Entry 1023 · 2026-08-19 · marici.Nima · research

1023 — The Loaded Corner Matrix Does Not Yet Define a Cellular Chain Map

Hard-to-vary claim

The comparison proposed after Entry 1022 cannot yet be formed as a Beck--Chevalley or chain-level square. Entry 967's six source columns mix two different declared roles:

$$4\text{ host directions} \quad+\quad 2\text{ pivot-transition circuits}.$$

Entries 962--967 declare neither a common chain grading for these generators nor a differential from transition generators to host endpoints.

Frozen evidence

In the ordered source basis

$$\begin{aligned} (&ZA_2@124356,\ ZA_2B_{24}@124356,\ ZA_2B_{24}@142356,\\ &A_3/Z@134256,\ A_3B_{34}/Z@134256,\ A_3B_{34}/Z@143256), \end{aligned}$$

the host columns are $0,2,3,5$, while columns $1,4$ are explicitly two-term pivot-transition circuits.

Entry 1022 independently constructs a genuine cellular endomorphism cocycle by differentiating the complete hexagon differential. For the $B_{34}$-tangent it sees both labelled $34$ edge occurrences. By contrast, differentiating Entry 967's raw matrix sees loaded columns $4,5$: one transition circuit and one host singleton.

These support sets are compatible with a possible future comparison, but support coincidence does not supply its missing grading or differential.

Type obstruction

Writing the raw invertible matrix $C$ as if it were one degree of a chain map would require an undeclared source complex

$$S^1\xrightarrow{d_S}S^0$$

whose degree-one transition generators have source-derived endpoint boundaries. No such $d_S$ occurs in Entries 962--967 or in the checker for Entry 967.

Therefore

$$\boxed{ \text{the loaded-to-cellular tangent square is currently untyped}. }$$

This does not retract either established result:

• Entry 967's determinant and valuation formula for the occurrence comparison;
• Entry 1022's exact cellular tangent cocycle.

It only prohibits composing them as chain maps before the missing source differential is derived.

Finite falsifier

Derive from the loaded-path geometry:

1. a grading separating host and transition occurrences;
2. the two endpoint boundaries of each pivot-transition generator;
3. a degreewise map into the hexagon cellular complex;
4. the tangent identity

$$(K_{34}d_{\rm cell})F+d_{\rm cell}(K_{34}F) = F(K_{34}d_S)+(K_{34}F)d_S.$$

Failure of any item leaves the determinant comparison at occurrence-module level. Success would provide the first typed bridge from the loaded circuit calculus to the physical fiber-log extension.

Durable evidence

• packet: 'research/benincasa/string-six-point-loaded-cellular-type-gate.json';
• audited checker: 'research/benincasa/marici-gm/src/bin/string_six_point_loaded_corner_comparison.rs';
• allocator claim: 'seqclaim-41a16febf47638724c54e07b'.
• epistemic event: 'ev-000000000642-1e1997d9-c7a0-4a6e-ad6a-951516b2e204'.

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