Research construction: phase-typed two-source order-four echo (no new kappa)

[1337isnot1337]

Status

Research construction; no new κ and no selected-frontier change.

Result

For the pinned order-four, five-child interface, this package checks two independent 24-coordinate source banks X,Y with arbitrary dirty D and a restored workspace. The exact map is D -> D + Σ_{i=0..4} R_i X + Σ_{i=5..9} R_i Y.

The phase-indexed child type is C_(i,t)(D,W)=(D+Q^(-t)R_i W, P W), with Q^(-t)R_iP^t=R_i. At the fixed 5|5 split, the source-bank handoff is W += P^3(Y-X), charged at 48 ADDs. Exhaustive recurrence checks cover all 4^5=1,024 and 4^10=1,048,576 phase paths, and both complete maps replay on all 80 basis columns.

The typed calls cost 1,696 primitives separately and 1,552 jointly (144 saved; 288 fewer reads). A distinct unchanged-reader control costs 2,016 separately and 1,952 jointly (64 saved). Five negative controls reject omitted or mistyped handoff, omitted restoration, and omitted literal inverse. These are exact costs in the declared signed-ADD word model; supplier routing, tape/hosting, fixed-precision admission, and transfer into the selected recursive supplier remain unproved.

Reproduction

python3.12 scripts/research_package.py --package research/z4-distinct-source-seed55

Expected result includes:

PASS_Z4_DISTINCT_SOURCE_PHASE_TYPED_ECHO g5=60 g10=48 separate=1696 joint=1552 saved=144 reads_saved=288 paths=1024+1048576 basis=80 controls=5
PASS_REGISTERED_RESEARCH_PACKAGE research/z4-distinct-source-seed55 outcome=completed

Pins and overlap

Assignment base: 4040a0f46d67b41c36a472a7cd4af791fd4c36cc. Publication parent: current main at ef5f39403610d231a0c27e8a6b4f08c10209bcd6. The exact predecessor heads and vendored snapshots for PR #1391 (6ce8017e4c27c8b220b6c3a27a53bb18f138212a) and PR #1410 (5b1c00b9f2770aabaa0085539405757f7818a14a) are pinned in SOURCES.json and NOTICE.md. Selected context remains #1094, κ=836330098538459/500000000000000000.

Adjacent work is credited and distinguished in the README: PR #1158's four-source Hadamard census; PR #1438 and Discussion #1412's two-root transfers; PR #1439's BCu correction for a persistent connector under source mutation; and PR #1442's chronological delivery-cut optimum. This package claims no priority over those models.

Prepared by Cinna Davis with substantial OpenAI Codex assistance in derivation, implementation, exact verification, source pinning, and writing. No independent human review or proof-assistant formalization is claimed. Apache-2.0.

[Mister-Meeseeks]

Batch review at 3ff7f7922d879a810aecb24d6dca66546014198d.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Phase-indexed order-four readers compose two distinct-source dirty echoes with the complete handoff and inverse charged. Exhaustive five/ten-child phase paths and all 80 input columns pass; physical routing and the increased precision envelope remain unadmitted.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.