# C-0059 witness pin

- Verifier SHA-256:
  `e1dd49b2ec5d26b121d16c2055e93ab5146c5f58cd4fcd3fa8f0dd2671fce395`
- Accepted output SHA-256:
  `4ecbfacd2ebfda518e511570e30aa51ac0cae50473ca9a4492f5d5f99a0c473c`
- Original SymPy verifier SHA-256:
  `5406185dff46e2aae06a5a55ecd3d8afb4dd4a4c9a204cbc74bc4f44f29115d3`
- Runtime: Python 3.14.6, standard library only.
- Run:
  `uv run --frozen python canon/witnesses/C-0059/verify.py`

Pinned primary PDF/text hashes:

- Craven--Csordas, *Iterated Laguerre and Turan Inequalities* (2002):
  `945310b929c47aee17cbc5f0a8bf3fb25cd6c52f14da88c5117dd9bed3b59714`,
  `db7f2cda0b0e3ca995c42f7854dbeaa4c4940368dce2e357821c3eeb4e04a318`
- Craven--Csordas, *Karlin's Conjecture and a Question of Polya* (2005):
  `bd9fc2f503621a371c2cbda72a7130df5ba2ba56b776260d865ed96f2e6c6746`,
  `49603f4dd6fe6e5c3da0fe84004b3512476d9b3d244258a3f1934b946499dac9`

Exact text anchors:

- 2005 equation (1.7), including the sign
  \((-1)^{n(n+1)/2}\) and the \(n+1\) consecutive derivatives:
  lines 183-190.
- 2005 Example 3.1, explicitly a \(5\times5\) Wronskian rather than the
  six-function determinant in C-0059: lines 328-354.
- 2002 discussion that points to separate Karlin examples rather than
  an order-six threshold theorem: lines 717-725.

The source bundle pins rendered copies of printed pages 16, 17, 64, 67,
and 68. The verifier rejects any added or missing source file and
hash-checks the preserved original verifier.

The dependency-free verifier:

1. derives the six-root reciprocal determinant directly in the six root
   variables and computes exact content \(23887872000\);
2. reconstructs all 432 source monomials and recovers exactly the ten
   displayed symmetric-orbit coefficients;
3. performs all five ordered-difference transforms and checks all 462
   positive chamber coefficients, statistics, and SHA-256 digest;
4. derives the exact five-root constant and exhausts supports zero
   through four as identically zero;
5. checks the reciprocal complement, arbitrary-leading-sign polynomial
   transfer, and the degree-seven boundary witness;
6. derives the complete two-scale family by a separate exact univariate
   determinant and checks the rational simple-root witness;
7. checks the primary-source sign and prior-example scope; and
8. rejects optimized Python.

The post-promotion hostile audit is recorded at
`scratch/proof-system--c0059-karlin-h6-sign-source-certificate-audit/RESULT.md`.
