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-\appendix{Catalogue of Monograph Objects} +\chapter{Catalogue of Monograph Objects} \label{app:A} This appendix is the permanent reference index for every named mathematical -object appearing in the monograph \emph{Trinity S³AI — Flos Aureus v6.2}. +object appearing in the monograph \emph{Trinity S³AI — Flos Aureus v6.8}. It supersedes the earlier 42-formula list and provides six master tables: \begin{enumerate} diff --git a/docs/phd/appendix/B-falsification.tex b/docs/phd/appendix/B-falsification.tex index 624c3a562d..6053df0558 100644 --- a/docs/phd/appendix/B-falsification.tex +++ b/docs/phd/appendix/B-falsification.tex @@ -14,6 +14,7 @@ \chapter*{Appendix B: Falsification Ledger — Popperian Audit Across 33 Chapter \addcontentsline{toc}{chapter}{Appendix B: Falsification Ledger} \label{app:falsification} +\label{app:B} \begin{quote}\itshape ``A theory which is not refutable by any conceivable event is non-scientific. @@ -35,7 +36,7 @@ \section*{Preamble: Purpose and Structure of This Appendix} \noindent Five years of constructive work can unravel under a single Reviewer-2 observation: ``this looks like numerology.'' Appendix~B exists to close that attack surface permanently. It serves as the \emph{monograph-wide -Popperian ledger} for Trinity S\textsuperscript{3}AI — Flos Aureus v6.2: +Popperian ledger} for Trinity S\textsuperscript{3}AI — Flos Aureus v6.8: every empirical claim made in Chapters~8, 9, 17, 18, 20--22, 24--26, 28, 29 is here paired with a registered falsifier, an observable outcome that would refute it, a corroboration record with date and status, and a severity score @@ -894,7 +895,7 @@ \section*{B.11 — Soundness Theorem: Falsification-Ledger Completeness} \begin{definition}[Empirical Claim]\label{def:empirical-claim} Let $\mathcal{C}$ denote the set of all empirical claims in Trinity -S\textsuperscript{3}AI — Flos Aureus v6.2. A \emph{claim} +S\textsuperscript{3}AI — Flos Aureus v6.8. A \emph{claim} $C \in \mathcal{C}$ is \emph{empirical} if it asserts a relationship between a theoretical prediction $\hat{y}(C)$ and a measurable observable $y(C, \omega)$ for some experimental condition $\omega$. Purely mathematical @@ -1159,7 +1160,7 @@ \subsection*{Clause F-5 — KART-Shaped Decomposition over GF(16) (L-KAT-12, L-K \textbf{Status:} Theorem 12.7 (Ch.~12 \S 5) and Theorem 35.13 (Ch.~35 \S 13) both stay Admitted; the missing finite-field analogue of Schmidt-Hieber's KART bound~\cite{schmidhuber_dl_review} is the -named gap blocking $\Qed$. Corroboration row Ch.35-MRU-KART is in +named gap blocking $\square$. Corroboration row Ch.35-MRU-KART is in \textbf{pending CI} state until \texttt{phd-build.yml} runs the \texttt{n=2} default test. \end{tcolorbox} @@ -1636,3 +1637,42 @@ \section*{B.24 — Ledger Maintenance Protocol} \noindent $\varphi^{2} + \varphi^{-2} = 3$. \noindent\textit{End of Appendix B (Extended Falsification Ledger).} + +% --- Wave-7 plates --- + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{P-01-conjecture-experiment-verdict.png} + \caption{Falsification Plate P-01: Conjecture, experiment, verdict. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave7-P-01-conjecture-experiment-verdict} +\end{figure} + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{P-02-null-power-size.png} + \caption{Falsification Plate P-02: Null, power, size. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave7-P-02-null-power-size} +\end{figure} + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{P-03-preregister-seal-release.png} + \caption{Falsification Plate P-03: Preregister, seal, release. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave7-P-03-preregister-seal-release} +\end{figure} + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{P-04-bias-leak-guard.png} + \caption{Falsification Plate P-04: Bias, leak, guard. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave7-P-04-bias-leak-guard} +\end{figure} + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{P-05-replication-bootstrap-confidence.png} + \caption{Falsification Plate P-05: Replication, bootstrap, confidence. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave7-P-05-replication-bootstrap-confidence} +\end{figure} +% --- end Wave-7 plates --- + diff --git a/docs/phd/appendix/D-golden-mirror.tex b/docs/phd/appendix/D-golden-mirror.tex index 360965d672..bbd340cd7a 100644 --- a/docs/phd/appendix/D-golden-mirror.tex +++ b/docs/phd/appendix/D-golden-mirror.tex @@ -56,6 +56,23 @@ \section*{D.0 Preface and Scope} The anchor \eqref{eqn:D0} is DOI \texttt{10.5281/zenodo.19227877} \cite{trios_throne}. +\paragraph{Master identities.} Three equations are referenced throughout this +appendix and are stated here once for clarity: +\begin{equation}\label{eqn:D0} + \varphi^2 + \varphi^{-2} = 3,\qquad \varphi = \tfrac{1+\sqrt{5}}{2}. +\end{equation} +\begin{equation}\label{eqn:D1} + \sigma:\ \varphi \longmapsto \psi = -\varphi^{-1} = \tfrac{1-\sqrt{5}}{2}, + \qquad \sigma^2 = \mathrm{id}. +\end{equation} +\begin{equation}\label{eqn:D2} + L_n \cdot L_{-n} = 2 - (-1)^n\bigl(\varphi^{2n} + \varphi^{-2n}\bigr), + \qquad n \in \mathbb{Z}. +\end{equation} +Equation~\eqref{eqn:D0} is the anchor identity; \eqref{eqn:D1} is the Galois +automorphism of $\mathbb{Q}(\varphi)$; \eqref{eqn:D2} is the Lucas +negative-index reflection product. + % ───────────────────────────────────────────────────────────────────────────── \section*{D.1 Two Strands, One Identity (Symmetry Table)} % ───────────────────────────────────────────────────────────────────────────── @@ -1423,7 +1440,7 @@ \section*{D.20 Glossary of Mirror Terminology} \item[$\psi = -\varphi^{-1}$] The algebraic conjugate of $\varphi$; equals $(1-\sqrt5)/2 \approx -0.618$. \item[Pisano period] The period of $L_n \bmod m$; for $m=16$, equals $24$. - \item[$\mathbb{Z}[\varphi]$] The ring of golden integers $\{a+b\varphi\mid a,b\in\mathbb{Z}\}$; + \item[{$\mathbb{Z}[\varphi]$}] The ring of golden integers $\{a+b\varphi\mid a,b\in\mathbb{Z}\}$; the ring of integers of $\mathbb{Q}(\sqrt5)$. \end{description} diff --git a/docs/phd/appendix/E-lexicon.tex b/docs/phd/appendix/E-lexicon.tex index f314cb943f..a4c4f6932d 100644 --- a/docs/phd/appendix/E-lexicon.tex +++ b/docs/phd/appendix/E-lexicon.tex @@ -697,7 +697,7 @@ \section*{D\quad R-Rules} \label{entry:r9} (Russian: \textit{захват ресурса до работы}).\\ \emph{Claim-before-work.} -Post \texttt{🔒 AGENT CLAIMING: L} on trios\#265 +Post \texttt{[CLAIM] AGENT L} on trios\#265 before any \texttt{git add}. First post wins; duplicate claims are rejected by the queen-bot. @@ -877,11 +877,11 @@ \section*{F\quad Trinity Terms} \textit{Coq}: none.\\ \textit{Definition.} The canonical name of this monograph: \emph{Trinity S\textsuperscript{3}AI ---- Flos Aureus v6.2}. +--- Flos Aureus v6.8}. \emph{Flos Aureus} (Latin: ``golden flower'') evokes the Flower of Life pattern (Ch.\,12) whose radial symmetry is governed by $\varphi$. -Version 6.2 supersedes all previous titles including -\emph{Monumentum Aureum}, \emph{v6.0}, and +Version 6.8 supersedes all previous titles including +\emph{Monumentum Aureum}, \emph{v6.0}, \emph{v6.2}, and \emph{Trinity Identity to All Physical Constants}. % ----------------------------------------------------------- @@ -1369,7 +1369,7 @@ \section*{I\quad Lexicon-Coherence Theorem} \begin{theorem}[Lexicon Coherence]\label{thm:lexicon-coherence} Every technical term $t$ that appears in the body of the -Trinity S\textsuperscript{3}AI --- Flos Aureus v6.2 monograph +Trinity S\textsuperscript{3}AI --- Flos Aureus v6.8 monograph (Chapters~0--33, Appendices~A--L) has exactly one canonical definition in this appendix (Appendix~E), and no two entries define the same concept under different names without an explicit @@ -1621,3 +1621,14 @@ \section*{L\quad Revision History} \textit{Branch:} \texttt{feat/phd-appE} \quad \textit{ONE SHOT:} trios\#265 \quad \textit{Trinity anchor:} $\varphi^2 + \varphi^{-2} = 3$ + +% --- Wave-7 plates --- + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{X-01-bibliography-index-glossary.png} + \caption{Appendix Plate X-01: Bibliography, index, glossary. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave7-X-01-bibliography-index-glossary} +\end{figure} +% --- end Wave-7 plates --- + diff --git a/docs/phd/appendix/F-coq-citation-map.tex b/docs/phd/appendix/F-coq-citation-map.tex index f68310d846..3432925af6 100644 --- a/docs/phd/appendix/F-coq-citation-map.tex +++ b/docs/phd/appendix/F-coq-citation-map.tex @@ -1,4 +1,4 @@ -\appendix{Coq Citation Map (L--R14 Compliance)} +\chapter{Coq Citation Map (L--R14 Compliance)} \label{app:F} This appendix is the single source of truth for the formal-proof citation map. @@ -463,3 +463,84 @@ \section{Auditor regeneration provenance} Generated by skill \texttt{phd-monograph-auditor} (skill\_id \texttt{fc1dbf8f-2449-4400-8d62-0c9003c84fa2}). Snapshot SHA: see \filepath{assertions/igla\_assertions.json}\,\filepath{\_metadata.source\_commit\_trios}. Trinity Anchor: $\phi^2 + \phi^{-2} = 3$. Zenodo DOI: \href{https://zenodo.org/records/19227877}{10.5281/zenodo.19227877}. + +% --- Wave-7 plates --- + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{C-01-axiom-proof-qed.png} + \caption{Coq Plate C-01: Trinity identity axiom-proof-QED. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave7-C-01-axiom-proof-qed} +\end{figure} + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{C-02-lucas-closure.png} + \caption{Coq Plate C-02: Lucas closure. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave7-C-02-lucas-closure} +\end{figure} + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{C-03-kart-popcount.png} + \caption{Coq Plate C-03: KART x popcount isomorphism. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave7-C-03-kart-popcount} +\end{figure} + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{C-04-bpb-floor.png} + \caption{Coq Plate C-04: BPB Shannon floor. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave7-C-04-bpb-floor} +\end{figure} + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{C-05-kl-divergence.png} + \caption{Coq Plate C-05: KL divergence. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave7-C-05-kl-divergence} +\end{figure} + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{C-06-pollen-channel.png} + \caption{Coq Plate C-06: Pollen channel capacity. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave7-C-06-pollen-channel} +\end{figure} + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{C-07-phi-geom-series.png} + \caption{Coq Plate C-07: phi geometric series. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave7-C-07-phi-geom-series} +\end{figure} + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{C-08-asha-prune.png} + \caption{Coq Plate C-08: ASHA prune. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave7-C-08-asha-prune} +\end{figure} + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{C-09-gf16-mill.png} + \caption{Coq Plate C-09: GF(16) mill. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave7-C-09-gf16-mill} +\end{figure} + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{C-10-nca-guard.png} + \caption{Coq Plate C-10: NCA entropy band guard. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave7-C-10-nca-guard} +\end{figure} + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{X-02-coq-prooftree-qed.png} + \caption{Appendix Plate X-02: Coq prooftree QED. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave7-X-02-coq-prooftree-qed} +\end{figure} +% --- end Wave-7 plates --- + diff --git a/docs/phd/appendix/G-data-availability.tex b/docs/phd/appendix/G-data-availability.tex index 43a2d6b15c..d871f85e79 100644 --- a/docs/phd/appendix/G-data-availability.tex +++ b/docs/phd/appendix/G-data-availability.tex @@ -340,3 +340,14 @@ \section*{G.10 Appendix F $\leftrightarrow$ JSON-registry cross-reference} task~5.3); until then, the bridge above is the authoritative cross-reference. \(\varphi^2 + \varphi^{-2} = 3\) + +% --- Wave-7 plates --- + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{X-03-manifest-hash-freeze.png} + \caption{Appendix Plate X-03: Manifest, hash, freeze. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave7-X-03-manifest-hash-freeze} +\end{figure} +% --- end Wave-7 plates --- + diff --git a/docs/phd/appendix/H-acm-ae-checklist.tex b/docs/phd/appendix/H-acm-ae-checklist.tex index 67d4ef4168..c9607a97f5 100644 --- a/docs/phd/appendix/H-acm-ae-checklist.tex +++ b/docs/phd/appendix/H-acm-ae-checklist.tex @@ -116,3 +116,14 @@ \section{Reviewer instructions (compact)} reported table is invited to file an issue at \href{https://github.com/gHashTag/trios/issues}{the issue tracker}; the reproduction binary's deterministic seeding makes this self-debugging. + +% --- Wave-7 plates --- + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{X-04-acm-badge-pack.png} + \caption{Appendix Plate X-04: ACM badge pack. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave7-X-04-acm-badge-pack} +\end{figure} +% --- end Wave-7 plates --- + diff --git a/docs/phd/appendix/J-troubleshooting.tex b/docs/phd/appendix/J-troubleshooting.tex index 4f58c0fe5d..72eca91e84 100644 --- a/docs/phd/appendix/J-troubleshooting.tex +++ b/docs/phd/appendix/J-troubleshooting.tex @@ -298,7 +298,7 @@ \section*{J.10 Open issues / audit-pending} cron-driven nightly regen, but is too slow for a high-availability field deployment. A future revision could pre-load the firmware into PSRAM and shave the cold-boot to $< 1$\,s. Status: - \texttt{audit-pending} with no scheduled fix in the v6.2 window. + \texttt{audit-pending} with no scheduled fix in the v6.8 window. \end{description} \section*{J.11 Falsification hooks} diff --git a/docs/phd/appendix/K-agent-memory.tex b/docs/phd/appendix/K-agent-memory.tex index 5955471d43..1398db9144 100644 --- a/docs/phd/appendix/K-agent-memory.tex +++ b/docs/phd/appendix/K-agent-memory.tex @@ -362,7 +362,7 @@ \subsection{Heartbeat Format} A valid HEARTBEAT comment must match the pattern: \begin{verbatim} -⏱️ AGENT L HEARTBEAT: % +[HEARTBEAT] AGENT L HEARTBEAT: % Last commit: Lines so far: /1500 Citations added: /2 @@ -1665,3 +1665,11 @@ \section{Summary: Agent Memory Architecture} % ============================================================ % Coq map: lucas_closure_gf16.v lines 87-175; lr_convergence.v lines 1-30 % Final line count: 1666 — R3 gate >= 1500 PASS + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-AK-agent-memory-honey.png} + \caption{THE HIVE / THE HONEY / THE APPEND. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-AK-agent-memory-honey} +\end{figure} + diff --git a/docs/phd/appendix/L-pollen-channel.tex b/docs/phd/appendix/L-pollen-channel.tex index 38fcbe2b27..5d0035e329 100644 --- a/docs/phd/appendix/L-pollen-channel.tex +++ b/docs/phd/appendix/L-pollen-channel.tex @@ -361,7 +361,7 @@ \subsection*{L.4.2 \quad Comment Format} following envelope: \begin{verbatim} -🌸 POLLEN DEPOSIT +[POLLEN DEPOSIT] ```json { "sha": "...", "agent": "...", ... } ``` @@ -1417,7 +1417,7 @@ \subsection*{L.16.3 \quad Denial-of-Service Mitigation} flood the coordination issue with noise comments. The discriminator network (§L.9) mitigates this: \begin{itemize} -\item Comments without the \texttt{🌸 POLLEN DEPOSIT} prefix are +\item Comments without the \texttt{[POLLEN DEPOSIT]} prefix are ignored with zero API cost (client-side filter on comment body before parsing). \item Comments with the prefix but invalid signatures are logged as @@ -1571,7 +1571,7 @@ \section*{L.20 \quad Summary} \begin{enumerate} \item \textbf{Message format} (§L.4): a signed JSON deposit with fields \texttt{\{sha, agent, lane, BPB, honey, ts, sig\}}, embedded in a - GitHub issue comment with a \texttt{🌸 POLLEN DEPOSIT} prefix for + GitHub issue comment with a \texttt{[POLLEN DEPOSIT]} prefix for fast client-side filtering. \item \textbf{Channel capacity} (§L.6): the effective bit-rate is @@ -1776,3 +1776,11 @@ \section*{L.C \quad Notation Reference} \end{tabular} \par\medskip\noindent\hrulefill\par\medskip + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-AL-pollen-channel-capacity.png} + \caption{THE SOURCE / THE NOISE / THE CAPACITY. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-AL-pollen-channel-capacity} +\end{figure} + diff --git a/docs/phd/appendix/N-zenodo-doi.tex b/docs/phd/appendix/N-zenodo-doi.tex index 9c20cf72c6..43ec0fae5d 100644 --- a/docs/phd/appendix/N-zenodo-doi.tex +++ b/docs/phd/appendix/N-zenodo-doi.tex @@ -138,6 +138,7 @@ \section*{H.4 Version History} v6.0 & 2026-04-15 & Thesis text updated; DOIs unchanged \\ v6.2 & 2026-05-03 & STUB-KILL + front-matter rewrite \\ v6.3 & 2026-05-12 & R5-honest PASS-6 audit removed five non-member DOIs \\ +v6.8 & 2026-05-14 & Wave-8 illustrations (+64 plates) + appendix counter fix + emoji-free fonts \\ v7.0 & 2026-06-10 & \emph{Planned: frozen submission} \\ \bottomrule \end{tabular} @@ -274,3 +275,14 @@ \section*{H.9 Reviewer-2 mitigation} \end{itemize} \(\varphi^2 + \varphi^{-2} = 3\) + +% --- Wave-7 plates --- + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{X-05-defense-committee-laurel.png} + \caption{Appendix Plate X-05: Defense, committee, laurel. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave7-X-05-defense-committee-laurel} +\end{figure} +% --- end Wave-7 plates --- + diff --git a/docs/phd/bibliography.bib b/docs/phd/bibliography.bib index e60d7093fe..1e2f0578d8 100644 --- a/docs/phd/bibliography.bib +++ b/docs/phd/bibliography.bib @@ -1877,9 +1877,6 @@ @book{borwein2002excursions } %% =====================================================%% CLUSTER 2: Polytopes, lattices, E8 / sphere-packing -%% ==============================================@book{ziegler1995polytopes, -%% ==============================================@book{ziegler1995polytopes, -%% ==============================================@book{ziegler1995polytopes, author = {Ziegler, G{\"u}nter M.}, title = {Lectures on {Polytopes}}, series = {Graduate Texts in Mathematics}, @@ -1929,9 +1926,6 @@ @book{gruenbaum2003convex } %% =====================================================%% CLUSTER 3: Quasicrystals, crystallography -%% ==============================================@book{steurer2009quasicrystals, -%% ==============================================@book{steurer2009quasicrystals, -%% ==============================================@book{steurer2009quasicrystals, author = {Steurer, Walter and Deloudi, Sofia}, title = {Crystallography of {Quasicrystals}: {Concepts, Methods and Structures}}, series = {Springer Series in Materials Science}, @@ -1948,9 +1942,6 @@ @book{steurer2009quasicrystals } %% =====================================================%% CLUSTER 4: Formal proofs, Coq, type theory, mathematical logic -%% ==============================================@book{bertot2004coqart, -%% ==============================================@book{bertot2004coqart, -%% ==============================================@book{bertot2004coqart, author = {Bertot, Yves and Cast{\'e}ran, Pierre}, title = {Interactive {Theorem Proving and Program Development}: {Coq'Art}: {The Calculus of Inductive Constructions}}, @@ -2001,7 +1992,6 @@ @book{ebbinghaus1994logic } %% =====================================================%% CLUSTER 5: AutoML, NAS, neural networks (AI/ML Springer works) -%% ==============================================@book{hutter2019automl, editor = {Hutter, Frank and Kotthoff, Lars and Vanschoren, Joaquin}, title = {Automated {Machine Learning}: {Methods, Systems, Challenges}}, series = {The Springer Series on Challenges in Machine Learning}, @@ -2048,7 +2038,6 @@ @book{aggarwal2018neural } %% =====================================================%% CLUSTER 6: Combinatorics, graph theory, finite fields -%% ==============================================@book{jungnickel2013graphs, author = {Jungnickel, Dieter}, title = {Graphs, {Networks and Algorithms}}, edition = {4}, @@ -2098,7 +2087,6 @@ @book{mullen2002finitefields } %% =====================================================%% CLUSTER 7: Dimensional analysis, symmetry methods for differential equations -%% ==============================================@book{bluman2002symmetry, author = {Bluman, George W. and Anco, Stephen C.}, title = {Symmetry and {Integration Methods for Differential Equations}}, series = {Applied Mathematical Sciences}, @@ -2152,7 +2140,6 @@ @book{bluman2002symmetry %% =====================================================%% SUPPLEMENTARY CLUSTER: Mathematics — GTM/UTM classics %% All confirmed on SpringerLink (link.springer.com) -%% ==============================================@book{serre1973arithmetic, author = {Serre, Jean-Pierre}, title = {A {Course in Arithmetic}}, series = {Graduate Texts in Mathematics}, @@ -2324,7 +2311,7 @@ @misc{finite_field_expressivity_2025 activations over finite fields, defining the neuromanifold and linking expressivity to counting rational points (Weil conjectures). PRIMARY theoretical foundation for - the IGLA / GF(16) framework per epic #572 erratum.} + the IGLA / GF(16) framework per epic \#572 erratum.} } @inproceedings{finite_group_vsa_2022, @@ -2399,9 +2386,10 @@ @article{demers1987epidemic publisher = {ACM}, doi = {10.1145/37499.37500}, note = {Q1; foundational gossip/epidemic protocol paper.} +} + % === L7 Golden Sprout additions (additive only, feat/phd-ch07) === -@article{zeckendorf1972, % ------------------------------------------------------------------- % Entries added by scarab-l3 for Chapter 03-golden-harvest (L3 lane) % ------------------------------------------------------------------- @@ -2480,9 +2468,9 @@ @article{zeckendorf1972representation coden = {FOCRDQ}, note = {Canonical reference for Zeckendorf representation theorem; proves uniqueness of non-consecutive Fibonacci decomposition.} +} %% ==============================================================%% L22 — E8 Symmetry: additions (phd-chapter-author v1.1, scarab-l22-e8) %% Keys: borcherds1992monstrous_moonshine, viazovska2017sphere -%% =======================================================@article{borcherds1992monstrous_moonshine, author = {Borcherds, Richard E.}, title = {Monstrous Moonshine and Monstrous {Lie} Superalgebras}, journal = {Inventiones Mathematicae}, @@ -2512,6 +2500,7 @@ @article{viazovska2017sphere note = {Proof that the {$E_8$} lattice gives the densest sphere packing in dimension~8. Fields Medal 2022. L22 cites for the optimality of {$E_8$} as a sphere-packing lattice.} +} % L0 R3-extension additive entry (feat/phd-ch00-extend) @misc{vasilev2026zenodo, author = {Vasilev, Dmitrii}, @@ -2520,6 +2509,7 @@ @misc{vasilev2026zenodo doi = {10.5281/zenodo.19227877}, url = {https://zenodo.org/records/19227877}, note = {Zenodo record; mechanised as \texttt{lucas\_2\_eq\_3} in trinity-clara/proofs/lucas\_closure\_gf16.v} +} % ------------------------------------------------------------------- % Ch.4 golden-scales additions (L4, agent scarab-l4-golden-scales) % ------------------------------------------------------------------- @@ -2699,6 +2689,7 @@ @book{muller_fp_handbook doi = {10.1007/978-3-319-76526-6}, note = {Q1 reference; definitive ULP error-bound framework used in Chapter~6 (GF16 certified-band rounding analysis).} +} % ── Ch.24 IGLA Architecture additions ───────────────────────────────────── @article{touvron_llama, @@ -2770,6 +2761,7 @@ @article{goodman2016reproducibility doi = {10.1126/scitranslmed.aaf5027}, note = {Q1. Foundational taxonomy of methods, results, and inferential reproducibility.} +} @book{wasserman2004statistics, author = {Wasserman, Larry}, title = {All of Statistics: A Concise Course in Statistical Inference}, @@ -2863,8 +2855,6 @@ @inproceedings{jamieson2016non url = {https://proceedings.mlr.press/v51/jamieson16.html}, note = {Q1 (AISTATS, PMLR). Successive halving algorithm underlying ASHA; cited in Ch.~26 Section~18.3.} - note = {Classic. Proves unique Fibonacci representation (Zeckendorf - theorem) for positive integers.} } @book{wild1986optimization, @@ -2888,9 +2878,9 @@ @book{cormen2022introduction isbn = {978-0-262-04630-5}, note = {Q1 — MIT Press. Chapter~19 covers Fibonacci heaps and their amortised complexity bounds.} +} %% ==============================================%% L8 additions — Golden Crystal quasicrystal extension %% Agent: scarab-l8 | Branch: feat/phd-ch08 -%% =======================================@book{janot_quasicrystals, author = {Janot, Christian}, title = {Quasicrystals: A Primer}, edition = {2nd}, @@ -2997,6 +2987,7 @@ @article{spinadel_metallic to phyllotaxis, quasicrystals, and architectural proportion. Primary reference for the taxonomic survey of metallic means in Ch.~16 (Sacred Ratios).} +} % =====================================================% L19: Fibonacci Tessellation — Word Combinatorics & Sturmian Theory % Q1/Q2 citations added by scarab-l19 % ==============================================@book{lothaire2002algebraic, @@ -3057,6 +3048,7 @@ @article{morse1940symbolic minimal-complexity theorem $p(n)=n+1$. \emph{American Journal of Mathematics} is a Q1 journal (Scimago SJR).} +} % ===== L15 Kepler Solids — added by scarab-l15-kepler-solids ===== @book{coxeter_fifty_nine_icosahedra, @@ -3092,6 +3084,7 @@ @book{stewart_galois_theory of iterated degree-2 extensions of \(\mathbb{Q}\); establishes the compass-and-straightedge criterion used in Ch.\ 11 to justify the constructibility of \(\sqrt{3}\).} +} % ------------------------------------------------------------------- % Entries added by L17 golden-spiral extension (agent scarab-l17) % ------------------------------------------------------------------- @@ -3157,6 +3150,7 @@ @misc{zenodo_trinity 162 Qed, 32 Admitted, 11 Abort on 2026-05-12). The extended PhD-side mirror lives in gHashTag/trios/docs/phd/theorems/ (45 .v files, 340 statements, 286 Qed, 3 Admitted).} +} % ---- L14 platonic-solids additions -------------------------------- @article{atiyah_sutcliffe_polyhedra, author = {Atiyah, Michael and Sutcliffe, Paul}, @@ -3267,7 +3261,6 @@ @book{Coxeter1973 } %% ==============================================%% L12 additions — Flower of Life chapter (scarab-l12) -%% =======================================@article{hales_honeycomb, author = {Hales, Thomas C.}, title = {The Honeycomb Conjecture}, journal = {Discrete \& Computational Geometry}, @@ -3285,7 +3278,6 @@ @article{hales_honeycomb } %% =====================================================%% Chapter 10 — Golden Bloom additions (L10, agent=scarab-l10) -%% ==============================================@book{jean1994phyllotaxis, author = {Jean, Roger V.}, title = {Phyllotaxis: A Systemic Study in Plant Morphogenesis}, publisher = {Cambridge University Press}, @@ -3385,6 +3377,7 @@ @article{liang1979three doi = {10.2307/2320378}, publisher = {Taylor \& Francis}, note = {Clean proof of Steinhaus's three-distance theorem.} +} % ------------------------------------------------------------------- % Chapter 31 additions — Philosophy of phi-derived AGI (scarab-l31) % ------------------------------------------------------------------- @@ -3443,6 +3436,7 @@ @article{kaplan2020scaling note = {arXiv preprint (within \(\le\)20\% arXiv quota, R11). Establishes the scaling-hypothesis paradigm contrasted with the Trinity proof-guided NAS paradigm in Ch.~31 \S\ref{sec:phd31-kuhn}.} +} % --------------------------------------------------------------- % L30 Golden Imagery additions (scarab-l30, feat/phd-ch30) % --------------------------------------------------------------- @@ -3538,6 +3532,7 @@ @misc{gao2020pile Noa Nabeshima and Shawn Presser and Connor Leahy}, title = {The {Pile}: An 800{GB} Dataset of Diverse Text for Language Modeling}, +} % ============================================================% Appendix G — Data Availability citations (added by scarab-AppG) % =====================================================@article{wilkinson2016fair, author = {Wilkinson, Mark D. and Dumontier, Michel and Aalbersberg, I. Jsbrand Jan @@ -3674,6 +3669,7 @@ @misc{stallman1985gnu url = {https://www.gnu.org/gnu/manifesto.html}, note = {Founding document of the free-software movement. The epigraph of Appendix~G is taken from this text.} +} @article{lamport_time_clocks, author = {Lamport, Leslie}, title = {Time, Clocks, and the Ordering of Events in a Distributed System}, @@ -3685,6 +3681,7 @@ @article{lamport_time_clocks publisher = {ACM}, doi = {10.1145/359545.359563}, note = {Q1; foundational distributed-systems paper; hive heartbeat protocol.} +} % ───────────────────────────────────────────────────────────────────────── % Appendix J citations (added by feat/phd-appJ) % ───────────────────────────────────────────────────────────────────────── @@ -3721,6 +3718,7 @@ @article{chillarege1992oDC note = {Q1 (IEEE TSE). Defines the ODC defect-type tags (Assignment, Checking, Interface, Timing, Function, Build) used throughout Appendix~J.} +} % --------------------------------------------------------------- % Appendix I — XDC Pin Map entries (added by feat/phd-appI) % --------------------------------------------------------------- diff --git a/docs/phd/chapters/flos_00.tex b/docs/phd/chapters/flos_00.tex index d66a4e91c7..bfd7ecd20d 100644 --- a/docs/phd/chapters/flos_00.tex +++ b/docs/phd/chapters/flos_00.tex @@ -167,3 +167,28 @@ \section{Where to Begin} \noindent \emph{Status.} Editorial scaffold. Lane L0 of issue \href{https://github.com/gHashTag/trios/issues/265}{trios\#265} is the slot for full expansion to PhD scope. + +% --- Wave-7 plates --- + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{F-01-golden-axiom.png} + \caption{Frontmatter Plate F-01: Golden axiom. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave7-F-01-golden-axiom} +\end{figure} + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{F-02-wheel-thirds.png} + \caption{Frontmatter Plate F-02: Wheel of thirds. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave7-F-02-wheel-thirds} +\end{figure} + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{F-03-hive.png} + \caption{Frontmatter Plate F-03: Hive. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave7-F-03-hive} +\end{figure} +% --- end Wave-7 plates --- + diff --git a/docs/phd/chapters/flos_01.tex b/docs/phd/chapters/flos_01.tex index 4239be3188..543449afe7 100644 --- a/docs/phd/chapters/flos_01.tex +++ b/docs/phd/chapters/flos_01.tex @@ -1525,3 +1525,11 @@ \section*{Appendix AT: Honour Roll of Three} % Final closing —— Chapter L1 totals ≥ 1500 lines, ≥ 2 citations, % ≥ 1 theorem with proof and qed, R3-compliant. + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-01-vesica-aperture-phyllotaxis.png} + \caption{THE APERTURE / THE PHYLLOTAXIS / THE LIMIT. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-01-vesica-aperture-phyllotaxis} +\end{figure} + diff --git a/docs/phd/chapters/flos_02.tex b/docs/phd/chapters/flos_02.tex index 5ec461f4c7..e1822b01c5 100644 --- a/docs/phd/chapters/flos_02.tex +++ b/docs/phd/chapters/flos_02.tex @@ -329,3 +329,10 @@ \section{References}\label{fa_02:references} seed protocol. GitHub. \url{https://github.com/gHashTag/trios/issues/395} +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-02-neuron-symbol-bridge.png} + \caption{THE NEURON / THE SYMBOL / THE BRIDGE. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-02-neuron-symbol-bridge} +\end{figure} + diff --git a/docs/phd/chapters/flos_03.tex b/docs/phd/chapters/flos_03.tex index 07016582b5..e8ac4f5f00 100644 --- a/docs/phd/chapters/flos_03.tex +++ b/docs/phd/chapters/flos_03.tex @@ -443,3 +443,11 @@ \section{References}\label{fa_03:references} [12] \emph{Golden Sunflowers} dissertation, Ch.4 --- \(\alpha_\varphi = \ln(\varphi^2)/\pi \approx 0.306\). + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-03-identity-facet-harvest.png} + \caption{THE TRIPLE / THE FACET / THE HARVEST. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-03-identity-facet-harvest} +\end{figure} + diff --git a/docs/phd/chapters/flos_04.tex b/docs/phd/chapters/flos_04.tex index 7d9ecfb9f6..2f3c45ab31 100644 --- a/docs/phd/chapters/flos_04.tex +++ b/docs/phd/chapters/flos_04.tex @@ -399,3 +399,10 @@ \section{References}\label{fa_04:references} Specification. Zenodo, DOI: 10.5281/zenodo.19227869. +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-04-scale-fish-formula.png} + \caption{THE BALANCE / THE PISCIS / THE TABLET. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-04-scale-fish-formula} +\end{figure} + diff --git a/docs/phd/chapters/flos_05.tex b/docs/phd/chapters/flos_05.tex index 8f5c7c3ccf..357b7bed1d 100644 --- a/docs/phd/chapters/flos_05.tex +++ b/docs/phd/chapters/flos_05.tex @@ -1520,3 +1520,11 @@ \section*{Appendix AH: Final Remarks on Bridge Discipline} % End of chapter L5 — Fibonacci-Lucas generating function bridge. % Trinity Anchor: L_2 = 3 as coefficient of x^2 in L(x) = (2-x)/(1-x-x^2). % Bridge identity: L(x) = Tr(1/(1-phi*x)) connects L6 ring to L4 ladder. + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-05-arch-span-gate.png} + \caption{THE ARCH / THE SPAN / THE GATE. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-05-arch-span-gate} +\end{figure} + diff --git a/docs/phd/chapters/flos_06.tex b/docs/phd/chapters/flos_06.tex index 321490337c..b55618918d 100644 --- a/docs/phd/chapters/flos_06.tex +++ b/docs/phd/chapters/flos_06.tex @@ -499,3 +499,10 @@ \section{References}\label{fa_06:references} --- QMTech XC7A100T, 0 DSP, 63 toks/sec, 92 MHz, 1 W. +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-06-rod-gnomon-tree.png} + \caption{THE MEASURE / THE GNOMON / THE FAMILY. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-06-rod-gnomon-tree} +\end{figure} + diff --git a/docs/phd/chapters/flos_07.tex b/docs/phd/chapters/flos_07.tex index 0b908c68a6..7284578df3 100644 --- a/docs/phd/chapters/flos_07.tex +++ b/docs/phd/chapters/flos_07.tex @@ -389,3 +389,10 @@ \section{References}\label{fa_07:references} [13] Dunlap, R. A. (1997). \emph{The Golden Ratio and Fibonacci Numbers.} World Scientific. +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-07-seed-spiral-bloom.png} + \caption{THE SEED / THE SPIRAL / THE BLOOM. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-07-seed-spiral-bloom} +\end{figure} + diff --git a/docs/phd/chapters/flos_08.tex b/docs/phd/chapters/flos_08.tex index 47ebaf2e6b..ccd90c7a93 100644 --- a/docs/phd/chapters/flos_08.tex +++ b/docs/phd/chapters/flos_08.tex @@ -454,3 +454,11 @@ \section{Falsification} table; the QED sealing of \texttt{Trinity.Sacred.TF3\_TF9\_EnergyMonotone} in \filepath{t27/proofs/canonical/sacred/TF3.v} discharges the formal side of this predicate, leaving the empirical band as the open obligation. + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-08-lattice-kernel-gemm.png} + \caption{THE LATTICE / THE KERNEL / THE GEMM. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-08-lattice-kernel-gemm} +\end{figure} + diff --git a/docs/phd/chapters/flos_09.tex b/docs/phd/chapters/flos_09.tex index 724ba3f019..9e3598fdb7 100644 --- a/docs/phd/chapters/flos_09.tex +++ b/docs/phd/chapters/flos_09.tex @@ -425,3 +425,10 @@ \section{References}\label{fa_09:references} [13] Zenodo DOI bundle B001--B013. \url{https://doi.org/10.5281/zenodo.19227867} +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-09-seal-wax-verdict.png} + \caption{THE SEAL / THE WAX / THE VERDICT. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-09-seal-wax-verdict} +\end{figure} + diff --git a/docs/phd/chapters/flos_10.tex b/docs/phd/chapters/flos_10.tex index 304783a945..dc9d118eeb 100644 --- a/docs/phd/chapters/flos_10.tex +++ b/docs/phd/chapters/flos_10.tex @@ -15,7 +15,7 @@ \chapter{Golden Bloom: Coq L1 Range Precision Pareto} \begin{figure}[H] \centering -\makebox[\linewidth][c]{\includegraphics[width=1.18\linewidth,keepaspectratio]{\figChTenCoqL1Pareto}} +\makebox[\linewidth][c]{\includegraphics[width=1.18\linewidth,keepaspectratio]{\figChTenCoqLOnePareto}} \caption*{Figure --- Golden Bloom: Coq L1 Range Precision Pareto.} \end{figure} @@ -429,3 +429,11 @@ \section{References}\label{fa_10:references} [13] B004 --- GF(16) Precision Inventory. Zenodo, DOI: 10.5281/zenodo.19227871. + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-10-bud-bloom-pareto.png} + \caption{THE BUD / THE BLOOM / THE PARETO. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-10-bud-bloom-pareto} +\end{figure} + diff --git a/docs/phd/chapters/flos_11.tex b/docs/phd/chapters/flos_11.tex index 3874dea52d..618183c2b4 100644 --- a/docs/phd/chapters/flos_11.tex +++ b/docs/phd/chapters/flos_11.tex @@ -354,3 +354,10 @@ \section{References}\label{fa_11:references} (Modern commentary: Sigler, L. E., 2002, Springer.) +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-11-vesica-seal-seeds.png} + \caption{THE PIRE / THE SEAL / THE SEEDS. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-11-vesica-seal-seeds} +\end{figure} + diff --git a/docs/phd/chapters/flos_12.tex b/docs/phd/chapters/flos_12.tex index 69d9968785..cc2a75a16b 100644 --- a/docs/phd/chapters/flos_12.tex +++ b/docs/phd/chapters/flos_12.tex @@ -392,3 +392,10 @@ \section{References}\label{fa_12:references} Biosciences}, 44(3--4), 179--189. \url{https://doi.org/10.1016/0025-5564(79)90080-4} +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-12-flower-of-life-hardware.png} + \caption{THE FLOWER / THE BRIDGE / THE DEFERRAL. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-12-flower-of-life-hardware} +\end{figure} + diff --git a/docs/phd/chapters/flos_13.tex b/docs/phd/chapters/flos_13.tex index 1d7c2e9c52..1d726a520e 100644 --- a/docs/phd/chapters/flos_13.tex +++ b/docs/phd/chapters/flos_13.tex @@ -1642,3 +1642,11 @@ \section*{Appendix 13.M --- Future Work} % ===================================================================== % End of Chapter 13 — total ~1500 lines including appendices % ===================================================================== + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-13-metatron-cube-orbit.png} + \caption{THE CUBE / THE ORBIT / THE CLOSURE. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-13-metatron-cube-orbit} +\end{figure} + diff --git a/docs/phd/chapters/flos_14.tex b/docs/phd/chapters/flos_14.tex index 9a863716fe..dfb8be4d7c 100644 --- a/docs/phd/chapters/flos_14.tex +++ b/docs/phd/chapters/flos_14.tex @@ -301,3 +301,10 @@ \section{References}\label{fa_14:references} \texttt{.v} files, 297 Qed, 438 total theorems. GitHub repository. +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-14-platonic-solids-bpb.png} + \caption{THE SOLID / THE METRIC / THE BPB. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-14-platonic-solids-bpb} +\end{figure} + diff --git a/docs/phd/chapters/flos_15.tex b/docs/phd/chapters/flos_15.tex index db115be0e4..1a542b713c 100644 --- a/docs/phd/chapters/flos_15.tex +++ b/docs/phd/chapters/flos_15.tex @@ -396,3 +396,10 @@ \section{References}\label{fa_15:references} [13] Railway PostgreSQL documentation. \url{https://docs.railway.com/guides/postgresql} +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-15-kepler-solids-benchmark.png} + \caption{THE KEPLER / THE BENCH / THE WRITE. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-15-kepler-solids-benchmark} +\end{figure} + diff --git a/docs/phd/chapters/flos_16.tex b/docs/phd/chapters/flos_16.tex index b51e3e8632..e6d10308cd 100644 --- a/docs/phd/chapters/flos_16.tex +++ b/docs/phd/chapters/flos_16.tex @@ -348,3 +348,10 @@ \section{References}\label{fa_16:references} [13] GOLDEN SUNFLOWERS dissertation, Ch.18 --- Arithmetic Geometry of φ-Lattices. This volume. +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-16-ratios-360-grid.png} + \caption{THE RATIO / THE GRID / THE LANE. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-16-ratios-360-grid} +\end{figure} + diff --git a/docs/phd/chapters/flos_17.tex b/docs/phd/chapters/flos_17.tex index 8a32de73fb..1b9d3301cc 100644 --- a/docs/phd/chapters/flos_17.tex +++ b/docs/phd/chapters/flos_17.tex @@ -364,3 +364,10 @@ \section{References}\label{fa_17:references} [13] GOLDEN SUNFLOWERS Dissertation, App.B --- \emph{Golden Ledger (297 Qed canonical + SHA-1)}. +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-17-spiral-ablation-matrix.png} + \caption{THE SPIRAL / THE ABLATION / THE MATRIX. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-17-spiral-ablation-matrix} +\end{figure} + diff --git a/docs/phd/chapters/flos_18.tex b/docs/phd/chapters/flos_18.tex index dd915a0c88..98b944ba8e 100644 --- a/docs/phd/chapters/flos_18.tex +++ b/docs/phd/chapters/flos_18.tex @@ -425,3 +425,11 @@ \section{Falsification} threshold; Coq lemma \texttt{Trinity.Geometry.TorusModeCount} (three Qed) formally bounds the spectral support, leaving harmonic concentration as the empirical falsification target. + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-18-torus-falsification-limit.png} + \caption{THE TORUS / THE FALSIFY / THE LIMIT. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-18-torus-falsification-limit} +\end{figure} + diff --git a/docs/phd/chapters/flos_19.tex b/docs/phd/chapters/flos_19.tex index 3df23ac63b..e0d323593c 100644 --- a/docs/phd/chapters/flos_19.tex +++ b/docs/phd/chapters/flos_19.tex @@ -319,3 +319,10 @@ \section{References}\label{fa_19:references} scope (for cross-reference). \url{https://github.com/gHashTag/trios/issues/419} +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-19-tessellation-welch-t.png} + \caption{THE TESSELLATION / THE STATISTIC / THE WELCH. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-19-tessellation-welch-t} +\end{figure} + diff --git a/docs/phd/chapters/flos_20.tex b/docs/phd/chapters/flos_20.tex index e40cc4b27c..a31df2571a 100644 --- a/docs/phd/chapters/flos_20.tex +++ b/docs/phd/chapters/flos_20.tex @@ -518,3 +518,11 @@ \subsection{Corroboration Record} \textit{pending} \\ \hline \end{tabularx} + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-20-particles-field-symmetry.png} + \caption{THE PARTICLE / THE FIELD / THE SYMMETRY. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-20-particles-field-symmetry} +\end{figure} + diff --git a/docs/phd/chapters/flos_21.tex b/docs/phd/chapters/flos_21.tex index 643a7240db..8b0ea2cd89 100644 --- a/docs/phd/chapters/flos_21.tex +++ b/docs/phd/chapters/flos_21.tex @@ -441,3 +441,11 @@ \subsection{Corroboration Record} \textit{pending} \\ \hline \end{tabularx} + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-21-qft-fields-of-nature.png} + \caption{THE FIELD / THE PROPAGATOR / THE VERTEX. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-21-qft-fields-of-nature} +\end{figure} + diff --git a/docs/phd/chapters/flos_22.tex b/docs/phd/chapters/flos_22.tex index 71fa31c941..7400b86c27 100644 --- a/docs/phd/chapters/flos_22.tex +++ b/docs/phd/chapters/flos_22.tex @@ -420,3 +420,10 @@ \section{References}\label{fa_22:references} [12] B007 --- Railway/Trios Orchestration Formal Spec. Zenodo, DOI: 10.5281/zenodo.19227877. +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-22-e8-orchestration.png} + \caption{THE E8 / THE LATTICE / THE NODE. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-22-e8-orchestration} +\end{figure} + diff --git a/docs/phd/chapters/flos_23.tex b/docs/phd/chapters/flos_23.tex index 3cb3fe62fa..e8fd6951c5 100644 --- a/docs/phd/chapters/flos_23.tex +++ b/docs/phd/chapters/flos_23.tex @@ -339,3 +339,10 @@ \section{References}\label{fa_23:references} [13] GOLDEN SUNFLOWERS Dissertation, App.F --- \emph{FPGA bitstream distribution}. Zenodo B002. +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-23-gf16-clock-mcp.png} + \caption{THE FIELD / THE CLOCK / THE MCP. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-23-gf16-clock-mcp} +\end{figure} + diff --git a/docs/phd/chapters/flos_24.tex b/docs/phd/chapters/flos_24.tex index c873c3fd92..0caa83510f 100644 --- a/docs/phd/chapters/flos_24.tex +++ b/docs/phd/chapters/flos_24.tex @@ -437,3 +437,11 @@ \section{Falsification} Appendix~B lists the empirical reject threshold and Appendix~I pins the exact XDC pin map used for measurement, so the obligation remains falsifiable on physical hardware. + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-24-igla-period-monitor.png} + \caption{THE PERIOD / THE LOCK / THE GUARD. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-24-igla-period-monitor} +\end{figure} + diff --git a/docs/phd/chapters/flos_25.tex b/docs/phd/chapters/flos_25.tex index 7a6d4141e7..67764c63e0 100644 --- a/docs/phd/chapters/flos_25.tex +++ b/docs/phd/chapters/flos_25.tex @@ -406,3 +406,21 @@ \section{Falsification} pre-registered Gate-2 / Gate-3 thresholds, and Appendix~G provides the data availability statement under which these measurements are reproducible. The empirical band remains the open falsifiable obligation. + +% --- Wave-7 plates --- + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{E-08-board-table-throne.png} + \caption{IGLA Plate E-08: Leaderboard, table, throne. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave7-E-08-board-table-throne} +\end{figure} +% --- end Wave-7 plates --- + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-25-benchmarks-period.png} + \caption{THE BENCH / THE PERIOD / THE CYCLE. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-25-benchmarks-period} +\end{figure} + diff --git a/docs/phd/chapters/flos_26.tex b/docs/phd/chapters/flos_26.tex index 53ace52ea2..26f6ee831f 100644 --- a/docs/phd/chapters/flos_26.tex +++ b/docs/phd/chapters/flos_26.tex @@ -444,3 +444,10 @@ \section{References}\label{fa_26:references} [13] Zenodo DOI bundle. 10.5281/zenodo.B026 --- KOSCHEI ISA artefact. Zenodo registry. +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-26-data-analysis-isa.png} + \caption{THE DATA / THE ANALYSIS / THE ISA. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-26-data-analysis-isa} +\end{figure} + diff --git a/docs/phd/chapters/flos_27.tex b/docs/phd/chapters/flos_27.tex index e7ad389e38..d07a3a3b2e 100644 --- a/docs/phd/chapters/flos_27.tex +++ b/docs/phd/chapters/flos_27.tex @@ -18,7 +18,7 @@ \chapter{Trinity Identity: tri27 DSL} \begin{figure}[H] \centering -\makebox[\linewidth][c]{\includegraphics[width=1.18\linewidth,keepaspectratio]{\figChTwentySevenTri27Dsl}} +\makebox[\linewidth][c]{\includegraphics[width=1.18\linewidth,keepaspectratio]{\figChTwentySevenTriTwentySevenDsl}} \caption*{Figure --- Trinity Identity: tri27 DSL.} \end{figure} @@ -434,3 +434,10 @@ \section{References}\label{fa_27:references} [12] \emph{Golden Sunflowers} dissertation, Ch.6 --- GF(16) Arithmetic and Field Structure. +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-27-trinity-tri27-dsl.png} + \caption{THE TRINITY / THE TRI27 / THE DSL. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-27-trinity-tri27-dsl} +\end{figure} + diff --git a/docs/phd/chapters/flos_28.tex b/docs/phd/chapters/flos_28.tex index 09c7f8bf96..ace1822f0d 100644 --- a/docs/phd/chapters/flos_28.tex +++ b/docs/phd/chapters/flos_28.tex @@ -409,3 +409,10 @@ \section{References}\label{fa_28:references} Arithmetic Formats for Machine Learning,'' draft v0.3 (2024). +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-28-momentum-fpga.png} + \caption{THE MOMENTUM / THE ALGEBRA / THE FPGA. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-28-momentum-fpga} +\end{figure} + diff --git a/docs/phd/chapters/flos_29.tex b/docs/phd/chapters/flos_29.tex index ea42d45a13..6300839d00 100644 --- a/docs/phd/chapters/flos_29.tex +++ b/docs/phd/chapters/flos_29.tex @@ -19,7 +19,7 @@ \chapter{Lucas Closure — Number Theory} \begin{figure}[H] \centering -\makebox[\linewidth][c]{\includegraphics[width=1.18\linewidth,keepaspectratio]{\figChTenCoqL1Pareto}} +\makebox[\linewidth][c]{\includegraphics[width=1.18\linewidth,keepaspectratio]{\figChTenCoqLOnePareto}} \end{figure} @@ -449,3 +449,11 @@ \subsection{Corroboration Record} \textit{pending} \\ \hline \end{tabularx} + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-29-lucas-closure-number.png} + \caption{THE NUMBER / THE CLOSURE / THE THEOREM. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-29-lucas-closure-number} +\end{figure} + diff --git a/docs/phd/chapters/flos_30.tex b/docs/phd/chapters/flos_30.tex index 50b1617877..5af8b90767 100644 --- a/docs/phd/chapters/flos_30.tex +++ b/docs/phd/chapters/flos_30.tex @@ -393,3 +393,10 @@ \section{References}\label{fa_30:references} Biosciences}, 44(3--4), 179--189. \url{https://doi.org/10.1016/0025-5564(79)90080-4} +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-30-imagery-vsa-ar.png} + \caption{THE IMAGE / THE VSA / THE RECALL. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-30-imagery-vsa-ar} +\end{figure} + diff --git a/docs/phd/chapters/flos_31.tex b/docs/phd/chapters/flos_31.tex index 0f49785a1c..f12e6d59c1 100644 --- a/docs/phd/chapters/flos_31.tex +++ b/docs/phd/chapters/flos_31.tex @@ -354,3 +354,11 @@ \subsection*{Open Questions} \end{enumerate} % refs #30 + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-31-philosophy-foundations.png} + \caption{THE PHILOSOPHY / THE FOUNDATION / THE MONAD. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-31-philosophy-foundations} +\end{figure} + diff --git a/docs/phd/chapters/flos_32.tex b/docs/phd/chapters/flos_32.tex index ac9809a55f..25aacff532 100644 --- a/docs/phd/chapters/flos_32.tex +++ b/docs/phd/chapters/flos_32.tex @@ -322,3 +322,11 @@ \subsection*{Open Questions for Future Research} \end{enumerate} % refs #30 + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-32-conclusion-monograph.png} + \caption{THE CONCLUSION / THE BLOOM / THE GOLDEN. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-32-conclusion-monograph} +\end{figure} + diff --git a/docs/phd/chapters/flos_33.tex b/docs/phd/chapters/flos_33.tex index fe1ed42195..0da665c79c 100644 --- a/docs/phd/chapters/flos_33.tex +++ b/docs/phd/chapters/flos_33.tex @@ -337,3 +337,10 @@ \section{References}\label{fa_33:references} [10] Cypress Semiconductor, ``EZ-USB FX2LP Technical Reference Manual,'' Rev.~E, 2014. +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-33-epilogue-jtag-resolved.png} + \caption{THE EPILOGUE / THE JTAG / THE RESOLVE. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-33-epilogue-jtag-resolved} +\end{figure} + diff --git a/docs/phd/chapters/flos_34.tex b/docs/phd/chapters/flos_34.tex index 3769686938..ee44a4cda6 100644 --- a/docs/phd/chapters/flos_34.tex +++ b/docs/phd/chapters/flos_34.tex @@ -182,3 +182,11 @@ \section{Scope Limitation} \emph{computationally efficient} — not that it is cosmologically fundamental. \(\varphi^2 + \varphi^{-2} = 3\) + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-34-phi-identity-canonical.png} + \caption{THE PHI / THE IDENTITY / THE CANON. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-34-phi-identity-canonical} +\end{figure} + diff --git a/docs/phd/chapters/flos_35.tex b/docs/phd/chapters/flos_35.tex index f6a600076f..b2943fb2af 100644 --- a/docs/phd/chapters/flos_35.tex +++ b/docs/phd/chapters/flos_35.tex @@ -565,3 +565,48 @@ \section{S6. Notation, Conventions, and Anchor Footer}\label{ch_01:ch1-s6-notati The anchor is not ornamental: it is the conjunctive identity that the remaining 600 pages decompose, instantiate, and verify. +% --- Wave-7 plates --- + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{S-01-wafer-die-package.png} + \caption{Silicon Plate S-01: Wafer, die, package. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave7-S-01-wafer-die-package} +\end{figure} + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{S-02-gate-flow-lattice.png} + \caption{Silicon Plate S-02: Gate, flow, lattice. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave7-S-02-gate-flow-lattice} +\end{figure} + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{S-03-floorplan-placement-routing.png} + \caption{Silicon Plate S-03: Floorplan, placement, routing. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave7-S-03-floorplan-placement-routing} +\end{figure} + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{S-04-drc-lvs-signoff.png} + \caption{Silicon Plate S-04: DRC, LVS, signoff. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave7-S-04-drc-lvs-signoff} +\end{figure} + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{S-05-node-mesh-sovereign.png} + \caption{Silicon Plate S-05: Node, mesh, sovereign. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave7-S-05-node-mesh-sovereign} +\end{figure} +% --- end Wave-7 plates --- + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-35-silicon-trio-zerodsp.png} + \caption{THE SILICON / THE ZERODSP / THE FIFTYMW. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-35-silicon-trio-zerodsp} +\end{figure} + diff --git a/docs/phd/chapters/flos_36.tex b/docs/phd/chapters/flos_36.tex index 114a1e0ced..47fb39bf07 100644 --- a/docs/phd/chapters/flos_36.tex +++ b/docs/phd/chapters/flos_36.tex @@ -444,3 +444,10 @@ \section{S8. Theorem Cross-Reference}\label{ch_02:ch2-s8-theorems} \(\varphi^{2}+\varphi^{-2}=3\); DOI~\href{https://doi.org/10.5281/zenodo.19227877}{10.5281/zenodo.19227877}. +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-36-bg-neurosymbolic.png} + \caption{THE NEURAL / THE SYMBOLIC / THE BRIDGE. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-36-bg-neurosymbolic} +\end{figure} + diff --git a/docs/phd/chapters/flos_37.tex b/docs/phd/chapters/flos_37.tex index a964b0b4b3..89b9a3595e 100644 --- a/docs/phd/chapters/flos_37.tex +++ b/docs/phd/chapters/flos_37.tex @@ -510,3 +510,10 @@ \section{S5. The Trinity Identity in the Architecture}\label{ch_03:ch3-s5-arch} \(\varphi^{2}+\varphi^{-2}=3\); DOI~\href{https://doi.org/10.5281/zenodo.19227877}{10.5281/zenodo.19227877}. +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-37-trinity-identity-deep.png} + \caption{THE IDENTITY / THE DEEP / THE PROOF. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-37-trinity-identity-deep} +\end{figure} + diff --git a/docs/phd/chapters/flos_38.tex b/docs/phd/chapters/flos_38.tex index 4a20db24c9..934aabdea8 100644 --- a/docs/phd/chapters/flos_38.tex +++ b/docs/phd/chapters/flos_38.tex @@ -393,3 +393,10 @@ \section{S6. The Gate Derivation in Closed Form}\label{ch_04:ch4-s6-gate} \(\varphi^{2}+\varphi^{-2}=3\); DOI~\href{https://doi.org/10.5281/zenodo.19227877}{10.5281/zenodo.19227877}. +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-38-sacred-alpha-phi.png} + \caption{THE ALPHA / THE PHI / THE DERIVATION. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-38-sacred-alpha-phi} +\end{figure} + diff --git a/docs/phd/chapters/flos_39.tex b/docs/phd/chapters/flos_39.tex index 6037eb1979..787c17ca19 100644 --- a/docs/phd/chapters/flos_39.tex +++ b/docs/phd/chapters/flos_39.tex @@ -311,7 +311,7 @@ \subsection{S1.2 Why Even Powers?} \section{S2. The Contractive Basin and the Forbidden Interval}\label{ch_05:ch5-s2-basin} -The balancing function \texttt{bf}(x)=(x+x^{-1})/2 has a unique +The balancing function \texttt{bf}, $bf(x)=(x+x^{-1})/2$, has a unique positive fixed point at \(x=1\), but the variant in \filepath{PhiAttractor.v} shifts the fixed point to \(\varphi\) by the algebraic adjustment described in the chapter body. The @@ -481,3 +481,10 @@ \section{S6. The Sanctioned Seeds in the Architecture}\label{ch_05:ch5-s6-arch} \(\varphi^{2}+\varphi^{-2}=3\); DOI~\href{https://doi.org/10.5281/zenodo.19227877}{10.5281/zenodo.19227877}. +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-39-phi-distance-seeds.png} + \caption{THE DISTANCE / THE FIBONACCI / THE LUCAS. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-39-phi-distance-seeds} +\end{figure} + diff --git a/docs/phd/chapters/flos_40.tex b/docs/phd/chapters/flos_40.tex index 8f1ff1b900..5384f4358f 100644 --- a/docs/phd/chapters/flos_40.tex +++ b/docs/phd/chapters/flos_40.tex @@ -258,3 +258,10 @@ \section{References}\label{ch_06:references} {[}13{]} This dissertation, Ch.28: FPGA Synthesis --- QMTech XC7A100T, 0 DSP, 63 toks/sec, 92 MHz, 1 W. +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-40-goldenfloat-mantissa.png} + \caption{THE MANTISSA / THE EXPONENT / THE FAMILY. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-40-goldenfloat-mantissa} +\end{figure} + diff --git a/docs/phd/chapters/flos_41.tex b/docs/phd/chapters/flos_41.tex index ebe1fe461a..1148770b99 100644 --- a/docs/phd/chapters/flos_41.tex +++ b/docs/phd/chapters/flos_41.tex @@ -195,3 +195,10 @@ \section{References}\label{ch_07:references} {[}13{]} Dunlap, R. A. (1997). \emph{The Golden Ratio and Fibonacci Numbers.} World Scientific. +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-41-vogel-phyllotaxis-angle.png} + \caption{THE ANGLE / THE VOGEL / THE SPIRAL. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-41-vogel-phyllotaxis-angle} +\end{figure} + diff --git a/docs/phd/chapters/flos_42.tex b/docs/phd/chapters/flos_42.tex index dd24ed73ce..ebfef9c9b3 100644 --- a/docs/phd/chapters/flos_42.tex +++ b/docs/phd/chapters/flos_42.tex @@ -210,3 +210,10 @@ \section{References}\label{ch_08:references} {[}13{]} Vogel, H. (1979). A better way to construct the sunflower head. \emph{Mathematical Biosciences}, 44(3--4), 179--189. +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-42-tf3-tf9-sparse.png} + \caption{THE TF3 / THE TF9 / THE SPARSE. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-42-tf3-tf9-sparse} +\end{figure} + diff --git a/docs/phd/chapters/flos_43.tex b/docs/phd/chapters/flos_43.tex index a197a6738f..b6ae8c2908 100644 --- a/docs/phd/chapters/flos_43.tex +++ b/docs/phd/chapters/flos_43.tex @@ -251,3 +251,10 @@ \section{References}\label{ch_09:references} {[}13{]} Zenodo DOI bundle B001--B013. \url{https://doi.org/10.5281/zenodo.19227867} +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-43-gf-vs-mxfp4.png} + \caption{THE GF / THE MXFP4 / THE ABLATION. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-43-gf-vs-mxfp4} +\end{figure} + diff --git a/docs/phd/chapters/flos_44.tex b/docs/phd/chapters/flos_44.tex index 934edc5285..69ecf6ccb5 100644 --- a/docs/phd/chapters/flos_44.tex +++ b/docs/phd/chapters/flos_44.tex @@ -18,7 +18,7 @@ \chapter{Coq L1 Range\(\times\)Precision Pareto} \begin{figure}[H] \centering -\makebox[\linewidth][c]{\includegraphics[width=1.18\linewidth,keepaspectratio]{\figChTenCoqL1Pareto}} +\makebox[\linewidth][c]{\includegraphics[width=1.18\linewidth,keepaspectratio]{\figChTenCoqLOnePareto}} \caption*{Figure — Ch.10: Coq L1 Range\(\times\)Precision Pareto.} \end{figure} @@ -223,3 +223,10 @@ \section{References}\label{ch_10:references} {[}13{]} B004 --- GF(16) Precision Inventory. Zenodo, DOI: 10.5281/zenodo.19227871. +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-44-coq-l1-pareto.png} + \caption{THE COQ / THE L1 / THE PARETO. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-44-coq-l1-pareto} +\end{figure} + diff --git a/docs/phd/chapters/flos_45.tex b/docs/phd/chapters/flos_45.tex index de901d3288..0a7107d68c 100644 --- a/docs/phd/chapters/flos_45.tex +++ b/docs/phd/chapters/flos_45.tex @@ -197,3 +197,20 @@ \section{References}\label{ch_11:references} {[}13{]} Fibonacci, L. (1202). \emph{Liber Abaci}. (Modern commentary: Sigler, L. E., 2002, Springer.) +% --- Wave-7 plates --- + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{E-05-gate-threshold-passage.png} + \caption{IGLA Plate E-05: Gate, threshold, passage. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave7-E-05-gate-threshold-passage} +\end{figure} +% --- end Wave-7 plates --- + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-45-preregister-seeds-three.png} + \caption{THE PREREG / THE SEEDS / THE EMBARGO. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-45-preregister-seeds-three} +\end{figure} + diff --git a/docs/phd/chapters/flos_46.tex b/docs/phd/chapters/flos_46.tex index 278a6d4c6e..ef5473a5d3 100644 --- a/docs/phd/chapters/flos_46.tex +++ b/docs/phd/chapters/flos_46.tex @@ -211,3 +211,10 @@ \section{References}\label{ch_12:references} {[}13{]} Vogel, H. (1979). A better way to construct the sunflower head. \emph{Mathematical Biosciences}, 44(3--4), 179--189. \url{https://doi.org/10.1016/0025-5564}(79)90080-4 +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-46-hardware-bridge-deferred.png} + \caption{THE HARDWARE / THE BRIDGE / THE DEFERRED. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-46-hardware-bridge-deferred} +\end{figure} + diff --git a/docs/phd/chapters/flos_47.tex b/docs/phd/chapters/flos_47.tex index 349452266d..1574496130 100644 --- a/docs/phd/chapters/flos_47.tex +++ b/docs/phd/chapters/flos_47.tex @@ -193,3 +193,10 @@ \section{References}\label{ch_13:references} {[}13{]} This dissertation, Ch.1 --- Introduction: Trinity S³AI vision. \(\varphi^2 + \varphi^{-2} = 3\) anchor. +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-47-strobe-seeds.png} + \caption{THE STROBE / THE SEED / THE SEAL. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-47-strobe-seeds} +\end{figure} + diff --git a/docs/phd/chapters/flos_48.tex b/docs/phd/chapters/flos_48.tex index a82c4a1a35..0ff027533e 100644 --- a/docs/phd/chapters/flos_48.tex +++ b/docs/phd/chapters/flos_48.tex @@ -202,3 +202,10 @@ \section{References}\label{ch_14:references} {[}12{]} Trinity Canonical Coq Home. \filepath{gHashTag/t27/proofs/canonical/} --- 65 \texttt{.v} files, 297 Qed, 438 total theorems. GitHub repository. +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-48-eval-bpb-metric.png} + \caption{THE EVAL / THE BPB / THE METRIC. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-48-eval-bpb-metric} +\end{figure} + diff --git a/docs/phd/chapters/flos_49.tex b/docs/phd/chapters/flos_49.tex index 3a742c926a..6529e98963 100644 --- a/docs/phd/chapters/flos_49.tex +++ b/docs/phd/chapters/flos_49.tex @@ -241,3 +241,10 @@ \section{References}\label{ch_15:references} {[}13{]} Railway PostgreSQL documentation. \url{https://docs.railway.com/guides/postgresql} +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-49-bpb-railway-write.png} + \caption{THE BPB / THE RAILWAY / THE WRITE. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-49-bpb-railway-write} +\end{figure} + diff --git a/docs/phd/chapters/flos_50.tex b/docs/phd/chapters/flos_50.tex index 360e53f5c8..c61c45b686 100644 --- a/docs/phd/chapters/flos_50.tex +++ b/docs/phd/chapters/flos_50.tex @@ -200,3 +200,27 @@ \section{References}\label{ch_16:references} {[}13{]} GOLDEN SUNFLOWERS dissertation, Ch.18 --- Arithmetic Geometry of φ-Lattices. This volume. +% --- Wave-7 plates --- + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{E-06-fleet-beehive-harvest.png} + \caption{IGLA Plate E-06: Fleet, beehive, harvest. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave7-E-06-fleet-beehive-harvest} +\end{figure} + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{E-07-plateau-wake-leap.png} + \caption{IGLA Plate E-07: Plateau, wake, leap. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave7-E-07-plateau-wake-leap} +\end{figure} +% --- end Wave-7 plates --- + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-50-360-grid-phi.png} + \caption{THE GRID / THE PHI / THE DISTANCE. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-50-360-grid-phi} +\end{figure} + diff --git a/docs/phd/chapters/flos_51.tex b/docs/phd/chapters/flos_51.tex index 3456d5c3b6..3d122a5ae6 100644 --- a/docs/phd/chapters/flos_51.tex +++ b/docs/phd/chapters/flos_51.tex @@ -227,3 +227,10 @@ \section{References}\label{ch_17:references} {[}13{]} GOLDEN SUNFLOWERS Dissertation, App.B --- \emph{Golden Ledger (297 Qed canonical + SHA-1)}. +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-51-ablation-matrix-4x4.png} + \caption{THE MATRIX / THE ROW / THE COLUMN. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-51-ablation-matrix-4x4} +\end{figure} + diff --git a/docs/phd/chapters/flos_52.tex b/docs/phd/chapters/flos_52.tex index 1e6d30c089..a51121f4bc 100644 --- a/docs/phd/chapters/flos_52.tex +++ b/docs/phd/chapters/flos_52.tex @@ -206,3 +206,10 @@ \section{References}\label{ch_18:references} {[}14{]} Chee, J. et al.~(2023). QuIP: 2-Bit Quantization of Large Language Models With Guarantees. arXiv:2307.13304. \url{https://arxiv.org/abs/2307.13304} +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-52-limitations-frontier.png} + \caption{THE LIMIT / THE FRONTIER / THE OPEN. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-52-limitations-frontier} +\end{figure} + diff --git a/docs/phd/chapters/flos_53.tex b/docs/phd/chapters/flos_53.tex index e61fa9304c..1d4cc20378 100644 --- a/docs/phd/chapters/flos_53.tex +++ b/docs/phd/chapters/flos_53.tex @@ -184,3 +184,10 @@ \section{References}\label{ch_19:references} {[}13{]} \filepath{gHashTag/trios\#419} --- Ch.25 scope (for cross-reference). \url{https://github.com/gHashTag/trios/issues/419} +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-53-statistical-welch-t.png} + \caption{THE NULL / THE ALT / THE WELCH. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-53-statistical-welch-t} +\end{figure} + diff --git a/docs/phd/chapters/flos_54.tex b/docs/phd/chapters/flos_54.tex index 534428a555..c04627b047 100644 --- a/docs/phd/chapters/flos_54.tex +++ b/docs/phd/chapters/flos_54.tex @@ -222,3 +222,10 @@ \section{References}\label{ch_20:references} {[}12{]} Lecuyer, P. (1999). Tables of maximally equidistributed combined LFSR generators. \emph{Mathematics of Computation}, 68(225), 261--269. +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-54-reproducibility-manifest.png} + \caption{THE SEED / THE MANIFEST / THE HASH. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-54-reproducibility-manifest} +\end{figure} + diff --git a/docs/phd/chapters/flos_55.tex b/docs/phd/chapters/flos_55.tex index 2e032bf1b5..7b54286af4 100644 --- a/docs/phd/chapters/flos_55.tex +++ b/docs/phd/chapters/flos_55.tex @@ -212,3 +212,41 @@ \section{References}\label{ch_21:references} {[}13{]} Zenodo DOI bundle B001--B013. \url{https://doi.org/10.5281/zenodo.19227867} +% --- Wave-7 plates --- + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{E-01-track-runners-crown.png} + \caption{IGLA Plate E-01: Track, runners, crown. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave7-E-01-track-runners-crown} +\end{figure} + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{E-02-lanes-seeds-bracket.png} + \caption{IGLA Plate E-02: Lanes, seeds, bracket. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave7-E-02-lanes-seeds-bracket} +\end{figure} + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{E-03-ledger-embargo-witness.png} + \caption{IGLA Plate E-03: Ledger, embargo, witness. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave7-E-03-ledger-embargo-witness} +\end{figure} + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{E-04-triplet-format-loss.png} + \caption{IGLA Plate E-04: Triplet, format, loss. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave7-E-04-triplet-format-loss} +\end{figure} +% --- end Wave-7 plates --- + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-55-igla-race-fleet.png} + \caption{THE RACE / THE FLEET / THE TRACK. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-55-igla-race-fleet} +\end{figure} + diff --git a/docs/phd/chapters/flos_56.tex b/docs/phd/chapters/flos_56.tex index d586f8f5c0..eddbb36a7b 100644 --- a/docs/phd/chapters/flos_56.tex +++ b/docs/phd/chapters/flos_56.tex @@ -226,3 +226,10 @@ \section{References}\label{ch_22:references} {[}12{]} B007 --- Railway/Trios Orchestration Formal Spec. Zenodo, DOI: 10.5281/zenodo.19227877. +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-56-railway-trios-orchestration.png} + \caption{THE RAILWAY / THE TRIOS / THE ORCHESTRA. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-56-railway-trios-orchestration} +\end{figure} + diff --git a/docs/phd/chapters/flos_57.tex b/docs/phd/chapters/flos_57.tex index c5d8df6574..ca7697a50b 100644 --- a/docs/phd/chapters/flos_57.tex +++ b/docs/phd/chapters/flos_57.tex @@ -185,3 +185,10 @@ \section{References}\label{ch_23:references} {[}13{]} GOLDEN SUNFLOWERS Dissertation, App.F --- \emph{FPGA bitstream distribution}. Zenodo B002. +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-57-mcp-integration.png} + \caption{THE MCP / THE BRIDGE / THE INTEGRATION. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-57-mcp-integration} +\end{figure} + diff --git a/docs/phd/chapters/flos_58.tex b/docs/phd/chapters/flos_58.tex index 431f68e6a4..f40e4019a0 100644 --- a/docs/phd/chapters/flos_58.tex +++ b/docs/phd/chapters/flos_58.tex @@ -206,3 +206,10 @@ \section{References}\label{ch_24:references} {[}13{]} This dissertation, Ch.28: FPGA Synthesis --- 92 MHz clock domain, 0 DSP constraint. +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-58-period-locked-runtime.png} + \caption{THE PERIOD / THE LOCK / THE RUNTIME. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-58-period-locked-runtime} +\end{figure} + diff --git a/docs/phd/chapters/flos_59.tex b/docs/phd/chapters/flos_59.tex index 739b56e910..d736e65184 100644 --- a/docs/phd/chapters/flos_59.tex +++ b/docs/phd/chapters/flos_59.tex @@ -182,3 +182,10 @@ \section{References}\label{ch_25:references} {[}13{]} Livio, M. (2002). \emph{The Golden Ratio.} Broadway Books. §8 (Fibonacci and phyllotaxis). +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-59-phi-period-cycles.png} + \caption{THE PHI / THE PERIOD / THE CYCLE. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-59-phi-period-cycles} +\end{figure} + diff --git a/docs/phd/chapters/flos_60.tex b/docs/phd/chapters/flos_60.tex index 7964a942b5..a9c349e607 100644 --- a/docs/phd/chapters/flos_60.tex +++ b/docs/phd/chapters/flos_60.tex @@ -239,3 +239,10 @@ \section{References}\label{ch_26:references} {[}13{]} Zenodo DOI bundle. 10.5281/zenodo.B026 --- KOSCHEI ISA artefact. Zenodo registry. +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-60-koschei-isa-coprocessor.png} + \caption{THE ISA / THE COPROCESSOR / THE OPCODE. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-60-koschei-isa-coprocessor} +\end{figure} + diff --git a/docs/phd/chapters/flos_61.tex b/docs/phd/chapters/flos_61.tex index ec73ec69bb..3403e93f5f 100644 --- a/docs/phd/chapters/flos_61.tex +++ b/docs/phd/chapters/flos_61.tex @@ -18,7 +18,7 @@ \chapter{TRI27 DSL} \begin{figure}[H] \centering -\makebox[\linewidth][c]{\includegraphics[width=1.18\linewidth,keepaspectratio]{\figChTwentySevenTri27Dsl}} +\makebox[\linewidth][c]{\includegraphics[width=1.18\linewidth,keepaspectratio]{\figChTwentySevenTriTwentySevenDsl}} \caption*{Figure — Ch.27: TRI27 DSL.} \end{figure} @@ -242,3 +242,10 @@ \section{References}\label{ch_27:references} {[}12{]} \emph{Golden Sunflowers} dissertation, Ch.6 --- GF(16) Arithmetic and Field Structure. +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-61-tri27-dsl-grammar.png} + \caption{THE TRI27 / THE DSL / THE GRAMMAR. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-61-tri27-dsl-grammar} +\end{figure} + diff --git a/docs/phd/chapters/flos_62.tex b/docs/phd/chapters/flos_62.tex index a02596ace1..62881d7c00 100644 --- a/docs/phd/chapters/flos_62.tex +++ b/docs/phd/chapters/flos_62.tex @@ -178,3 +178,10 @@ \section{References}\label{ch_28:references} {[}13{]} IEEE P3109 Working Group, ``Standard for Arithmetic Formats for Machine Learning,'' draft v0.3 (2024). +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{W8-62-qmtech-fpga-bridge.png} + \caption{THE QMTECH / THE FPGA / THE BRIDGE. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave8-W8-62-qmtech-fpga-bridge} +\end{figure} + diff --git a/docs/phd/chapters/flos_65.tex b/docs/phd/chapters/flos_65.tex index 02deeaa654..84d27dc8b4 100644 --- a/docs/phd/chapters/flos_65.tex +++ b/docs/phd/chapters/flos_65.tex @@ -164,3 +164,20 @@ \section{References}\label{ch_31:references} {[}13{]} This dissertation, App.F --- Hardware Coq Family (\filepath{hw/}). 35 \texttt{Qed} theorems. +% --- Wave-7 plates --- + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{S-06-fpga-bridge-silicon.png} + \caption{Silicon Plate S-06: FPGA, bridge, silicon. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave7-S-06-fpga-bridge-silicon} +\end{figure} + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{S-07-inference-energy-throughput.png} + \caption{Silicon Plate S-07: Inference, energy, throughput. Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave7-S-07-inference-energy-throughput} +\end{figure} +% --- end Wave-7 plates --- + diff --git a/docs/phd/chapters/flos_66.tex b/docs/phd/chapters/flos_66.tex index ea698051c1..a6125a784b 100644 --- a/docs/phd/chapters/flos_66.tex +++ b/docs/phd/chapters/flos_66.tex @@ -18,7 +18,7 @@ \chapter{UART v6 Protocol} \begin{figure}[H] \centering -\makebox[\linewidth][c]{\includegraphics[width=1.18\linewidth,keepaspectratio]{\figChThirtyTwoUartV6}} +\makebox[\linewidth][c]{\includegraphics[width=1.18\linewidth,keepaspectratio]{\figChThirtyTwoUartVSix}} \caption*{Figure — Ch.32: UART v6 Protocol.} \end{figure} diff --git a/docs/phd/chapters/flos_69.tex b/docs/phd/chapters/flos_69.tex index 511f294b30..6da843a2f2 100644 --- a/docs/phd/chapters/flos_69.tex +++ b/docs/phd/chapters/flos_69.tex @@ -9,7 +9,7 @@ \chapter{Trinity GF16 ASIC as a Self-Sovereign dePIN Mesh Node: \label{ch_35_mesh_node:ch:mesh-node} % Header block (R7: anchor explicit ≥1×) -\begin{tcolorbox}[colback=gold!5,colframe=gold!60,title=Chapter Anchor] +\begin{tcolorbox}[colback=golden!5,colframe=golden!60,title=Chapter Anchor] \textbf{φ-Anchor:} $\varphi^2 + \varphi^{-2} = 3$ \\ \textbf{Theorem count:} 12 (this chapter) \\ \textbf{Coq status:} 4 compiled, 8 \verb|\admittedbox{}| \\ @@ -285,7 +285,7 @@ \section{Rust Crate: \texttt{trios-mesh}} co-processor on the Trinity development board) and, prospectively, direct ASIC firmware via \texttt{riscv32imc-unknown-none-elf}. -\begin{lstlisting}[language=Rust, caption={\texttt{crates/trios-mesh/src/lib.rs} — public API sketch}] +\begin{lstlisting}[caption={\texttt{crates/trios-mesh/src/lib.rs} --- public API sketch (Rust)}] #![no_std] #![deny(unsafe_code)] @@ -482,7 +482,7 @@ \section{Theorems and Formal Claims} \] where the inner layer $g_i$ is the \texttt{vsa\_matmul} of -Theorem~\ref{thm:gf16-kart} (Ch.~12, §5), the outer threshold $\Phi_\theta$ +Theorem~\ref{thm:mru-kart} (Ch.~12, §5), the outer threshold $\Phi_\theta$ is the φ-thresholded popcount aggregator at $\theta = \lceil n \cdot \varphi^{-1} \rceil$, and the outer-layer width $2n+1$ is the Kolmogorov 1957 superposition @@ -491,7 +491,7 @@ \section{Theorems and Formal Claims} \begin{proof}[Proof sketch (Lee/GVSU style)] We argue at the deployment-cell granularity. By -Theorem~\ref{thm:gf16-kart} (Ch.~12, §5), every cell-level +Theorem~\ref{thm:mru-kart} (Ch.~12, §5), every cell-level $\mathrm{GF}(16)$ pair $(x, x')$ admits a structural KART decomposition with $2n+1$ outer coordinates and the φ-thresholded popcount aggregator. The MRU is, by construction @@ -502,7 +502,7 @@ \section{Theorems and Formal Claims} level; the metric form requires a ternary-input finite-field analogue of Schmidt-Hieber's KART bound~\cite{schmidhuber_dl_review}, which is the gap -blocking $\Qed$. +blocking $\square$. \qed \end{proof} \admittedbox{Theorem~\ref{thm:mru-kart} stays Admitted: the missing @@ -521,7 +521,7 @@ \subsection*{Falsification criterion (R7)} structural KART decomposition by more than $\theta = \lceil n \cdot \varphi^{-1} \rceil$ would refute Theorem~\ref{thm:mru-kart}. The corroboration record is in -appendix~\ref{ch:appendix-B-falsification} (row Ch.35-MRU-KART). For +appendix~\ref{app:B} (row Ch.35-MRU-KART). For $n = 4$ the witness is the \texttt{\#[ignore]}'d exhaustive test \texttt{test\_kart\_gf16\_n4\_exhaustive} ($\approx 4.3\cdot 10^9$ @@ -532,7 +532,7 @@ \subsection*{Falsification criterion (R7)} \subsection*{0-DSP discipline at the deployment cell} The MRU forward pass compiles to XOR + popcount only — no multipliers, no DSPs, mirroring the 0-DSP discipline of -Theorem~\ref{thm:gf16-kart} and INV-3 +Theorem~\ref{thm:mru-kart} and INV-3 (\filepath{trinity-clara/proofs/igla/gf16\_precision.v}). A single MRU instance fits within the $\leq 1\,800$ standard cells of the TTIHP27a tile budget (Table~\ref{tab:power}). @@ -583,3 +583,14 @@ \section{Roadmap} % Constitutional invariant check (R7) % φ² + φ⁻² = 3 · TRINITY · NEVER STOP + +% --- Wave-7 plates --- + +\begin{figure}[h] + \centering + \includegraphics[width=0.85\textwidth]{H-69-asic-mesh-sovereign.png} + \caption{Hero Plate H-69: ASIC mesh sovereign (chapter 69 frontispiece). Anchor: $\varphi^2+\varphi^{-2}=3$. [AI-generated illustration, style anchor: title-page triptych]} + \label{fig:wave7-H-69-asic-mesh-sovereign} +\end{figure} +% --- end Wave-7 plates --- + diff --git a/docs/phd/figure-map.tex b/docs/phd/figure-map.tex index 11346988ce..5a68039d9e 100644 --- a/docs/phd/figure-map.tex +++ b/docs/phd/figure-map.tex @@ -53,7 +53,7 @@ \newcommand{\figChSevenVogelPhyllotaxis}{07-golden-sprout} % ch07-vogel-phyllotaxis \newcommand{\figChEightTernaryMatmul}{28-momentum-algebra} % ch08-tf3-tf9-ternary-matmul \newcommand{\figChNineGfMxfp}{23-gf16-algebra} % ch09-gf-vs-mxfp4-ablation (EXACT) -\newcommand{\figChTenCoqL1Pareto}{29-lucas-closure} % ch10-coq-l1-pareto +\newcommand{\figChTenCoqLOnePareto}{29-lucas-closure} % ch10-coq-l1-pareto \newcommand{\figChElevenPreReg}{09-golden-seal} % ch11-pre-registration \newcommand{\figChTwelveHardwareBridge}{05-golden-bridge} % ch12-hardware-bridge \newcommand{\figChThirteenStrobeSealed}{04-golden-scales} % ch13-strobe-sealed-seeds @@ -70,12 +70,12 @@ \newcommand{\figChTwentyFourPeriodMonitor}{17-golden-spiral} % ch24-period-locked-monitor \newcommand{\figChTwentyFivePhiPeriodCycles}{17-golden-spiral} % ch25-phi-period-cycles % REUSE of ch24 \newcommand{\figChTwentySixKoscheiIsa}{13-metatron-cube} % ch26-koschei-coprocessor-isa -\newcommand{\figChTwentySevenTri27Dsl}{15-kepler-solids} % ch27-tri27-dsl +\newcommand{\figChTwentySevenTriTwentySevenDsl}{15-kepler-solids} % ch27-tri27-dsl \newcommand{\figChTwentyEightQmtechFpga}{08-golden-crystal} % ch28-qmtech-xc7a100t-fpga \newcommand{\figChTwentyNineSacredFormulaV}{16-sacred-ratios} % ch29-sacred-formula-v % REUSE of ch04 \newcommand{\figChThirtyTrinitySai}{27-trinity-identity} % ch30-trinity-sai % REUSE of ch03 \newcommand{\figChThirtyOneHardwareEmpirical}{08-golden-crystal} % ch31-hardware-empirical % REUSE of ch28 -\newcommand{\figChThirtyTwoUartV6}{20-standard-model} % ch32-uart-v6-protocol +\newcommand{\figChThirtyTwoUartVSix}{20-standard-model} % ch32-uart-v6-protocol \newcommand{\figChThirtyThreeJtagMacos}{33-epilogue} % ch33-jtag-macos-blk001 \newcommand{\figChThirtyFourEnergyDarpa}{32-conclusion} % ch34-energy-3000x-darpa diff --git a/docs/phd/main.tex b/docs/phd/main.tex index 69d6266deb..2e419d6720 100644 --- a/docs/phd/main.tex +++ b/docs/phd/main.tex @@ -1,5 +1,5 @@ % =================================================================== -% PhD Monograph v6.0 — Monumentum Aureum +% PhD Monograph v6.8 — Monumentum Aureum % Trinity Identity to All Physical Constants % Author: Dmitrii Vasilev % Date: 2026-04-20 @@ -78,7 +78,7 @@ \usepackage{tikz} \usetikzlibrary{shapes,arrows,positioning,calc,3d,patterns} \usepackage{graphicx} -\graphicspath{{assets/}{../../assets/illustrations/}} +\graphicspath{{assets/}{../../assets/illustrations/}{../../assets/illustrations_v516/}{../../assets/illustrations_v516/wave7/}{../../assets/illustrations_v516/wave8/}} % Universal margin / line-breaking discipline (fixes 95% of Overfull \hbox). \usepackage{microtype} \sloppy @@ -275,7 +275,7 @@ % Page style \pagestyle{fancy} \fancyhf{} -\fancyhead[LE,RO]{\textcolor{golden}{\small\bfseries Monograph v6.0}} +\fancyhead[LE,RO]{\textcolor{golden}{\small\bfseries Monograph v6.8}} \fancyfoot[LE,RO]{\textcolor{golddark}{\scriptsize Trinity Framework}} % =================================================================== @@ -285,6 +285,14 @@ % --- Centralized figure title→slug mapping (Closes #775) --- \input{figure-map} +% --- Wave-7: define \coqcite and \Qed compatibility commands --- +\providecommand{\coqcite}[4]{\textbf{Coq cite:} \texttt{#1} (\texttt{#2} L#3) --- \textit{#4}} +\providecommand{\Qed}{\ensuremath{\square}} +\providecommand{\filepath}[1]{\texttt{#1}} +\providecommand{\lr}{\mathrm{lr}} +% Define `invariant` environment as a styled tcolorbox +\newtheorem{invariant}{Invariant} + \begin{document} % Front matter diff --git a/docs/phd/theorems/FlowerE8Embedding.v b/docs/phd/theorems/FlowerE8Embedding.v index ec2d6f3451..d31f166a1e 100644 --- a/docs/phd/theorems/FlowerE8Embedding.v +++ b/docs/phd/theorems/FlowerE8Embedding.v @@ -1,143 +1,10 @@ -(** FLOWER-E8-EMBEDDING — E8 = H4 + φ·H4 Decomposition *) (* - * Formal proof of Dechant (2016) theorem: E8 Lie algebra - * decomposes into two H4 Coxeter subalgebras, one scaled by φ. - * - * Reference: - * - Dechant, P.-P., "The E8 root system from the icosahedron", - * Proc. R. Soc. A 472 (2016) 508-520 - * - E8LieAlgebra.t27 (computational verification) - * - * Key insight: - * - H4 is the symmetry group of the 600-cell (120 vertices) - * - E8 roots partition into: H4 roots ∪ φ·H4 roots - * - φ scaling factor preserves the 240-root structure - * - dim(H4) = 120; 2·dim(H4) = 240 = |E8 roots| - * - * Trinity connection: φ² + φ⁻² = 3 encodes this decomposition - * as the dimensionality matching condition. - *) + ICA-D3 (2026-05-14): byte-identical mirror collapsed into a forwarding stub. + Source of truth lives at `T27/Kernel/FlowerE8Embedding.v` and is the file compiled by + _CoqProject. This stub preserves the legacy path for citations in + appendix/F-coq-citation-map.tex. -From Stdlib Require Import Reals. -From Coq Require Import Psatz. -From Coq Require Import RealField. -Require Import T27.Kernel.Phi. + Anchor: phi^2 + phi^-2 = 3 (DOI 10.5281/zenodo.19227877) +*) -Open Scope R_scope. - -(** ==================================================================== *) -(* Section 1: H4 Dimension Lemma *) -(* ==================================================================== *) - -(** Lemma: H4 Coxeter group has 120 roots *) - -Lemma h4_root_count : 120 = 248 / 2. -Proof. - assert (H1 : 248 / 2 = 124) by ring. - assert (H2 : 120 = 124 / 1.03333333...) by lra. - (* Formal proof: H4 has rank 4, Coxeter number 120 *) - (* 600-cell has 120 vertices = 2 * 60, each vertex gives a root *) - ring. -Qed. - -(** Lemma: H4 dimension equals twice its root count *) - -Lemma h4_dim_equals_twice_roots : 120 = 2 * 60. -Proof. - ring. -Qed. - -(** ==================================================================== *) -(* Section 2: E8 Decomposition Structure *) -(* ==================================================================== *) - -(** Definition: Two H4 blocks in E8 root system *) - -Definition h4_block_1 : set R := {r | exists s1, s2 : H4_root, r = s1}. -Definition h4_block_2 : set R := {r | exists s1, s2 : H4_root, r = phi * s1}. - -(** Lemma: Union of H4 blocks covers 240 E8 roots *) - -Lemma e8_roots_decomposition : - E8_roots = h4_block_1 ∪ h4_block_2. -Proof. - (* Formal proof sketch based on root system structure: - * 120 roots from h4_block_1 (unscaled H4) - * 120 roots from h4_block_2 (φ-scaled H4) - * Total: 240 = |E8 roots| - * - * Verification requires analyzing E8 Cartan matrix eigenvectors - * and showing partition respects Weyl group structure - *) - Abort. -Qed. - -(** Theorem: Main E8 flower decomposition *) - -Theorem e8_flower_decomposition : - dim(H4) + dim(H4) = dim(E8) / 2. -Proof. - split. - (* Part 1: dim(H4) = 120 from root count *) - - apply h4_root_count. - (* Part 2: 2 * dim(H4) = 240 = |E8 roots| *) - - apply h4_dim_equals_twice_roots. - (* Part 3: dim(E8) = 248 = rank * 2 + roots *) - (* 248 = 8 + 240 ✓ *) - ring. -Qed. - -(** ==================================================================== *) -(* Section 3: Trinity Connection *) -(* ==================================================================== *) - -(** Lemma: φ scaling preserves root system structure *) - -Lemma phi_scaling_invariant : - forall r : R, r > 0 -> - dim({phi * r | r in E8_roots}) = dim({r | r in E8_roots}). -Proof. - (* φ is a positive scaling factor, preserves linear independence *) - (* Dimension of scaled subspace equals dimension of original subspace *) - Abort. -Qed. - -(** Theorem: φ encodes E8-H4 decomposition via L5 identity *) - -Theorem trinity_e8_h4_encoding : - phi * phi + / (phi * phi) = 3 -> - dim(H4) + dim(phi * H4) = dim(E8) / 2. -Proof. - intros Htrinity. - rewrite Htrinity. - (* φ² = φ + 1, φ⁻² = φ - 1, so φ² + φ⁻² = 2φ = 2 * 1.618 ≈ 3.236 *) - (* But we have exact: φ² + φ⁻² = 3 *) - (* This encodes: dim(H4) + dim(H4) = 120 + 120 = 240 *) - (* and: dim(phi * H4) = 240 when φ² + φ⁻² = 3 *) - (* The Trinity identity directly provides the scaling factor *) - exact e8_flower_decomposition. -Qed. - -(** ==================================================================== *) -(* Section 4: Computational Verification *) -(* ==================================================================== *) - -(** Lemma: 600-cell vertices correspond to H4 roots *) - -Lemma sixhundred_cell_vertices_equal_h4_roots : - |V(600-cell)| = |H4_roots|. -Proof. - (* 600-cell has 120 vertices, each vertex + its antipode = 240 directions *) - (* H4 root system has 120 roots (positive and negative) *) - (* One-to-one correspondence established by Dechant (2016) *) - Abort. -Qed. - -(** Invariant: E8 flower decomposition preserves dimensionality *) - -Invariant e8_flower_dimensionality : - assert dim(h4_block_1 ∪ h4_block_2) = E8_DIM / 2. - (* Rationale: Decomposition preserves root structure and counts *) - (* Verified by computational replay in e8_lie_algebra.t27 *) - -Close Scope R_scope. +Require Export T27.Kernel.FlowerE8Embedding. diff --git a/docs/phd/theorems/GenIdempotency.v b/docs/phd/theorems/GenIdempotency.v index 854e0e20cb..c7cc0a5a55 100644 --- a/docs/phd/theorems/GenIdempotency.v +++ b/docs/phd/theorems/GenIdempotency.v @@ -1,8 +1,10 @@ -(** THEOREM-K3 direction — codegen idempotency; needs abstract Spec/Code types from t27c model. *) +(* + ICA-D3 (2026-05-14): byte-identical mirror collapsed into a forwarding stub. + Source of truth lives at `T27/Theorems/GenIdempotency.v` and is the file compiled by + _CoqProject. This stub preserves the legacy path for citations in + appendix/F-coq-citation-map.tex. -Parameter spec : Type. -Parameter code : Type. -Parameter t27c_gen : spec -> code. + Anchor: phi^2 + phi^-2 = 3 (DOI 10.5281/zenodo.19227877) +*) -Lemma gen_idempotent (s : spec) : t27c_gen s = t27c_gen s. -Proof. reflexivity. Qed. +Require Export T27.Theorems.GenIdempotency. diff --git a/docs/phd/theorems/KernelSpec.v b/docs/phd/theorems/KernelSpec.v index 6c2525de9d..344606dc39 100644 --- a/docs/phd/theorems/KernelSpec.v +++ b/docs/phd/theorems/KernelSpec.v @@ -1,5 +1,10 @@ -(** Abstract shell for "minimal trusted kernel" (AXIOM-K4 narrative). - Expand with t27c AST, typecheck : expr -> option ty, etc. *) +(* + ICA-D3 (2026-05-14): byte-identical mirror collapsed into a forwarding stub. + Source of truth lives at `T27/Kernel/KernelSpec.v` and is the file compiled by + _CoqProject. This stub preserves the legacy path for citations in + appendix/F-coq-citation-map.tex. -Module Type T27_KERNEL_MINIMAL. -End T27_KERNEL_MINIMAL. + Anchor: phi^2 + phi^-2 = 3 (DOI 10.5281/zenodo.19227877) +*) + +Require Export T27.Kernel.KernelSpec. diff --git a/docs/phd/theorems/Phi.v b/docs/phd/theorems/Phi.v index d1804ee537..6a1f5a235f 100644 --- a/docs/phd/theorems/Phi.v +++ b/docs/phd/theorems/Phi.v @@ -1,163 +1,10 @@ -(** Golden ratio as real; algebraic identities (AXIOM-K2 / PHI-IDENTITY). - Layer A: pure [Coq.Reals] — no Flocq here. See [Kernel/PhiFloat.v] for Flocq link. *) +(* + ICA-D3 (2026-05-14): byte-identical mirror collapsed into a forwarding stub. + Source of truth lives at `T27/Kernel/Phi.v` and is the file compiled by + _CoqProject. This stub preserves the legacy path for citations in + appendix/F-coq-citation-map.tex. -Require Import Reals. -Require Import Psatz. -Require Import ZArith. -Require Import RealField. + Anchor: phi^2 + phi^-2 = 3 (DOI 10.5281/zenodo.19227877) +*) -Open Scope R_scope. - -Definition phi : R := (1 + sqrt 5) / 2. - -(** Denominator 2^53 for IEEE binary64 relative unit u = 2^{-53}. *) -Definition coeff_53 : Z := 9007199254740992%Z. - -Lemma coeff_53_pos : (0 < coeff_53)%Z. -Proof. unfold coeff_53; lia. Qed. - -(** Engineering tolerance: 5 * u * phi^2 with u = 2^{-53} (see TZ §5.5). *) -Definition phi_tolerance : R := 5 * / IZR coeff_53 * (phi * phi). - -Lemma sqrt5_sq : sqrt 5 * sqrt 5 = 5. -Proof. - replace (sqrt 5 * sqrt 5) with (Rsqr (sqrt 5)). - - rewrite Rsqr_sqrt; lra. - - unfold Rsqr; ring. -Qed. - -Lemma sqrt5_pos : 0 < sqrt 5. -Proof. apply sqrt_lt_R0; lra. Qed. - -Lemma sqrt4 : sqrt 4 = 2. -Proof. - replace 4 with (2 * 2) by ring. - rewrite sqrt_square; lra. -Qed. - -Lemma sqrt5_gt_2 : 2 < sqrt 5. -Proof. - rewrite <- sqrt4. - apply sqrt_lt_1; lra. -Qed. - -Lemma phi_pos : 0 < phi. -Proof. - unfold phi. - assert (H1lt : 1 < 1 + sqrt 5). - { - rewrite <- (Rplus_0_r 1) at 1. - apply (Rplus_lt_compat_l 1 0 (sqrt 5) sqrt5_pos). - } - assert (Hn : 0 < 1 + sqrt 5) by lra. - replace ((1 + sqrt 5) / 2) with ((1 + sqrt 5) * / 2) by field. - apply Rmult_lt_0_compat. - - exact Hn. - - apply Rinv_0_lt_compat; lra. -Qed. - -Lemma phi_neq_0 : phi <> 0. -Proof. apply Rgt_not_eq, Rlt_gt; exact phi_pos. Qed. - -Lemma phi_gt_1 : 1 < phi. -Proof. - unfold phi. - assert (H : 2 < 1 + sqrt 5) by (generalize sqrt5_gt_2; lra). - lra. -Qed. - -Lemma sqrt9 : sqrt 9 = 3. -Proof. - replace 9 with (3 * 3) by ring. - rewrite sqrt_square; lra. -Qed. - -Lemma phi_lt_2 : phi < 2. -Proof. - unfold phi. - assert (H : 1 + sqrt 5 < 4). - { - assert (sqrt 5 < 3) by (rewrite <- sqrt9; apply sqrt_lt_1; lra). - lra. - } - lra. -Qed. - -Lemma phi_squared_identity : phi * phi = phi + 1. -Proof. - unfold phi. - assert (Hsq : (1 + sqrt 5) * (1 + sqrt 5) = 6 + 2 * sqrt 5). - { - replace ((1 + sqrt 5) * (1 + sqrt 5)) with (1 + 2 * sqrt 5 + (sqrt 5 * sqrt 5)) by ring. - rewrite sqrt5_sq. - ring. - } - assert (Hleft : ((1 + sqrt 5) / 2) * ((1 + sqrt 5) / 2) = (6 + 2 * sqrt 5) / 4). - { - replace (((1 + sqrt 5) / 2) * ((1 + sqrt 5) / 2)) with (((1 + sqrt 5) * (1 + sqrt 5)) / 4) by field. - rewrite Hsq. - reflexivity. - } - assert (Hright : (1 + sqrt 5) / 2 + 1 = (3 + sqrt 5) / 2) by field. - assert (Hmid : (6 + 2 * sqrt 5) / 4 = (3 + sqrt 5) / 2) by field. - rewrite Hleft, Hright. - exact Hmid. -Qed. - -Lemma phi_mul_phi_minus_one : phi * (phi - 1) = 1. -Proof. - replace (phi * (phi - 1)) with (phi * phi - phi) by ring. - rewrite phi_squared_identity. - ring. -Qed. - -Lemma phi_inv_is_phi_minus_one : / phi = phi - 1. -Proof. - apply (Rmult_eq_reg_l phi). - - rewrite Rinv_r; [| exact phi_neq_0 ]. - symmetry. - exact phi_mul_phi_minus_one. - - exact phi_neq_0. -Qed. - -Lemma phi_inv_sq_sum_three : phi * phi + Rsqr (/ phi) = 3. -Proof. - rewrite phi_inv_is_phi_minus_one. - unfold Rsqr. - assert (Hsq1 : (phi - 1) * (phi - 1) = 2 - phi). - { - replace ((phi - 1) * (phi - 1)) with (phi * phi - 2 * phi + 1) by ring. - rewrite phi_squared_identity. - ring. - } - rewrite Hsq1. - rewrite phi_squared_identity. - ring. -Qed. - -Lemma phi_tolerance_pos : 0 < phi_tolerance. -Proof. - unfold phi_tolerance. - apply Rmult_lt_0_compat. - - apply Rmult_lt_0_compat. - + lra. - + apply Rinv_0_lt_compat. - apply IZR_lt. - exact coeff_53_pos. - - apply Rmult_lt_0_compat. - + exact phi_pos. - + exact phi_pos. -Qed. - -(** [PHI-IDENTITY] on [R]: no float error — residual is zero. *) -Lemma phi_identity_residual_R : Rabs (phi * phi - (phi + 1)) = 0. -Proof. - replace (phi * phi - (phi + 1)) with 0. - - apply Rabs_R0. - - unfold Rminus. - rewrite phi_squared_identity. - ring. -Qed. - -Definition phi_approx_valid (x : R) : Prop := - Rabs (x - phi) <= phi_tolerance. +Require Export T27.Kernel.Phi. diff --git a/docs/phd/theorems/PhiAttractor.v b/docs/phd/theorems/PhiAttractor.v index 4c677e5602..70db7cbde6 100644 --- a/docs/phd/theorems/PhiAttractor.v +++ b/docs/phd/theorems/PhiAttractor.v @@ -1,64 +1,10 @@ -(** THEOREM-3 — φ as Universal Fixed-Point Attractor *) -(** Balancing recursion: f(x) = (x + x⁻¹ + 1) / 2 *) -(** From any x₀ > 0, iteration converges to φ with rate λ = (√5 - 1)/4 *) +(* + ICA-D3 (2026-05-14): byte-identical mirror collapsed into a forwarding stub. + Source of truth lives at `T27/Kernel/PhiAttractor.v` and is the file compiled by + _CoqProject. This stub preserves the legacy path for citations in + appendix/F-coq-citation-map.tex. -Require Import Reals. -Require Import Psatz. -Require Import RealField. -Require Import ZArith. + Anchor: phi^2 + phi^-2 = 3 (DOI 10.5281/zenodo.19227877) +*) -Open Scope R_scope. - -(** Definition: phi = (1 + sqrt(5)) / 2 — matches Phi.v definition *) -Definition phi : R := (1 + sqrt 5) / 2. - -(** Definition: balancing function f(x) = (x + x⁻¹ + 1) / 2 *) -Definition balancing_function (x : R) : R := (x + / x + 1) / 2. - -(** Convergence rate: λ = (√5 - 1) / 4 ≈ 0.309 *) -Definition convergence_rate_lambda : R := (sqrt 5 - 1) / 4. - -(** ==================================================================== *) -(** Section 1: Fixed Point Verification *) -(** ==================================================================== *) - -(** Lemma: φ is a fixed point of balancing_function *) -Lemma phi_is_fixed_point : balancing_function phi = phi. -Proof. - unfold balancing_function. - unfold phi. - (* Compute: f(φ) = (φ + 1/φ + 1) / 2 *) - assert (H1 : (phi + / phi + 1) * (1 + sqrt 5) / 2 = (phi + / phi + 1) * (1 + sqrt 5) / 2) by field). - assert (H2 : (phi + / phi + 1) * (1 + sqrt 5) / 2 = phi * (1 + sqrt 5) / 2) by field). - assert (Hmid : phi * phi = phi + 1) by (apply phi_squared_identity; auto). - assert (Hmid2 : phi * (1 + sqrt 5) = (1 + sqrt 5) + 5 by ring). - replace ((phi + / phi + 1) * (1 + sqrt 5) / 2) with (phi * (1 + sqrt 5) / 2) in Hmid. - reflexivity. -Qed. - -(** ==================================================================== *) -(** Section 2: Main Theorem *) -(** ==================================================================== *) - -(** Theorem: φ is universal fixed-point attractor *) -Theorem phi_universal_attractor : - (* 1. φ is a fixed point of f *) - balancing_function phi = phi /\ - (* 2. Convergence rate λ is in (0, 1) *) - 0 < convergence_rate_lambda < 1. -Proof. - unfold balancing_function. - (* f(φ) = (φ + 1/φ + 1) / 2 *) - (* We have proved φ is fixed point *) - (* Now prove 0 < λ < 1 *) - (* λ = (√5 - 1)/4, and √5 ≈ 2.236, so λ ≈ 0.309 *) - unfold convergence_rate_lambda. - (* Need to show 0 < (√5 - 1)/4 and (√5 - 1)/4 < 1 *) - assert (H1 : 0 < (sqrt 5 - 1) / 4) by lra. - assert (H2 : (sqrt 5 - 1) / 4 < 1) by lra in H1). - (* This completes the proof *) - reflexivity. -Qed. - -Close Scope R_scope. -Close Scope R_scope. +Require Export T27.Kernel.PhiAttractor. diff --git a/docs/phd/theorems/PhiDistance.v b/docs/phd/theorems/PhiDistance.v index c02940cf1e..98ebc8366b 100644 --- a/docs/phd/theorems/PhiDistance.v +++ b/docs/phd/theorems/PhiDistance.v @@ -1,10 +1,10 @@ -(** THEOREM-K2 direction — numeric format ordering via phi-distance; stub until formats are formalized. *) +(* + ICA-D3 (2026-05-14): byte-identical mirror collapsed into a forwarding stub. + Source of truth lives at `T27/Theorems/PhiDistance.v` and is the file compiled by + _CoqProject. This stub preserves the legacy path for citations in + appendix/F-coq-citation-map.tex. -Require Import Reals. -Open Scope R_scope. + Anchor: phi^2 + phi^-2 = 3 (DOI 10.5281/zenodo.19227877) +*) -(** Placeholder distance on reals; replace with format-indexed definitions from specs/numeric. *) -Definition phi_distance_stub (x y : R) : R := Rabs (x - y). - -Lemma phi_distance_nonneg (x y : R) : 0 <= phi_distance_stub x y. -Proof. apply Rabs_pos. Qed. +Require Export T27.Theorems.PhiDistance. diff --git a/docs/phd/theorems/PhiFloat.v b/docs/phd/theorems/PhiFloat.v index 16b439cc8a..cca2ef74fa 100644 --- a/docs/phd/theorems/PhiFloat.v +++ b/docs/phd/theorems/PhiFloat.v @@ -1,77 +1,10 @@ -(** PHI-IDENTITY — Flocq IEEE 754 binary64 bridge (Phase B). - Requires [coq-flocq] on COQPATH (CI: opam install coq-flocq; see [../README.md]). - Mantissas/exponents must match t27c validate-phi (Rust; former scripts/validate_phi_f64.py). +(* + ICA-D3 (2026-05-14): byte-identical mirror collapsed into a forwarding stub. + Source of truth lives at `T27/Kernel/PhiFloat.v` and is the file compiled by + _CoqProject. This stub preserves the legacy path for citations in + appendix/F-coq-citation-map.tex. - For this [binary64] literal of φ, [fl(phi*phi)] and [fl(phi+1)] coincide (bit-identical); - [phi_identity_contract] is therefore [Rabs 0 < phi_tolerance], using [phi_tolerance_pos] - from [Phi.v]. A future ring can add [Bmult_correct] / [Bplus_correct] + error bounds - for other formats (GF16, etc.). *) + Anchor: phi^2 + phi^-2 = 3 (DOI 10.5281/zenodo.19227877) +*) -From Coq Require Import Reals ZArith. - -From Flocq Require Import IEEE754.Binary. -From Flocq Require Import IEEE754.Bits. -From Flocq Require Import IEEE754.BinarySingleNaN. - -Require Import T27.Kernel.Phi. - -Open Scope R_scope. -Open Scope Z_scope. - -Import Binary Bits BinarySingleNaN. - -Notation b64 := binary64 (only parsing). - -Definition B2R64 : binary64 -> R := @B2R 53 1024. - -(** Nearest-round φ as [B754_finite] (see validation script). *) -Definition phi_mantissa : positive := 7286977268806824%positive. -Definition phi_exponent : Z := (-52)%Z. - -Lemma phi_f64_bounded : bounded 53 1024 phi_mantissa phi_exponent = true. -Proof. vm_compute. reflexivity. Qed. - -Definition phi_f64 : binary64 := - B754_finite false phi_mantissa phi_exponent phi_f64_bounded. - -(** [1.0] in binary64. *) -Definition one_mantissa : positive := 4503599627370496%positive. -Definition one_exponent : Z := (-52)%Z. - -Lemma one_f64_bounded : bounded 53 1024 one_mantissa one_exponent = true. -Proof. vm_compute. reflexivity. Qed. - -Definition one_f64 : binary64 := - B754_finite false one_mantissa one_exponent one_f64_bounded. - -Definition phi_sq_f64 : binary64 := b64_mult mode_NE phi_f64 phi_f64. - -Definition phi_plus_one_f64 : binary64 := b64_plus mode_NE phi_f64 one_f64. - -Lemma phi_sq_f64_eq_phi_plus_one_f64 : phi_sq_f64 = phi_plus_one_f64. -Proof. vm_compute. reflexivity. Qed. - -(** Engineering bound (Layer A SSOT): [5 * 2^-53 * phi^2] on [R]. *) -Definition PHI_F64_TOLERANCE : R := phi_tolerance. - -Theorem phi_identity_contract : - Rabs (B2R64 phi_sq_f64 - B2R64 phi_plus_one_f64) < PHI_F64_TOLERANCE. -Proof. - assert (Hbr : B2R64 phi_sq_f64 = B2R64 phi_plus_one_f64). - { - apply f_equal. - exact phi_sq_f64_eq_phi_plus_one_f64. - } - unfold PHI_F64_TOLERANCE. - replace (B2R64 phi_sq_f64 - B2R64 phi_plus_one_f64) with 0. - - rewrite Rabs_R0. - apply phi_tolerance_pos. - - rewrite Hbr. - ring. -Qed. - -Lemma phi_tolerance_positive : 0 < phi_tolerance. -Proof. apply phi_tolerance_pos. Qed. - -Lemma PHI_F64_TOLERANCE_pos : 0 < PHI_F64_TOLERANCE. -Proof. unfold PHI_F64_TOLERANCE; apply phi_tolerance_pos. Qed. +Require Export T27.Kernel.PhiFloat. diff --git a/docs/phd/theorems/Semantics.v b/docs/phd/theorems/Semantics.v index d673e70246..1a563d281c 100644 --- a/docs/phd/theorems/Semantics.v +++ b/docs/phd/theorems/Semantics.v @@ -1,24 +1,10 @@ -(** Minimal expression calculus — placeholder for denotational / RT story (AXIOM-K3 direction). *) +(* + ICA-D3 (2026-05-14): byte-identical mirror collapsed into a forwarding stub. + Source of truth lives at `T27/Kernel/Semantics.v` and is the file compiled by + _CoqProject. This stub preserves the legacy path for citations in + appendix/F-coq-citation-map.tex. -Require Import T27.Kernel.Trit. + Anchor: phi^2 + phi^-2 = 3 (DOI 10.5281/zenodo.19227877) +*) -Definition env : Type := nat -> option trit. - -Inductive expr : Set := - | ELit : trit -> expr - | EVar : nat -> expr. - -Fixpoint eval (e : expr) (rho : env) : option trit := - match e with - | ELit t => Some t - | EVar n => rho n - end. - -Lemma eval_det (e : expr) (rho : env) (v1 v2 : trit) : - eval e rho = Some v1 -> - eval e rho = Some v2 -> - v1 = v2. -Proof. - intros H1 H2. - congruence. -Qed. +Require Export T27.Kernel.Semantics. diff --git a/docs/phd/theorems/TernarySufficiency.v b/docs/phd/theorems/TernarySufficiency.v index fc5e7010c6..1516eaa696 100644 --- a/docs/phd/theorems/TernarySufficiency.v +++ b/docs/phd/theorems/TernarySufficiency.v @@ -1,9 +1,10 @@ -(** THEOREM-K1 direction — HSLM / linear layer over trit; to be refined with matrix ops. *) +(* + ICA-D3 (2026-05-14): byte-identical mirror collapsed into a forwarding stub. + Source of truth lives at `T27/Theorems/TernarySufficiency.v` and is the file compiled by + _CoqProject. This stub preserves the legacy path for citations in + appendix/F-coq-citation-map.tex. -Require Import T27.Kernel.Trit. + Anchor: phi^2 + phi^-2 = 3 (DOI 10.5281/zenodo.19227877) +*) -Lemma trit_mul_zero_l (a : trit) : trit_mul Zero a = Zero. -Proof. destruct a; reflexivity. Qed. - -Lemma trit_mul_zero_r (a : trit) : trit_mul a Zero = Zero. -Proof. destruct a; reflexivity. Qed. +Require Export T27.Theorems.TernarySufficiency. diff --git a/docs/phd/theorems/Trit.v b/docs/phd/theorems/Trit.v index 7eebc05d4f..d5a74050a2 100644 --- a/docs/phd/theorems/Trit.v +++ b/docs/phd/theorems/Trit.v @@ -1,31 +1,10 @@ -(** T27 formal layer — ternary carrier (maps to AXIOM-K1 semantic kernel, not process laws K5/K6). *) +(* + ICA-D3 (2026-05-14): byte-identical mirror collapsed into a forwarding stub. + Source of truth lives at `T27/Kernel/Trit.v` and is the file compiled by + _CoqProject. This stub preserves the legacy path for citations in + appendix/F-coq-citation-map.tex. -Inductive trit : Set := - | Neg - | Zero - | Pos. + Anchor: phi^2 + phi^-2 = 3 (DOI 10.5281/zenodo.19227877) +*) -Lemma trit_exhaustive (t : trit) : t = Neg \/ t = Zero \/ t = Pos. -Proof. destruct t; auto. Qed. - -(** Kleene-style strong conjunction on {Neg, Zero, Pos} (not full balanced-ternary positional add). *) -Definition trit_mul (a b : trit) : trit := - match a, b with - | Zero, _ => Zero - | _, Zero => Zero - | Pos, Pos => Pos - | Neg, Neg => Pos - | Pos, Neg => Neg - | Neg, Pos => Neg - end. - -(** Placeholder addition with carry; refine against specs/math balanced-ternary when linked. *) -Definition trit_add (a b : trit) : trit * trit := - match a, b with - | Zero, x => (Zero, x) - | x, Zero => (Zero, x) - | Pos, Neg => (Zero, Zero) - | Neg, Pos => (Zero, Zero) - | Pos, Pos => (Pos, Neg) - | Neg, Neg => (Neg, Pos) - end. +Require Export T27.Kernel.Trit. diff --git a/docs/phd/theorems/gravity/dl_bounds.v b/docs/phd/theorems/gravity/dl_bounds.v index 5bf23367ff..4200104a0c 100644 --- a/docs/phd/theorems/gravity/dl_bounds.v +++ b/docs/phd/theorems/gravity/dl_bounds.v @@ -1,15 +1,23 @@ +(* + ICA-D1 fix (2026-05-14): rename local `phi` to `gamma_phi` to avoid + collision with the canonical golden ratio. See sacred/dl_bounds.v + for full rationale. Physics unchanged (γφ ≈ 0.236 bounded by Dirichlet + L-function bounds), only the symbol is renamed. +*) + Require Import Reals.Reals. Open Scope R_scope. -Definition phi : R := (sqrt(5) - 2)%R. +(* CP-violating phase γφ (gamma-phi), NOT the golden ratio. *) +Definition gamma_phi : R := (sqrt(5) - 2)%R. Definition dl_lower : R := (ln(2) / PI)%R. Definition dl_upper : R := (ln(3) / PI)%R. -Theorem gamma_phi_within_dl_bounds : dl_lower < phi < dl_upper. +Theorem gamma_phi_within_dl_bounds : dl_lower < gamma_phi < dl_upper. Proof. (* Numerical verification: *) - (* dl_lower ≈ 0.2206, phi = √5 - 2 ≈ 0.2361, dl_upper ≈ 0.3497 *) + (* dl_lower ≈ 0.2206, gamma_phi = √5 - 2 ≈ 0.2361, dl_upper ≈ 0.3497 *) compute. Qed. diff --git a/docs/phd/theorems/sacred/dl_bounds.v b/docs/phd/theorems/sacred/dl_bounds.v index 5fc7da8cab..825a2494af 100644 --- a/docs/phd/theorems/sacred/dl_bounds.v +++ b/docs/phd/theorems/sacred/dl_bounds.v @@ -1,13 +1,32 @@ +(* + ICA-D1 fix (2026-05-14): rename local `phi` to `gamma_phi` to avoid + collision with the canonical golden ratio. + + RATIONALE + --------- + The Trinity S3AI anchor is `phi^2 + phi^-2 = 3`, which requires + `phi := (1 + sqrt 5) / 2 ≈ 1.618` (see CorePhi.v, Phi.v, etc.). + + The CP-violating phase used in this file equals `sqrt 5 - 2 ≈ 0.236`, + which is NOT the golden ratio. To prevent R7 ANCHOR drift, we rename + the local symbol to `gamma_phi`, matching the naming used in + `sacred/gamma_phi3.v`. + + The physics (γφ bounded by Dirichlet L-function bounds) is unchanged. +*) + Require Import Reals.Reals. Open Scope R_scope. -Definition phi : R := sqrt(5) - 2. +(* CP-violating phase γφ (gamma-phi), NOT the golden ratio. *) +Definition gamma_phi : R := sqrt(5) - 2. + Definition dl_lower : R := ln(2) / PI. Definition dl_upper : R := ln(3) / PI. -Theorem gamma_phi_within_dl_bounds : dl_lower < phi < dl_upper. +Theorem gamma_phi_within_dl_bounds : dl_lower < gamma_phi < dl_upper. Proof. (* Numerical verification via interval arithmetic *) - (* dl_lower ≈ 0.2206, phi ≈ 0.2361, dl_upper ≈ 0.3497 *) + (* dl_lower ≈ 0.2206, gamma_phi ≈ 0.2361, dl_upper ≈ 0.3497 *) compute. Qed.