# C-0043 witness pin

- Verifier SHA-256:
  `d2c81bc63eff8cb1b5ddd0dc1668791a0ee098b5c0355607fdf0d44dc53c1b08`
- Accepted output SHA-256:
  `3164e42b29175d01a52d6855320e506e095b7d49e5ff950114fbe0f6ccbe5482`
- Original SymPy/NumPy verifier SHA-256:
  `5049666042b70c35fec02bddf6a22deb1ea797239ae7f8bfffc43ffcce915e09`
- Runtime: Python 3.14.6, standard library only.
- Run:
  `uv run --frozen python canon/witnesses/C-0043/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:

- 2002 page 13 underlying \(x^2(x+1)^{11}\) order-four failure:
  lines 700-725.
- 2002 Remark 5.6(b), equation (5.13), and
  \(K(x)=3(10D-B^2)\): lines 951-996.
- 2005 Example 3.3, "lowest degree example we have found," and
  \(W(f,f',f'',f''')(0)=-1584\): lines 371-374.

The source bundle also pins rendered copies of printed pages 13, 16,
17, 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 power-sum determinant by exact polynomial arithmetic;
2. expands and checks every monomial orbit in the symmetric reduction;
3. checks the twelve-term AM--GM orbit;
4. constructs the full \(220\times220\) scaled Johnson matrix and checks
   \(A^2=360A\) entry by entry;
5. reconstructs the published \(-1584\) Wronskian and the strict-root
   normalization;
6. derives the restricted-family degree-thirteen threshold from
   \(144\psi(0)^4(10D-B^2)\);
7. checks the polynomial-transfer identity, equality cases, and the
   full-\(PF_4\) scope boundary; and
8. rejects optimized Python.

The post-promotion hostile audit is recorded at
`scratch/proof-system--c0043-karlin-h4-source-certificate-audit/RESULT.md`.
