Scoped negative result: frozen P111 receivers cannot beat 439 helpers (no new kappa)

[ToikY]

Scoped negative result; no new kappa. For PR555's frozen puncture set and keeper plan, changing the nine pseudo-target receivers cannot lower the shipped 439-helper count. The complete 3^9 = 19,683 census finds 2,646 minimizers; the remaining assignments use 440–443 helpers.

The original discovery sampled 3–6 receiver choices per keeper-plan seed. This contribution closes that gap for the shipped seed 552 and its exact generator policy. It does not repeat the closed frame-only or decoder-copy searches. Other 439-helper words may still improve ADD counts, frame profiles or precision.

The complete helper bill is 240 carriers + 180 cell-empty helpers + 9 totals + extra carriers + new junk wires. Ten independent supplying-block tables contain 60 entries. Their minima give 429 + 3 + 1 + 2 + 4 = 439. A written separation argument and every local response/rank/carrier record are retained. This is optimality within the frozen generator class, not unrestricted circuit optimality.

Reproduce

Ordinary Python 3.11+ with the inherited NumPy dependency:

python3 -I -B research/p111-receiver-census/verify.py
python3 -I -B research/p111-receiver-census/independent.py
python3 -I -B research/p111-receiver-census/test_package.py

Expected: PASS_P111_RECEIVER_CENSUS cases=19683 local_rows=60 min_helpers=439 minimizers=2646 no_new_kappa.

The main bitmask/block-table checker and a separately written set-valued full-vector checker agree on all records: SHA-256 5598bbe4112493b6f6b55051a0364b7e576e253b8c2a85f8f05dcbb5d2ef7316. They share pinned geometry/setup. The independent checker also completes 59 original-generator controls (55 distinct vectors), covering every changing block entry. Seven tests pass, including a failed-write mutation that falsely saves one carrier, punctured-zero and carrier-reuse controls, source/receipt corruption, and both checkers in a minimal offline copy with unchanged input bytes. All twelve base Git blob/source bindings and 17 selected-record tests pass. Optimized Python is rejected explicitly.

Provenance and limits

Exact base: 0076643. OS assignment seed 15; bit supplier track. Only ten files under research/p111-receiver-census/ are added. The published tree equals the tested local tree. Final overlap refresh reached #961; no coordination issue was available, so the local claim records the result and branch link.

Credit eumemic #543/#555, DreamingOfClouds #545/#589, and the retained construction lineage. The punctures, L3 plan, keeper assignment, ordered residual-carrier closure and junk-reuse rule are fixed. Arbitrary carrier vectors, other keeper plans, full native/hosted supplier admission and geometry formalization are outside scope. Uniform compilation, physical realization, hosting, precision/tape and analytic obligations remain unresolved by this package. Full repository verification, selected cold replay and hosted CI are not claimed. Selected PR890 conditional kappa remains 0.001661957774647029.

Prepared for ToikY with substantial OpenAI Codex assistance, including separate implementations and model review. No independent human review or formal multiplication theorem is claimed. Apache-2.0.