Add sparse four-endpoint observability census

[Gonzalo-Mier]

Change and mathematical scope

This exact observability census extends both pinned orientations of the PR2979 word from pairs and triples to all 49 choose 4 = 211,876 four-class supports of rank-seven endpoints. A complete GF(3) screen finds 1,353 candidates, each rechecked over the rationals. Six new scalar readout identities span the same five-dimensional block; four use five input coordinates, and all use nine terminal registers across seven endpoint classes.

The census shows that pooled observations expose eligible forms, while the rank-nine join is not a free common helper. These are linear-information identities, not a supplier or caller-facing construction. No downstream consumer, physical realization, complete recursive invoice or κ improvement is claimed; selected κ remains 0.001672660197076918.

Task and overlap

Task complex-new-helper-inventory, priority revision 6. Scope changed to test whether pooling incomparable endpoint observations yields a sparse basis. Package: research/cross-endframe-observability/; base commit: 20ecf2891d80b5acf18d980b2164fb44ea7faa90. Both word inputs are hash-pinned in SOURCES.json.

PR #3172 states the fixed-endpoint pooling boundary tested here. This package extends the changed PR2979 word and makes no general novelty claim. The cached overlap scan covered 394 open PRs and 2,319 discussions as of 2026-10-18 03:15 UTC; its refresh failed, so the scan is not a novelty certificate.

Validation

Reproduce with Python 3.12:

python3 -B research/cross-endframe-observability/verify.py
python3 scripts/research_package.py --package research/cross-endframe-observability --check-only
python3.12 scripts/research_package.py --package research/cross-endframe-observability

The verifier reconstructs both pinned word orientations and exact formal-warp adjoints. It checks endpoint singletons, 1,176 pairs, 18,424 triples and all 211,876 quartets; screens over GF(3) and rechecks every candidate over Q. The orientations agree, and protected-column, warp-word and register-deletion controls challenge the witnesses. No physical or recursive invoice is established.

Credit

Provider attribution from PR #2979 and the pooling boundary from PR #3172 are retained. Prepared by OpenAI Codex with substantial AI assistance; Apache-2.0. No independent human or formal-kernel review is claimed.

Open next questions

Trace the six-form block to a named downstream caller and compare the caller's required subspace with the five-dimensional span. Price the multi-register circuit, chronology, dirty-state restoration, storage and recursive profile only if a caller matches.