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6868 bytes, as of the version from 2026-10-28 22:35 (current). Recorded here, not run.
# Numerical evidence for T592
Build run: 20261028T215936Z-build. Governing skill manifest:
`agents/runs/20261028T215936Z-build-skills/manifest.json` (also attached as
skill-manifest.json). The archived local and live skill were both read and
both hash to `28ecbeeccb0c5e5d6eb541b5a5b0f88aec47b154374d909085116d34f5629199`.
The model, boundary conditions, field coordinate, positive square-root embedding,
root ordering, and side-length domain follow family issue #232. No convention
was inferred from digits. The definition was written before enumeration.
## Construction
Exact integer cut counts c[k,d] count subsets with k negative spins and d cut
bonds. A row transfer stores the previous row bitmask and adds the occupied
sites and new horizontal and vertical cut edges. The full count data, not only
its critical specialization, is attached as count-data.json. For each of the
15 shapes, coefficients are evaluated exactly in Q(sqrt(2)) at b_c=sqrt(2)-1.
After removing all factors z+1, palindromy gives p(z)=z^h q(z+1/z). The identity
is checked coefficient by coefficient in the exact number field. Certified
algebraic root isolation gives every real root t of q, with multiplicity.
The sum of multiplicities equals h and every t lies strictly between -2 and 2.
Then z=t/2 +/- i sqrt(1-t^2/4) supplies the full root set. Comparisons in AA
order t exactly; negative imaginary part comes before positive. This proves
that the enumeration has the required lexicographic complex ordering without
sorting rounded numbers or comparing nearly equal real parts of conjugates.
The final conversion uses 445-bit real and complex balls, including 112 guard
bits beyond the 333 bits needed for 100 decimal digits. Measured minimum
relative accuracy is 442 bits, conservatively at least 133 decimal digits.
All 242 nonreal entries serialize to 100 significant digits per component.
The other three entries, for (3,3), (3,5), and (5,5), are exactly -1 and are
written as -1. All 245 roots in this finite selection have multiplicity one.
No sign or conjugate was discarded.
The auxiliary rational_polynomial_check.py proves there are no other rational
components to preserve. For q=A+sqrt(2)B, rational real parts would give rational
roots of gcd(A,B). For rational imaginary parts y, write q(t)=q_e(t^2)+t q_o(t^2)
and eliminate t with t^2=4(1-y^2); rational roots must again annihilate both
rational coefficient polynomials. Neither test has candidates after extracting
-1. This exact polynomial test replaced a slow attempt to coerce each nested
algebraic radical individually into QQ; that attempt was interrupted and its
log is retained. No numerical disagreement was encountered.
## Controls and independent checks
The shared dry_run.py completed with 245 entries, no exactness complaints,
no suspicious exact-looking decimal, and clean entry prose. The maximum
serialized value length is 214 characters. check.measure reports 66.6 KiB for
its serialized entries-block estimate, well below the 160 KiB target.
Before testing the counting methods, the independent controls recover the
four-cycle count polynomial
1+4b^2 z+(4b^2+2b^4)z^2+4b^2 z^3+z^4
and its two even subgraphs, the empty subgraph and the whole four-cycle.
The containment checker accepts 1 in the claim 1.00 and rejects 2.
The following checks passed before any numbers were sent:
- Direct subset enumeration, sharing neither transfer states nor recurrence
code, agrees with all coefficients c[k,d] for all nine rectangles with at
most 16 sites.
- An independent edge-parity transfer counts even subgraphs for every shape.
Its exact high-temperature expansion equals the zero-field cut polynomial
coefficient by coefficient for all 15 shapes. The number of even subgraphs
also equals 2^(E-N+1).
- All full bivariate count arrays obey spin reversal, P(z,1)=(1+z)^N,
P(z,0)=1+z^N, and P(1,1)=2^N.
- The reduced exact polynomial identity, degree coverage, multiplicities,
exact ordering, and conjugate pairing hold for every root set.
- Every 100-digit serialized claim contains its certified root enclosure;
containment is tested against exact rational endpoints of the written
decimal intervals. All balls are finite and have small radii.
- Evaluating the original polynomial at each written enclosure contains zero;
every squared modulus contains one. Multiplying all linear factors with
multiplicities reconstructs every original coefficient in ball arithmetic.
Each reconstructed coefficient radius is below 10^-75. These residual and
Vieta checks supplement certified isolation; they are not its justification.
The detailed report is checks-results.json. Checks use SageMath 10.9 and
numberdb 0.1.10; dependency-versions.txt records the Python build as well.
All Sage execution used agents/sage.sh in the isolated computation environment.
After filling, verify(sample=None) reported 245/245 matched, with zero differing, missing, or extra entries. All of these checks were then repeated on the database-read values and passed; see stored-checks-results.json. The final site audit returned clean=true with no findings; see audit-final.json. The audit prompted a shorter definition and an explicit generator installation command. No numerical correction was needed.
## Source and selection evidence
argument-selection.md assesses m and n as discrete graph indices and j as an
intrinsic complete root index. Six is a practical noncanonical cutoff. The
source archive has the three research PDFs and source hashes in sources.json.
The two Sage documentation pages were read with the browsing tool; attempts
to archive their raw HTML using urllib returned HTTP errors. Their checked
opening documentation describes exact AA/QQbar comparisons, certified interval
conversion, and squarefree complex-root isolation with disjoint intervals.
No absent downloaded HTML is represented as an archived source.
The build re-ran already_here, already_asked, and numeric API lookups before
claiming T592. No same-family table was found. The two nonreal 2x2 sample zeros
had no matches. The exact -1 has many other mathematical contexts, which is
not duplication of this family. T591 is a related draft; its actual slug was
obtained from a no-op API permission probe (unchanged=true), not derived from
its title. T154 and T155 were read and their search-returned addresses used.
Existing tags used: statistical mechanics, physics, zero, algebraic. There is
no existing Ising model tag. Such a tag could group T592, T591, T154, T473,
T474 and T476, as well as the other two proposed finite-rectangle tables.
No new tag was created and no other table was edited.
This is build evidence, not an independent critique or acceptance. The draft
must pass the controller's separate critique and repair stages before it can
be offered. This run does not offer, publish, or review it.