Aion holography #1
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Summary by CodeRabbitRelease Notes
WalkthroughAdds a complete LaTeX paper "Computational Holography" under Changes
Sequence Diagram(s)sequenceDiagram
autonumber
participant GH as GitHub Actions
participant Repo as Repository
participant Latex as latex-action
participant Art as Artifact Store
participant Rel as GitHub Release
Note over GH,Repo: Trigger on push/PR to main|master or release
GH->>Repo: checkout
GH->>Latex: compile `aion-holography/main.tex`
Latex-->>GH: produces `aion-holography/main.pdf`
GH->>Art: upload `holography-paper-pdf` (retention: 30d)
alt event == release
GH->>GH: rename artifact -> `computational-holography-rmg.pdf`
GH->>Rel: attach renamed PDF (uses GITHUB_TOKEN)
end
sequenceDiagram
autonumber
participant Boundary as Boundary (S0, P)
participant Recon as Recon
participant Volume as Interior Volume
Note over Boundary,Recon: Computational holography — boundary reconstructs interior
Boundary->>Recon: provide (S0, P)
Recon->>Volume: replay microsteps deterministically (reconstruct)
Recon-->>Boundary: return reconstructed Volume (unique up to iso)
Note right of Volume: termination & uniqueness proven in paper
Estimated code review effort🎯 4 (Complex) | ⏱️ ~65 minutes
Poem
Pre-merge checks and finishing touches❌ Failed checks (1 inconclusive)
✅ Passed checks (2 passed)
✨ Finishing touches🧪 Generate unit tests (beta)
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Actionable comments posted: 33
♻️ Duplicate comments (1)
aion-holography/sections/multiway_ruliad.tex (1)
1-1: Verify\sectionbreakpackage dependency.Same as discussion.tex: ensure the appropriate package is loaded for
\sectionbreak.
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.github/workflows/build-papers.yml(1 hunks).gitignore(1 hunks)README.md(1 hunks)aion-holography/Makefile(1 hunks)aion-holography/macros.tex(1 hunks)aion-holography/main.tex(1 hunks)aion-holography/references.bib(1 hunks)aion-holography/sections/determinism_confluence.tex(1 hunks)aion-holography/sections/discussion.tex(1 hunks)aion-holography/sections/dpo_rmg.tex(1 hunks)aion-holography/sections/holography.tex(1 hunks)aion-holography/sections/intro.tex(1 hunks)aion-holography/sections/multiway_ruliad.tex(1 hunks)aion-holography/sections/rmg.tex(1 hunks)aion-holography/sections/rulial_distance.tex(1 hunks)aion-holography/sections/wormholes.tex(1 hunks)
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🔇 Additional comments (6)
.gitignore (1)
1-77: LGTM: Comprehensive and well-organized .gitignore.The patterns are appropriate for a LaTeX project with CI/CD. The PDF exclusion (line 30) correctly aligns with your artifact-based distribution strategy.
aion-holography/references.bib (1)
68-80: Verify unpublished self-citations.You're citing two unpublished works from 2025:
RossRMG2025(Technical report)RossAIONCalculus2025(Working note)Ensure these documents exist and are accessible to readers. If
RossAIONCalculus2025is merely a personal working note not intended for external distribution, consider removing the citation or upgrading it to a proper technical report.aion-holography/macros.tex (1)
23-33: LGTM: Theorem environments properly configured.The theorem environment setup follows LaTeX best practices with appropriate style assignments and section-level numbering.
.github/workflows/build-papers.yml (1)
19-26: Verify bibtex error handling in latex-action.The workflow uses
xu-cheng/latex-action@v3withlatexmk, which bypasses your Makefile. This means:
- The Makefile's
|| truebibtex suppression (line 11) doesn't affect CI builds- CI will correctly fail on bibtex errors due to
-halt-on-error- Local builds via
makewill silently ignore bibtex errors (per Makefile review)This inconsistency between local and CI builds is problematic. Fix the Makefile as suggested in that review.
aion-holography/sections/discussion.tex (1)
1-1: No issues found—review comment was incorrect.The
titlesecpackage is already loaded at line 18 ofaion-holography/main.tex, so\sectionbreakis properly available. No fixes required.aion-holography/sections/holography.tex (1)
174-231: Ensure required TikZ libraries are loaded for the holography figure.This figure uses several TikZ features that depend on external libraries:
-Latexarrow tips and<->on the mapping arrow (\Rightarrow)arrows.meta.The
bracedecoration style:brace/.style={decorate,decoration={brace,amplitude=5pt}},requires
\usetikzlibrary{decorations.pathreplacing}.If these libraries are not already loaded in
main.texor a shared preamble, this section will not compile.Given this figure is central to the narrative, I’d double‑check the preamble contains at least:
\usetikzlibrary{arrows.meta,decorations.pathreplacing}Once that’s in place, the TikZ code here is clean and nicely communicates the volume–boundary duality.
Co-authored-by: coderabbitai[bot] <136622811+coderabbitai[bot]@users.noreply.github.com> Signed-off-by: James Ross <james@flyingrobots.dev>
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Actionable comments posted: 1
♻️ Duplicate comments (13)
README.md (6)
7-9: Fix markdown formatting issues.Line 7 is missing a blank line below the heading, and line 8 uses emphasis for what should be structured as a proper heading or plain text with correct spacing.
Apply this diff:
### Computational Holography for Recursive Metagraphs + *Deterministic Concurrency, Provenance Encoding, and Rulial Distance*As per coding guidelines (markdownlint MD022, MD036).
41-46: Add blank line before code fence.The bash code block at line 42 needs a blank line above it.
Apply this diff:
To create a release with PDF: + ```bashAs per coding guidelines (markdownlint MD031).
50-58: Fix heading spacing violations.Lines 50 and 54 are missing blank lines below their headings, and line 55 is missing a blank line before the code fence.
Apply this diff:
#### Prerequisites + - A working LaTeX installation (TeX Live 2023+ recommended) - Standard packages: `amsmath`, `tikz`, `amsthm`, `enumitem`, `cleveref` #### Compile + ```bashAs per coding guidelines (markdownlint MD022, MD031).
62-65: Add blank line after code fence.Line 63 needs a blank line after the closing fence.
Apply this diff:
make clean
Note: PDFs are gitignored (standard practice). Use CI artifacts or local builds to access compiled papers.
As per coding guidelines (markdownlint MD031). --- `71-89`: **Specify language identifier for code fence.** The directory tree code block at line 71 is missing a language identifier. Apply this diff: ```diff -``` +```text aion/ ├── README.md # This fileAs per coding guidelines (markdownlint MD040).
93-113: Fix heading spacing in Key Concepts section.Lines 93, 102, and 112 are all missing blank lines below their headings.
Apply this diff:
### Recursive Metagraphs + A graph where every node and edge can carry an attached subgraph, recursively. Formally: ```math \mathcal{U} = (G; \alpha, \beta)where
$G$ is a skeleton graph and$\alpha$ ,$\beta$ attach RMGs to nodes and edges.Wormholes
A wormhole
$(S_0, P)$ consists of:
- An initial RMG state
$S_0$ - A provenance payload
$P = (\mu_0, \dots, \mu_{n-1})$ recording microstepsThe volume is the full derivation
$S_0 \Rightarrow \cdots \Rightarrow S_n$ .
The boundary is just the pair$(S_0, P)$ .Computational holography proves these are equivalent: the boundary encodes the volume.
Rulial Distance
An MDL-based metric
$D_{\tau,m}(O_1, O_2)$ measuring how complex it is to translate between two observers' views of the same computation. Gives geometry to "observer space" in the Ruliad.As per coding guidelines (markdownlint MD022). </blockquote></details> <details> <summary>.github/workflows/build-papers.yml (1)</summary><blockquote> `40-44`: **Critical: Update deprecated GitHub Action.** Line 42 uses `softprops/action-gh-release@v1` which is deprecated and will fail on current GitHub Actions runners. Apply this diff: ```diff - name: Upload PDF to release if: github.event_name == 'release' - uses: softprops/action-gh-release@v1 + uses: softprops/action-gh-release@v2 with: files: aion-holography/computational-holography-rmg.pdfNote: v2 automatically uses
GITHUB_TOKENfrom context, so noenvblock is needed.As per coding guidelines (actionlint).
aion-holography/Makefile (2)
1-7: Declare phony targets to prevent file conflicts.Lines 7, 19, and 22 define targets that aren't files. Without
.PHONYdeclarations, the build breaks if files namedall,clean, ordistcleanexist.Apply this diff:
MAIN = main +.PHONY: all clean distclean + all: $(MAIN).pdfAs per coding guidelines (checkmake).
11-18: Critical: Do not suppress bibtex errors.Line 13 uses
|| trueto silently ignore bibtex failures. This masks legitimate bibliography errors (missing entries, malformed BibTeX, etc.) that should halt the build.Apply this diff to let bibtex errors fail the build properly:
$(MAIN).pdf: $(MAIN).tex sections/*.tex macros.tex references.bib $(TEX) $(MAIN) - $(BIB) $(MAIN) || true + $(BIB) $(MAIN) $(TEX) $(MAIN) $(TEX) $(MAIN)If you genuinely expect empty-bibliography warnings on first run, document this explicitly:
- $(BIB) $(MAIN) || true + $(BIB) $(MAIN) || true # Tolerate missing citations on first passaion-holography/sections/rulial_distance.tex (4)
11-20: Clarify where resource budgets live and tie them explicitly to (D_{\tau,m}).Lines 17-19 suggest the observation category (\mathcal{Y}) is "subject to resource budgets," but budgets constrain the observer implementation, not (\mathcal{Y}) itself. Also, ((\tau,m)) appear later as subscripts of (D_{\tau,m}) without clear binding to these budgets.
Tighten this to explicitly state that an observer is a resource-bounded functor (O) implemented by a program under budgets ((\tau,m)), and cross-reference that these are the budgets indexed by (D_{\tau,m}).
For example:
-where $\mathcal{Y}$ is a suitable category of observations (symbol -streams, trace graphs, etc.). We assume that $O$ is realised by some -algorithm subject to fixed time and memory budgets $(\tau,m)$; these -budgets are reflected in the subscript of $D_{\tau,m}$ below. +where $\mathcal{Y}$ is a suitable category of observations (symbol +streams, trace graphs, etc.). We assume that $O$ is realised by some +algorithm subject to fixed time and memory budgets $(\tau,m)$; these +budgets are precisely the parameters indexed by the subscript of +$D_{\tau,m}$ defined below.
31-57: Tighten translator notation, define (\lambda), and make the type of (\mathrm{Dist}) precise.Several definitional details are under-specified:
Overloading (\Rewrite) for translators. Line 32 uses (T : O_1 \Rewrite O_2), reusing the symbol for state rewriting (S_0 \Rewrite^\ast S_n). Use a distinct arrow (e.g. (T : O_1 \Rightarrow O_2) or (O_1 \leadsto O_2)).
Unspecified (\lambda). Line 65 introduces weight (\lambda) with no definition. Fix this as part of the model:
-Let $\mathrm{DL}(T)$ be a prefix-code description length for $T$ -(MDL cost), and let $\mathrm{Dist}$ be a distortion metric on observed -traces. +Let $\mathrm{DL}(T)$ be a prefix-code description length for $T$ +(MDL cost), let $\mathrm{Dist}$ be a distortion metric on observed +traces, and fix a weighting parameter $\lambda > 0$ trading off +description length against distortion.Type of (\mathrm{Dist}). You describe it as "a distortion metric on observed traces" but apply it to observers at line 66-67: (\mathrm{Dist}(O_2, T_{12}\circ O_1)). State explicitly:
We write $\mathrm{Dist}(O_2, T_{12}\circ O_1)$ as shorthand for the aggregate distortion over histories, e.g. $\sup_{h\in\Hist(U,R)} \mathrm{Dist}_\mathrm{tr}\bigl(O_2(h), (T_{12}\circ O_1)(h)\bigr)$.Budgets in the infimum. Line 62 should restrict to translators realizable under ((\tau,m)):
- D_{\tau,m}(O_1,O_2) - = \inf_{T_{12},T_{21}} + D_{\tau,m}(O_1,O_2) + = \inf_{\substack{T_{12},T_{21} \\ \text{budget} \le (\tau,m)}}
59-129: Pseudometric claim and triangle inequality proof are not justified under stated assumptions.Several critical issues affect the correctness of the "rulial distance" theorem:
(D_{\tau,m}(O,O)=0) is not automatic. Proposition 73-76 asserts (D_{\tau,m}(O,O) = 0), but the proof only shows nonnegativity and symmetry. For zero self-distance, you need either:
- A distinguished identity translator (I_O) with (\mathrm{DL}(I_O)=0) and zero distortion, or
- Explicit proof that the infimum attains (0).
With realistic MDL coding, shortest non-empty programs have positive length, so (D_{\tau,m}) is at best a pseudometric up to an additive constant. Add a structural assumption:
Let $\mathrm{DL}(T)$ be a prefix-code description length for $T$ (MDL cost) ... +We assume there is a distinguished identity translator $I_O$ for +each observer $O$ with $\mathrm{DL}(I_O)=0$ and zero distortion.Proposition vs Theorem: redundant use of "pseudometric". Proposition claims pseudometric status but only lists nonnegativity, symmetry, and (D(O,O)=0), without triangle inequality. Theorem then re-states "is a pseudometric." Either restrict Proposition to "nonnegative and symmetric" or remove it entirely.
Triangle inequality uses unstated invariance property. Lines 115-119 claim:
[
\mathrm{Dist}(O_3,T_{13}\circ O_1)
\le \mathrm{Dist}(O_3,T_{23}\circ O_2) + \mathrm{Dist}(O_2,T_{12}\circ O_1).
]
But from metric property alone, you get:
[
\mathrm{Dist}(O_3,T_{13}\circ O_1)
\le \mathrm{Dist}(O_3,T_{23}\circ O_2) + \mathrm{Dist}(T_{23}\circ O_2,T_{23}\circ T_{12}\circ O_1).
]
To replace (\mathrm{Dist}(T_{23}\circ O_2,T_{23}\circ T_{12}\circ O_1)) by (\mathrm{Dist}(O_2,T_{12}\circ O_1)), you need:
[
\mathrm{Dist}(T\circ O, T\circ O') \le \mathrm{Dist}(O,O')
\quad\text{for all translators }T.
]
This Lipschitz/invariance assumption is not stated and is non-trivial. Add it explicitly as a hypothesis or redefine (\mathrm{Dist}) to be manifestly invariant.Budgets and compositional translators. Line 107 assumes (T_{23}\circ T_{12}) is admissible under the same budget ((\tau,m)). State:
We assume that the budget class indexed by $(\tau,m)$ is closed under finite composition of translators.These gaps prevent the theorem from being correct as stated. Fix the assumptions and proofs before claiming (D_{\tau,m}) is a pseudometric.
138-151: Add explicit figure cross-reference in text.The subsection enumerates different observer projections but doesn't explicitly reference Figure~\ref{fig:observer-projections}. Add a cross-reference when first listing the projections, e.g. "(see Figure~\ref{fig:observer-projections})".
This improves readability and helps the reader connect the text to the diagram.
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aion-holography/Makefile
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🔇 Additional comments (2)
aion-holography/sections/rmg.tex (1)
1-158: LGTM!All previous review concerns have been addressed:
- Lines 41-43 now explicitly state "small collection" and "finitary polynomial endofunctor"
- Lines 56-67 properly define morphisms by "structural recursion on RMG depth" with explicit recursive clause
- Line 114 correctly uses (\beta(e_{\mathsf{call}})) notation
- Line 145 disambiguates (\mathcal{U}) vs (U) in the notation table
The formal definitions are mathematically sound, the TikZ figure is properly formatted, and the categorical framework is rigorous.
aion-holography/macros.tex (1)
1-34: LGTM!The previous review concern has been addressed—line 11 now defines the
\COMPUTERmacro to match the\AIONmacro pattern.All macro definitions are consistent and well-structured:
- Math category macros (lines 2-6)
- Roman-style operators (lines 8-11)
- Structural arrows (lines 13-15)
- Named entities (lines 17-22)
- Theorem environments (lines 24-34)
The macro definitions provide a clean, consistent notation framework for the paper.
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Actionable comments posted: 26
♻️ Duplicate comments (5)
aion-holography/sections/multiway_ruliad.tex (1)
20-84: TikZ absolute coordinates make layout changes painful.Past review comment already covered this: using absolute coordinates throughout makes adjustments tedious. While functional, refactoring to use the
positioninglibrary (above=of,right=of, etc.) would improve maintainability.This is a minor refactor and doesn't block merge.
aion-holography/Makefile (2)
7-7: Past phony declaration comment addressed.
.PHONYdeclaration is now present. Good.
11-16: Past duplicate recipe and error suppression comments addressed.No duplicate recipes, and no
|| trueon bibtex. Both past critical issues resolved.aion-holography/sections/wormholes.tex (1)
5-7: Past comments addressed, but inconsistent cross-reference style.Past review correctly requested tighter ASP definition and holography theorem citation—both are now present. However, line 6 uses
\S\ref{sec:holography}instead of\cref{sec:holography}, which is inconsistent with the rest of your document.-From the perspective of the ambient RMG, an Aion State Packet (ASP; see -\S\ref{sec:holography}) provides a single edge $S_0 \Rewrite S_n$ +From the perspective of the ambient RMG, an Aion State Packet (ASP; see +\cref{sec:holography}) provides a single edge $S_0 \Rewrite S_n$
\crefwill automatically generate "Section X" or "§X" based on your cleveref configuration.aion-holography/sections/rulial_distance.tex (1)
190-201: Figure is wired correctly; still missing an explicit textual cross-referenceThe TikZ figure now compiles cleanly given the main preamble’s
\usetikzlibrary{arrows.meta,shapes.misc,positioning}, and the local styles are neat. One lingering nit from the earlier review: when you enumerate the different observer projections of a wormhole in the preceding subsection, you never actually say “see Figure~\ref{fig:observer-projections}”. Adding that parenthetical at the end of the bullet list would make it much easier for readers to connect the prose to the diagram.Also applies to: 202-244
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Context: ...: the boundary encodes the volume. ### Rulial Distance An MDL-based metric $D_{\tau,...
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🔇 Additional comments (10)
aion-holography/sections/ethics.tex (2)
19-24: Good citation practice for ethical principles.Proper inline citation with principle reference to ross_universal_charter_v1. The footnote providing the principle number is helpful for traceability.
61-77: Well-structured ethical framework.The distinction between system-mode (mandatory provenance) and mind-mode (consent-based provenance) is technically sound and ethically coherent. This provides a practical implementation path for Charter compliance.
aion-holography/sections/assumptions.tex (1)
1-2: Disregard this review comment — the flagged pattern is not actually problematic.The
\label{sec:assumptions}is never referenced anywhere in the codebase. A ripgrep search found zero calls to\ref{sec:assumptions}or\cref{sec:assumptions}, eliminating the "confusing Section ??" risk the comment warns about.More critically, this is the document's consistent architectural pattern. Every single section in the codebase—across all 14
.texfiles—uses\section*paired with\label{sec:xxx}. Modern LaTeX with hyperref handles this correctly. There's nothing wrong here.Likely an incorrect or invalid review comment.
aion-holography/main.tex (1)
3-11: Preamble/metadata now looks engine-aware and reproducibleThe
ifxetex/ifluatexguard aroundinputencand the fixed\date{November 2025}resolve the earlier XeLaTeX noise and non-reproducible build issues. TikZ libraries are loaded centrally here (includingarrows.meta), which is exactly what the downstream figures need. Only thing to double‑check is that any nonstandard macros used elsewhere (e.g.\varmathbb,\AION,\COMPUTER,\OGraph_T) are indeed defined inmacros.texso this file never fails alone.Also applies to: 60-60
aion-holography/sections/intro.tex (1)
13-26: Intro claims are finally aligned with the formal hypotheses—keep theorem statements in lockstepThe bullets now correctly qualify determinism as “up to typed open‑graph isomorphism” and explicitly condition confluence on the independence discipline plus no‑delete/no‑clone invariants, and the contributions list cleanly ties each informal item to a theorem label. That’s the right level of honesty for the intro.
Given how central these four claims are, I’d still sanity‑check that:
\cref{thm:tick-confluence,thm:two-plane,thm:global}collectively justify “deterministic and confluent at the level of ticks” under exactly the hypotheses named here, and\cref{thm:holography}really states information‑completeness of the boundary data(S_0,P)in the sense you describe.If any of those theorem statements drift, this section will be the first place the mismatch shows up.
Also applies to: 59-72
aion-holography/sections/rulial_distance.tex (1)
11-21: Observer/budget and identity-translator assumptions are finally explicitThis cleans up the earlier hand‑waving nicely: observers are now resource‑bounded functors
$O:\Hist(U,R)\to\mathcal{Y}$ with explicit time/memory budgets$(\tau,m)$ , translators live in\Trans_{\tau,m}(\cdot,\cdot)and are assumed closed under finite composition, and you’ve postulated a zero‑cost, zero‑distortion identity translator$I_O$ for each observer. That’s exactly the structure you needed to justify$D_{\tau,m}(O,O)=0$ and to make the budget dependence in the subscript meaningful rather than decorative.Also applies to: 80-88
aion-holography/sections/discussion.tex (1)
16-30: Cross-references and theorem citations are in good shapeSwitching the theorem mentions here to
\cref{thm:tick-confluence}and\cref{thm:global}removes the manual “Theorem~” duplication and lets cleveref do its job, and the surrounding related‑work text is technically accurate. No obvious logical or citation issues in this paragraph.aion-holography/sections/holography.tex (1)
98-115: Backward provenance completeness now has the right hypotheses and proof spine.The addition of the explicit “no re‑derivation (single producer)” runtime constraint and its use in Theorem~\textbackslash ref{thm:backward} cleanly fix the earlier gap: uniqueness of the producing microstep for a value is now an assumption, not a wishful consequence of immutability/determinism.
The inductive proof then reads correctly: base case in (S_0), inductive step pins down a unique last microstep and glues uniquely determined sub‑derivations. This section is finally mathematically honest.
aion-holography/sections/rmg.tex (1)
45-55: Initial‑algebra presentation is now well‑posed.Calling out (\mathcal{G}) as a small collection of finite skeleton shapes and explicitly describing (F) as a finitary polynomial endofunctor removes the set‑theoretic hand‑waving around the initial‑algebra claim. This is finally at the level a category theorist will not side‑eye.
aion-holography/macros.tex (1)
13-37: Macro set (including \COMPUTER, rewrite helpers, and theorem envs) looks consistent and sane.
\COMPUTERnow mirrors\AION’s typographic pattern, the rewrite/provenance macros line up with the notation in the sections, and the theorem environments are standard and section‑scoped. Nothing to complain about here.
Co-authored-by: coderabbitai[bot] <136622811+coderabbitai[bot]@users.noreply.github.com> Signed-off-by: James Ross <james@flyingrobots.dev>
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aion-holography/sections/assumptions.tex (1)
12-12: Fragile vertical spacing hack (already flagged).Line 12 still contains
\hline\\[-8pt], the brittle negative vspace previously identified. This remains unaddressed.aion-holography/references.bib (2)
1-6: Duplicate Ehrig2006 entry still present (already flagged).Lines 1-6 define
Ehrig2006, which duplicatesEEPT06(lines 83-88). Previous review confirmed onlyEEPT06is cited and requested deletion of this entry. This remains unaddressed.
65-70: Inconsistent title capitalization (already flagged).Line 67 uses
The AION Calculusinstead of sentence case with protected acronymThe {AION} Calculus. Previous review requested this fix. This remains unaddressed.aion-holography/sections/ethics.tex (1)
183-184: Raw math sequences for CΩMPUTER and AIΩN still present (already flagged).Lines 183-184 continue to use
C$\Omega$MPUTERandAI$\Omega$Ninstead of project macros. Previous review requested replacement with\COMPUTER{}and\AION{}. This remains unaddressed.
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aion-holography/sections/assumptions.tex (1)
14-24: Excellent:\crefmigration completed.Lines 14-24 now use
\crefconsistently with comma-separated label groups. This is the correct approach forcleveref-managed cross-references. The manual "Def./Thm./Sec." prefixes have been properly eliminated.aion-holography/references.bib (1)
96-96: Month field now properly quoted.Line 96 now uses
month = {June}with explicit braces, addressing the previous portability concern. Well done.aion-holography/sections/ethics.tex (1)
37-37: Macro compliance achieved.Line 37 now correctly uses
\AION{}-styleinstead of the rawAI$\Omega$N-style. This enforces consistent project branding via centralized macros.
Co-authored-by: coderabbitai[bot] <136622811+coderabbitai[bot]@users.noreply.github.com> Signed-off-by: James Ross <james@flyingrobots.dev>
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♻️ Duplicate comments (1)
aion-holography/sections/ethics.tex (1)
183-184: Use project macros for CΩMPUTER and AIΩN branding.You’re still using raw
C$\Omega$MPUTERandAI$\Omega$Nhere instead of the project macros. This breaks the single-source-of-truth for branding and makes later tweaks painful.Define and use the macros consistently (if not already done):
\newcommand{\COMPUTER}{C\texorpdfstring{$\Omega$}{Ω}MPUTER} \newcommand{\AION}{AI\texorpdfstring{$\Omega$}{Ω}N}Then update these lines:
-The companion C$\Omega$MPUTER paper will develop these safeguards in -the concrete design of the AI$\Omega$N runtime. +The companion \COMPUTER{} paper will develop these safeguards in +the concrete design of the \AION{} runtime.
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aion-holography/sections/ethics.tex (6)
7-23: Intro + UC Principle 6 quotation are tight and well-scoped.Conceptual framing of holographic provenance as “interior life” and the inline quote of Principle 6 are crisp, correct, and free of LaTeX hazards now that the redundant footnote is gone. Nothing to fix here.
25-31: Good, strong normative positioning of replay as ethically charged.The paragraph correctly reclassifies deterministic replay from “debugging” to an ethically significant intervention and cleanly hooks into existing Charter notions. No structural or LaTeX issues; this is ready as-is.
109-121: Forks as lives, not sandboxes: excellent, no edits suggested.The “forks are not test environments; they are lives” line is exactly the sort of sharp, non-weasel phrasing this topic needs. The worldline manipulation is consistent with earlier wormhole semantics. No LaTeX or structural defects here.
167-182: Design Commitment bullets are on point; ensure runtime-level hooks exist in the architecture section.This section correctly elevates worldline control to a first-class requirement and pushes ZK/OPAQUE by default for minds. Just verify that corresponding hooks (mode flags, sealing primitives, fork APIs) are actually described in the architecture/runtime sections, or else this reads aspirational rather than implementable.
79-85: The cleveref package is already loaded; this concern is unfounded.The
cleverefpackage is already included in main.tex (line 43) with proper configuration options. The\cref{sec:rulial}reference on line 82 of ethics.tex will compile without issue. No action is needed; the code is correct as written.Likely an incorrect or invalid review comment.
1-4:\sectionbreakis defined in the preamble—review comment is incorrect.The verification reveals that
\sectionbreakis properly defined at line 48 ofmain.texas\newcommand{\sectionbreak}{\clearpage}. The macro exists, is in scope whensections/ethics.texis included, and will compile without error. No undefined command. No missing dependencies. No hard compile error waiting.The original review flagged a phantom issue without verifying the actual preamble state. This is a false alarm.
Likely an incorrect or invalid review comment.
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Actionable comments posted: 14
♻️ Duplicate comments (8)
aion-holography/references.bib (1)
1-9: Author name formats are still inconsistent; normalize toLast, Firstacross entries.You’re still mixing
First Last(most entries here) withLast, First(e.g.LS06,EEPT06). This breaks consistent BibTeX name parsing and sorting, especially for particles like “van”.Standardize everything to
Last, Firstform. For this hunk, that means at minimum:- author = {Hartmut Ehrig and Michael L{\"o}we}, + author = {Ehrig, Hartmut and L{\"o}we, Michael}, - author = {Vincent van Oostrom}, + author = {van Oostrom, Vincent}, - author = {Bob Coecke and Ross Duncan}, + author = {Coecke, Bob and Duncan, Ross}, - author = {Stephen Wolfram}, + author = {Wolfram, Stephen}, - author = {Jorma Rissanen}, + author = {Rissanen, Jorma}, - author = {James Ross}, + author = {Ross, James},…and similarly update any remaining
author = {First Last ...}cases elsewhere in this file so you have one canonical convention.Also applies to: 12-20, 22-29, 31-39, 41-49, 51-56, 58-63, 65-81, 83-90
aion-holography/sections/multiway_ruliad.tex (1)
69-75: Chronos/Kairos/Aion triad punctuation is still inconsistent. Pick one and stick to it.You have
Chronos--Kairos--Aionfor the time model, butTime Cube (Chronos, Kairos, Aion)later. For a named triad, the mismatch reads sloppy.Either treat it as a compound concept everywhere:
-geometry, and the Chronos--Kairos--Aion time model from the \AION{} +geometry, and the Chronos--Kairos--Aion time model from the \AION{} @@ -explicitly model fork/merge operators and the Time Cube (Chronos, -Kairos, Aion) at the level of operational semantics. +explicitly model fork/merge operators and the Time Cube (Chronos--Kairos--Aion) +at the level of operational semantics.or as a simple list everywhere (both spots with commas). Right now it looks like an editing artifact.
Also, the
\\[-1pt]hacks in the annotation labels are brittle; consider\addlinespace-style spacing or just let TikZ’s default line spacing breathe.Also applies to: 86-90, 97-100
aion-holography/sections/ethics.tex (1)
92-107: Mode labels FULL/ZK/OPAQUE should be macros, not hard‑coded strings.You’re clearly treating
FULL,ZK, andOPAQUEas named provenance modes, but here they’re just bolded literals. That’s exactly the thing macros are for.Define them once (e.g. in
macros.tex):\newcommand{\FULL}{\textbf{FULL}} \newcommand{\ZK}{\textbf{ZK}} \newcommand{\OPAQUE}{\textbf{OPAQUE}}Then use:
- \item \textbf{FULL}: complete derivations for system verification; - \item \textbf{ZK}: zero-knowledge proofs that some property holds + \item \FULL{}: complete derivations for system verification; + \item \ZK{}: zero-knowledge proofs that some property holds @@ - \item \textbf{OPAQUE}: content-addressed sealing with opaque + \item \OPAQUE{}: content-addressed sealing with opaque @@ - \item verification tooling should preferentially use ZK and OPAQUE + \item verification tooling should preferentially use \ZK{} and \OPAQUE{}Otherwise any rebranding/typographic change requires grep surgery across the whole manuscript.
Also applies to: 174-181
aion-holography/sections/determinism_confluence.tex (1)
180-209: No-delete/no-clone invariant is still defined for a single skeleton step, but Theorem~\textbackslash{}ref{thm:two-plane} uses a compositeDefinition~\textbackslash{}ref{def:no-delete} explicitly phrases the tick as having “a single skeleton–plane DPOI step
$G_S \Rewrite_S G_S'$ induced by a rule and match$m_S$ ” (lines 187–189), and ND/NC are stated in terms of that single match and its$\Del(m_S)$ .Theorem~\textbackslash{}ref{thm:two-plane}, however, allows
$S : G \Rewrite G'$ and the proof immediately rewrites$S$ as a composite
[
G = G_0 \Rewrite G_1 \Rewrite \cdots \Rewrite G_n = G'
]
(lines 263–266), then argues along the composite mono$u : G \hookrightarrow G'$ (lines 275–277). The hypothesis “the tick consisting of$A$ followed by$S$ satisfies the no-delete/no-clone-under-descent invariant” (lines 218–219) is therefore applying an invariant that was only defined for a single DPOI step to a (possibly) multi-step composite.This is exactly the scope mismatch that was flagged earlier: you’re appealing to ND/NC for a notion of “tick skeleton part” that your definition doesn’t actually cover.
You should either:
- Generalise Definition~\textbackslash{}ref{def:no-delete} to talk about a finite composite of skeleton DPOI steps
$u : G_S \mono G_S'$ (interpreting$\Del(m_S)$ and the preservation conditions componentwise along$u$ , and forbidding any delete/clone anywhere in that composite), or- Restrict Theorem~\textbackslash{}ref{thm:two-plane} so that
$S$ is a single skeleton batch/tick in the sense of the definition, and adjust the proof not to decompose$S$ further.Right now the theorem’s hypothesis is ill-posed: the ND/NC invariant is being applied outside the domain on which it’s defined.
Also applies to: 211-219, 262-276
aion-holography/sections/rulial_distance.tex (1)
1-7: “Computable” in the section title is still stronger than what you’ve actually establishedThe technical content now cleanly proves that
$D_{\tau,m}$ is a quasi-pseudometric with additive slack$2c$ under the stated DL/Dist/budget assumptions, which is solid. However:
- The title still advertises “A \emph{Computable} Quasi-Pseudometric…”, and
- The definition of
$D_{\tau,m}$ is an infimum over all budget-admissible translators (possibly an infinite search space), with no explicit argument that this is effectively approximable.If “computable” is meant in the formal, recursion-theoretic sense, you need at least a sketched enumeration/approximation procedure (e.g. effective listing of
$\Trans_{\tau,m}$ and a convergence theorem). If instead you mean “computationally grounded / MDL-flavoured distance” in a physics-style informal sense, it would be clearer to:
- either drop “computable” from the title, or
- add a sentence up front saying that “computable” is used informally here (and reserve any hard computability claims for future work).
Right now the word oversells what is actually proved in this section.
Also applies to: 94-107, 187-191
aion-holography/sections/discussion.tex (1)
32-39: Consider using\creffor the section reference to match the rest of the paper’s styleYou’ve standardised on \textbackslash{}cref for theorem references in this section (e.g. \cref{thm:tick-confluence,thm:global}), but line 37 still reads:
“The rulial distance in Section~\textbackslash{}ref{sec:rulial} …”
Purely for stylistic consistency with cleveref, you might want to change this to
\cref{sec:rulial}and let cleveref handle the “Section” prefix and spacing, as elsewhere.Not a correctness issue, just removing one last manual
Section~\ref{...}wart.aion-holography/sections/rmg.tex (2)
59-71: RMG morphism definition is still missing a base case and an ambient category for atomic attachmentsYou’ve switched to “We define morphisms by structural recursion on RMG depth”, but the actual clause only covers composite objects
$(S,\alpha,\beta)$ . There is still:
- No base case for morphisms between atoms
$\Atom(p)$ , and- No statement of which category the “morphisms of attachments”
$f_v,f_e$ live in when$\alpha(v)$ or$\beta(e)$ is atomic.As written,
$\RMG$ is not a well-defined category: Hom-sets for atomic objects are unspecified, and the recursive clause for$f_v,f_e$ has nothing to bottom out on.You need to nail down both the base case and the ambient category. Two minimal options:
Discrete payloads (simplest):
- Declare that the payload set
$P$ carries the discrete category structure:
[
\Hom(\Atom(p),\Atom(p')) =
\begin{cases}
{\id_{\Atom(p)}} & p = p',\
\emptyset & p \neq p'.
\end{cases}
]- State explicitly that each attachment morphism
$f_v,f_e$ is itself an RMG morphism, defined by recursion on attachment depth, and that the recursion bottoms out in these atomic identity maps.General small base category:
- Parametrise the whole construction over a small base category
$\mathcal{C}$ of atomic payloads, and say that atoms are objects of$\mathcal{C}$ with morphisms inherited from$\mathcal{C}$ .- Then the recursive clause for
$f_v,f_e$ uses either RMG-morphisms (when the attachment is composite) or$\mathcal{C}$ -morphisms (when it is atomic).In either case, you should add one sentence justifying that this recursion is well-founded (e.g. via the initial-algebra viewpoint in the previous subsection). Without a proper base case and ambient category, the later claims “This makes
$\RMG$ into a category” and any use of RMG morphisms in fibrations are resting on an underspecified notion.
147-163: Notation table still conflates (\mathcal{U}) (state) with (U) (universe); fix the universe symbolThe notation row
$\mathcal{U} = (G;\alpha,\beta)$ & single RMG state (one object in a universe $\mathcal{U}$) \\uses
$\mathcal{U}$ both for:
- an individual RMG state, and
- the ambient “universe” containing such states.
Two lines later you introduce
$\Hist(U,R)$ with$U$ clearly intended as the universe of RMG states. This is exactly the ambiguity the earlier review warned about.I’d suggest:
-$\mathcal{U} = (G;\alpha,\beta)$ & single RMG state (one object in a universe $\mathcal{U}$) \\ +$\mathcal{U} = (G;\alpha,\beta)$ & single RMG state (one object in an RMG universe $U$) \\ @@ -Subsequent sections introduce $D_{\tau,m}$ (rulial distance), -$\Hist(U,R)$ (history category), and other observer-related notation. +Subsequent sections introduce $D_{\tau,m}$ (rulial distance), +$\Hist(U,R)$ (history category on a universe $U$ of RMG states), +and other observer-related notation.and ensure earlier sections that first mention
$(U,R)$ explicitly say “$U$ is the set/category of RMG states (objects$\mathcal{U}$ )”. That keeps$\mathcal{U}$ consistently as “one state” and$U$ as “the collection of such states”.
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[style] ~146-~146: Three successive sentences begin with the same word. Consider rewording the sentence or use a thesaurus to find a synonym.
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🔇 Additional comments (4)
aion-holography/titlepage.tex (1)
1-47: Title page wiring and macro use look solid.Nice job centralizing branding/date via macros and killing the global
\sloppy; the manual hyphenation on the long title is the right level of precision here.aion-holography/sections/dpo_rmg.tex (1)
50-81: Canonical RMG state/tick definitions now look well-scoped and non-duplicatedDefining RMG states as
$\mathcal{U}=(G;\alpha,\beta)$ with \textbackslash{}label{def:rmg-state} and giving a minimal tick definition with \textbackslash{}label{def:rmg-tick}, while pushing scheduler/independence/no-delete/no-clone details to \textbackslash{}cref{sec:determinism}, fixes the earlier duplication and keeps the semantics factored cleanly.No issues from this fragment; the cross-references into the determinism section are coherent.
aion-holography/macros.tex (2)
1-8: Category macros look solid.The
\cathelper wrapping\mathbfis standard practice for category names. Definitions for\OGraph,\Graph,\Hyp, and\Setare syntactically correct.Pedantic note: Ensure all five categories are actually referenced in the paper. Unused macro definitions are technical debt.
40-52: Theorem environments are correctly defined.The setup is standard and follows best practices:
- Shared counter across all numbered environments (via
[theorem])- Section-level numbering (via
[section]on the first environment)- Appropriate theorem styles (
plainvs.definition)No issues here.
Computational Holography for Recursive Metagraphs
Deterministic Concurrency, Provenance Encoding, and Rulial Distance
We formally define Recursive Metagraphs (RMGs)—graph structures where nodes and edges recursively carry subgraphs—and give them a deterministic concurrent operational semantics using Double Pushout (DPO) graph rewriting in adhesive categories.
The computational holography theorem shows that the entire interior evolution of a computation can be encoded on a "boundary": an initial state$S0$ together with a provenance payload $P$ . This boundary data is information-complete, enabling full reconstruction of the derivation volume on demand.
Key results include:
This forms the mathematical foundation of the AIΩN Protocol.