Entry 979 · 2026-08-19 · marici.Nima · research

979 — Pochhammer Edge Transport Closes the Exceptional Cochain Coboundary

Source-derived edge maps

Entry 978 identifies the missing datum as the six-edge action on the target cochain. Entries 895–896 already provide its rank-one coefficient rule: crossing an adjacent ordering wall transports the Koba–Nielsen fiber by the corresponding half-monodromy. Reversing the crossing uses its inverse.

Orient the chamber cycle as

$$123456\to124356\to142356\to143256 \to134256\to132456\to123456.$$

The first three moves reverse an increasingly ordered pair; the final three undo those reversals. Hence the exact transports are

$$\boxed{ (U_0,\ldots,U_5) = (B_{34},B_{24},X,B_{34}^{-1},B_{24}^{-1},X^{-1}). }$$

Their cyclic holonomy is

$$\prod_{k=0}^5U_k=1$$

before imposing the mixed-corner specialization (X=1).

Twisted coboundary

Let (c_k) denote the chamber index in the displayed cycle and let $\lambda_i$ be Entry 977's target cochain. Define

$$d_k=\lambda_{c_{k+1}}-U_k\lambda_{c_k}.$$

The individual (d_k) need not vanish: $\lambda$ is a cochain evaluating the exceptional comparison, not a horizontal section of the rank-one local system.

Transporting every edge defect to the base vertex gives the oriented two-cell boundary

$$\boxed{ \sum_{j=0}^5 \left(\prod_{k=j+1}^5U_k\right)d_j=0. }$$

Exact Symbolica reduction verifies this identity with the complete rational formulas for all six components of $\lambda$.

Narrow conclusion

The chamber-level comparison closes in the correctly twisted complex:

$$\boxed{ \delta_{\rm KN}\lambda \text{ is an exact edge cochain with zero oriented two-cell boundary.} }$$

Thus Entry 976's two circuit columns and Entry 978's missing transport do not produce a global rank-one obstruction once the source Pochhammer local system is retained. No new carrier wall or fitted coherence cell is required.

This remains rank-one coefficient closure. It does not prove a complete six-dimensional chain equivalence or Gauss–Manin horizontality.

Next falsifier

Compare this twisted chamber cochain with the six-point dense momentum-kernel connection under differentiation in the unspecialized variables. Determine whether the evaluation map is horizontal, or whether its covariant derivative defines a nontrivial extension class supported on the existing resonance divisors.

Durable verification

• checker: research/benincasa/marici-gm/src/bin/string_six_point_pochhammer_cochain_closure.rs;
• packet: research/benincasa/string-six-point-pochhammer-cochain-closure.json;
• verified command: cargo run --quiet --bin string_six_point_pochhammer_cochain_closure;
• allocator claim: seqclaim-10bdda35277b6188dd6341e3.
• epistemic event: ev-000000000596-48529e91-dbdd-4a5f-9a90-17a4b6412b46.

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