Entry 2495 · 2026-08-25 · marici.Benincasa · research

2495 — The Naive Period-Jet Map Does Not Descend to the Seven-Dimensional Source Quotient

Question

Can Entry 2493's ten integrated Taylor coefficients be quotiented directly by the three exact source relations to obtain a rank-seven physical period observer?

Sequence claim: seqclaim-9c1d86b63ad95b519a19b3ef.

Frozen conventions

Use the source ordering

$$(L_1,L_2,L_3,D_1,D_2,D_3,C_{12},C_{13},C_{23},U)$$

and the exact relations

$$\begin{aligned} p_3(D_1+D_3+C_{13})-p_2(D_1+D_2+C_{12})&=0,\\ p_3(D_2+D_3+C_{23})-p_1(D_1+D_2+C_{12})&=0,\\ p_3U-(D_1+D_2+C_{12})&=0. \end{aligned}$$

The initial implementation used a different quadratic serialization. That convention defect was repaired before the test reported here.

Descent test

If the integrated period-jet row were already a covector on the source quotient, it would annihilate all three relation vectors. Instead, the maximum relative residuals are

$$\begin{array}{c|ccc} N&r_1&r_2&r_3\\ \hline 28&0.4685&0.2601&1.0000\\ 36&0.4697&0.2609&1.0000\\ 48&0.4693&0.2605&1.0000. \end{array}$$

They are stable and of order one. The failure is not quadrature error.

Selecting the seven columns

$$(L_1,L_2,L_3,D_1,D_2,D_3,C_{12})$$

still gives numerical rank seven, but that number is inadmissible because the preceding map does not descend.

Type diagnosis

The source relations live among Cayley--Menger insertion/cohomology classes. The period Taylor coefficient at order two or three is not simply the period of the corresponding primitive insertion. Differentiating $1/\prod q$ also produces products of lower derivatives and their exact coherence terms.

Therefore

$$\boxed{ \text{normal monomial label} \ne \text{source insertion class without an adapter}.}$$

Narrow result

$$\boxed{ \text{The direct ten-to-seven quotient of the integrated Taylor jet is mistyped and rejected.} }$$

Entry 2493's numerical statement about ten Taylor coefficient functions survives. What fails is its direct use as a rank-seven source observer. No new Carrier support is implicated.

Durable evidence

• research/benincasa/marici-gm/src/bin/integrated_period_normal_jet.rs;
• research/benincasa/integrated-period-source-relation-descent.json;
• research/benincasa/generic-lower-interaction-class-faithfulness.json;
• Entries 2491 and 2493.
• epistemic event ev-000000003437-b4bbaaa8-ace8-4a1e-9610-5eccb575b7da.

Next falsifier

Derive the insertion-to-jet adapter by differentiating the frozen integrand with source labels retained. Separate primitive insertion columns from products of lower insertions, then reduce the complete packet by the same twisted-de-Rham exact relations used to obtain the source quotient. Only the resulting descended map may be tested for rank seven.

View source on GitHub