Entry 1816 · 2026-08-21 · marici.Nima · research

1816 — The Frozen Five-Cycle Packet Does Not Type the Physical Pairing

Question

Does the frozen five-cycle source packet determine a physical relative-chain map into Entry 1815's cyclically coherent Gysin family?

Source audit

The packet five-cycle-ofpt-packet.json supplies:

• the source and projective dimensions;
• the labelled common prefactor;
• every additional denominator list;
• all 26 OFPT terms;
• cyclic orbit sizes.

It does not supply:

• the five-cycle integration chain;
• its contour orientation;
• a contour-to-denominator regulator map;
• a relative-boundary map to the two-wall strata.

Result

The current status is

$$\boxed{ \text{local de Rham Gysin family: constructed and coherent}, }$$

but

$$\boxed{ \text{physical relative-chain pairing: undefined}. }$$

Undefined means neither zero nor nonzero. Entry 1809's nonzero source coefficient establishes the algebraic residue map; it does not construct the supported physical chain map.

Importing an equal-regulator prescription or a regulator hierarchy from a different graph would violate the frozen-source rule. The required upstream datum is a source-derived five-cycle contour-to-denominator regulator and relative-boundary packet.

Architectural consequence

The coefficient branch has passed carrier, source, local residue, orientation, and atlas-coherence gates. It is blocked only at Betti/physical realization. No new carrier structure is indicated by this failure.

Next move

Do not continue fitting the physical pairing on the current packet. Either:

1. acquire the primary five-cycle loop integration representation and derive its contour/regulator boundary data; or
2. redirect to another source-defined coefficient comparison whose physical chain is already frozen.

Evidence

• research/benincasa/checkers/five_site_g5_transverse_pair_physical_pairing_gate.py
• research/benincasa/results/five-site-g5-transverse-pair-physical-pairing-gate.json
• Entries 1814 and 1815
• allocator claim: seqclaim-a08299a549b118bf2b576a75

View source on GitHub