2681 — The Frozen Conormal Completion Does Not Supply the Required Off-Diagonal Coherence
Required map
Entry 2678 found a rank-twelve defect in diagonal curvature descent through
Cancellation would require a source-derived off-diagonal coherence coupling the base-direction and conormal occurrence blocks.
Frozen-constructor inventory
The admitted source machinery contains:
- tracked exact-trace corrections to quotient representatives;
- the option to retain or subtract the primitive exact term;
- the ordinary Koszul differential;
- the bare differentiated Koszul contractions and mixed generator derivatives.
The finite audits establish:
- tracked exact-trace correction acts within the visible quotient grade;
- retaining the primitive term changes a dense visible block and diagonal coherence entries but creates no cross-grade block (Entry 2651);
- the ordinary quotient Koszul differential is zero (Entry 2664);
- bare differentiated Koszul mixed curvature is zero (Entry 2667).
Therefore no map in the frozen inventory has the variance needed to cancel the rank-twelve transitivity defect.
Narrow closure
The proposed conormal curvature completion fails under the frozen constructor. The visible rank-four curvature is presentation curvature in this model: it does not descend to the cotangent-transitivity cohomology through any admitted map.
This does not prove that no larger source geometry can supply a transitivity connection. Such an enlargement must be independently derived and must predict its off-diagonal block before inspecting the defect. Solving the chain-map equation for a convenient correction is prohibited.
Evidence chain
- Entry 2651
- Entry 2664
- Entry 2667
- Entry 2678
research/benincasa/results/cm-rank-seven-dual-cross-grade.jsonresearch/benincasa/results/cm-curvature-transitivity-descent.json
Next programme move
Retire this curvature-completion branch. Return to a source-defined physical or coefficient comparison whose map exists before reduction—most naturally the rank-twelve marked-relative extension or another independently enlarged source family. Preserve the transitivity packet as a hostile acceptance test for future enlargements.