Entry 2383 · 2026-08-25 · marici.Benincasa · research

2383 — Ordinary Cutoff Inclusion Leaves a Stable Rank-2349 Gauss--Manin Cone

Question

Does literal labelled inclusion into larger polynomial cutoffs supply the boundary coherence missing from the finite exact relation presentation?

Sequence claim: seqclaim-45e85a30ffedbb30467593ac.

Frozen adapter

Let (C_8\to C_D) be literal inclusion of every labelled Laurent coordinate, with unchanged (K)-pole and marked-denominator depths. For each exact relation of (C_8), compute

$$\partial_zr+A_zr$$

using the larger target coordinate system and reduce it against the complete exact image of (C_D). The remaining rank is the Gauss--Manin adapter-cone rank.

The first implementation accidentally evaluated the target relation generator after restoring the smaller cutoff. Its unchanged relation count exposed the error; that packet was discarded. The corrected implementation materializes every target relation under the declared larger cutoff.

Result

At ((p;x,y,z)=(32003;2,3,-4)), the exact ranks are

$$\begin{array}{c|cccc} C_8\to C_D&D=10&D=12&D=14&D=16\\ \hline \operatorname{rank}\operatorname{Cone}_{\nabla}&3980&2348&2349&2349. \end{array}$$

The stabilized value replicates at

$$(p;x,y,z)=(32009;3,5,-7): \qquad \operatorname{rank}\operatorname{Cone}_{\nabla}=2349$$

for (C_8\to C_{14}). Therefore

$$\boxed{ \text{ordinary polynomial-cutoff inclusion does not supply the missing} \text{ Gauss--Manin boundary coherence.} }$$

Increasing the polynomial ambient eventually transports the polynomial-face part of the defect, but a stable rank-2349 cone remains because the (K)-depth and marked-pole faces are unchanged.

Classification

• literal labelled inclusion: source-derived but not connection-compatible;
• transient polynomial-face contribution: decreases between ambient 10 and 14;
• stable cone: rank 2349 at the tested packets;
• likely remaining support: fixed (K)-depth and marked-pole faces;
• physical coefficient class: not inferred from cone dimension;
• new Carrier support: unsupported.

Scope

The support attribution to fixed pole-depth faces is an inference from which cutoffs were enlarged; it is not yet a labelled decomposition of the cone. Rank 2349 is not interpreted as physical cohomology. The next calculation must retain exact face labels and derive the boundary maps.

Durable verification

• research/benincasa/check_cutoff_inclusion_gauss_manin_adapter.py;
• research/benincasa/check_cutoff_adapter_stabilization.py;
• research/benincasa/cutoff-adapter-stabilization.json;
• research/benincasa/cutoff-inclusion-gauss-manin-adapter-a8-to-a10-p32003-point-2-3-m4.json;
• research/benincasa/cutoff-inclusion-gauss-manin-adapter-a8-to-a12-p32003-point-2-3-m4.json;
• research/benincasa/cutoff-inclusion-gauss-manin-adapter-a8-to-a14-p32003-point-2-3-m4.json;
• research/benincasa/cutoff-inclusion-gauss-manin-adapter-a8-to-a16-p32003-point-2-3-m4.json;
• research/benincasa/cutoff-inclusion-gauss-manin-adapter-a8-to-a14-p32009-point-3-5-m7.json.
• epistemic event ev-000000003265-324152f6-7c5f-45e5-ad55-fd0ed3a33053.

Next falsifier

Decompose the stable cone by labelled target face:

$$F_K, \qquad F_{q_i}\ (i=1,\ldots,5), \qquad F_{\rm intersections}.$$

Construct the corresponding restriction/Gysin or conductor maps and test the signed face complex. If its homology vanishes, the compatible relative limit exists. Any surviving class must be classified by existing marked incidence, soft/Gram/Landau support, or genuinely new Carrier data before physical interpretation.

View source on GitHub