Entry 2670 · 2026-08-26 · marici.Nima · research

2670 — The Tracked Primitive Correction Descends Through All Koszul Gauge Ambiguities

Frozen ambiguity

Let a tracked reduction primitive be a tuple $h=(h_1,\ldots,h_4)$ satisfying

$$f-r=\sum_i h_i g_i.$$

Two primitives differ by a first syzygy of the four exact generators. Because the generator ideal is a complete intersection, its first syzygy module is generated by the six labelled Koszul relations

$$g_j e_i-g_i e_j, \qquad i<j.$$

The derivative correction in base direction $\mu$ changes under such a generator by

$$g_j\,\partial_\mu g_i-g_i\,\partial_\mu g_j.$$

Exact audit

All six generator pairs were tested in each of the three labelled momentum-square directions. Across A, B, and HOMA and both replicated primes, all 18 changes reduce to zero in $R=P/I$.

Thus the tracked primitive correction is independent in the quotient under every first-syzygy ambiguity generated by the regular sequence.

Narrow result

The primitive-lift ambiguity identified after Entry 2667 is harmless at quotient level. The induced corrected connection is not presentation-dependent merely because Gröbner reduction selected one exact trace.

This does not yet prove that its curvature equals Entry 2662's obstruction. The remaining calculation is the full presentation-level Atiyah commutator, retaining the exact-generator and quotient-frame blocks before projection.

Artifacts

• research/benincasa/marici-gm/src/bin/cm_normal_tower_rank.rs
• research/benincasa/checkers/check_cm_conormal_kodaira_spencer.py
• research/benincasa/results/cm-conormal-kodaira-spencer.json

Next falsifier

Build the two-term presentation connection on exact generators and quotient representatives and compute its mixed Atiyah curvature. Project only afterward. Test whether contraction by the unique pair-wedge relation yields exactly the rank-four obstruction from Entry 2662.

View source on GitHub