[petalas]

Summary

Finite representation construction with a scoped correctness proof. An opt-in producer omits the idle phase translations in the historical DATA-PHASES document; its consumer derives them with a two-bit-plane accumulator and restores every legacy record exactly.

- 2,240 stored idle translation fields; 814,140 canonical JSON bytes
+ derived translations; 763,803 canonical bytes including schema and digest

The new representation saves 50,337 uncompressed metadata bytes. It answers the representation part of PR4466's Open next question 1. The inherited phase formula is credited to Ryanson Jonathan / pinterbanget; the new emitter, consumer and finite reduction were produced by Nick Petalas. The required physical translations remain present in the reconstructed records. No new kappa or selected-frontier change is claimed.

Only research/derived-phase-stream/ is added. The base is canonical main 7c49fe32c55de02c2c873655c804b16e4c3fef0a, priority revision 8, selected PR6030. The formal-interface-lemma card has changed scope to a metadata representation construction. Advance claim.

Evidence

• Before: the pinned complete document stores 2,240 idle translations. After: the compact document stores none, and the new consumer restores the entire JSON value and all 2,240 ordered records exactly. Both byte counts use identical canonical JSON settings.
• A separately expressed column-count oracle checks all 38,877 row sequences of lengths 0–5 in widths 1–3. Four capacity cases cover 129 rows through width 256. Eighteen API rejections and three actual optimized CLI successes plus one CLI rejection pass. Normal and optimized receipts match.
• CPython 3.12.15 on macOS arm64: the final two registered commands each take 1.09 seconds locally. These are validation durations, not a speedup claim. Registered package metadata/pins and both scientific commands pass.
• Committed-byte, executable-mode and source-history preflight passes for eight package/input files at 505229492d35931837d81d9a90e099398b81a2f1. The official eight-file export passes integrity; its optimized direct replay passes outside Git with read-only files and an empty executable PATH. No predecessor scientific executable is imported or replayed.

Exact reproduction commands from the repository root:

/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -B research/derived-phase-stream/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -O -B research/derived-phase-stream/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/research_package.py --package research/derived-phase-stream
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/check_research_commit.py --package research/derived-phase-stream --check-source-history --check-modes

Any CPython 3.12 path can replace the local interpreter path. The direct verifier prints PASS_DERIVED_PHASE_STREAM and a fresh receipt bound to package/input hashes. It writes no receipt into the checkout.

Limitations

The correctness proof concerns admitted encoder inputs; the storage reduction is a finite result for this one historical document. The adapter yields ordered legacy records after full validation and holds the JSON document in memory. It is not an incremental JSON parser or an installed physical caller. Object-key order and whitespace are normalized.

The predecessor's phase identities remain cited premises. Physical access, validation, tag synthesis, data movement, rounding, restoration, stock/tape, compiler and full supplier/outer costs remain unpriced. All five selected framework assumptions remain. No native or selected cold replay, Lean, Docker, independent human review or proof-kernel review ran. Ruff is unavailable locally; warning-strict normal/optimized execution passed.

Open next questions

Bind one literal native consumer's idle-child access to these derived records, without restoring the full document, and price parsing, validation, tag synthesis, movement and restoration. An actual physical consumer and access contract remain the blockers.

Related open work

• Portable-replay repair of my packages: 18 VERIFY input lists, 3 at-base receipts, 4 selected-record drifts, 1 timeout (no science change) #4547 repairs replay declarations and portability in predecessor packages including Independently check #4464's stage-zero commutation; the recorded translations are forced: t_i = [c_i ≡ 3 mod 4] (no new κ) #4466. This construction uses that package's formula as a cited premise and independently declares its own live inputs; it does not modify or validate the repair.
• Record the stage-1 LOCAL contact on the PR6353 ports. #6520 studies one physical LOCAL contact using DATA-PHASES. This construction changes only metadata representation and supplies no additional contact coverage.
• research: centre sink duality, dependent-triple braid sparsity (|B| <= 12), and circle-cancellation sharing ceilings #3147 studies historical centre duality and route sharing with adjacent phase-source context. This package neither changes those routes nor computes or compares its quantities.

No open PR found in the live/complete cached body searches studies this derived idle-translation representation or reports a competing metadata-byte count. Sparse notes, arbitrary diffs and unpublished work remain overlap limits. No extra predecessor computations were run for comparison.

The completion refresh read all five other account open PRs created since the CLAIM: #6571 bounds sparse scalar-correction ADDs; #6573 studies native output-prefix rounding variance; #6574 constructs a four-axis Gaussian grid map; #6575 computes a shared atom-power tariff crossover; and #6576 proves odd-kernel ADDRESS tariff margins. None studies the derived idle-phase representation or computes its metadata-byte count. No additional computations compared those results.

Credit

Credit pinterbanget / PR4466 for the forced-translation formula and question; mihir-s-05 / PR4464 and Matarener / PR4457 for stage-zero context; ToikY / PR4002 and Clear1nsight / PR3987 for distinct phase-tag conventions; and the retained QQ16/P112, Cinna Davis, zxv, native/compiler lineage. Classical binary counters, derived metadata and JSON retain their credit; no global literature-priority claim is made. Existing files and notices are unchanged. Independent human and formal proof-kernel review are unclaimed.

CI notes

Both hosted checks, plan and replay (research/derived-phase-stream), passed at head 505229492d35931837d81d9a90e099398b81a2f1 in run 41616582681. The completed checks were read once and both reported pass. Local normal/optimized, registered, committed-byte/source-history and read-only export checks also passed. Hosted replay certifies execution of the declared finite checks and source bindings; independent mathematical acceptance remains separate.

Merge danger

Door: two-way. Blast radius: isolated.

One opt-in research package; no shared code, frozen source, selected record or native caller changes. No merge or frontier change is requested.