v1.0.6 — arXiv submission presentation

Version 1.0.6 is the arXiv-facing presentation and bibliography release.
The theorem, mathematical claims, and proof strategy are unchanged.

Highlights:

• keeps both long tables within the sections that introduce them;
• revises the abstract, transition prose, related-work discussion, and
  availability statement for clarity;
• corrects and completes bibliographic page, issue, editor, and series data;
• compacts the references and removes the one-entry final bibliography page;
• updates the manuscript and citation metadata to Version 1.0.6, dated
  September 4, 2026;
• rebuilds the manuscript as a clean 30-page PDF.

No verifier source, exported witness, deterministic proof log, dependency
lock, or mathematical certificate changed. The only changed file listed in
the proof payload is the Makefile, whose SOURCE_DATE_EPOCH now matches this
release date. The v1.0.4 complete replay profile and v1.0.5 independent
software-assurance profile are retained as records for the unchanged
computations. No fresh complete replay or independent human sign-off is
claimed for v1.0.6; the attached sanitized transcript retains its original
v1.0.5 filename for that reason.

Final release checks:

• make paper completed successfully;
• the LaTeX log contains no box, citation, reference, or package warnings;
• all PDF fonts are embedded, and MuPDF parses all 30 pages;
• all 22 cited bibliography keys resolve, with no unused entries;
• make verify passed both stored hash lists;
• the extracted source archive passed all 39 payload and 57 full-manifest
  checks, and its PDF matches the separately attached PDF byte-for-byte.

Snapshot commit:
7955273411dd42d6102d0e8858da869b6fa8f204

Proof-payload SHA-256:
0856e33af616ca7883835a449e2e1ee2b9a28c91bdc946ed5a2e752b47e02681

PDF SHA-256:
eb0a00b4994537111cde37ea35fbd61e8af4735f3dba5502f6ea4fed02ee4f45

GitHub is the distribution mirror. A DOI-bearing archival deposit remains
planned for an accepted journal snapshot.

v1.0.5 — independent verification layer

Version 1.0.5 adds an independent software-verification layer while leaving
the theorem and proof strategy unchanged.

Highlights:

• standalone C++ exact checking of exported polynomial, factor, Sturm, and
  resultant witnesses: 537 checks, 0 failures;
• a structurally independent Boost/two-parent Pascal scan through D = 1200:
  289,261,901 top-half cells, 0 negative Turán steps;
• twelve injected scan and certificate mutations, all rejected;
• atomic witness exports, hard-failure gates, long-stage progress reporting,
  expanded reviewer maps, and CI integration;
• rebuilt 31-page manuscript with the independent-assurance trust boundary
  and v1.0.5 artifact identifiers.

The local component runs and make audit-fast passed. The separate clean
replay by a second person has not been performed: the included sign-off form
is intentionally unsigned, and the release does not represent it as complete.

Snapshot commit:
93ed17920c044650e4a69a69ba4fbdc2d5fc4212

Proof-payload SHA-256:
8659c3004354cc7dbf95a8509bb3e4ed7787c352ed4ff69586c3e92f7fcbdbaa

PDF SHA-256:
dd0d018a5b9f9062347098e5bd674ebebe74c63c8a2e575452eea9bd5be1c1bb

The accepted snapshot remains intended for deposit in a persistent,
DOI-bearing archive.

v1.0.4 — AI-use disclosure

Submission artifact v1.0.4.

This revision adds an AI-use disclosure identifying GPT-5.6 Sol
(gpt-5.6-sol) at max reasoning effort and stating the author's direction,
verification, and responsibility. It also updates the manuscript version and
date, citation metadata, deterministic PDF source date, PDF, and hash records.

The theorem, mathematical argument, proof generators, exact logs,
dependencies, and replay commands are unchanged from v1.0.3. The successful
complete replay recorded there therefore remains the replay record for this
snapshot: 1:15:18 wall time, 338764 KiB peak resident memory, and 289,261,901
top-half cells checked through D = 1200 with zero negative Turán steps.

Proof-payload SHA-256:
b8d918147e24d23461f492805c56ebbd4ab388f8ce2620514d4fb4fac7865c2f

PDF SHA-256:
907561982fdd7f7661cef17cd268117f1268e102efc0ba7554c4711b179783bf

The accepted snapshot remains intended for deposit in a persistent,
DOI-bearing archive.

v1.0.3 — referee-ready submission artifact

Submission artifact v1.0.3.

This revision incorporates the final referee-requested manuscript and artifact
changes without altering the main theorem or proof strategy:

• corrects the archival wording and identifies GitHub as a distribution mirror;
• adds explicit BSD-3-Clause and CC BY 4.0 component licensing;
• replaces the optimization-removable verifier assertion with a hard gate;
• updates the finite-offset source documentation and denominator convention;
• adds a digest- and snapshot-pinned replay environment and fast CI audit;
• applies the requested proof clarifications, copy edits, link breaking, and
  bibliography additions, including Bustoz--Ismail;
• records a clean complete replay under the v1.0.3 sources.

The complete replay exited successfully in 1:15:18 with 338764 KiB peak
resident memory. The exact GMP scan covered 289,261,901 top-half cells through
D = 1200 and found zero negative Turán steps.

Proof-payload SHA-256:
cef4ab11ed2905f7d71a8140290808f215771bd32f6b8d29fb89b4e086a94c0b

PDF SHA-256:
c75d0c02c024628e0901b08f6b5c422818b88f2cbfa055384ef3369a8ac979ed

The accepted snapshot remains intended for deposit in a persistent,
DOI-bearing archive.

v1.0.2 — privacy-sanitized submission artifact

Privacy-sanitized immutable submission snapshot. The mathematical proof payload is unchanged; this revision adds explicit statement domains to Lemmas 4.4 and 6.1, removes prior confidential development history from the public repository, omits detailed shared-host metadata, and publishes a replay transcript whose working-directory path is normalized to .