F1 run_checks.sh exited 1 on any machine WITH SageMath. set -euo pipefail made
the declared-optional cross-checks fatal, so the script passed without the
optional tooling and failed with it. Optional calls are now guarded by
run_optional(), failures are counted and reported non-fatally, and the script
ends exit 0 with a summary line.
F2 false assertion in p28_lattice_hypotheses_certificate.sage. Component 1 read
216 + 108x + 46x; b2 = (1,2,1,0) contributes 216x, so the true value is
216 + 216x + 46x. The load-bearing identity below it (Bcomb == 4x*Crow) was
always correct, so no mathematics changes.
F3 Sage 10.9 raised 'keys do not match self's parent' at the subs() call: q
lives in the fraction field K while .numerator()/.denominator() return elements
of the underlying polynomial ring. The substitution key is now coerced into the
polynomial parent. This error had been MASKING F2.
Verified after the fixes:
run_checks.sh exit 0, 48 mandatory PASS (up from 43 -- the previously failing
certificate now runs to completion), 0 optional failures
falsifiability intact: 64R-44 -> 64R-43 exits 1, and 236337691420383 -> ...384
exits 1
pdflatex x3: 0 errors, 0 warnings, 0 undefined, 17 pages, 0 broken refs
Documentation: states plainly that no base is claimed superior to any other --
the non-injectivity holds for every b >= 2, [0,1] and [1] collide in decimal
exactly as in octal, and both repairs are stated for general b. Base 8 is only
the inherited worked example. Without this a reader could take the radix work
for a claim that base 8 beats base 10 or binary, which is not claimed anywhere.
Housekeeping: removes three Sage preparser .sage.py outputs that an earlier
'git add -A' in this branch had wrongly committed, and adds a .gitignore for
Sage and LaTeX build artifacts. Release zip and PDF rebuilt.
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01WY6SfRYvm8zFKMX9GcjS8u
Renames THE_ENCODER_APPROACH.md -> HOW_THE_SOLUTION_WAS_FOUND.md and rewrites
it to answer the question a reader actually has -- why these moves -- rather
than arguing for novelty.
Removed: all self-assessment of distinctiveness. Replaced with a plain statement
of the relevant standard practice (PSLQ/LLL, Inverse Symbolic Calculator;
canonical numeration systems, base-k recognisable sets, Cobham) so a reader can
place the work without being told what to think of it.
The narrative now explains each move that looks arbitrary in isolation:
- why the seed data was treated as generated rather than given
- why a bijective codec was needed first, which is what the Radix framing and
DFA canonicalisation work is for
- why the Pascal basis was not a search: the matrix's own second row
(-u^3, -3u^2, -3u, -1) is a signed Pascal row, visible before any fitting
- what decoded (A, B, S) and why exact agreement makes it evidence
- how A, B factor through s2(tau_163) to reduce the problem to one CM value
- why the encoding is only a lead, with the proof built independently
- why the deformation r = 1/x exists: without it there is no contour
Adds a 'What did not work' section recording the three closed routes with their
witnesses (t-line intertwiner impossibility, L_U monodromy exclusion, Sym^2 V
set aside), since the indirectness of the final route is explained by them.
Retains the honest limits: 3.54x is not compression, and the claim should be
rejected.
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01WY6SfRYvm8zFKMX9GcjS8u
Reconstructs the Problem 2.8 data directly from the challenge statement
(R, u=2n+3, w, the 4x4 M(n), both integer seed rows) and verifies by exact
rational arithmetic that the manuscript's specialisation reproduces it:
M_N(x_0) == official M(N), all 16 entries, at N = 0,1,2,3,5,8,17,40
A_0 = A*C - (5/4)H_0 == official first seed row
A_1 = S*C == official second seed row
(14R-567)/9 == 236337691420383 (the deformed coefficient restores)
18 assertions, three with explicit negative controls. fractions.Fraction
throughout; no floating point, no CAS.
Closes the one gap no existing certificate covered: the other four verify
statements about the deformed family, none verified that the family is the
official object.
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01WY6SfRYvm8zFKMX9GcjS8u
