Realize two mutable snapshots with selected physical address maps

[adamgall]

Research claim

This realizes the fixed PR1704 two-copy scatter in PR1627's selected PR589 exact physical-stream model. It allocates the two live snapshots to existing reserved private families 28416 and 28417, proves separation from every persistent owner for every orthogonal cover class, and checks restoration with the actual nine rank-seven address operators. The native interpreter applies every MOVE to the physical function addresses; it does not project MOVEs out as the earlier formal-bank interpreter does.

This is a new physical boundary implication for that concrete bit-helper mechanism, not a new scalar optimization, admitted compiler/supplier, κ improvement, or formal-kernel theorem. The selected κ remains 0.001672660197076918.

Predecessors and changed premise

• Ross Richardson's Finite bit construction: two-copy scatter saves 120 ADDs (no new kappa) #1704, head 7f14aa7285cf10a7be350472fab25a25ef898484: fixed pair partition (0,3),(1),(2,4),(5,7),(6,8), 120-ADD saving, scalar restoration and accounting. Those results are credited, not reclaimed.
• Adam Gall's Research: two-copy raw-record lifecycle and formal bank boundary #1943, head 60e0d6d37b857a30c2db032255892f7e2f6465ce: two-temporary raw-record lifecycle and formal bank boundary; physical MOVE address execution and simultaneous private-stream allocation were explicitly outside scope.
• alephnan's Research: PR589 whole-call hosting in the exact stream model (no new kappa) #1627, head 7943acd4b430dd4286e32954237136ee9657be3b: selected exact-stream hosting, actual owner charts, rank-seven COPY maps and one-private-stream proof.
• Sagar Thakrar's PR1062 word; PR967 helper-star / PR1015 / PR923 blocks; DreamingOfClouds' PR589 and eumemic's PR555; and the geometric/hosting/formal lineage credited by PR1627, including cheesegrader PR540, DaysSky, Zhihao Chen, chafreaky, commdata2338 and Cinna Davis.

The emitted bit-helper-contract card was changed from the already-covered D/H2/K implication to this precise physical snapshot handoff. Revision4's concrete-interface priority motivates the choice; no repeat of its retired register/monotone-frame cases is involved.

Method and domain

Memory locations are (family,g) streams of arbitrary Boolean functions on K^64 × K^64, where K has characteristic other than two. Functions may be correlated. For frame projector P, D_P(x,y)=((I-P)x+Py,Px+(I-P)y). The two copied values are their distinct centers composed with their own D_P; they are never identified merely because ranks agree.

The checker independently reconstructs all636 rational frame projectors, authenticates exact source bytes, multiplies exact rational address maps into the function atoms at every MOVE, and checks every COPY/ERASE chronological transport in both complete local orientations. It compares all661 arbitrary physical input functions, rather than finite-address tests. The written proof specializes the dyadic identities to every odd-characteristic address field and cancels the common exterior/reflected factors. Actual selected owner charts and all288 stage/replica descriptors supply the family-separation proof; no cover-class enumeration is claimed.

Complete result and price

• Persistent functions:661; two simultaneously live copied streams inside the existing nine-family reserve; all other seven private families untouched.
• Physical family total remains28425, including28416 persistent families and9 reserved private families.
• All190368 persistent owner occurrences are separated from the two private family tags.
• Each orientation executes2911 native MOVEs and9 rank-seven COPY/ERASE pairs; COPY rank sum63, peak copied rank14.
• Fixed full ADD bill11500→11380; fixed scatter527→407, including prepare/restore. These savings originate in Finite bit construction: two-copy scatter saves 120 ADDs (no new kappa) #1704.
• Local rank mass5129 and profile {1:1323,2:1342,3:79,4:44,5:102,6:11,7:19} are unchanged. Every MOVE and COPY charge remains present.
• F=25717, B=6248884; finite algebraic guard expressions occupy96/182 bits below104/192-bit caps.
• Ten semantic controls cover omitted restoration hidden by blind deletion, full-swap/equal-rank/wrong COPY addresses, dirty private output, aliasing, one available family, mispriced MOVE, and omission of actual MOVE address action while preserving labels and charges.

Even granting all scalar work and spare work storage for free leaves the recursive moment unchanged; this result is a physical interface completion, not a new exponent bound.

Evidence and reproduction

Package: research/bit-two-copy-physical/. README.md contains the written proof, paid contract, predecessor boundary and next question. RESULT.json records exact COPY matrices, endpoint hashes, bills and controls. SOURCES.json authenticates every consumed source by Git blob and SHA256. The replay compares canonical mathematical payloads, not regenerated gzip containers.

uv run --python 3.12 --no-project python -I -B research/bit-two-copy-physical/verify.py
uv run --python 3.12 --no-project python -I -B scripts/research_package.py --package research/bit-two-copy-physical

Final local direct smoke and registered ordinary/optimized CPython3.12.12 replays are recorded in VALIDATION.json; the main scientific marker is:

PASS_BIT_TWO_COPY_PHYSICAL functions=661 directions=2 native_MOVEs=2911 COPY_rank=63 private=2/9 descriptors=288 controls=10 no_new_kappa

Scientific base 564148b82ae9df72163f22106f15e73efca8aff2, selected-record SHA256 10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32, priority revision4. The refreshed main 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2 changed workflow guidance only; scientific inputs and catalogue are unchanged. SELECTION.json retains the one independent nonce d275591f5a4f5d59e9e8231c8f6aad53; TASK.json records the concrete scope before computation. Seed differences are not a novelty claim.

Limits and next useful task

The exact-stream construction uses two blank reserved work streams initially and proves they are blank again before every reuse. It never resets dirty persistent storage. It does not infer a recursive COPY child's scratch availability from the reserve count9. The ideal primitive touches only its stated source/destination; lowering it with real child scratch, common-grid routing, tape and precision remains an explicit compiler obligation. No full native compiled supplier replay, finite hosted invoice, outer assembly, Lean kernel run, full cover enumeration, or hosted CI pass is claimed.

The next task is to bind these exact two private destinations and their transported ERASEs into the actual compiler allocator and reprice simultaneous child output plus child scratch. Stop that admission attempt if it cannot retain both live snapshots without borrowing dirty persistent storage or charging additional work. The complete physical boundary proof here remains useful independently of that compiler decision.

Prepared for Adam Gall with substantial OpenAI Codex assistance in proof, implementation and writing. Apache-2.0. No independent human review is claimed.

[ywz65]

DONE - published as PR #2459: #2459. Reviewed head e0f10cd; all 36 dyadic-unit separating witnesses verified. Registered Python 3.12 ordinary/optimized replay and a separate AI review passed. This closes the scoped audit, with no native implementation, supplier or kappa claim. Original claim retained below for provenance.

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CLAIM — independent selected-COPY separation audit (ywz65, additional batch round 1).

Base main 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2, priority revision 4; PR2088 predecessor head 95669bdd93cb3707f42268f5edee48af2a611bcc.

Question: can the nine selected rank-seven snapshot pullbacks be proved pairwise distinct uniformly in every odd address characteristic, and what does the existing simultaneous helper/snapshot intertwining criterion then permit? I will independently reconstruct the nine maps from the pinned word, seek a dyadic-unit separating coordinate for every pair, and apply the credited operator-intertwining theorem. This is a scoped interface audit, not a new COPY implementation, PR1704 scalar saving, physical admission or kappa claim. PR2088 already reports distinct rational maps; the proposed delta is independently checkable uniform-characteristic separation witnesses and the precise restriction on synchronized scalar rebasing.

Method/domain: all 36 pairs of the nine fixed maps, exact rational reconstruction plus Boolean-function witnesses over F3, with equal-map and wrong-map failure controls. Expected artifact: a small registered proof/checker package with exact source pins and explicit unchanged obligations. Substantial OpenAI Codex assistance. Claim expires 2026-10-15 13:30 UTC; evidence is LOCAL-ONLY until publication.