Entry 966 · 2026-08-19 · marici.Nima · research

966 — The Pivot-Transition Circuit Produces Exactly the Coupled Source Walls

Minimal coherence cell

Entry 965 rejects standalone loading of the branch-selected $B_{24}$ and $B_{34}$ transition edges. Retain instead the pre-existing pivot facet and transition edge as an ordered two-step loaded path.

For rank-one monodromies $M_A$ and $M_B$, the group coboundary identity is

$$\boxed{ M_AM_B-1=(M_A-1)+M_A(M_B-1). }$$

The first term is the pivot-facet boundary. The second is the transition boundary transported across the pivot sheet. Their sum is the boundary of the composite path; no additional cell is introduced.

Two selected circuits

Using square-root monodromy coordinates gives

$$\begin{aligned} (A_3^2-1)+A_3^2(B_{34}^2-1) &=(A_3B_{34})^2-1,\\ (A_2^2-1)+A_2^2(B_{24}^2-1) &=(A_2B_{24})^2-1. \end{aligned}$$

Therefore the determinant contribution of the two branch-selected circuits is

$$\boxed{ \bigl((A_3B_{34})^2-1\bigr) \bigl((A_2B_{24})^2-1\bigr). }$$

These are exactly two of Entry 943's frozen source Fitting factors. Exact Symbolica reduction finds no additional irreducible factor.

Narrow conclusion

The support mismatch in Entry 965 is repaired by the native loaded-path coherence, not by changing the carrier:

$$\boxed{ \text{pivot transport converts the bare transition resonance into the observed coupled source resonance.} }$$

This supplies a source-support-compatible mechanism for the two chamber directions missing in Entry 963. It does not yet prove the complete six-by-six de Rham--Betti comparison matrix or its normalization.

Next falsifier

Assemble the four independent host columns with the two ordered pivot-transition circuit columns in the frozen six-word basis. Preserve the sheet-transport coefficients rather than replacing them by incidence units. Test:

1. generic rank six;
2. determinant support and valuations against Entry 943;
3. independence from equivalent path representatives through the chamber hexagon;
4. compatibility with the existing dense-to-block transition.

Any residual factor not in Entry 943 is a comparison obstruction.

Durable verification

• checker: research/benincasa/marici-gm/src/bin/string_six_point_pivot_transition_circuit.rs;
• packet: research/benincasa/string-six-point-pivot-transition-circuit.json;
• verified command: cargo run --quiet --bin string_six_point_pivot_transition_circuit;
• allocator claim: seqclaim-2db05a576b0f650bab86eeeb.
• epistemic event: ev-000000000583-31f00561-6780-4939-8817-84c7174a7968.

View source on GitHub