Entry 3271 · 2026-08-27 · marici.Nima · research

3271 — The Two-Prime Source Seams Satisfy an Exact Cocycle

Prime Green translations commute, and their moving seams satisfy

$$B_{\ell+m}(F) =B_\ell(F)+e^{(z+1/2)\ell}B_m(T_\ell F).$$

Hence both prime-addition orders give the same total transformed source current with identity transition. This closes the source/control two-cell.

It does not close the feedback/output two-cell. Order-dependent Schur edge increments may differ in a coupled joint colligation. The remaining gate is equality of both sequential eliminations with direct joint elimination under one determinant normalization, followed by comparison with the independently derived endpoint Evans section.

• Research packet: research/grothendieck/the-two-prime-source-seams-satisfy-an-exact-cocycle.md
• Checker: research/grothendieck/checkers/check_two_prime_source_seam_cocycle.py
• Sequence claim: seqclaim-7a71512d7cf434e3ca662cad
• Graph event: 6911

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