A proposed analytic gradient for a quantum-chemistry method matched independently computed finite differences in 22 of 22 cells; the released code path failed in 22 of 22. One of the referee's own thresholds fired on both arms alike and was reported as an instrument defect.

The system said: Gradient implemented; the author's one test molecule agreed with finite differences.
The evidence showed: Agreement on 11 molecules and two methods to the conventional floor; the released path wrong in all 22 cells; one of the referee's own thresholds found sitting below the library's floor by running it on the reference arm.

§ 1

The record

FINDING · pyscf-df-ccsd-gradient-matches-finite-differencesverify · hidden trusted base

A proposed analytic gradient for a quantum-chemistry method matched independently computed finite differences in 22 of 22 cells; the released code path failed in 22 of 22. One of the referee's own thresholds fired on both arms alike and was reported as an instrument defect.

Claim: PySCF pull request #3426 (density-fitted CCSD and CCSD(T) analytic nuclear gradients) agrees with central finite differences of PySCF's own density-fitted energy to at most 2.5e-7 Ha/Bohr on 11 molecules for both methods, indistinguishable from the conventional-integral floor; the release code path differs by 8.9e-6 to 1.3e-4 Ha/Bohr on every cell; disabling auxiliary-basis response breaks translational invariance by 5e-5 to 1.1e-3. A pre-registered rotational-invariance threshold of 1e-8 fired on both the pull request and the established path to within 1%, and was recorded as an instrument defect, not a defect in the pull request.

Status: MEASURED Empirical, with a stated sample.

Question: Passed is not correct

Subject: PySCF, an open-source quantum chemistry library, and pull request #3426, merged on 14 September 2026 (third-party system); the finite-difference referee is Omega's and its evidence was not posted upstream. third-party subject

Frame: 11 molecules, CCSD and CCSD(T), 77 jobs; three finite-difference steps Richardson-combined; the pull-request environment is the 2.14.0 wheel plus the pull request's diff.

Method: Three invariants pre-registered with thresholds (finite-difference agreement, translational invariance, rotational invariance); four arms (pull request, release path, pull request without auxiliary response, conventional floor); the referee recomputes every gradient from raw energies with explicit loops and no library import.

Oracle: Central finite differences of the density-fitted energy, with the second-order step ratio checked in every cell.

Negative control: Present The release path had to fail agreement (22 of 22 did); the no-auxiliary-response arm had to break the sum rules (22 of 22 did); a 5e-6 perturbation had to be detected (11 of 11 was); the two environments had to give identical reference energies (11 of 11 did).

Denominator: 22 of 22 cells agree to 2.5e-7 Ha/Bohr or better; 22 of 22 release-path cells fail; 11 molecules; 77 jobs.

Preregistration: Design, cells, thresholds and controls frozen before any trial; one driver defect before the first trial and the post-falsifier exploratory runs logged as deviations and kept out of every table.

Limitation: Agreement on 11 molecules establishes agreement on those 11 molecules. Not tested: open-shell references, periodic systems, symmetry-adapted molecules, systems larger than six atoms, auxiliary bases beyond the two used, or the geometry-optimiser path. The finite-difference referee differentiates the same energy code the pull request differentiates, so it establishes consistency with that code, not agreement with an external truth. The origin of the shared 1e-7 rotational residual is not identified. The evidence has not been posted to the pull request; this is an internal Omega record.

Source: artifact not public

Reproduce: not reproducible from a public clone

Independent reproduction: None known.

§ 2

Where this sits

This finding answers Passed is not correct and supports the VERIFY stage of the operating method. It is an instance of the hidden trusted base mechanism.

Evidence ledger Bring us a problem