# C-0056 witness pin

- Verifier SHA-256:
  `4d5a17fea7113c4a0dead5c3218eb267e090bc7fb6139fe8a12216cf310c709e`
- Accepted output SHA-256:
  `db2d4610d0dd82d53824b79b9506dc428b8f4f69c52186714b70dab3c05813a2`
- Original SymPy verifier SHA-256:
  `81705c43d0db60f5d5dbed189ae8220bb4943cf307407cf74f3bee82c8ec4623`
- Runtime: Python 3.14.6, standard library only.
- Run:
  `uv run --frozen python canon/witnesses/C-0056/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 Example 3.1 and the full \(5\times5\) Wronskian:
  lines 328-342.
- 2005 strict-root examples and simple-root perturbation:
  lines 347-354.
- 2002 order-four restricted-family formulas, confirming that source is
  not an order-five classification: lines 951-996.

The source bundle pins rendered copies of printed pages 16, 17, 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 reciprocal determinant in elementary-symmetric variables
   and checks exact content \(82944\);
2. proves that all possible root monomials lie in the 46-dimensional
   degree-15, seven-variable, exponent-at-most-five symmetric basis;
3. recovers the unique 46 orbit coefficients from an exact evaluation
   system whose matrix is invertible modulo \(2^{61}-1\), verifies the
   equations over the integers, and recovers exactly the displayed 20
   nonzero orbits;
4. reconstructs all 6496 source monomials and all six ordered-difference
   transforms;
5. checks all 48503 positive chamber coefficients, their statistics, and
   SHA-256 digest;
6. checks the reciprocal complement, published witnesses,
   positive-leading transfer, sign reversal, lower-support continuity,
   and the O-0160 scope counterfeit; and
7. rejects optimized Python.

The post-promotion hostile audit is recorded at
`scratch/proof-system--c0056-karlin-h5-source-certificate-audit/RESULT.md`.
