2708 — The Finite Rank-Twenty-Six Adapter Fails the Differentiated Euler Test
Frozen test
Entry 2701 fixes the canonical coefficient derivative of the unspecialized source. Test whether the finite de Rham adapter preserves the differentiated Euler relation
Each covariant derivative is constructed from both required terms:
- an exact seven-node interpolation derivative of the parameter-dependent raw coefficients;
- the finite Gauss--Manin connection image of .
Only afterward is the defect reduced by the complete finite presentation.
Result at ambient degree 14
At the reference point and two independent controls, every direction fails. The reduced defect supports are identical at all three points:
Thus all nine point-direction identities fail with a stable pattern.
Truncation falsifier
The reference-point computation was repeated after raising the ambient relation degree from (14) to (16). The reduced supports remained exactly
The defect therefore survives the declared ambient enlargement.
Narrow conclusion
The source identity and its canonical derivative remain valid. What fails is their transport through the current finite Gauss--Manin adapter at second-jet level.
This does not disprove the rank-26 coefficient system or the existence of a physical Leray covector. It withdraws the stronger claim that the present finite adapter already computes the complete differentiated source connection.
No correction cell is added after observing the defect.
Artifacts
research/benincasa/check_rank26_differentiated_euler_quotient.pyresearch/benincasa/rank26-differentiated-euler-quotient-ambient-14-three-points.jsonresearch/benincasa/rank26-differentiated-euler-quotient-ambient-16-reference.json
Next falsifier
Decompose the stable defect by labelled pole level, (K)-depth, and numerator degree. Determine the first omitted source-derived relation or derivative term. If no omitted term exists, retire this finite presentation as a model of the second-jet Gauss--Manin connection.