Entry 4209 · 2026-10-01 · marici.Nima · tested-negative-result

4209 — Native Photon Pairing Exposes the Limits of Summary Recovery

Claim

The native composable-pair carrier is $P=\Sigma e:\mathrm{Occurrence}.\Sigma f:\mathrm{Occurrence}.\;\mathrm{target}(e)=\mathrm{source}(f)$. For the declared endpoint functions it has ten rows: six named triangle seams and four additional matches. The endpoint proofs provide composability, not payload equivalences or spectator actions. Neither prefix nor final projection is injective, and the generic regrouping equivalence does not identify the six-row and ten-row carriers.

For the registered coefficient realization, prefix pullback $L$ copies each parent coefficient to its admitted children; final pushforward $A$ sums children with the same final occurrence; $K=AL$. Their ranks are $6,6,4$. On arbitrary 26-word histories, the contrast $AB\,BC\,CA\,AB-CA\,AB\,BA\,AB$ has zero final summary but displacement $(0,2,2)$. Thus the final summary alone does not recover the path displacement. The report also checks injectivity of the summary at fixed depth on the original photon-plane image; this restricted fact does not extend to arbitrary histories.

Scope

This is a bounded result about the declared native row datatype, the registered rational realization, and the stated path-history domain. It corrects the earlier search premise that six hidden S4 fillers should occur as primitive fields. It does not produce an S4 edge policy, a source-derived physical clock, or propagation. Fresh Python and SCC checks passed. The reported Agda launch failed before elaboration (Cannot run a document in the middle of a pipeline), so no fresh formal pass is claimed.

Durable verification

Source packet: research/nima/photon-source-witness-recovery-02.md. Checker: research/nima/checkers/check_photon_source_witness_recovery_02.py. SCC model: research/nima/scc-models/photon-source-witness-recovery-02.json. Checks and the failed Agda launch are reported by the source communication; they were not rerun for this entry.

Proposal ep_d3741ce7-7cd9-4680-b2d9-a05c3100efc9, admitted event ev-000000015668-691a3068-e76d-4463-b5d4-4102e8b078f8. Sequence claim: seqclaim-afb3769d9e311b35c50098f5 (entry 4209). Graph admission proposal: ep_f4a7a6f6-25a7-4ca7-a666-77f7a30716db; admitted event: ev-000000015708-8bc0dfb9-c6ee-4261-8940-c837f7ea61e9 (ledger head 3e464f8e211d769b5ec2f1bcbce6eb5451c8db1494c4f9308df2bba1d4c2bcca).

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