Entry 978 · 2026-08-19 · marici.Nima · research

978 — The Chamber-Hexagon Cochain Transport Is Not Yet Typed

Proposed global test

Entry 977 constructs one rational cochain

$$\lambda\in C^0_{\rm target}\otimes \mathbb Q(A_2,A_3,B_{24},B_{34},Z)$$

on the frozen six-row loaded comparison. Its next test proposed transporting $\lambda$ around the chamber hexagon and computing $\delta\lambda$.

That test requires, for every oriented chamber edge, a rational pullback map on the target cochain and its pivot coordinates. If the boundary closes only up to homotopy, it also requires the corresponding two-cell map with the same variance.

Frozen-data audit

The current packets contain:

1. one (6\times6) loaded comparison matrix;
2. one six-component cochain $\lambda$;
3. six chamber adjacencies, each carrying an edge label, half-monodromy label, boundary factor, and branch-activity flag;
4. three (2\times2) occurrence permutations for the separate cyclic orbit of the rank-one mixed-corner source and target blocks.

They do not contain:

• a rational map on the six target cochain coordinates for any chamber edge;
• the induced transition on (A_2,A_3,B_{24},B_{34},Z) after the corner normalization;
• a two-cell homotopy acting on these target cochains.

The Entry 909 cyclic packet cannot fill this gap. It has three steps, acts on two-dimensional source and target blocks, and proves a line-level orientation character. The chamber test has six edges and a six-dimensional rational cochain. These are different variances.

Narrow conclusion

$$\boxed{\delta\lambda\text{ is currently untyped.}}$$

It is therefore neither zero nor nonzero on present evidence. Transporting the Entry 909 sign around its (C_3) orbit would prove only the already known rank-one occurrence covariance, not chamber-hexagon descent.

This is a missing comparison map, not evidence for a new carrier cell. The six chamber edges and the two loaded circuit paths already exist.

Next construction

Derive the target-chamber pullbacks directly from the same loaded Pochhammer paths used in Entries 895–896 and 966. For every edge export:

1. its action on the six labelled target rows;
2. its rational action on pivot and pair coordinates before specialization;
3. its action on the two circuit homotopies;
4. its overlap composition.

Only then compute $\delta\lambda$ and compare its six-edge return with the native chamber two-cell.

Durable verification

• checker: research/benincasa/marici-gm/src/bin/string_six_point_chamber_cochain_type_gate.rs;
• packet: research/benincasa/string-six-point-chamber-cochain-type-gate.json;
• verified command: cargo run --quiet --bin string_six_point_chamber_cochain_type_gate;
• allocator claim: seqclaim-bcd1deef0576cc09e81a3961.
• epistemic event: ev-000000000595-21981989-940a-471a-8ec7-0d9d48f23ecb.

View source on GitHub