From 35cf06a9d35b20701550b5517f4d69afd43c0ca7 Mon Sep 17 00:00:00 2001 From: Clear Insight Date: Sun, 18 Oct 2026 21:02:54 +1100 Subject: [PATCH 1/3] research: retain exact P104 feasibility source inputs and notices --- .../consumer/inputs/ALL_PAIR_README.md | 217 + .../consumer/inputs/PR2744_PREDECESSORS.json | 68 + .../consumer/inputs/PR2744_RESULT.json | 222 + .../consumer/inputs/PR3574_README.md | 73 + .../consumer/inputs/PR3574_verify.py | 126 + .../consumer/inputs/PR3605_CLAIM.json | 33 + .../consumer/inputs/PR3605_DERIVATION.md | 152 + .../consumer/inputs/PR3605_PROFILE.json | 10 + .../consumer/inputs/PR3605_README.md | 119 + .../consumer/inputs/PR3609_RECEIPT.json | 4120 ++++++ .../consumer/inputs/SELECTED.json | 222 + .../physical/inputs/FRAME-SA504-NOTICE.md | 24 + .../physical/inputs/LICENSE | 201 + .../physical/inputs/NATIVE-LINEAGE-NOTICE | 14 + .../physical/inputs/NOTICE | 415 + .../physical/inputs/ORIGINAL_NATIVE.json.gz | Bin 0 -> 49610 bytes .../physical/inputs/PR1862-NOTICE.md | 50 + .../physical/inputs/PR1972-NOTICE.md | 11 + .../physical/inputs/PR3382_PROOF.md | 445 + .../physical/inputs/PR3416_PROOF.md | 117 + .../physical/inputs/PR3609_NATIVE.json | 4412 +++++++ .../physical/inputs/PR3609_PROGRAM.json | 10905 ++++++++++++++++ .../physical/inputs/PR3609_PROOF.md | 188 + .../physical/inputs/WORD.json | 6124 +++++++++ 24 files changed, 28268 insertions(+) create mode 100644 research/p104-caller-feasibility/consumer/inputs/ALL_PAIR_README.md create mode 100644 research/p104-caller-feasibility/consumer/inputs/PR2744_PREDECESSORS.json create mode 100644 research/p104-caller-feasibility/consumer/inputs/PR2744_RESULT.json create mode 100644 research/p104-caller-feasibility/consumer/inputs/PR3574_README.md create mode 100644 research/p104-caller-feasibility/consumer/inputs/PR3574_verify.py create mode 100644 research/p104-caller-feasibility/consumer/inputs/PR3605_CLAIM.json create mode 100644 research/p104-caller-feasibility/consumer/inputs/PR3605_DERIVATION.md create mode 100644 research/p104-caller-feasibility/consumer/inputs/PR3605_PROFILE.json create mode 100644 research/p104-caller-feasibility/consumer/inputs/PR3605_README.md create mode 100644 research/p104-caller-feasibility/consumer/inputs/PR3609_RECEIPT.json create mode 100644 research/p104-caller-feasibility/consumer/inputs/SELECTED.json create mode 100644 research/p104-caller-feasibility/physical/inputs/FRAME-SA504-NOTICE.md create mode 100644 research/p104-caller-feasibility/physical/inputs/LICENSE create mode 100644 research/p104-caller-feasibility/physical/inputs/NATIVE-LINEAGE-NOTICE create mode 100644 research/p104-caller-feasibility/physical/inputs/NOTICE create mode 100644 research/p104-caller-feasibility/physical/inputs/ORIGINAL_NATIVE.json.gz create mode 100644 research/p104-caller-feasibility/physical/inputs/PR1862-NOTICE.md create mode 100644 research/p104-caller-feasibility/physical/inputs/PR1972-NOTICE.md create mode 100644 research/p104-caller-feasibility/physical/inputs/PR3382_PROOF.md create mode 100644 research/p104-caller-feasibility/physical/inputs/PR3416_PROOF.md create mode 100644 research/p104-caller-feasibility/physical/inputs/PR3609_NATIVE.json create mode 100644 research/p104-caller-feasibility/physical/inputs/PR3609_PROGRAM.json create mode 100644 research/p104-caller-feasibility/physical/inputs/PR3609_PROOF.md create mode 100644 research/p104-caller-feasibility/physical/inputs/WORD.json diff --git a/research/p104-caller-feasibility/consumer/inputs/ALL_PAIR_README.md b/research/p104-caller-feasibility/consumer/inputs/ALL_PAIR_README.md new file mode 100644 index 0000000000..1182dfdff6 --- /dev/null +++ b/research/p104-caller-feasibility/consumer/inputs/ALL_PAIR_README.md @@ -0,0 +1,217 @@ +# An all-pair-count screen for the current P104 forward and dual + +Scoped conditional obstruction. No supplier admission or new kappa. + +The pinned PR2458 forward and PR2712 physical dual cannot meet the selected +saving in the paired-chain coverage model below, for **any integer pair count +`p >= 1`**, even with 416 rank units forgiven per dual and the other 102 forward +corrections supplied free. Any finite number of fully paid auxiliary banks +also fails. The selected frontier and predecessor files are unchanged. + +This extends Jose Manuel / `jmbarrancoml`'s +[four-pair Discussion calculation](https://github.com/CrocSwap/integer-mult-bounds/discussions/2619#discussioncomment-18955566). +It is not another local fusion or endpoint-rank result. The new step covers +all pair counts with the actual changing width `m=16p+9`, rather than +extrapolating the four-pair width 73. + +## Exact contract and evidence + +Fix these local positive-child profiles, independently recounted from the +retained transport events using exact binary elimination: + +| Rank | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | Rank mass | +| --- | ---: | ---: | ---: | ---: | ---: | ---: | ---: | ---: | ---: | +| PR2458 forward F | 1216 | 74 | 86 | 104 | 48 | 42 | 68 | 8 | 3070 | +| PR2712 dual D | 1498 | 60 | 74 | 92 | 58 | 56 | 92 | 8 | 3542 | +| Optimistic dual D* | 1082 | 60 | 74 | 92 | 58 | 56 | 92 | 8 | 3126 | + +Exact source heads: + +- PR2458, Ross Richardson (`RossRichardson`), `3170afd2fc13a990bfe28f5ab6421bcda4ffd0f6`. +- PR2712, ywz65, `afa5d6649460dcdb93489babd74f0ee9d01a4911`. + +`PREDECESSORS.json` binds the retained data and original README notices to +SHA256 and original Git blobs. `SOURCES.json` binds live inputs and historical +assignment provenance. No predecessor Python is imported or executed. The +checker also recounts net endpoint progress as 2312 original plus 702 added +forward units and 3014 dual units. Crediting those units to global coverage +is conditional. Native correctness and complete forward/dual boundaries +remain inherited, not newly verified here. The forward count combines the original PR1972 word retained +by PR1991 with PR2458's two insertion lists; this is an invoice recount, not a +new chronology or native proof. + +The conditional consumer has, per replica: + +- `p+1` forward calls, `p` dual calls, `m=16p+9` and `W=208p` live data families. +- One unpaid coordinate per live data family. +- At most `C=104*8+104*8+150*9=3014` units of persistent endpoint progress per + call. We grant that entire amount to every call, including descending paths + and the discounted dual, without requiring an actual compatible owner map. +- With `B_aux>=0` fully paid auxiliary banks, residual coverage at least + `I_B=max(0,(m-1)W+m*B_aux-(2p+1)C)`. Without banks write `I=I_0`. + We grant residual children rank `m`, above the retained halving guard. +- Every other obligation free, including missing forward corrections, scalar + and monomial work, allocation, movement, precision and restoration overhead. + +The template formulas come from Dominik Scholz's retained `larger-gain` model +and the explicitly conditional P104 substitution in +[`p104-terminal-correction-floor`](../p104-terminal-correction-floor/README.md). +This is not a claim that its coverage law, inventory or owner windows have +been realized for these nonmonotone words. A consumer with extra unpaid +coordinates, different coverage, different call multiplicities, shared work +that changes the profiles, or different endpoint progress is outside the +result. Costs cannot simply be removed while retaining endpoint credit from +a different contract. + +## Proof + +Write `a0=836330098538459/500000000000000000`, the selected kappa. Testing at +this smaller value favors the candidate: the retained transfer requires a +primitive saving strictly larger than kappa, and each child cost is +nondecreasing in the saving. + +For `0= (m-1)W+m*B_aux-(2p+1)C` directly. It gives paid-plus-idle +mass at least `m*(W+B_aux)+56-40p`, a strict **16-unit** excess at `p=1`. +Since `(r/m)^(1-a)>=r/m`, this rejects every nonnegative saving. The stronger +4066-unit zero-bank margin must not be reused unchanged after adding banks. + +For `p>=2`, `I=3328*(p-2)^2+8948*(p-2)+1570>=0`. The zero-bank +paid-plus-idle mass is + +``` +sum_r n_r(p)*r + I = mW + 56 - 40p. +``` + +Use `exp(x)>=1+x` to get + +``` +M_p,0(a0) >= 1 + [56-40p + a0*L_p] / (mW), +L_p = sum_r n_r(p)*r*log(m/r). +``` + +The executable uses only rational lower bounds for these logarithms. For +`x>=1`, put `t=(x-1)/(x+1)`. Integrating the finite geometric series for +`1/(1-t^2)` gives + +``` +log(x) >= 2*sum_{j=0}^{127} t^(2j+1)/(2j+1). +``` + +It rounds this sum down to six decimal places. No floating-point sign decision +or numerical root enters acceptance. + +For each of `p=2,3,4,5,6,7`, substituting these bounds makes the excess +numerator strictly greater than **46**. For every `p>=8`, `m>=137`, so use the +single fixed table of lower bounds for `log(137/r)`. It gives + +``` +56-40p+a0*L_p >= A*p+B, +A > 2/3, B > 76. +``` + +The exact certified values are +`A=6793028173440143209107/10000000000000000000000` and +`B=19117566126860375528272583/250000000000000000000000`. +They prove the entire infinite tail, not a sampled large-p range. +Consequently `M_p,0(a0)>1` for every positive integer p, and the same holds +at any required primitive saving `a>=a0` below one. + +For `p>=2`, nonnegative `I` gives `I_B=I+m*B_aux`. The same positive +excess numerator is therefore divided by `m*(W+B_aux)`, rather than `mW`. +It remains strictly positive for every finite `B_aux`. The clamped `p=1` +case was handled separately above. Banks receive no unpaid-coordinate +credit; granting that credit changes the contract. + +## Reproduce + +Standard-library Python 3.12 or later, from the repository root: + +```sh +python3 -I -B research/p104-all-pair-consumer-budget/verify.py +python3 -I -O -B research/p104-all-pair-consumer-budget/test_verify.py +python3 scripts/research_package.py --package research/p104-all-pair-consumer-budget +``` + +Expected marker: `PASS_P104_ALL_PAIR_CONSUMER_BUDGET all_p>=1 finite=6 tail_from=8 no_new_kappa`. +The normal verifier is read-only and compares its complete recomputed receipt +with `RESULT.json`. Only explicit `--write` replaces that receipt. +Tests exercise the credited p=4 profile as a positive fixture, lower-saving +non-rejection, wrong mass/rank/nesting, duplicate JSON keys, source and receipt +corruption, optimized Git-free replay and equivalent gzip recompression. +A separate set-span census checks all 3584 transport occurrences without +using the primary elimination routine. + +Local validation passes on CPython 3.12.15 through the registered hook and +CPython 3.13.5 with optimized execution. All 11 package tests pass. The 70 +research-workflow tests pass with two skips. Ruff `E,F,I,UP,B` diagnostics +pass. No hosted-CI or independent human review is claimed. + +## Expansion decision and limitations + +Pause extensions that only change pair count, repack idle coverage or add +fully paid banks to these exact profiles under this exact consumer. Local +native and fusion contributions remain useful. Reopen with a source-bound +changed profile or consumer and a new complete coverage/cost ledger. + +This does not bound every P104 decoder, interleaved correction, changed +producer/consumer or multiplication algorithm. No native cold replay, +all-size proof, physical owner/routing construction, precision/tape admission, +selected-supplier replay or formal-kernel check is claimed. + +Python allocates managed integers and fractions during this bounded check. +JSON payloads are capped at 2 MB; each word has at most 6000 events, each frame +uses at most 18 nine-bit vectors, and each logarithm uses exactly 128 terms. +The all-p proof uses six base cases and one tail, not an unbounded loop. +Source JSON contains varying event shapes, so its parsed representation is +dynamic; rank/frame and source bindings validate the proof-relevant boundary. + +## Open next questions + +Can a changed P104 consumer provide enough additional unpaid-coordinate or +endpoint-progress credit without repaying it in restoration? First write its +actual boundary and replace `I` above with a justified coverage law. The +blocker is a compatible physical consumer, not another optimizer seed. + +Can a changed complete local profile escape this screen? First recount both +directions, including all missing corrections, then replace F and D in the +same optimistic screen. The current words correct only two forward rows; +finishing the other rows at unchanged cost was merely a favorable assumption. + +## Credit + +Jose Manuel / `jmbarrancoml` supplied the p=4 screen and 416-unit discount +argument in Discussion2619. ywz65 supplied PR2458's native binding, PR2497 and +PR2586's physical-dual lineage, and PR2712's retiming. commdata2338 supplied +PR2662's endpoint fusion; Nick Petalas supplied PR2550's complementary-frame +method. Ross Richardson / PR2445 supplied the two-target correction. + +Retain Chafik Boukhalfa / PR1991, Rohan Arun / PR1972, Adam Gall / PR1940, +Josie Elliston / PR1071, Ali Romman / PR1125 and PR1862, icekylinx and the +retained geometry/compiler lineage. Dominik Scholz supplied the larger-gain +stage template; Sagar Thakrar / PR1012 supplied the coverage context; Douglas +Colkitt supplied the selected-word ceiling context. Original notices remain +in the retained predecessor READMEs. The selected construction's complete +attribution remains in its selected review. + +New all-p theorem, checker and tests by Nick Petalas. Apache-2.0. diff --git a/research/p104-caller-feasibility/consumer/inputs/PR2744_PREDECESSORS.json b/research/p104-caller-feasibility/consumer/inputs/PR2744_PREDECESSORS.json new file mode 100644 index 0000000000..04f6326a99 --- /dev/null +++ b/research/p104-caller-feasibility/consumer/inputs/PR2744_PREDECESSORS.json @@ -0,0 +1,68 @@ +{ + "schema_version": 1, + "files": [ + { + "commit": "3170afd2fc13a990bfe28f5ab6421bcda4ffd0f6", + "source": "research/p104-two-target-native/inputs/CIRCUIT.json", + "local": "inputs/PR2458-CIRCUIT.json", + "sha256": "c34d94128decc426e7528302ab2570967293a1b293f184fdd89fd376addd61f9", + "git_blob": "17b0a10eafaf6e6c0db78690f01dc48505c63a4d" + }, + { + "commit": "3170afd2fc13a990bfe28f5ab6421bcda4ffd0f6", + "source": "research/p104-two-target-native/README.md", + "local": "inputs/PR2458-README.md", + "sha256": "a9aacd624c17ec6ba97583d866a1833c5f027866d1eeb181cc8b2ada48b7ec08", + "git_blob": "979be231f8e5994e8be3bcac178c09775120c5c5" + }, + { + "commit": "afa5d6649460dcdb93489babd74f0ee9d01a4911", + "source": "research/p104-shared-chart-retiming/WORD.json", + "local": "inputs/PR2712-WORD.json", + "sha256": "f395a54f747eea8dd5d54b0959a6ab4bfa8c5bed6447c9dd2586f2f68b0eed74", + "git_blob": "e071eb090efe6a7a98db70c594d1081c1530272c" + }, + { + "commit": "afa5d6649460dcdb93489babd74f0ee9d01a4911", + "source": "research/p104-shared-chart-retiming/README.md", + "local": "inputs/PR2712-README.md", + "sha256": "2435c9fe9adbcde892840975d9875fc0e36c9211330f851a53a256dddaaa6493", + "git_blob": "a1890be765dc7a266d9cb4816f1ca04acb57eb70" + }, + { + "commit": "71d24b655c2fdddc063b9aaf285e8425ce197499", + "source": "research/p104-dual-add-retiming/WORD.json", + "local": "inputs/PR2725-WORD.json", + "sha256": "d1a5484fbb9b89f1b4297b68db143ac21afdd64b0ba000dac222af1594745e60", + "git_blob": "8a52dc63784261235701f952ec535ee45b28d198" + }, + { + "commit": "71d24b655c2fdddc063b9aaf285e8425ce197499", + "source": "research/p104-dual-add-retiming/README.md", + "local": "inputs/PR2725-README.md", + "sha256": "b413a463a81f9499f2af766a513f2d6d642ac372dc77a2cc912bf9c1d1b75373", + "git_blob": "d1d1b24054a99992540a0ab2a5c29e58cf8a3dbe" + } + ], + "context_only": [ + { + "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/2619#discussioncomment-18955566", + "author": "Jose Manuel / jmbarrancoml", + "checked_at_utc": "2026-10-15T19:23:30Z", + "claim": "Fixed five-forward/four-dual consumer misses the selected target even after416 rank units forgiven per dual.", + "status": "Provisional Discussion result independently audited here; original finding credited." + }, + { + "pr": 2729, + "head": "6b29cc86ca040cf1f23e4a104b5d279afd3dce73", + "path": "research/p104-fusion-cost-headroom/README.md", + "scope": "Local headroom result, explicitly distinct from consumer screen" + }, + { + "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/2619#discussioncomment-18956430", + "author": "Nick Petalas / petalas", + "checked_at_utc": "2026-10-15T19:23:30Z", + "scope": "Local-only claim for the all-positive-pair2458/2712 extension. Not a consumed proof or a verified public artifact; this package stays at four pairs and separately checks2725." + } + ] +} diff --git a/research/p104-caller-feasibility/consumer/inputs/PR2744_RESULT.json b/research/p104-caller-feasibility/consumer/inputs/PR2744_RESULT.json new file mode 100644 index 0000000000..cf47566a35 --- /dev/null +++ b/research/p104-caller-feasibility/consumer/inputs/PR2744_RESULT.json @@ -0,0 +1,222 @@ +{ + "schema_version": 1, + "status": "PASS_P104_CONSUMER_BUDGET_AUDIT", + "contract": { + "width": 73, + "original_families": 832, + "forward_calls": 5, + "dual_calls": 4, + "unpaid_per_original_family": 1, + "maximum_original_progress_per_call": 3014, + "rank_deletion_per_dual": 416, + "remaining_child_rank_cap": 73, + "scope": "Fixed profiled calls, per-child integer rank deletion only; no other fusion, resynthesis, shared children or additional unpaid bank coordinates." + }, + "censuses": { + "forward2458": { + "events": 4734, + "operations": { + "add": 3064, + "copy": 8, + "erase": 8, + "transport": 1646, + "zero": 8 + }, + "profile": { + "1": 1216, + "2": 74, + "3": 86, + "4": 104, + "5": 48, + "6": 42, + "7": 68, + "8": 8 + }, + "rank_mass": 3070, + "persistent_endpoint_progress": 3014, + "role_types": { + "X": 104, + "Y": 104, + "dirty": 150 + }, + "descending_transports": 8, + "program_sha256": "25894f3c1b9eb37bafe5979fb94e48e7eb1b745260e07f41d8eead74599f9cbb" + }, + "dual2712": { + "events": 5266, + "operations": { + "add": 3104, + "erase": 8, + "sign": 208, + "transport": 1938, + "zero": 8 + }, + "profile": { + "1": 1498, + "2": 60, + "3": 74, + "4": 92, + "5": 58, + "6": 56, + "7": 92, + "8": 8 + }, + "rank_mass": 3542, + "persistent_endpoint_progress": 3014, + "role_types": { + "X": 104, + "Y": 104, + "dirty": 150 + }, + "descending_transports": 216, + "program_sha256": "e6815a9baac749db227bb904a69fc98ffd3bacb16fff2c4b188f2b25deb3ee80" + }, + "dual2725": { + "events": 5268, + "operations": { + "add": 3104, + "erase": 8, + "sign": 208, + "transport": 1940, + "zero": 8 + }, + "profile": { + "1": 1502, + "2": 58, + "3": 74, + "4": 93, + "5": 57, + "6": 56, + "7": 91, + "8": 9 + }, + "rank_mass": 3542, + "persistent_endpoint_progress": 3014, + "role_types": { + "X": 104, + "Y": 104, + "dirty": 150 + }, + "descending_transports": 216, + "program_sha256": "e6344064de59850b7e9b38b01ff08e1947eedb1a937f0003b8be2d679eb57cc2" + } + }, + "bills": { + "dual2712": { + "original_profile": { + "1": 12072, + "2": 610, + "3": 726, + "4": 888, + "5": 472, + "6": 434, + "7": 708, + "8": 72 + }, + "discounted_profile": { + "1": 10408, + "2": 610, + "3": 726, + "4": 888, + "5": 472, + "6": 434, + "7": 708, + "8": 72 + }, + "original_local_mass": 29518, + "discounted_local_mass": 27854, + "remaining_coverage_mass": 32778, + "raw_zero_saving_ratio": "599/584", + "discounted_zero_saving_ratio": "583/584", + "log_slope": 76524, + "lower_bounds": { + "selected_kappa": { + "a": "836330098538459/500000000000000000", + "moment_strictly_above": "7594999831115139259129/7592000000000000000000", + "numerator_margin": "2999831115139259129/125000000000000000", + "minimum_additional_unpaid_units_for_this_guard_to_stop_rejecting": 24 + }, + "selected_primitive": { + "a": "67018507072324140917/40000000000000000000000", + "moment_strictly_above": "607602131058800633139883127/607360000000000000000000000", + "numerator_margin": "242131058800633139883127/10000000000000000000000", + "minimum_additional_unpaid_units_for_this_guard_to_stop_rejecting": 25 + } + }, + "bank_extension": "For every finite integer B>=0: M_B(a)>1+(slope*a-104)/(73*(832+B)). Banks earn no unpaid-coordinate credit and do not rewrite the fixed profiled calls." + }, + "dual2725": { + "original_profile": { + "1": 12088, + "2": 602, + "3": 726, + "4": 892, + "5": 468, + "6": 434, + "7": 704, + "8": 76 + }, + "discounted_profile": { + "1": 10424, + "2": 602, + "3": 726, + "4": 892, + "5": 468, + "6": 434, + "7": 704, + "8": 76 + }, + "original_local_mass": 29518, + "discounted_local_mass": 27854, + "remaining_coverage_mass": 32778, + "raw_zero_saving_ratio": "599/584", + "discounted_zero_saving_ratio": "583/584", + "log_slope": 76556, + "lower_bounds": { + "selected_kappa": { + "a": "836330098538459/500000000000000000", + "moment_strictly_above": "7595006521755927566801/7592000000000000000000", + "numerator_margin": "3006521755927566801/125000000000000000", + "minimum_additional_unpaid_units_for_this_guard_to_stop_rejecting": 25 + }, + "selected_primitive": { + "a": "67018507072324140917/40000000000000000000000", + "moment_strictly_above": "607602667206857211733010463/607360000000000000000000000", + "numerator_margin": "242667206857211733010463/10000000000000000000000", + "minimum_additional_unpaid_units_for_this_guard_to_stop_rejecting": 25 + } + }, + "bank_extension": "For every finite integer B>=0: M_B(a)>1+(slope*a-104)/(73*(832+B)). Banks earn no unpaid-coordinate credit and do not rewrite the fixed profiled calls." + } + }, + "elementary_bounds": { + "e_upper": "49/18", + "log_lower_claims": [ + "ln(73)>4", + "ln(73/r)>2 for integer2<=r<=8" + ], + "scope_witness": { + "profile": { + "1": 17, + "9": 3093 + }, + "local_mass": 27854, + "construction": "5*(341H9+H1) +4*(347H9+3H1)", + "log_upper": { + "1": "9/2", + "9": "17/8" + }, + "taylor_degree": 10, + "taylor_lower": { + "1": "4102015261/45875200", + "9": "32623638623621489/3896394330931200" + }, + "selected_primitive": "67018507072324140917/40000000000000000000000", + "moment_upper": "768756558943453721588036545458749049905049480382613/768812344366283572579075775027782729118100104964256", + "uniform_a_max": "1/580", + "uniform_moment_upper": "53862115339/53863448288", + "scope": "Abstract same-mass profile only, with fractional rank73 remainder; no realizable circuit, owner packing, or supplier is supplied. Not permitted by the fixed-profile rank-deletion contract." + } + }, + "boundary": "Conditional consumer rejection, not a native/owner construction or a universal P104 obstruction. Scalar inverse-transpose identities are separately checked; physical recipes remain inherited." +} diff --git a/research/p104-caller-feasibility/consumer/inputs/PR3574_README.md b/research/p104-caller-feasibility/consumer/inputs/PR3574_README.md new file mode 100644 index 0000000000..4f3dc91f1d --- /dev/null +++ b/research/p104-caller-feasibility/consumer/inputs/PR3574_README.md @@ -0,0 +1,73 @@ +# Rank-1 hosting of 1127 meets the selected saving + +**Partial. No new exponent.** + +The native channel histogram is + +```text +1074 H1 + 58 H2 + 86 H3 + 104 H4 + 48 H5 + 24 H6 + 8 H7 + 8 H8 +``` + +with rank mass 2,368. The minimizing side correction is 208 unit-step +helpers, nine rank-one steps each, adding 1,872. The local mass is 4,240. +On the template `W=832/9`, centre 56 and total mass 6,712, the idle mass is +2,472, which is `824/17` ideal rank-51 children. + +At the selected saving the moment of that bill is `0.9988962438816702`, +below one. The same bill still beats the selected saving after 1,126 extra +rank-1 hosting units. At 1,127 units the moment goes above one. Both counts +fit inside the idle room. + +The geometric budget leaves native ADDs, owners, routing, precision and tape +unpriced. This cut is the rank-1 hosting threshold for that omission. + +## What was executed + +The checker rebuilds the histogram and calls `ceiling.relax` at the selected +saving. It does not rerun the 208-flag matching or the two-type optimizer. + +`scripts/research_baseline.py` needs +`research/community-frontier1094-audit/ASSEMBLY.json`, which this checkout +does not have. The orientation used here is the channel histogram and the +geometric-budget sentences. + +## Scope and evidence + +Original card: `p104-side-correction`, priority revision 6, refined to this +hosting cut. [TASK.json](TASK.json) records the scope change. +[RESULT.json](RESULT.json) is the executed receipt and is not rewritten. +[SOURCES.json](SOURCES.json) pins the two notes, the ceiling function and +the selected record. No selected frontier file changes. + +Upstream checkpoint: `20ecf2891d80b5acf18d980b2164fb44ea7faa90`, priority +revision 6, checked 2026-10-18 06:15 UTC. Catalogue and selected record match +that commit. Handoff discussion #1166, through the PR3564 note at 2026-10-18 +06:15 UTC, was released work. Draw seed +`b35d4e81a6bbaab3024f2cde36708828`, track `complex-mechanisms`, third card +`p104-side-correction`. + +## Reproduce + +From the repository root, standard-library Python 3.12: + +```sh +python3.12 -B research/p104-hosting-threshold/verify.py +python3.12 -B research/p104-hosting-threshold/test_verify.py +python3.12 -B scripts/research_package.py --package research/p104-hosting-threshold +``` + +The moment checks finish in about a second. + +## Open next questions + +The 1,126/1,127 rank-1 cut is this template's hosting decision. + +## Credit + +The channel histogram is Rohan Arun's PR1972, with the native recipes +prepared for Chafik Boukhalfa. The two-history budget and the 208-unit +minimum are Nick Petalas's. The interval engine is Douglas Colkitt's packing +ceiling, with Claude (Anthropic). The selected kappa is the #1094 record. + +Prepared by jwr with substantial Cursor agent assistance. No independent human +review is claimed. Apache-2.0. diff --git a/research/p104-caller-feasibility/consumer/inputs/PR3574_verify.py b/research/p104-caller-feasibility/consumer/inputs/PR3574_verify.py new file mode 100644 index 0000000000..3a253a9e7e --- /dev/null +++ b/research/p104-caller-feasibility/consumer/inputs/PR3574_verify.py @@ -0,0 +1,126 @@ +#!/usr/bin/env python3 +"""Price the P104 channel plus its unit-step side correction. + +The published histogram plus 208 nine-step helpers is the local bill. +Extra rank-1 hosting is added until the moment at the selected saving +crosses one. +""" + +import hashlib +import json +import sys +from fractions import Fraction +from pathlib import Path + +ROOT = Path(__file__).resolve().parents[2] +PACKAGE = Path(__file__).resolve().parent +sys.path.insert(0, str(ROOT / "research/complex-local-word-ceiling")) +import ceiling as ceiling_mod # noqa: E402 + +MARKER = "PASS_P104_HOSTING_THRESHOLD moment_below_one=true no_new_kappa" +CHANNEL = {1: 1074, 2: 58, 3: 86, 4: 104, 5: 48, 6: 24, 7: 8, 8: 8} +UNITS = 208 +STEP = 9 +TOTAL = 6712 +SHOWN = "0.9988962438816702" + + +def fail(message): + raise SystemExit("FAIL_P104_HOSTING_THRESHOLD " + message) + + +def require(condition, message): + if not condition: + fail(message) + + +def sha256(path): + digest = hashlib.sha256() + with path.open("rb") as handle: + for block in iter(lambda: handle.read(1 << 20), b""): + digest.update(block) + return digest.hexdigest() + + +def authenticate(): + sources = json.loads((PACKAGE / "SOURCES.json").read_text(encoding="utf-8")) + pinned = {row["path"]: row for row in sources["files"] if row["usage"] == "input"} + expected = { + "research/p104-endpoint-geometric-budget/README.md", + "research/p104-native-channel/README.md", + "research/complex-local-word-ceiling/ceiling.py", + "certificates/selected-result.json", + } + require(set(pinned) == expected, "input inventory changed") + for path, row in pinned.items(): + require(sha256(ROOT / path) == row["sha256"], "input drift " + path) + + +def mass(profile): + return sum(rank * count for rank, count in profile.items()) + + +def bill(): + paid = dict(CHANNEL) + paid[1] += UNITS * STEP + return paid + + +def moment(profile, saving): + return ceiling_mod.relax(profile, 73, 832, 9, 56, saving, unpaid=1) + + +def evaluate(): + authenticate() + budget = (ROOT / "research/p104-endpoint-geometric-budget/README.md").read_text(encoding="utf-8") + native = (ROOT / "research/p104-native-channel/README.md").read_text(encoding="utf-8") + selected = json.loads((ROOT / "certificates/selected-result.json").read_text(encoding="utf-8")) + for sentence in ( + "1074 H1 + 58 H2 + 86 H3 + 104 H4 + 48 H5 + 24 H6 + 8 H7 + 8 H8.", + "Its rank mass is 2368. Every added lifetime consumes nine more rank units,", + "The minimizing profile has `H1=2946`", + "local rank mass 4240 and idle rank mass 2472", + SHOWN, + "Native ADDs, owners, routing, precision, tape and\nall other physical charges are unknown and additional.", + "centre charge 56, total paid\nrank mass 6712", + ): + require(sentence in budget, "the budget sentence moved") + require("chronological global hosting, precision and all-size admission remain open." in native, "the hosting sentence moved") + require(mass(CHANNEL) == 2368, "the channel mass moved") + paid = bill() + require(paid[1] == 2946 and mass(paid) == 4240, "the side-correction bill moved") + idle = TOTAL - mass(paid) + require(idle == 2472 and Fraction(idle, 51) == Fraction(824, 17), "the idle children moved") + kappa = Fraction(selected["kappa"]) + saving = kappa / (1 - kappa) + low, high = moment(paid, saving) + require(high < 1 and f"{float(low):.16f}" == SHOWN and f"{float(high):.16f}" == SHOWN, "the side-correction moment moved") + below = dict(paid) + below[1] += 1126 + above = dict(paid) + above[1] += 1127 + require(moment(below, saving)[1] < 1, "1126 rank-1 hosting met moment one") + require(moment(above, saving)[0] > 1, "1127 rank-1 hosting stayed under moment one") + require(1127 <= idle, "the hosting cut left the template") + return { + "channel_mass": 2368, + "unit_steps": UNITS * STEP, + "local_mass": 4240, + "idle_mass": idle, + "idle_children": "824/17", + "moment_below_one": True, + "hosting_rank1_below": 1126, + "hosting_rank1_above": 1127, + "no_new_kappa": True, + } + + +def main(): + observed = evaluate() + stored = json.loads((PACKAGE / "RESULT.json").read_text(encoding="utf-8")) + require(observed == stored, "RESULT.json does not match the execution: " + json.dumps(observed, sort_keys=True)) + print(MARKER) + + +if __name__ == "__main__": + main() diff --git a/research/p104-caller-feasibility/consumer/inputs/PR3605_CLAIM.json b/research/p104-caller-feasibility/consumer/inputs/PR3605_CLAIM.json new file mode 100644 index 0000000000..445e6a83a4 --- /dev/null +++ b/research/p104-caller-feasibility/consumer/inputs/PR3605_CLAIM.json @@ -0,0 +1,33 @@ +{ + "calls": 6660, + "dimension": 73, + "generated_package_manifest_sha256": "d516ed4734f0d10d99fd157db769d72fe372ca09947e1d2c5ac93a27f0142dda", + "kappa": "17300065495388418470049999999999999999999998999999999999999999999999/10000000000000000000000000000000000000000000000000000000000000000000000", + "kappa_decimal": "0.0017300065495388418470049999999999999999999998999999999999999999999999", + "live": 663040, + "local_publication_head": "ac92a027c78b0c9bb0ada739b26959afda489d0e", + "owner_payload_sha256": "653085641ff2e9470e25aedfc92861ec34e5cf594d52123e8b28b6f0ec20b9f8", + "physical": 663549, + "profile": { + "1": 16417896, + "2": 4835160, + "3": 1540174, + "4": 679321, + "48": 283185, + "5": 143992, + "6": 3, + "8": 53280 + }, + "release_receipt_sha256": "ce1ce9d9ad3ac9440057534d19e06b7cb4fb8da98ba5e72e01ce538b59eb2f40", + "replicas": 740, + "roles": 2717280, + "root_interval": [ + "346001309907768369401/200000000000000000000000", + "865003274769420923503/500000000000000000000000" + ], + "scope": "Complete fixed T740 source/native/owner/physical/prefix/outer release bound to the stated exact endpoint. All inherited all-size/compiler/uniform-cost/hosting/bootstrap-time/PR559/rounding/tape/recovery/analytic/BIT H1-H5 hypotheses remain. No unconditional or formal-kernel theorem or selected-record update.", + "source_manifest_sha256": "adb145b4f36ca330c34c0dbdb847351dafdc4ca9cd7bb4e1de01ed634d96bfe1", + "status": "CONDITIONAL_RELEASE_BOUND", + "unchanged_bit_endpoint": "0.001733427039589844234749", + "validation_binding": "evidence/FINAL-BINDING.json" +} diff --git a/research/p104-caller-feasibility/consumer/inputs/PR3605_DERIVATION.md b/research/p104-caller-feasibility/consumer/inputs/PR3605_DERIVATION.md new file mode 100644 index 0000000000..30710a70b9 --- /dev/null +++ b/research/p104-caller-feasibility/consumer/inputs/PR3605_DERIVATION.md @@ -0,0 +1,152 @@ +# Conditional transfer for the staged 644/660 supplier + +The original full strict release and separate source/native/owner/physical/prefix/outer +binding pass; see evidence/RELEASE-RECEIPT.json and evidence/FINAL-BINDING.json. + +The historical model is PR3133's native complex supplier composed with PR3148's +T740 owner geometry and PR3531's modern outer transfer. The native complex +moment has no conservative complex surcharge. The unchanged BIT supplier keeps +its conservative surcharge and certified endpoint +`0.001733427039589844234749`. All compiler, physical realization, rounded +recursive precision and analytic hypotheses of that model remain explicit. + +There are `9*740=6660` complete supplier calls, dispatched as 2500 gauge44 and +4160 extra calls. Both actual local words have the same paid profile +`L={1:2439,2:726,3:224,4:102,5:20,8:8}`. The corrected literal chronological +owner journal has 2,717,280 whole helper roles. Its complete idle profile is +`I={1:174156,3:48334,4:1,5:10792,6:3,48:283185}`. Consequently the complete +recursive histogram is `H=6660*L+I`: + +| rank | paid children | +| --- | ---: | +| 1 | 16,417,896 | +| 2 | 4,835,160 | +| 3 | 1,540,174 | +| 4 | 679,321 | +| 5 | 143,992 | +| 6 | 3 | +| 8 | 53,280 | +| 48 | 283,185 | + +These are actual rank-six children, rather than numerical rounding residues. +Generic pending-axis emission and audits retain that stratum. The exact totals +are 23,953,011 children and rank mass 48,165,120. With dimension `m=73` and live +stock `W=896*740=663040`, `mW=48,401,920`, so the deficit is +`236800=320*740`. These invariants alone would not certify the moment; all eight +rank strata above enter the calculation. + +The stipulated complete moment is + +``` +M(b) = (1/(73*663040)) * sum_r r*H[r]*(73/r)^b. +``` + +Every occupied rank lies strictly between zero and 73, so each summand is +strictly increasing in `b`. Independent outward rational log/exp arithmetic +locates adjacent endpoints + +``` +C = 0.001730006549538841847005 +D = 0.001730006549538841847006. +``` + +The PR3531 positive-binomial engine and both retained moment implementations +independently certify `upper M(C)<1 0.00173. +``` + +Both independent modern outer engines pass 63 strict inequalities and 17 +rejecting controls; the retained bootstrap passes all 47 strict inequalities +and its four controls. The unchanged BIT endpoint exceeds `C`, so the complex +supplier remains binding. This arithmetic does not replace the complete finite +source/native/owner/physical/prefix release. + +The fixed physical stock is `663040+8+408+91+2=663549` families. The complete +ambient conversion includes + +``` +|Sp(72,2)| = 2^(36^2) * product_(j=1..36) (2^(2j)-1). +``` + +The exact integer `|Sp(72,2)|*663549` has bit length 2647. Thus its square root +is below `2^1324`. The actual local scalar/Horner prefix bound is 95 bits in +both-provider maximum, versus the retained reserve 128. Under the whole-owner +tensor block context that full release checks separately (nine calls and nine +bridges per replica), the bound is + +``` +actual prefix = 95 + 37 + 18 + 1324 + 1 + 4 = 1479, +paid reserve = 128 + 37 + 18 + 1324 + 1 + 4 = 1512 < 2048. +``` + +The universal sufficient inequality is written in +`research/tensor-block-kappa/PROOF.md`, section “Universal sufficient energy +bound” (SHA256 `3fa62afc4cee9315f236e8cae94484b40d2dedc271d654b08eb5eaf86a96a425`). +It assumes unitary helper residuals within each physical family and at most +eighteen norm-at-most-two data shears/bridges per owner block. It proves +`E_t(r)<=4^18 E_0(r)` and the summed bound for arbitrary correlated inputs. +The historical T114/72-buffer/local70 application in that file is not reused +as the new finite parameter check. No fresh Lean or axiom validation was run. + +The local endpoint check covers every one of the 632 arbitrary data/helper +columns, literal centre first/terminal clearing, all 91 allocated and cleared +zero buffers, both orientations and both providers. All helper roles, including +the changed rank-seven residual interfaces, retain paid native frame/phase and +primitive contracts. Preparation and the full global replay regenerate actual +source access, scalar coefficients, adapter, controller, physical stock and +prefix invoices; none is inferred merely from the local rank saving. + +This is finite evidence at the fixed T740 geometry, together with an exact +conditional transfer calculation. The completed original full release is recorded by +`evidence/RELEASE-RECEIPT.json`, with exact source binding in +`evidence/FINAL-BINDING.json`. Neither that finite gate nor this +derivation proves an all-size dispatcher/compiler, common-label or mutable-source +physical realization, uniform scalar/COPY/CLEAR and zero-allocation mechanism, +whole-call hosting, internal recursive rounding precision, tape complexity, +exact recovery, analytic transfer or BIT H1-H5. No formal-kernel proof or +maintainer-selected frontier update is asserted. + +At endpoint precision 24, the explicit modern parameters are +`r0=10^-104`, `delta=(1025/1024)r0`, `epsilon=1-delta`, +`beta=1-3delta`, `b=C-r0`, and `q=C-2r0`. Since +`0 0.00173` +under the inherited hypotheses below. + +The staged 644/660 construction has a literal owner allocation at 740 replicas, +6,660 calls and 2,717,280 helper roles. The complete histogram is +`{1:16417896,2:4835160,3:1540174,4:679321,5:143992,6:3,8:53280,48:283185}`. +The fresh arithmetic check encloses the complex root in +`[0.001730006549538841847005,0.001730006549538841847006]` and checks the +modern outer inequalities. The completed original full strict release and separate +exact binding are recorded in `evidence/RELEASE-RECEIPT.json` and +`evidence/FINAL-BINDING.json`. The binding source-hash inventory preserves the +raw receipt/script hashes and normalizes only run-root paths. + +[DERIVATION.md](DERIVATION.md) gives the complete histogram, joint BIT/complex +convention, exact outer parameters, stock/prefix calculation and inherited +conditional hypotheses. + +The two local words, arbitrary-input cleanup, exact phase and full native proofs +are in the sibling `staged-644-660-width-reduction` package. This package preserves +that independent local replay. It adds a compact exact integer-flow witness, +a deterministic standard-library realization, an independent complete literal +audit, and fresh rigorous moment/outer arithmetic. Its registered check requires +no optimizer, Git history, network access or stored success receipt. + +## Reproduction and scope + +From the repository root, with Python 3.12 and NumPy 2.5.4: + +```sh +python3 -B research/staged-644-660-conditional-release/verify.py +``` + +The registered verifier checks four aggregate corruptions, regenerates all owner +rows, derives both native frame tables freshly from the sibling's frozen words, +and audits complete helper identities, strict/closed source windows, physical +family uniqueness, every chronological pending prefix and the full paid invoice. +It then derives the root using exact rational interval arithmetic, verifies the +strict bracket with three arithmetic engines, and runs all 63 modern outer +inequalities and 17 controls plus 47 bootstrap inequalities and four controls. +The literal audit's five local predicate controls are separately identified; +they are not advertised as whole-journal corruption replays. + +The public new validation gates use explicit exceptions. Historical assertion +checks execute only in fresh unoptimized children with `PYTHONOPTIMIZE` removed; +the owner and integral-network programs also reject optimized execution. The +registered parent can itself run under `-I -O`. Gzip stream bytes are provenance; +the complete regenerated payload is compared semantically. + +The separate long cold replay requires the historical Git objects in FETCH.txt +and the inherited full dependency set. It reconstructs the unchanged source +closure rather than vendoring it again. A fresh retained bootstrap is the default: + +```sh +python3 -B research/staged-644-660-conditional-release/reproduce.py \ + --repo /absolute/path/to/repository \ + --word-package /absolute/path/to/research/staged-644-660-width-reduction \ + --work /absolute/path/to/fresh-output +``` + +`--retained /absolute/path/to/retained` explicitly reuses a completely +source/receipt/cache-authenticated predecessor. `--prepare-only` stops before +complete admission and makes no release claim. The bounded check does not run +the long cold command. The new long wrapper passed its preparation-only replay, including fresh +source/native and owner preparation. Its complete release tail was not run; +a Git-free full cold replay is not claimed. The source overlay +recreates exactly 648 files with manifest +`adb145b4f36ca330c34c0dbdb847351dafdc4ca9cd7bb4e1de01ed634d96bfe1`. + +## Mathematical boundaries + +The complete conditional transfer still requires the inherited all-size compiler, +physical common-label and mutable-source realization, rounded recursive precision, +tape bound, exact recovery, analytic transfer and BIT H1–H5 hypotheses. Finite +source/native/owner/physical/prefix/outer checks do not prove these hypotheses. +No formal-kernel theorem, unconditional multiplication bound or selected-record +change is supplied. The copied-flow realization lemma in owners/PROOF.md is a +written all-parameter lemma under its integer-flow and source-window premises; +feasibility of this concrete witness is finite exact computation. + +The actual prefix is 1,479 bits, the sufficient reserve is 1,512, and the paid +reserve is 2,048. The physical stock is `896*740+408+8+91+2=663549`; all 91 private cleanup buffers +remain charged. The new local profile is +`{1:2439,2:726,3:224,4:102,5:20,8:8}`. The helpers' actual widths change from 8 to 7; +this does not establish the earlier proposed 7-to-6 extraction. + +## Sources and credit + +Exact source PR3133 is dcharb78's +`51eb9c4ee9e4722010d308aa3309e039d3940cc2`; prior owner/cap machinery is Jeremy +Diviney's PR3148 `f2927a4b8afcf0701a6b945e14f30de1d94f5176`. The source notices +and credits are retained verbatim in owners/SOURCE-CREDITS.md and SOURCE-NOTICE; +“new here” in that copied credit file describes PR3133, not this contribution. +Credit Yiyang Lu's staged-kernel/flow lineage, Nick Petalas's copied owners, +Tekalign's independent owner checker, Marius-Paul Dumitrean's endpoint/native +work, and Jeremy Kothe's preload/source work. The tiny arithmetic vendor is +PR3531 `550a660a97308d3aeb3620ee1f4218f77e2c2742`, preserving its source notice +and dataisfire/PR3361 bootstrap attribution. + +Ross Richardson prepared this contribution with substantial OpenAI Codex +assistance. Separate AI review is not independent human or formal-kernel review. + +## Open next questions + +The complete original full release and exact binding have passed. The separate +portable long wrapper has only been executed through preparation. Replaying its +full tail and obtaining independent human review are open validation tasks; the +all-size inherited hypotheses remain mathematical obligations. +Any later packing or scalar-network change requires a new complete invoice and +the repository's family-level budget gate; this package makes no claim that the +finite primal is globally optimal. + +Historical metadata caveats are recorded in STAGE-SCOPE.json. The immutable +outer template prose retains old 3000/3080-digit wording; the new numeric SPEC +and LEDGER use endpoint precision 24. The inherited verify summary says 15 +controller controls, while actual ASYNC-AUDIT and SPEC cover 25. The actual +numeric fields and audit coverage govern; historical receipts are preserved. diff --git a/research/p104-caller-feasibility/consumer/inputs/PR3609_RECEIPT.json b/research/p104-caller-feasibility/consumer/inputs/PR3609_RECEIPT.json new file mode 100644 index 0000000000..6faa5157f2 --- /dev/null +++ b/research/p104-caller-feasibility/consumer/inputs/PR3609_RECEIPT.json @@ -0,0 +1,4120 @@ +{ + "SOURCES_sha256": "d160d608c2bd3b7d5470b268ac746ad604bbfcb9e0d41b3a29175c623ca33f5d", + "artifact_sha256": { + "NATIVE.json": "795a8c4e096a42a2f2c5875c354a4d4b56515cf8ffdfd5767a82713cf7f84dbd", + "PROGRAM.json": "608c5c66a6eb7af2fc75d32e2b353a8074a50ef0bdb848c7211c59f3b7a176e6" + }, + "dirty_controls": { + "compared_banks": 197, + "controls": [ + { + "all_Y_restored": true, + "control": "omit_precondition", + "differing_banks": [ + { + "bank": "X10", + "expected_multiple_of_u": "0", + "observed_multiple_of_u": "1" + }, + { + "bank": "X16", + "expected_multiple_of_u": "0", + "observed_multiple_of_u": "-1" + }, + { + "bank": "X17", + "expected_multiple_of_u": "0", + "observed_multiple_of_u": "-1" + }, + { + "bank": "X25", + "expected_multiple_of_u": "0", + "observed_multiple_of_u": "-1" + }, + { + "bank": "X26", + "expected_multiple_of_u": "0", + "observed_multiple_of_u": "-1" + }, + { + "bank": "X34", + "expected_multiple_of_u": "0", + "observed_multiple_of_u": "-1" + }, + { + "bank": "X37", + "expected_multiple_of_u": "0", + "observed_multiple_of_u": "1" + }, + { + "bank": "X41", + "expected_multiple_of_u": "0", + "observed_multiple_of_u": "1" + }, + { + "bank": "X47", + "expected_multiple_of_u": "0", + "observed_multiple_of_u": "-1" + }, + { + "bank": "X5", + "expected_multiple_of_u": "0", + "observed_multiple_of_u": "1" + }, + { + "bank": "X53", + "expected_multiple_of_u": "0", + "observed_multiple_of_u": "-1" + }, + { + "bank": "X57", + "expected_multiple_of_u": "0", + "observed_multiple_of_u": "-1" + }, + { + "bank": "X6", + "expected_multiple_of_u": "0", + "observed_multiple_of_u": "1" + }, + { + "bank": "X60", + "expected_multiple_of_u": "0", + "observed_multiple_of_u": "1" + }, + { + "bank": "X63", + "expected_multiple_of_u": "0", + "observed_multiple_of_u": "-1" + }, + { + "bank": "X69", + "expected_multiple_of_u": "0", + "observed_multiple_of_u": "-1" + }, + { + "bank": "X73", + "expected_multiple_of_u": "0", + "observed_multiple_of_u": "-1" + }, + { + "bank": "X76", + "expected_multiple_of_u": "0", + "observed_multiple_of_u": "1" + }, + { + "bank": "X82", + "expected_multiple_of_u": "0", + "observed_multiple_of_u": "-1" + }, + { + "bank": "X86", + "expected_multiple_of_u": "0", + "observed_multiple_of_u": "-1" + }, + { + "bank": "X91", + "expected_multiple_of_u": "0", + "observed_multiple_of_u": "-1" + }, + { + "bank": "X97", + "expected_multiple_of_u": "0", + "observed_multiple_of_u": "-1" + } + ], + "executed_program_operations": 991, + "input_multiples_of_u": { + "X11": 1 + }, + "status": "REJECTED_BY_OUTPUT" + }, + { + "all_Y_restored": true, + "control": "late_precondition", + "differing_banks": [ + { + "bank": "X16", + "expected_multiple_of_u": "-2", + "observed_multiple_of_u": "0" + }, + { + "bank": "X21", + "expected_multiple_of_u": "-2", + "observed_multiple_of_u": "0" + }, + { + "bank": "X25", + "expected_multiple_of_u": "-2", + "observed_multiple_of_u": "0" + }, + { + "bank": "X30", + "expected_multiple_of_u": "-2", + "observed_multiple_of_u": "0" + }, + { + "bank": "X38", + "expected_multiple_of_u": "-2", + "observed_multiple_of_u": "0" + }, + { + "bank": "X41", + "expected_multiple_of_u": "2", + "observed_multiple_of_u": "0" + }, + { + "bank": "X43", + "expected_multiple_of_u": "2", + "observed_multiple_of_u": "0" + }, + { + "bank": "X5", + "expected_multiple_of_u": "-2", + "observed_multiple_of_u": "0" + }, + { + "bank": "X51", + "expected_multiple_of_u": "-2", + "observed_multiple_of_u": "0" + }, + { + "bank": "X53", + "expected_multiple_of_u": "-2", + "observed_multiple_of_u": "0" + }, + { + "bank": "X56", + "expected_multiple_of_u": "2", + "observed_multiple_of_u": "0" + }, + { + "bank": "X61", + "expected_multiple_of_u": "-2", + "observed_multiple_of_u": "0" + }, + { + "bank": "X67", + "expected_multiple_of_u": "-2", + "observed_multiple_of_u": "0" + }, + { + "bank": "X69", + "expected_multiple_of_u": "-2", + "observed_multiple_of_u": "0" + }, + { + "bank": "X72", + "expected_multiple_of_u": "2", + "observed_multiple_of_u": "0" + }, + { + "bank": "X77", + "expected_multiple_of_u": "-2", + "observed_multiple_of_u": "0" + }, + { + "bank": "X82", + "expected_multiple_of_u": "-2", + "observed_multiple_of_u": "0" + }, + { + "bank": "X91", + "expected_multiple_of_u": "-2", + "observed_multiple_of_u": "0" + }, + { + "bank": "X97", + "expected_multiple_of_u": "-2", + "observed_multiple_of_u": "0" + } + ], + "executed_program_operations": 1238, + "input_multiples_of_u": { + "Y3": 4 + }, + "status": "REJECTED_BY_OUTPUT" + } + ], + "interpretation": "Normalized multiples of one B9 vector u; native charts omitted", + "oracle": "X_initial + C*A*Y_initial/2; all other banks unchanged", + "original_full_bank_oracle_matches": 2, + "original_program_operations": 1238, + "precondition_ADDs": 247, + "status": "PASS" + }, + "global_phase_control": "Altered scalar i rejected by exact global-phase anchor.", + "implementation_and_proof_sha256": { + "COSTS.md": "07768c7c42cfdb99f780e96423d13787ade1faefda66d44df9986da67a646e6c", + "PROOF.md": "e72a2a0a34ba1c3c226da1e99326ec14e2fb913a74788463bb7013aa8d4954af", + "README.md": "7a65c25d71acb7d8cc9752d0e220679857c05f9c43af93a953a463a1a04fe6b0", + "TASK.json": "6b5227217bda70e24efc9f2d99637dd0973421847d0e0c14586237a83cdc40be", + "VERIFY.json": "de8f0a49a154857ed0fbffeb4d4fc478a1496e0bfc1f9077c0747d8be2ac5efb", + "controls.py": "f5967b3627405efe453dfffa75f546f1e96e6c948d5ccbe5632697b4c8ad27d6", + "invoice.py": "8910efa1b0cbe803d3f47b9ed803b4584a9ff0065d704af4e2c59dfe07edfbee", + "native.py": "28b26fbfcd67008cfd1c158427755f48041ed5e20551c3dd97e96920f9d2838b", + "physical.py": "fc5c00d735a493ef97f978c473b433b12f4c02ee89ca99910570a11cd383931f", + "primary.py": "031660f98b56e703a7e5fe0fdbaafd5a188ecdd629cb74b2ec35208f86b2703f", + "verify.py": "856793b59bcef5d5ab0411e4e0ad17f0a42fc128303d72531c2025f74a01ed7d" + }, + "input_sha256": { + "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "NOTICE": "b49022cb4104d90b182e4c335f670faf45529025b15db77bf0291835083c28bd", + "research/gmx-t74-borrow43-handoff/new/fastnative/NATIVE-LINEAGE-NOTICE": "ee0c73ca35877aad0e0b6adc560a3881cb82276dba4cf2d4fc58cd19e57cc420", + "research/gmx-t74-borrow43-handoff/new/fastnative/vendor/native/new/code/borrow/vendor/clifford/clifford_exact.py": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962", + "research/p104-consumer-budget-audit/README.md": "13694215d0c1a245b392f7155e8395b9c4bad9c5db3558833c784d9449616417", + "research/p104-native-channel/notices/FRAME-SA504-NOTICE.md": "a92f49c5ced455160fbedcc8954e3c9255e3605e88ad12ae5a84f1c4302986f1", + "research/p104-native-channel/notices/PR1862-NOTICE.md": "d86f31a4c0bafd4271fe0c0e087a7fc1cd72d5b705e3739c4ba3e9241b7ba3f9", + "research/p104-native-channel/notices/PR1972-NOTICE.md": "2d9c60fdeda14a8609f2b210fe0873ee0318788130637db9e5e79d487243ab7d", + "research/p104-omitted-completion/CERTIFICATE.json": "f68a2e6f3bd771b9692772909df200102350a80deda35532f3cc348b75d0c044", + "research/p104-omitted-frame-adapters/ADAPTERS.json": "db424edfb316f06f4913946b2b0cafa2f200b75392cacb35244b8705db02387c", + "research/p104-omitted-frame-adapters/inputs/ORIGINS.json": "c28888fb28c6c4defab5dd4b17150001d7435a6e7346a705ca0a266b67e1598c", + "research/p104-omitted-frame-adapters/inputs/PR3416_verify.py": "d9fa70e7feb0032048b84b7a3e63628d56b206030b2f6b6a5c001b470bb9d049", + "research/p104-rounded-collector/inputs/NATIVE.json.gz": "ab91c78835c3e10cf3b2cb8a5d4e0b7cfc3df1ae5a811298d27842f2193e1e3d", + "research/p104-rounded-collector/inputs/WORD.json": "cec1fb3fbd0067b500ad5119a62ba60685be718e769374d7ec8abdd2beaa7e50", + "research/p104-stagewise-entrance/inputs/PR3382_PROOF.md": "1ca8c0e7e78f0f39de6cff7accc68ccd3901bfb50759bf7a2e2896bcf63bf081", + "research/p104-stagewise-entrance/inputs/PR3416_PROOF.md": "0dc1c35158902299fc8748c8baf89205483562f041e9050580e6579c331ebeb5" + }, + "invoice": { + "changed_full": { + "coordinate_C_pairs": 906752, + "native_calls": 1742, + "native_profile": { + "1": 1316, + "2": 61, + "3": 74, + "4": 86, + "5": 33, + "6": 25, + "7": 46, + "8": 8, + "9": 93 + }, + "native_rank_mass": 3542, + "new_private_C_lifetimes": 0, + "original_private_C_lifetimes": 8, + "scalar_exact_half_and_double_change_each": 7168, + "scalar_exact_real_halves": 2757632, + "scalar_real_ADD_change": -488448, + "scalar_real_ADDs": 3969024, + "scalar_real_doublings": 2757632 + }, + "closure": { + "event_sha256": "66113bcd513a17eac24f43944a8759bdae1bb2a85e2b9900122f281c5c676dc8", + "events": 4027, + "inputs": 265, + "omitted_banks": 93, + "projection_reads_or_writes_omitted": false + }, + "conditional_consumer_stop": { + "W": 832, + "auxiliary_bank_scope": "every finite B>=0; fixed m, fully paid 73 units per added bank", + "dual_calls": 4, + "exp2_rational_upper": "134800213/18243225", + "exp4_rational_upper": "377139364267/6907548375", + "forgiven_profile": { + "1": 9680, + "2": 614, + "3": 726, + "4": 864, + "5": 372, + "6": 310, + "7": 524, + "8": 72, + "9": 372 + }, + "forgiven_rank_mass": 27854, + "forgiven_zero_saving_bound": "583/584", + "forward_calls": 5, + "fully_paid_B_lower_bound": "1 + (75068*a-104)/(73*(832+B))", + "kappa": "836330098538459/500000000000000000", + "linear_lower_slope": 75068, + "m": 73, + "no_bank_selected_lower_bound": "7594695406959271260053/7592000000000000000000", + "persistent_credit_per_call": 3014, + "rank_forgiveness_per_dual": 416, + "remaining_coverage_mass": 32778, + "remaining_hypotheses": [ + "unchanged forward profile", + "new dual decomposition fixed apart from allowed rank deletion", + "all other positive children rank<=73", + "coverage law and endpoint credit unchanged", + "all other charges nonnegative; source admission and ownership not supplied" + ], + "scope": "Conditional new fixed-profile substitution under the retained PR2744 five-forward/four-dual coverage assumptions; not a universal P104 barrier", + "slope_times_kappa_minus_104": "2695406959271260053/125000000000000000", + "unforgiven_zero_saving_bound": "599/584" + }, + "entrance_completion": { + "A_l1": 393, + "A_nonzeros": 385, + "C_nonbasis_l1": 247, + "C_nonbasis_nonzeros": 201, + "basis": [ + "X0", + "X33", + "X101", + "X102", + "X11", + "X12", + "X15", + "X24" + ], + "basis_identity_checked": true, + "exact_real_doublings": 105472, + "exact_real_halves": 105472, + "inactive_Y": [ + "Y1" + ], + "native_calls": 145, + "native_profile": { + "1": 52, + "9": 93 + }, + "native_rank_mass": 889, + "new_private_Gaussian_banks": 0, + "real_ADDs": 908288, + "schedule": "Xnonbasis-=C_N*Xbasis; Xbasis+=A*Y/2 by source columns; Xnonbasis+=C_N*Xbasis", + "temporarily_halved_restored_Y_banks": 103, + "unit_Gaussian_bank_ADDs": 887, + "weighted_ADDs": 787 + }, + "evidence_limits": "Exact symbolic structure, coefficient and rational tariff checks; no native matrix/rounded replay or full-word endpoint proof is performed by this module.", + "native_concavity_gain": { + "equal_mass": 889, + "majorization_prefixes_checked": 473, + "new_calls": 145, + "new_tariff": "52 + 93*9^s", + "old_calls": 473, + "old_minus_new_lower_bound": "41*(9-9^s)", + "old_tariff_lower_bound": "421 + 52*9^s", + "positive_sqrt_chord_control": { + "certified_gain_at_least": 246, + "new_exact": 331, + "old_lower": 577, + "s": "1/2" + }, + "prefix_difference_sha256": "4fd4aef216cbc83a4b9916b372ea77002c35d383765345ab422e27792997dbb5", + "scope": "Strict improvement for 0<=s<1; equality at s=1; native-only profile tariff, with monomials and all physical/outer charges separate" + }, + "native_occurrences_bound": 2070, + "not_priced": [ + "actual source preparation", + "monomial swaps and phases", + "native-pair temporary implementation", + "global ownership and routing", + "caller heights and widths", + "idle packing realization", + "recursive/all-size transfer", + "actual physical-machine runtime" + ], + "original_full": { + "coordinate_C_pairs": 906752, + "native_calls": 2070, + "native_profile": { + "1": 1632, + "2": 74, + "3": 86, + "4": 104, + "5": 48, + "6": 42, + "7": 76, + "8": 8 + }, + "native_rank_mass": 3542, + "operations": { + "add": 3104, + "erase": 8, + "sign": 208, + "transport": 2070, + "zero": 8 + }, + "scalar_exact_half_bank_passes": 2686, + "scalar_exact_real_halves": 2750464, + "scalar_real_ADDs": 4457472, + "scalar_source_restoring_real_doublings": 2750464, + "scalar_unit_Gaussian_bank_ADDs": 4353, + "weighted_ADD_coefficients": { + "-1": 258, + "-1/2": 95, + "-1/4": 714, + "-2": 642, + "1": 159, + "1/2": 95, + "1/4": 534, + "2": 607 + } + }, + "projection": { + "coordinate_C_pairs": 679168, + "native_calls": 1597, + "native_profile": { + "1": 1264, + "2": 61, + "3": 74, + "4": 86, + "5": 33, + "6": 25, + "7": 46, + "8": 8 + }, + "native_rank_mass": 2653, + "operations": { + "add": 2310, + "erase": 8, + "sign": 104, + "transport": 1597, + "zero": 8 + }, + "scalar_exact_half_bank_passes": 2590, + "scalar_exact_real_halves": 2652160, + "scalar_real_ADDs": 3060736, + "scalar_source_restoring_real_doublings": 2652160, + "scalar_unit_Gaussian_bank_ADDs": 2989, + "weighted_ADD_coefficients": { + "-1": 175, + "-1/2": 47, + "-1/4": 714, + "-2": 342, + "1": 114, + "1/2": 47, + "1/4": 534, + "2": 337 + } + }, + "removed_program": { + "coordinate_C_pairs": 227584, + "native_calls": 473, + "native_profile": { + "1": 368, + "2": 13, + "3": 12, + "4": 18, + "5": 15, + "6": 17, + "7": 30 + }, + "native_rank_mass": 889, + "operations": { + "add": 794, + "sign": 104, + "transport": 473 + }, + "scalar_exact_half_bank_passes": 96, + "scalar_exact_real_halves": 98304, + "scalar_real_ADDs": 1396736, + "scalar_source_restoring_real_doublings": 98304, + "scalar_unit_Gaussian_bank_ADDs": 1364, + "weighted_ADD_coefficients": { + "-1": 83, + "-1/2": 48, + "-2": 300, + "1": 45, + "1/2": 48, + "2": 270 + } + }, + "scalar_invoice_contract": "Integer weighted ADDs repeat unit Gaussian ADDs. Each original fractional ADD temporarily divides its mutable source, performs its signed unit ADD, and restores the source by doubling before the next original event. The source-row audit proves exact divisibility at those reads. 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The 38 projection N-source count is a read inventory, not a new minimal-domain theorem. 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"e78b42372973e9f794b17cd0ff9dca0bd444b8af63ad28b4ddad1154a1dc67d2", + "scope": "One complete dense local physical fixture, exact primitive controls, and supplied schedule binding. Universal recipe covariance and B9 invariance are separate proof inputs. No full-WORD arbitrary-input admission, register-owner, routing, total width/cost or frontier claim.", + "source_object_sha256": { + "completion": "4eca9be38c194b8bcc9fe984ac4a5eb6e58503e204574d56f35a0a4b85ce9212", + "empty_to_full": "701ea529d1e7b171655c05debd974b1aa7e0a0cff2fb8e0a9a0753dd9c11ea9c", + "word": "c00db0d99b75817e7805b254f8b33af37d534bd11f0612aca80e16f140159315", + "x_to_empty": "05b5ee6a5e7069915ab756b612fa7abc8e3b486ccd9b4a247782a146b3aa6d5c" + }, + "status": "PASS_INDEPENDENT_LOCAL_PHYSICAL_INPLACE_COMPLETION", + "width_convention": "H_Y denotes actual unhalved common-frame Y. The 8H_X+95H_Y row attains the equal-bound peak103H; it is not a uniform two-parameter bound. Use the primary Pareto envelope for independent H_X,H_Y. Native adapters and temporaries are additional.", + "work_component_magnitude_bits_limit": 8224 + }, + "primary": { + "common_sufficient_admission": { + "N_in_2B9": 78, + "Y_in_4B9": 104, + "all_scalar_increments_module_integral": true, + "minimality_claimed": false, + "native_and_chart_module_lemmas": "Pinned PR3382 and PR3416 proofs, not re-proved by this matrix check.", + "other_in_B9": 176 + }, + "controls": { + "omit_Y0_redoubling": "complete Y source restoration", + "weaken_N100_to_B9": "non-module increment at 312" + }, + "endpoint_matrix_sha256": "8e738751d18e85e1395fa0a7affa2a81d283e41a1e7bdaa8a58b05b97d111e7d", + "entrance": { + "convex_reduced_scalar_envelope": [ + { + "after_prelude_operation": 929, + "bank": "X17", + "twice_y_weight": 190, + "x_weight": 8 + }, + { + "after_prelude_operation": 926, + "bank": "X17", + "twice_y_weight": 128, + "x_weight": 11 + }, + { + "after_prelude_operation": 925, + "bank": "X17", + "twice_y_weight": 98, + "x_weight": 12 + }, + { + "after_prelude_operation": 90, + "bank": "X17", + "twice_y_weight": 0, + "x_weight": 14 + } + ], + "operations": { + "add": 887, + "double": 103, + "half": 103, + "native": 145 + }, + "scalar_peak_after_entering_empty_frame": { + "after_prelude_operation": 929, + "bank": "X17", + "twice_equal_bound": 206, + "twice_y_weight": 190, + "x_weight": 8 + }, + "two_bound_scalar_envelope": [ + { + "after_prelude_operation": 929, + "bank": "X17", + "twice_y_weight": 190, + "x_weight": 8 + }, + { + "after_prelude_operation": 928, + "bank": "X17", + "twice_y_weight": 156, + "x_weight": 9 + }, + { + "after_prelude_operation": 926, + "bank": "X17", + "twice_y_weight": 128, + "x_weight": 11 + }, + { + "after_prelude_operation": 925, + "bank": "X17", + "twice_y_weight": 98, + "x_weight": 12 + }, + { + "after_prelude_operation": 924, + "bank": "X17", + "twice_y_weight": 49, + "x_weight": 13 + }, + { + "after_prelude_operation": 90, + "bank": "X17", + "twice_y_weight": 0, + "x_weight": 14 + } + ], + "width_interpretation": "Maximum of the displayed x_weight*H_X + twice_y_weight*H_Y/2 rows;103H when H_X=H_Y=H. H_X is after entrance conversion and H_Y is unhalved. Native conversions/temporaries are additional." + }, + "native_occurrences_bound": 2070, + "new_program_sha256": "e78b42372973e9f794b17cd0ff9dca0bd444b8af63ad28b4ddad1154a1dc67d2", + "normalised_endpoint_fields_checked": 358, + "normalised_matrix_entries_checked": 128164, + "original_opcode_counts": { + "add": 3104, + "erase": 8, + "sign": 208, + "transport": 2070, + "zero": 8 + }, + "projection_event_sha256": "66113bcd513a17eac24f43944a8759bdae1bb2a85e2b9900122f281c5c676dc8", + "projection_never_reads_or_writes_omitted": true, + "residual_nonzero_coefficients": 2500, + "residual_nonzero_rows": 52, + "retained_opcode_counts": { + "add": 2310, + "erase": 8, + "sign": 104, + "transport": 1597, + "zero": 8 + }, + "status": "PASS_SOURCE_BOUND_ENTRANCE_MATRIX_AND_ADMISSION" + }, + "schema_version": 1, + "scope": "An actual local in-place entrance completion, a source-bound all358 endpoint/module implication, one independent dense literal prefix, and a conditional rejected consumer budget. No global owner, full physical bill, all-size supplier, or new selected saving.", + "status": "PASS_P104_INPLACE_ENTRANCE", + "typed_receipt_control": "Boolean true is distinct from integer1." +} diff --git a/research/p104-caller-feasibility/consumer/inputs/SELECTED.json b/research/p104-caller-feasibility/consumer/inputs/SELECTED.json new file mode 100644 index 0000000000..b1fea0c944 --- /dev/null +++ b/research/p104-caller-feasibility/consumer/inputs/SELECTED.json @@ -0,0 +1,222 @@ +{ + "status": "Maintainer-reviewed conditional finite construction; see the integration receipt for publication and PR resolution status", + "kappa": "836330098538459/500000000000000000", + "decimal": "0.001672660197076918", + "source_prs": [ + 1094, + 1087, + 1082, + 1074, + 1068, + 1065, + 1063, + 1061, + 1056, + 1055, + 1053, + 1050, + 1042, + 1031, + 1028, + 1022, + 1018, + 1005, + 1004, + 987, + 942, + 890, + 870, + 869, + 858, + 799, + 741, + 699, + 685, + 676, + 664, + 660, + 659, + 656, + 655, + 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Local review and submission packaging used OpenAI Codex. +The new work is the same-partition 504-helper scalar architecture, its frozen +entrance selection, delivery-frame coalescing, literal global allocation, +targeted certificate reuse and complete new finite recount. + +The included Hamming inputs, Gaussian-dyadic Clifford compiler, primitive +scalar routines, rational moment engines and outer assembly descend from the +authors recorded in `SOURCES.json` and `inputs/PR523-ANCESTRY.json`. Original +source notices are retained. In particular, DreamingOfClouds' gauge/kernel +and paid-wrapper files retain their notice crediting Claude Opus 5.5 assistance; +those files are not presented as newly authored work. + +Dugongue's PR522 rank-sector coordinate-total principle was inspected and is +credited as a related idea. This increment does not import its ranksector99 +patch or add its reported gain arithmetically. Higherbeing's PR520 face-packet +geometry helped direct the structural investigation; its code is not copied. +The latest numerical comparison, Rohan Arun's PR527, is a comparison source. + +The reproduction wrapper deliberately separates fresh changed-word/global +checks from reuse of the byte-pinned completed baseline and unchanged bit +operator. Old finite receipts never stand in for the changed local word. diff --git a/research/p104-caller-feasibility/physical/inputs/LICENSE b/research/p104-caller-feasibility/physical/inputs/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/research/p104-caller-feasibility/physical/inputs/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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We also recommend that a + file or class name and description of purpose be included on the + same "printed page" as the copyright notice for easier + identification within third-party archives. + + Copyright [yyyy] [name of copyright owner] + + Licensed under the Apache License, Version 2.0 (the "License"); + you may not use this file except in compliance with the License. + You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + + Unless required by applicable law or agreed to in writing, software + distributed under the License is distributed on an "AS IS" BASIS, + WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + See the License for the specific language governing permissions and + limitations under the License. diff --git a/research/p104-caller-feasibility/physical/inputs/NATIVE-LINEAGE-NOTICE b/research/p104-caller-feasibility/physical/inputs/NATIVE-LINEAGE-NOTICE new file mode 100644 index 0000000000..380e979f0e --- /dev/null +++ b/research/p104-caller-feasibility/physical/inputs/NATIVE-LINEAGE-NOTICE @@ -0,0 +1,14 @@ +Anticipatory dirty borrowing: PR2226 (Cinna Davis / 1337isnot1337, with substantial OpenAI Codex assistance) is credited first. Its alias rule, changed-reference K_G handoffs, initial compensation and exact free-operator replay (vendored under new/code/borrow/vendor, see new/code/borrow/NOTICE-PR2226.md) are applied here to the T74 pivot-566+554 words; the native lowering, window-exact owner fill and independent audit of the borrow words are new in this package. Bootstrap carried-cutoff repair: PR1956 (Josie Elliston); Lemma G label/adapter checks and X/Y/Z mutants: PR1964 (thakrarsagar), extended here with borrow warp/zero-buffer controls. + +New research prepared by Rohan Arun with substantial OpenAI Codex assistance. Apache-2.0. Parent words and build recipe method derive from Jeremy Kothe PR1274 and Rohan Arun PR1218, with lineage credited in README.md. All inherited mathematical qualifications are retained. +Additional pivot555 and567 composition by Rohan Arun with substantial OpenAI Codex assistance. + +T74 exact-fill owner construction by Rohan Arun with substantial OpenAI Codex assistance. + +PR1377 grid refinement credited to Jeremy Kothe. Outer witness refinement by Rohan Arun with OpenAI Codex assistance; construction unchanged. + +Pivot-566 kernel, words, edits, rebuild.py and rebind.py: PR1625 (mdumitrean). Endpoint/outer-witness stacking, fine_cache.py and oracle stage by jeremykothe2 with oh-my-pi assistance. + +The preceding paragraphs are inherited source notices, not attribution of this derivative. +This joint twelve-source construction, generator, independent replay, hosting composition and package: Tekalign (@tekuuu), with substantial OpenAI Codex assistance. No independent human review claimed. +Credits: Cinna Davis/PR2226 anticipatory dirty borrowing; Tekalign/PR2436 four lifted targets; Jeremy Kothe/PR2462,2588,2673 source pipeline, source-label swap and order/fill; zxv/PR2530 eight aliases; Mason Hale/PR2696 concentrated source-partner assignment and independent local interpreter; Philippe Van Velzen/PR2559,2679 evacuation, six pre-life hosts and refit/alias; themilkman216/PR2621 priority order; Marius-Paul Dumitrean/PR2733 independent concentrated/pre-life composition; Vlado Vojdanovski/PR2322 generator utilities. PR2720's fixed-old-path cut obstruction motivates the changed premise. The retained owner/native/bit/modern outer lineage and their notices remain in the pinned source. New work Apache-2.0. diff --git a/research/p104-caller-feasibility/physical/inputs/NOTICE b/research/p104-caller-feasibility/physical/inputs/NOTICE new file mode 100644 index 0000000000..59d8e0cf31 --- /dev/null +++ b/research/p104-caller-feasibility/physical/inputs/NOTICE @@ -0,0 +1,415 @@ +A sharper exponent for integer multiplication +Copyright 2026 Douglas Colkitt + +This project includes unmodified source files from OpenAI's manuscript +"Integer multiplication below n log n" and its accompanying repository: +https://github.com/openai/math +Commit: adc7f1241b42e322a6451854ab7e4b4c146bf78a + +The original manuscript identifies OpenAI as its author. Its Apache-2.0 +license is retained at upstream/LICENSE. The exact source URLs and hashes +are recorded in upstream/manifest.json. Proposed modifications are supplied +as separate files under patches/; upstream source files remain unchanged. + +The original local research note, scripts, certificates, patches, and +documentation were prepared by Douglas Colkitt with assistance from OpenAI +Codex. The community release incorporates work by the contributors identified +in the notices below; it is not solely Douglas Colkitt's work. +This project is not an official OpenAI release or an OpenAI endorsement. + +Related contributions (not imported in this checkpoint): +Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset +motif, finite-alphabet transfer and a different compressed producer: +https://github.com/CrocSwap/integer-mult-bounds/pull/7 +The present checkpoint claims no priority for that motif. Related compressed +complex-network work was submitted by eumemic in PR #3: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +The pending contributions and their stronger bounds require their own review; +this notice does not represent adoption or verification of their claims. + +Additional community work, including parallel and superseded submissions, is +acknowledged in CONTRIBUTORS.md, with pinned submission metadata in +docs/research/contribution-snapshot.json. These acknowledgements do not imply +joint authorship of the checkpoint, incorporation of pending code, or verification +of submitted mathematical claims. Original source-specific notices remain in force. + +Community release (accepted by conditional maintainer audit): +The following original contributor notices apply to the imported PR #39 chain. +The preceding non-import statements describe the preserved 2^-30 checkpoint. + +Ternary five-subset construction and common-four-point resynthesis +Copyright 2026 Zhihao Chen (jacklightChen) + +This is Zhihao Chen's first submission of this specific construction to this +repository. Research, proof development, code and verification were prepared +with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by +the contributor. This is not independent review or an OpenAI endorsement. +Future research building on this contribution should explicitly acknowledge +Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and +retain the preceding contributors' attribution. This notice records research +provenance; the repository's Apache-2.0 license remains unchanged. + +Dependencies retained from eumemic's Claude-assisted PRs #3 and #5: +https://github.com/CrocSwap/integer-mult-bounds/pull/3 +https://github.com/CrocSwap/integer-mult-bounds/pull/5 +PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893 +These include complex_circuit.py, complex_network.py, fast_gaussian.py, +their generators, construction notes and certificates. The Gaussian input +scaling proof is corrected in this derivative; see the modification notice below. +Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank +sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6. +Their results and ideas are credited separately from this new construction. + +Bulk recursion and controlled tensor basis, 8 October 2026 +Copyright 2026 icekylinx + +The new projector batching, controlled simultaneous basis, mixed-width tape +recursions, whole-residual complex recursion, and dependency-path precision +guard in the batched-23 proof package are contributed by icekylinx, developed +with substantial OpenAI GPT-6 Astra assistance. Review corrections and +repository integration were prepared with OpenAI Codex assistance. They build on the retained +PR #7 finite producers and the preceding contributions credited above. +The new package retains the repository's Apache-2.0 license and the original +authors' attribution. It is not an official OpenAI release or endorsement. + +Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian +proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2). +The P=34p precision budget and asymptotic exponent are unchanged. New batching +checks are integrated into make verify. Existing attribution and licenses +are retained. + +Partial-swap extension, 8 October 2026 +Copyright 2026 icekylinx + +The partial-swap framing, binary retained-total triple construction, +dependency-preserving positive labels and carrier reuse, unequal (25,23,57) +common basis, improved complex batching, and exact assembly are contributed +by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance. +This extension directly inherits PR #10, commit +62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters +modify the retained paired-exclusion and shared-point implementations credited +above. The original licenses, attribution, and Gaussian correction are retained. + +Endpoint-gauge extension, 8 October 2026 +Copyright 2026 icekylinx + +The complementary auxiliary endpoint gauges, (32,30,40) controlled basis, +general nondegenerate binary phase residuals, retained-center complex producer, +updated path guard and exact assembly are contributed by icekylinx with +substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits +f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable +adapters retain the paired-exclusion and shared-point contributions credited +above. Original licenses, notices and the Gaussian correction are retained. + +Structured-basis and semantic-bulk extension, 8 October 2026 +Copyright 2026 icekylinx + +The selected (32,30,36) bit construction, A1/A5 block refinements, fixed +middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic +complex centers, complete data-front batching and circuit-specific assembly +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505. + +The semantic/bulk compatibility argument, literal scalar charge, product row +stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23, +commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints +are adopted from the same contributor's PR #21, +commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame +work and the earlier nested-basis contributions. + +Completed-child semantic precision, arbitrary-coordinate routing, phase-cell +Gaussian inversion and bulk tape transfer are credited to the RaD project +(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through +PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof +sources retain their separate CC0 license and original NOTICE under +references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI +Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra +assistance. These are source attributions, not claims about this session's +runtime model. Related contributions by Rohan Arun and Aurel Prosz remain +acknowledged in the imported notices. No exclusive priority or additional +license condition is asserted. + +Copied retained-center extension, 8 October 2026 +Copyright 2026 icekylinx + +The copied retained-center schedule in both orientations, its complex-phase +transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance. This extension inherits PR #32 at +0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work. + +The two-stage topology and paid copied-stream endpoint correction are due +to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab, +through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition, +9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil +Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a. + +The contiguous corner method, incidence factorization and exact partition +certificates are due to Rohan Arun (PR #31), method commit +02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate +specializes Dominik Scholz's parameterization (PR #33), +a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof +snapshots are preserved in references/copied-centers. Historical OpenAI +Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to +the respective imported sources. Existing PR #21/#23 and RaD attribution, +licenses and the Gaussian correction remain in force. + +Copied centers with reversed (23,25) data corners, 2026-10-08 +Rohan Arun with substantial OpenAI Codex assistance supplies the composition, +exact dimension23 controls and cost/assembly integration. James Chang's PR34 +supplies the reversed boundary family; icekylinx's PR36 supplies copied retained +centers and the selected complex graph. The balanced assembly remains attributed +to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan +Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx, +eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses. +This is not a claim of formal verification, new foundational rank identities, +global optimality or measured runtime speedup. + +Fixed middle basis with copied reversed corners (2026-10-08): +Rohan Arun, with substantial OpenAI Codex assistance. Composition and +simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34, +Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures, +eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed. + +Changed-graph composition with copied centers and fixed bases, 8 October 2026 +Prepared with OpenAI Codex assistance. +The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J +projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument, +Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and +Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods, +Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc) +PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40 +reversed integration, modular data tests and both-fixed baseline; +RaD (hipotures) PR41 changed scalar DAGs, alternating point order and +independent role compiler; RaD balanced routing/bulk interfaces, and all +retained predecessors. +Complete attribution and the conditional proof boundary are recorded in +research/copied-fixed/PROOF.md; imported originals and source pins are retained. +Original Apache-2.0 and CC0 notices remain applicable. + +Community follow-up integration (PRs #49, #45 and #26), 8 October 2026: +Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out +orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction +composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and +reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD / +hipotures's alternating pair order and independent physical role compiler (#41). +All predecessor attribution and conditional proof interfaces remain in force. + +Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic +proofs, finite tensor execution, profile precision accounting and mixed-center +reference checks (#45), with substantial OpenAI Codex assistance. See +research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution. +Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic +frame/movement/guard lemmas and independent paired-circuit checks (#26). Original +source notices and historical snapshots are preserved. Neither formal package +claims a full formal proof of the multiplication algorithm or a new kappa. + +Joint frame compilation of skip-prefix strips + +The local compiler and exact finite witnesses were prepared by eumemic with +substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic +Claude assistance supplied the unmodified PR #53 skip-prefix producer. +The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating +Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang, +Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt, +OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors +credited in the retained sources. See references/frame-compiler/pr48/NOTICE +and references/frame-compiler/pr53/NOTICE for their original attribution. +No authorship or review by those predecessors is claimed for this compiler. + +Joint dual-skip/frame-compiler composition (2026-10-08) +--------------------------------------------------- +Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip +scalar graph; original LICENSE and NOTICE are retained under +references/frame-compiler/pr55. eumemic with substantial OpenAI Codex +assistance: PR57 joint reversible frame compiler, serialized physical-word +replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex +assistance: this composition, independent integration and exact certificate. +Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all +predecessor authors retain the notices above and in pinned source files. +No original copyright or Apache-2.0 notice is removed. + +Ranked reclamation after the PR58 joint-dual composition (2026-10-08) +---------------------------------------------------------------- +Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical +slots by descending current frame rank, retaining slot ID as the tie-breaker; +complete replay, exact profiles, comparison and adversarial controls. +The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57 +compiler. Its original shared compiler remains byte-identical. The PR55 +producer and all preceding attribution remain unchanged. The complete PR58 +comparison certificate and its original source/proof provenance are retained +under references/frame-compiler/pr58. + +Skip-prefix strip producer, 8 October 2026 +By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5) +assistance. The skip-prefix leave-one-out strip layout in +research/skip-strips/skip_graph.py is new. Everything else reuses Chafik +Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification +code, exact data recovery and support-order sorting, together with: +- Rohan Arun's PR #44 weighted carrier matching optimizer; +- RaD (hipotures) PR #41 alternating point order; +- every predecessor credited above. +Complete attribution and the conditional proof boundary are recorded in +research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain +applicable. + +Local split-pair skip-prefix research continuation (2026-10-08) +Prepared with substantial OpenAI Codex assistance at the user's request. +New contribution: singleton/pair recursive partition refinement, finite summand +order and moment search, and verified composition with inherited paid clones. +Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips. +Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone +specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51 +whole-chain/source-partition cloning and earlier producer/interfaces. +Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all +stated historical AI assistance. All predecessor notices remain applicable. + +Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones): +Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain +source-partition clone operation is adapted from RaD / hipotures, PR #51, +with original envelopes retained here. The scalar base is Avi Eisenberg's +PR #53 skip-prefix layout, prepared with Anthropic Claude assistance. +All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain +in force. This extension is provided under the repository's Apache-2.0 terms. + +Community review checkpoint #50–#61, 8 October 2026 +Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex. +Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude. +Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance) +and dual-suffix strips (#55, Anthropic Claude assistance). +Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex. +Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked +reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame +composition (#56), with Anthropic Claude and stated Codex validation assistance. +RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones +(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone +composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter +refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with +his disclosed multi-tool and Codex assistance. +Parallel #50/#52 records are reviewed and credited without replacing the earlier +climbed-48 implementation; their exact commit history is retained. The separate +#51 witness is retained as research; its source-graph/negative-basis data proof +has not received the same full replay as #56's consumed compiler machinery. +See docs/research/community-round2-review.md for precise validation boundaries. +All earlier licenses, contributions and notices remain applicable. + +Interval strips and core-aware pair assembly + +The interval leave-one-out strips and the core-aware group-pair assembly in +research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic +Claude assistance. They build on PR #53's skip-prefix pipeline and its +inherited PR #48 sources. The stacked witness in research/pair-assembly/frame +uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier +are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and +verify_skip_frame.py. Original notices are retained. + +Stopped product-ring extension, 9 October 2026 +Copyright 2026 icekylinx + +The opposite-bank generic projector factorization, componentwise atom-ring +adapters, stopped recurrence and outer ordinary-interchange conversion, +aligned pair-star producer with rational centers, exact denominator-21 +grid and selected (23,23)/(24,24) composition are contributed by icekylinx +with substantial OpenAI GPT-6 Astra and Codex assistance. This extension +builds on merged PR #36, 11817ccacb564bb7f98789c20dc11d3fece207e3, and is +integrated on upstream main 56b66d58297deca1d7dd130247d720e960f77a37. + +The retained ordinary leaf uses the preceding projector, corner and +copied-center proofs. The selected two-stage topology retains Aurel Prosz +(Paureel), Swapnil Jain and Zhihao Chen's credits; the semantic assembly +retains PR #21/#23 and RaD's attribution. Paired producers, carrier matching, +original source notices and each imported license remain unchanged. + +Partial-gauge extension, 9 October 2026 +Copyright 2026 icekylinx + +The pair-first cube assembly, compatible backward frame enlargement, +partial source-gauge schedule and stopped whole-projector composition are +contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex +assistance, extending PR #104 at 948ce1510df750f4c18b96bdaef436a86f8bf834. + +The physical deferred bit word, reflected event accounting, fan-order +clarification and signed two-stage endpoint are adopted from Zhihao Chen +(jacklightChen), PR #97, e15350b66e4bf796153a68c240a6cc1b788abe3e, with +Codex assistance. Its deferred readouts, V leaves, lifted frames and frozen +witness originate in Swapnil Jain's 741e7aa078392553815df7926ee17ac5e25a8c38, +with the original Claude disclosure retained. Cyclic interval and core-aware +pair primitives build on Avi Eisenberg (ikeboy), PR #62, +ad0f25ff7b23cff7f08ad237c2254e6ecf74257e, with Anthropic Claude assistance. +Prior two-stage, copied-center, ordinary-leaf, semantic/bulk, routing and +precision credits remain in force. Imported source notices and licenses +are preserved under references/partial-gauge/; see SOURCES.json. + +Three-stage cover extension, 9 October 2026 +Copyright 2026 icekylinx + +The arbitrary-subspace Clifford frame theorem, three-stage Cayley geometry, +weighted q-adic GL cover, unit-lower weighted compiler, charged local-ring +fallback, uniform batching, internal row borrowing and exact composition +are contributed by icekylinx with substantial OpenAI GPT-6 Astra assistance. This +repository integration uses Codex assistance and extends +PR #115, cf60442983c153a3a0f5272ea4713f99eba13c86. + +The selected local complex DAG and support/label replay are adopted from +Copyright 2026 eumemic, PR #117, cbb05ce504d571546d9b7794c186a613c659c3bf, +with its original Apache-2.0 terms and Claude assistance disclosure. +The unchanged bit physical word retains Zhihao Chen (jacklightChen), +PR #97, and Swapnil Jain's underlying witness and assistance notices. +The prior opposite-bank, stopped ordinary-leaf, copied-center, topology, +semantic/bulk, precision and analytic credits remain applicable. +Original source notices and license bytes are preserved in +references/three-stage-cover/pr117/ and references/partial-gauge/. + +Paired-cube and shared-core extension, 9 October 2026 +Copyright 2026 icekylinx + +The paired-coordinate triple-cube identity, signed overlap channels, +original-source involution, coordinate-star centers, concrete frame/carrier +compiler, chronological source gauges, PR97 gauge-subset selection, +orthogonal cross-stage routing and exact supplier/assembly integration +are contributed by icekylinx with substantial OpenAI GPT-6 Astra assistance. +Repository integration uses Codex assistance and extends PR #130 at +6a9970a530119174507904e23592fd59ede19a5d. + +The substantial completed-core workspace-sharing principle is credited to +an664, PR #128, 530588a019b4a74f09180680c9e3961bf649ec89, with its reported +OpenAI Codex assistance. No source code, partition or serialized witness +from that PR is imported. The new routing and paired-motif integration +are described separately and claim no exclusive priority for broad sharing, +paired-coordinate, Fourier or carrier-matching ideas. + +Selected coarse queries restrict the retained eumemic PR #117 positive DAG; +its original Apache-2.0 and Claude assistance notices remain unchanged. +The bit word and original frames retain Zhihao Chen's PR #97 and Swapnil +Jain's frozen witness, notices and historical assistance disclosures. +Earlier generalized Clifford, three-stage, uniform weighted recursion, +ordinary-leaf, semantic/bulk, precision and analytic credits remain in force. +Source-specific license bytes are preserved under references/. + +October 9 recycled-bit integration: +DaysSky (#150), William Porter/hpst3r (#147), Thomas Marchand/Th0rgal (#146), +Rohan Gupta/gupt1156 (#148), James Chang/jamesyc (#124), SovereignSteak (#122). +The original notices and assistance disclosures are retained under research/, +including research/recycled-bit-integration/NOTICE. Andrew Barnes/Bortlesboat +(#101) repairs shared verifiers using rfu08's #64 counterexample. rfu08's +scoped finite and formal-transfer packages are included separately; they do +not establish the full multiplication theorem. Earlier and parallel credits +remain applicable. Douglas Colkitt integrated these with OpenAI Codex assistance. + +SovereignSteak PR151 independently supplies the matching gauge/recycling +composition and the selected 473/10^6 atom refinement; its original package +and assistance disclosure are retained under research/gauge-recycling/. + +October 9 coordinated-frame and completed-entrance-bank integration: +Dugongue PR186, 166a34d75e853e933855f0f7e940fe77c4bb6b8d, builds on +Chafik Boukhalfa/chafreaky's PR181, 7fb2194801e3a10f54772c7f0d5505035a4fc0ad, +and eumemic's PR168 v4, 4a3c769e5c5430e7114c4d3e099ff34664677f17. +The frozen package and prerequisite archive preserve all author, source-license +and assistance notices, including PR175's compiler optimization. DaysSky's +carrier closure, James Chang's terminal substitution and balanced assembly, +geckods' stopping refinements and all preceding framework credits remain. +Rohan Arun's PR185 bootstrap and chafreaky's PR182 bit refinement are reviewed +parallel contributions; their gains are not added to the selected witness. +Douglas Colkitt integrated the package and supplied the bank scheduling +supplement with OpenAI Codex assistance, under Apache-2.0. 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zz{y_5OrKY7AnuRLPi;fVsdM?po({Ijeyn_xidx$D$~QH4zntFJ<(p#nx5_u#26|BW zCVx-m8`T!u1yqYu`qKf`04o1f=U*(g*L(p|{Z}_s=Z~s4q%VCu*AJn3Q$brYEcgTi zn6voZ2{s)ScUM*1-BQEUt!<>GRl4(?cPj3biX#mjR%;SR?bg3 zylwD-6dSF!cQTT9n@=;IyYFJQM&4~2#`A~a+j@E&-|hd>R)BQ_b!lkNXRJOUI7;Pr zWP&85OQtpT2qOs b?U1q5Vu4EI0{rj){m=gci66iEb|wb^K8bPS literal 0 HcmV?d00001 diff --git a/research/p104-caller-feasibility/physical/inputs/PR1862-NOTICE.md b/research/p104-caller-feasibility/physical/inputs/PR1862-NOTICE.md new file mode 100644 index 0000000000..24461eddc1 --- /dev/null +++ b/research/p104-caller-feasibility/physical/inputs/PR1862-NOTICE.md @@ -0,0 +1,50 @@ +# Source attribution and license + +New research, code, and verification used substantial OpenAI Codex +assistance under the user's direction. Separate agents developed the +input construction and reviewed its algebra, native phases, and literal +programs. No independent human review is claimed. New material uses the +repository's Apache-2.0 license. + +The package reads immutable source objects at commit +`bce54fb3f895cbe5cd4c0eb477c3afeed100190f`. It does not change the frozen +source archive or copy a predecessor package. Exact source pins are in +[SOURCES.json](SOURCES.json). The original notices are retained as exact +files under `notices/`. + +The local word comes from the gauge44 lineage. Its +[notice](https://github.com/CrocSwap/integer-mult-bounds/blob/bce54fb3f895cbe5cd4c0eb477c3afeed100190f/research/gauge44-slots-t16/NOTICE.md) +credits @icekylinx, with OpenAI GPT-6 Astra assistance, for the source +gauge and related local construction. The +[construction notice](https://github.com/CrocSwap/integer-mult-bounds/blob/bce54fb3f895cbe5cd4c0eb477c3afeed100190f/research/gauge44-slots-t16/construction/NOTICE.md) +preserves the factory, K-triangle, porting, joint-prefix, and HPE lineage. + +The retained +[t16 notice](https://github.com/CrocSwap/integer-mult-bounds/blob/bce54fb3f895cbe5cd4c0eb477c3afeed100190f/research/gauge44-slots-t16/t16/NOTICE.md) +credits Hao Yan (@FanPUYen) for the integration; Jeremy Kothe +(@jeremykothe2) for the [PR #799](https://github.com/CrocSwap/integer-mult-bounds/pull/799) +local supplier; and Chafik Boukhalfa (@chafreaky) for the +[PR #741](https://github.com/CrocSwap/integer-mult-bounds/pull/741) +frame work. These sources and their earlier attribution are retained +inputs, not new results of this package. Name-to-account evidence is in +the pinned +[contributor record](https://github.com/CrocSwap/integer-mult-bounds/blob/bce54fb3f895cbe5cd4c0eb477c3afeed100190f/CONTRIBUTORS.md). + +The complete +[upstream notice](https://github.com/CrocSwap/integer-mult-bounds/blob/bce54fb3f895cbe5cd4c0eb477c3afeed100190f/research/gauge44-slots-t16/UPSTREAM-NOTICE.md) +retains DreamingOfClouds, earlier cold-end and joint-prefix work, other +contributors, source pins, licenses, and AI disclosures. It is copied +without edits. The selected slot-word lineage also credits @rohanarun +for [PR #987](https://github.com/CrocSwap/integer-mult-bounds/pull/987) +and NewBArch for [PR #869](https://github.com/CrocSwap/integer-mult-bounds/pull/869) +in the pinned +[local README](https://github.com/CrocSwap/integer-mult-bounds/blob/bce54fb3f895cbe5cd4c0eb477c3afeed100190f/research/gauge44-slots/README.md). +NewBArch is the credited source name; no account identity is inferred. + +The portable source loader, sparse replay, and exact native interpreter +come from this centre-encoding campaign. They retain the same source +objects used in [PR #1719](https://github.com/CrocSwap/integer-mult-bounds/pull/1719), +but this package does not depend on that PR being merged. The new verifier +does not import the source-code producer or the exploratory native +compiler. The historical global owner map and final invoice are not +replayed or improved by this local package. diff --git a/research/p104-caller-feasibility/physical/inputs/PR1972-NOTICE.md b/research/p104-caller-feasibility/physical/inputs/PR1972-NOTICE.md new file mode 100644 index 0000000000..eb4ac7c07f --- /dev/null +++ b/research/p104-caller-feasibility/physical/inputs/PR1972-NOTICE.md @@ -0,0 +1,11 @@ +New material: Rohan Arun, with substantial OpenAI Codex assistance. Apache-2.0. +Vendored PR1940 verifier and schedule: Adam Gall, with substantial OpenAI +Codex (gpt-6-astra) assistance; Apache-2.0. The source docstring is retained. +The P104 fixture comes from Josie Elliston / PR1071, with substantial Claude +Opus 5.5 assistance, through the hash-pinned PR1940 input. The decoder, +32-path bound and their lineage belong to PR1071, Ali Romman / PR1125, +themilkman216 / PR968, DreamingOfClouds / PR717, PR446/PR595 and GamingPuzzled +/ Joel Pulikkan / PR620. None of those results is claimed new here. +The generic dirty-cancellation identity is not claimed new. PR673 and the +existing dirty-helper source/target compensation methods are adjacent +precedents. No literature-priority guarantee or independent human review. diff --git a/research/p104-caller-feasibility/physical/inputs/PR3382_PROOF.md b/research/p104-caller-feasibility/physical/inputs/PR3382_PROOF.md new file mode 100644 index 0000000000..10b3202c78 --- /dev/null +++ b/research/p104-caller-feasibility/physical/inputs/PR3382_PROOF.md @@ -0,0 +1,445 @@ +# A phase-complete Gaussian entrance for one literal P104 collector + +This result changes the admissible numerical states of one fixed collector. +It does not change its scalar/frame word, claim a new precision threshold, +or provide the missing complete P104 correction and supplier invoice. +The construction is motivated by Clifford-invariant and Barnes–Wall lattice +methods. The proof below uses the repository's exact Gaussian normalization; +it does not invoke a lattice classification theorem or claim a new lattice +family. + +The source is ywz65's PR #2586, head +`7953c9a8f788a8de5cf2ced63d9a61b67c22c6f1`, retained at +`research/p104-rounded-collector/inputs/WORD.json` and `NATIVE.json.gz`. +Tekalign's PR #3025 binds its first collector and supplies the literal signed +floor pair. Ross Richardson's PR #3068, head +`7d2c519a1fdcc6bf66f6f08757eed7c48762d3f2`, supplies the neighboring +period-domain contract and explicitly leaves a larger state exactness domain +open. Their constructions, inverses, source binding and earlier bounds retain +their credit. Exact consumed bytes and the isolated replay are recorded by +the accompanying source manifest and receipt. + +## 1. Coordinates and the explicit code + +Put `pi = 1+i`, so `pi^2 = 2i` and `1/pi = (1-i)/2`. An array of +`2^r` Gaussian integers is a function on the binary cube. It has unique +multilinear Newton coefficients: + +\[ + f(x)=\sum_{S\subseteq\{0,\ldots,r-1\}}a_S x^S, + \qquad x^S=\prod_{j\in S}x_j. +\] + +Uniqueness follows by Boolean differences, or by the triangular evaluation +matrix indexed by subsets. Define the Gaussian module + +\[ + \mathcal B_r=\{f:a_S\in\pi^{|S|}\mathbb Z[i]\text{ for every }S\}. +\] + +Its encoder is explicit: + +\[ + E_r=E_1^{\otimes r},\qquad + E_1=\begin{pmatrix}1&0\\1&\pi\end{pmatrix}. +\] + +Thus a coefficient pair `(c0,c1)` becomes `(c0,c0+pi*c1)`. Bit `j` is +the address bit `1< x xor y = x+y-2xy`, and gives + +\[ + (a,b,c,d)\longmapsto + (a,\ b+c+\pi d,\ c,\ (i-1)c-d). +\] + +The phase `CZ=(-1)^{xy}=1-2xy` gives + +\[ + (a,b,c,d)\longmapsto + (a,\ b,\ c,\ ia+(i-1)(b+c)-d). +\] + +These formulas use `x^2=x`, `y^2=y` and `2=-i*pi^2`. The other bits contribute +the same common coefficient factors, so the formulas apply at every rank. +Bit swaps simply permute coefficient indices. The listed self-inverse gates +remain self-inverse under conjugation; `C` and `S` have the integral inverses +shown above. Global Gaussian units preserve the module. Thus every full source +wrapper, and its inverse, preserves `B_r`. + +No unrestricted phase or permutation is admitted by this argument. For example, +the cubic phase `(-1)^(x0*x1*x2)` applied to the constant one produces Newton +coefficient `-2` at degree three. It is not divisible by `pi^3`, so the result +leaves `B_3`. The quadratic source schema matters. + +The old structured phase witness is a positive control here. The constant one +and `i^{x_j}=1+(i-1)x_j` both belong to `B_r`, because `i-1=i*pi`. +The latter leaves the older `Gamma` period lattice, as credited in PR #3068. +That earlier counterexample did not claim that it creates a lifting error. + +## 5. One complete source-bound collector + +Use zero-based events **2025–2039** of the retained PR #2586 word. They are: + +1. Allocate zero private `C` at the common source frame. +2. Add `D31,D30,D29,D28,D27` to `C`, in that order. +3. Apply the literal rank-seven transport `U` at event 2031. +4. Add `C` to the arbitrarily dirty query `Q7` at its common frame. +5. Apply the separately archived return `V` at event 2033. +6. Subtract the five original sources in reverse order; erase exact zero `C`. + +The source arrays have 512 complex entries and nine address bits. Both native +recipes have the form `M_left C_0 ... C_6 M_right`. The complete surrounding +wrapper acts on all nine bits, so the contract is `B_9`, not an unproved +rank-seven block restriction. Source authentication binds the two event +occurrences, their frames, the common-chart ADDs and their actual recipes. +The predecessor's exact native interpretation is retained; the finite operator +check of `VU=I` is separate from the lattice exactness argument. + +Assume the five source arrays and the initial query belong to `2^-f B_9`. +They are otherwise arbitrary, independently dirty and potentially correlated. +The five sources remain available and unchanged across this whole interval. +The private `C` is owned and starts zero. No alias of those distinct roles or +nonzero private initialization is granted. + +Let `s` be the sum of the five sources. Module closure gives `s in 2^-f B_9`. +By Sections 3–4 both actual transports execute their exact ideal maps on this +domain. The query becomes `Q7+U*s`. Since `VU=I`, the private register returns +to `s`; subtracting the unchanged sources makes it exactly zero. Thus the +literal endpoint is + +\[ + (D31,\ldots,D27,Q7,C=0) + \longmapsto(D31,\ldots,D27,Q7+U\sum_jD_j,C=0). +\] + +The query remains in the same declared lattice and grid. There is no rounded +query defect, per-input grid selection, residue history or numerical downcast +in this restricted-state execution. This permits the separately archived `V`; +the unrestricted approximate lifting contract instead needs its paired inverse. +They must not be interchanged when counting operations. + +This is a boundary assumption at the actual collector cut. The earlier producer +has not been proved to supply this state for arbitrary unrestricted inputs. +The later whole word also has additional operations. A repeated collector is +valid only when its sources, frames, permissions and declared lattice are +available at its own cut. + +## 6. Quarter ADD and the exact meaning of an encoder + +Whole-array ADD by any Gaussian-integer coefficient preserves `B_r`. For an +integral array `z`, a quarter source `z/4` belongs to `B_r` exactly when +`z` belongs to `4B_r`. Integral components alone do not imply that condition. +At rank one `(4,0)` belongs to `B_1`, but `(4,0)/4=(1,0)` does not. Extend +the pair constantly in the other eight bits for the actual nine-bit counterexample. +Conversely `z=4E_r c` always has the admissible quarter `E_r c`. +The named collector contains only unit ADDs, so this counterexample marks the +external interface; no quarter instruction is treated as free within its bill. + +Encoding arbitrary raw coefficients `c` as `E_r c` changes the logical action +of a physical native map `U` to + +\[ + T=E_r^{-1}UE_r. +\] + +The gate formulas prove that `T` is an explicitly described Gaussian-integral +automorphism for the stated alphabet. They do **not** say `UE_r=E_rU`. +Already `C E_1 != E_1 C`; a control checks this distinction. Substituting this +representation into a caller expecting a different map requires its own +intertwining adapters and their complete costs. + +For clarity, one fully specified optional cold preparation realizes this +different `T` contract. Keep five arbitrary raw Gaussian coefficient source +arrays borrowed and unchanged, and give the query mutable ownership. Allocate +five zero source banks, copy the borrowed sources into them by five full-array +ADDs, and encode the five banks and query. Run the original collector on these +six encoded fields. Decode the query and all five banks. Each source bank is +then exactly its original raw source; subtract that borrowed source, check zero +and dispose of the bank. The query endpoint is `q+T*sum(sources)`. + +This construction uses six encodes, six decodes, five copy ADDs, five cleanup +ADDs and five additional owned array lifetimes. It demonstrates a complete +logical codec schedule with literal restoration. It does not admit that `T` +as a requested recursive caller, give a free borrowed-input conversion, or +establish an advantage over an existing `U` implementation. + +## 7. Gate, codec and storage ledger + +All counts in this section concern a direct scalar reference with explicit +array access. They are not tape time, native child tariffs or a lower bound. +Gaussian units, signed arithmetic and addressing are separate operations. + +An encode or decode sweep has `r*2^(r-1)` tensor pairs. Encoding a pair uses +one multiplication by `pi` and one Gaussian ADD. Decoding uses one Gaussian +subtraction and one exact division by `pi`. Multiplication by `pi` is +`(a-b,a+b)`; exact division is `((a+b)/2,(b-a)/2)`. Thus each encode pair costs +four real additions/subtractions, while each decode pair adds two exact real +halvings. Each loads four real components and writes two. An in-place sweep +uses the owned numerical array and four real work words; loop/control storage +and physical routing are additional. Borrowed input cannot be overwritten to +obtain this in-place price. + +At `r=9`, each direction has **2,304 pairs**. The optional cold schedule therefore +adds 13,824 `pi` multiplications, 13,824 exact `pi` divisions, 110,592 real +additions/subtractions, 27,648 exact real halvings and its ten full-array copy/ +cleanup ADDs. Those ten ADDs add 10,240 real additions/subtractions, 20,480 +real-component reads and 10,240 writes. The codecs add 110,592 component reads +and 55,296 writes. Five extra owned banks add 2,560 complex words and 5,120 +component initializations and zero checks each. These quantities are additional +to the direct collector below; they are not paid by an abstract rank count. + +For the literal collector, both seven-stage transforms use `7*512=3,584` +pair applications altogether. Each credited signed-floor pair costs eight +real additions/subtractions, four real floor halvings and one Gaussian quarter +turn. The eleven field ADDs cost `22*512` more real additions/subtractions. +The four actual wrapper cycle counts, in chronological order, are + +\[ + U_{right}:64,\quad U_{left}:128,\quad V_{right}:160,\quad V_{left}:64. +\] + +The credited one-zero-Gaussian-scratch cycle algorithm uses `N+c` swaps for a +wrapper with `c` cycles and `N` unit phase applications. Here it gives **416 +cycles and 2,464 swaps**, plus 2,048 phase applications. The old paired-inverse +schedule's 384 cycles and 2,432 swaps do not price these separately archived +return wrappers. The phase acts on the cycle scratch before each swap, so its +arithmetic is counted without an extra full-array phase pass. + +| Direct collector operation | Count | +|---|---:| +| Signed-floor pair applications | 3,584 | +| Real additions/subtractions, including all eleven field ADDs | 39,936 | +| Real floor halvings | 14,336 | +| Pair Gaussian quarter turns | 3,584 | +| Actual wrapper Gaussian swaps | 2,464 | +| Actual wrapper unit phase applications | 2,048 | +| Butterfly real-component reads / writes | 14,336 / 14,336 | +| Field-ADD real-component reads / writes | 22,528 / 11,264 | +| Wrapper-swap component reads / writes, including scratch | 9,856 / 9,856 | +| Private initialization / zero-check component inspections | 1,024 / 1,024 | + +The 10,240 source-component reads are a subtotal of the field-ADD reads, not an +extra charge. The direct contract has five borrowed source arrays, one mutable +query, one owned zero private array and one zero Gaussian wrapper scratch, +with constant pair work. The optional cold schedule supplies the five source +arrays by additional owned copies. Source plans, range/type validation, +permissions, address/control work, physical movement, allocator behavior, +recursive children, precision metadata and final endpoint consumption require +their actual caller's tariff. They do not acquire a zero price from these +scalar counts. + +## 8. Finite headroom + +Let `H` bound the absolute value of every real and imaginary component at a +codec's own entrance. During an encode the exact largest real component row +sum after at most `r` factors is bounded by + +\[ + M_r=\sum_{k=0}^r {r\choose k} + (|\Re\pi^k|+|\Im\pi^k|). +\] + +This follows by expanding a tensor row; its entries are powers of `pi`, one +for each subset. A smaller partial row is covered by the same nonnegative +bound. For `r=9`, `M_r=3363`. Thus `M_r H` bounds stored encoder components; +`3 M_r H` is a conservative bound for its two-step arithmetic temporaries. + +A row of a `k`-factor inverse sweep is a signed sum of `2^k` inputs divided by +`pi^k`. Its real component row sum is +`2^k (|Re pi^-k|+|Im pi^-k|)=|Re pi^k|+|Im pi^k|`, at most +`2^ceil(r/2)`. Therefore decoder components are bounded by `2^ceil(r/2) H`, +and its subtraction/numerator temporaries by four times that amount. These +are sufficient arithmetic bounds, not a compression or precision advantage. + +For the direct collector suppose its six admitted entrance fields have +integer numerator components bounded by `H`. The sum of five sources has +Hilbert norm at most `5 sqrt(2N) H`. Every exact native prefix is unitary, +including each wrapper. At `N=512`, **160 H** bounds every native-prefix real +component; **161 H** bounds the updated query. A conservative signed-floor +pair scratch bound is **800 H**. Gathers and ungathers are bounded sums of at +most five unchanged sources. Partially written stages store either preceding +or completed pair values, so these same bounds cover the entire execution. + +For the optional cold caller, now let `H` bound its **raw coefficient** entrance. +Encoding gives `3363 H`; the collector therefore gives an encoded query bound +`161*3363 H=541443 H`. Decoding that query gives at most +`32*161*3363 H=17326176 H`. The conservative complete scratch bound is four +times this last quantity, **69304704 H**, which also dominates the encoder, +native pair, source-bank decoding and cleanup temporaries. These composed +bounds make the optional caller's finite-width obligation explicit; they are +not measured peaks or necessary widths. + +For a nonnegative integer component bound `M`, +`1+ceil_log2(M+1)` signed bits suffice. This states an explicit finite range; +an actual fixed-width implementation must use that range, retain the required +grid and charge its bit arithmetic. The older sharp scalar-grid/Clifford +denominator results remain credited and unchanged. + +## 9. Evidence boundary and stopping decision + +The written arguments hold at every finite rank. The new managed-Python model +and finite source checks are bounded by nine address bits, 512 complex entries +and 8,192 magnitude bits per admitted input or returned array component. +Signed storage may require another bit; exact arithmetic temporaries have the +additional finite headroom derived above. The functional model allocates fresh +lists, while the direct ledger prices the separately specified in-place codec +and credited cycle-scratch algorithm. It is not a measurement of Python +allocation. Membership checks and snapshots inside verification are test work; +a production caller must establish or pay for its lattice entrance. +Managed allocation and verification snapshots are not a physical memory +implementation. Exact checks use explicit exceptions, including under Python +optimization. + +Finite verification binds the two archived recipes, checks exact operators and +both literal directions on admitted states, tests dirty collector endpoints, +and exercises the missing-prefix, phase-alphabet, wrong weighting, quarter-ADD, +intertwiner and source/invoice failure boundaries. The separate checker uses +its own representation and does not derive a nonlinear universal theorem from +finite basis samples. Source-native correctness, physical ownership, eventual +recursive prices and human/proof-kernel admission remain separate premises. + +The result stops at a phase-compatible exactness theorem, one actual complete +local collector, an explicit codec/intertwiner, and their full direct logical +ledger. It neither proves that earlier arbitrary P104 inputs satisfy the +entrance nor extends the contract to the later quarter ADDs. A larger caller +needs an actual admitted source of this state and a compatible fully charged +consumer. No selected frontier, all-size supplier, new scalar-grid guard, +physical storage saving or new kappa follows. + +Prepared by Clear1nsight with substantial OpenAI assistance. Separate automated +derivation and review are not independent human or formal-kernel verification. +Apache-2.0; predecessor authors and original source notices retain their credit. diff --git a/research/p104-caller-feasibility/physical/inputs/PR3416_PROOF.md b/research/p104-caller-feasibility/physical/inputs/PR3416_PROOF.md new file mode 100644 index 0000000000..276f61cb64 --- /dev/null +++ b/research/p104-caller-feasibility/physical/inputs/PR3416_PROOF.md @@ -0,0 +1,117 @@ +# Exact covariance of the archived P104 native recipes + +All statements concern the two frozen PR2586 inputs in SOURCES.json, at nine +address bits. The ground field is Q(i), and arrays have 512 complex entries. +The word and native archive are ywz65's work. This package supplies a separate +finite verification of their native change-of-chart identities. It does not +construct a new native word or strengthen the original native invoice. + +## Canonical charts and the precise claim + +Write computational basis vectors as |x>, for x in F_2^9. For an independent +ordered frame W=(w_0,...,w_(r-1)), complete these columns greedily with the +standard basis e_0,...,e_8. Let G be the resulting binary matrix, A=G^-1, +and Q=I+A^T A over F_2. Set + + q(x) = sum_j Q_jj x_j + 2 sum_(j = i^q(x) |A x>. + +The phases use the binary representatives 0 and 1 of Q. Define + + C(a,b) = ((a+b+i(a-b))/2, (a+b-i(a-b))/2). + +For 0 to i^p(x) |B x+b>, using its archived address rows, offset, +linear Z4 phase, quadratic binary rows and constant Gaussian phase. The +verifier validates bijectivity and all numeric ranges before computing its +operator. All arithmetic is integral or Gaussian dyadic, with no numerical +tolerance and no floating point. + +The certified finite theorem is + + U = Delta_new Delta_old^-1 + +for every one of the 1,245 archived records, as operators on every vector in +Q(i)^512. Their 2,070 occurrences are each matched to the literal word's +recorded old frame, new frame and positive rank. Their chronological incoming +frames, all ADD common-frame constraints, private frame lifetimes and final +frames are checked. This covariance theorem does not itself prove the scalar +word's dirty restoration or zero erasure values. Those are separate obligations. + +## Complete operator comparison + +Use P(p,x,z)=i^p X^x Z^z, so + + P(p,x,z)|v> = i^(p+2 z.v)|v+x>, + P(p,x,z) P(q,u,w) = P(p+q+2 z.u, x+u, z+w). + +Phases are reduced modulo 4 and binary sums are XOR. A signed tableau records +the exact conjugates of the nine X_j and nine Z_j, including their phases. +For a one-coordinate C, + + C X C^-1 = X, + C Z C^-1 = -Y = i^3 XZ. + +Its inverse sends Z to Y=i XZ. These formulas follow directly from the +stated two-by-two matrix. `c_table` uses those identities. For every monomial +appearing in an actual recipe or canonical chart, `monomial_table` reconstructs +its candidate Pauli images, then checks each identity on all 512 computational +columns. In particular, for M|v>=i^q(v)|a(v)>, conjugation has address difference +`a(v+x)+a(v)` and phase difference `p+q(v+x)-q(v)+2 z.v`. +The check compares these with the proposed output Pauli at every v. No +inference from rank, unsigned symplectic data, or a few sampled inputs is used. +The product law then composes the exact signed actions through each circuit. + +Here is why those 18 identities determine an operator up to a scalar. +If invertible U and V have the same signed conjugation action, V^-1 U +commutes with every Z_j and X_j. Commuting with all Z_j makes V^-1 U diagonal +in the computational basis, because distinct addresses have different joint +Z eigenvalues. Commuting with every X_j makes its diagonal entries equal +along every cube edge. The cube is connected, so V^-1 U=lambda I. All factors +here are unitary and hence invertible. No external irreducibility theorem is +needed for this finite argument. + +Finally the checker compares the complete, exact nonzero column U|0> with +V|0>. Equality forces lambda=1. The column is stored as Gaussian integer +numerators over one power of two. Removing only common factors of two gives +a unique representation for a nonzero dyadic column. The stored receipt +contains a digest of each fully compared tableau and anchor, alongside frames, +rank and occurrences. Digests summarize the comparisons; the verifier does not +accept an identity by comparing hashes of operators. + +This criterion is established predecessor mathematics. In particular, +Tekalign's PR3218 supplies a separate Pauli-plus-anchor comparator and proof. +The present contribution is its independent implementation and exhaustive +application to the PR2586 corpus required by PR3406's stated proof dependency. + +## Connection to the Newton source theorem + +PR3406 at `18a054fd585ab4b2010770ec83cba0c9f28184e3` proves its sharp source +criterion under these exact native identities. This certificate supplies that +finite inherited premise. With the other hypotheses and proof of that pending +result retained, its entrance remains 4 B_9 on 104 independent Y inputs, +2 B_9 on 78 independent N inputs, and B_9 on the other 176 public inputs. +Here B_9 is the Gaussian Newton module introduced for this application by +Clear1nsight/PR3382. This does not independently recertify every other lemma or +turn that conditional restricted-state contract into an actual-caller theorem. + +The result is author-checked exact arithmetic, with a separately implemented +comparison path and independent dense controls. It has no human or proof-kernel +review. Physical storage, owners, routing, rounded recursive children, actual +input preparation, a favorable complete bill, tensor-depth transfer and the +selected multiplication theorem remain outside scope. 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New material is Apache-2.0; +predecessor authorship and notices remain in force. + +## Statement and source boundary + +The supplied program replaces the omitted part of the pinned 5,398-event P104 +word by a 1,238-operation entrance program, followed by the unchanged +4,027-event projection. It has the same complete physical endpoint map, +including arbitrary admitted dirty offsets and all 358 final frames. The +result closes a chronological, common-frame access obligation. It does not +establish a complete physical supplier or a new multiplication exponent. + +The projection is credited to [PR #3446](https://github.com/CrocSwap/integer-mult-bounds/pull/3446), +Hiroki Kumazaki; the rank-eight residual and integer factorization to +[PR #3462](https://github.com/CrocSwap/integer-mult-bounds/pull/3462), Nick Petalas; +and the endpoint-adapter construction to +[PR #3469](https://github.com/CrocSwap/integer-mult-bounds/pull/3469), Nick Petalas. +Their exact retained sources, the original WORD/native lineage, and executable +dependencies are bound in [SOURCES.json](SOURCES.json). + +The method of using dirty outputs as accumulators while restoring modified +inputs is general: see Jean-Guillaume Dumas and Bruno Grenet, +[In-place accumulation of fast multiplication formulae](https://arxiv.org/abs/2307.12712), +ISSAC 2024. The contribution here is its source-bound P104 realization and bill, +not that general accumulation principle or the predecessor factorization. + +## 1. Why the correction can move to the entrance + +Let $J_f$ denote the retained Delta chart of frame $f$. Work first with +chart-normalized public fields: the physical value of normalized $z$ in frame +$f$ is $J_fz$. Let $W$ be the original normalized endpoint operator and $S$ +the normalized operator of the projection. The source reconstruction proves + +$$ +W=S+K,\qquad K_{X,Y}=\frac12 CA, +$$ + +where $A$ has eight rows and 104 Y columns, and $C$ has 52 X rows and eight +columns. Every other block of $K$ is zero. + +The dependency reconstruction retains exactly the predecessor's event-index +digest. Every retained event neither reads nor writes any of the 93 omitted +public banks. Consequently $S$ acts identically on them and has no dependence +on their initial values in its other outputs. It also preserves every +normalized Y field. Since the image of $K$ lies in the omitted X banks and +$K$ reads only Y, + +$$ +SK=KS=K,\qquad K^2=0,\qquad W=S(I+K)=(I+K)S. +$$ + +These equalities concern the normalized operators. Physical frames are still +owed. At the actual entrance all Y banks are in the empty frame. The new +prefix computes $I+K$ there and delivers all 93 omitted banks in their required +full frame + +$$F=[256,128,64,32,16,8,4,2,1].$$ + +It restores every retained public field to its identical entrance value and +frame. Thus the original retained trace executes from exactly its original +state, including its eight private lifetimes. Its disjointness makes the +already completed omitted banks irrelevant to that trace. + +## 2. Dirty-output accumulation and source return + +Use the following ordered eight pivot X banks: + +```text +X0, X33, X101, X102, X11, X12, X15, X24. +``` + +The actual rows of $C$ on these banks are $I_8$. Write their values as $x_P$, +and the other 44 X values as $x_T$. First move all 52 X banks from their +actual singleton entrance frames to the empty frame. Then perform + +$$ +x_T\leftarrow x_T-C_Tx_P,\qquad +x_P\leftarrow x_P+\frac12 AY,\qquad +x_T\leftarrow x_T+C_Tx_P. +$$ + +The entire first stage precedes every gather. The last stage uses the updated +pivots, so its result is +$x_T-C_Tx_P+C_T(x_P+AY/2)=x_T+C_TAY/2$. +The pivots themselves have their required updates because $C_P=I_8$. +No dirty value is assumed zero or discarded. + +For each active Y column, halve that bank once, execute its signed unit ADDs +into the eight pivots, then double it immediately. This realizes coefficients +of magnitude two by repeated unit ADDs and returns the source before advancing +to the next column. Exactly 103 columns are active. Y1 is unused by this +correction but remains live and is used by the retained projection. + +Finally move all 52 X and the other 41 omitted banks from empty to $F$. +The latter are 38 N banks and G2, G3, G9; they retain their normalized dirty +values. Sources and outputs have distinct physical roles. The prefix needs +temporarily writable, restored Y access and no additional Gaussian bank. +Arithmetic registers, monomial workspace, routing and controllers still need +their own implementations. + +## 3. The new native maps include their phases + +There are 52 actual singleton-to-empty maps of rank one and a shared +empty-to-full map of rank nine, used 93 times. Each requested map is +$J_{\rm new}J_{\rm old}^{-1}$. The pinned compiler synthesizes its affine +quadratic-phase monomials and positive native child. + +The separately written PR #3416 checker compares each of the 53 distinct +recipes with the direct canonical-chart expression. It checks all 18 signed +Pauli actions and a complete 512-entry exact Gaussian-dyadic anchor. Equality +of the signed actions makes the ratio commute with all binary X and Z: +commutation with Z makes it diagonal, and commutation with X makes it scalar. +The nonzero anchor fixes that scalar to one. This covers global phase as well +as address action. An extra-$i$ control specifically fails the anchor check. + +An additional elimination computes the requested B-block rank, and separately +enumerated monomial maps agree with the checker's maps. These are 53 new-map +certificates; the historical 1,245-class native census is inherited, not +reexecuted. The common rank-nine recipe also matches PR #3469's retained +certificate. Total new native work is 145 calls, rank mass 889, and 227,584 +Gaussian pairs in the fixed 512-coordinate model. + +## 4. Exactness domains and the universal implication + +Put $R=\mathbb Z[i]$, $\pi=1+i$, and + +$$B_9=E_9R^{512},\qquad +E_9=\begin{pmatrix}1&0\\1&\pi\end{pmatrix}^{\otimes9}.$$ + +The pinned [PR #3382](https://github.com/CrocSwap/integer-mult-bounds/pull/3382) +module lemmas and [PR #3416](https://github.com/CrocSwap/integer-mult-bounds/pull/3416) +covariance theorem supply the chart/native interpretation. Their admitted +monomials and native coordinate factors preserve $B_9$; on this domain the +literal signed-floor pairs equal their integral ideal pairs. + +Locally, all 93 physical dirty inputs may lie in $B_9$, and all 104 Y inputs +must lie in $4B_9$. Inverse entrance charts preserve the dirty domain. +Temporary Y halves lie in $2B_9$; integer ADDs preserve $B_9$; subsequent +charts therefore have exact literal executions. The halves are exact also +for negative components. + +For a common sufficient domain of the complete old and new programs, require +all 104 Y banks in $4B_9$, all 78 N banks in $2B_9$, and the other 176 public +banks in $B_9$. This stronger domain is not claimed minimal. Assign one +independent $B_9$ symbol to each normalized entrance bank, with weights +respectively four, two and one. The exact rational row interpreter checks +that every fractional ADD increment and every resulting state has integer +symbol coefficients, throughout both programs. Every private erasure has +the zero symbolic row. This induction, together with the pinned native +lemmas, proves universal literal admission and equality. It checks 128,164 +final matrix entries and all 358 final frames. Weakening N100 alone fails the +increment condition at original event 312. + +## 5. Finite evidence, costs and limits + +The independent physical engine imports no candidate or predecessor executable. +It reconstructs charts directly, executes the serialized 1,238-operation +prefix on one dense signed fixture, checks all 227,584 completed floor pairs, +and compares all 93 dirty outputs and 104 returned Y arrays. This finite +fixture complements the universal symbolic and native arguments; it does not +replace them. + +The prefix has 887 unit Gaussian ADD/SUBs, 103 field halves and 103 field +doublings. Its local native tariff is $52+93\,9^s$. For $0\le s\le1$, +concavity gives + +$$r^s\ge1+(r-1)(9^s-1)/8\quad(1\le r\le9).$$ + +The original omitted 473 calls have rank mass 889, hence tariff at least +$421+52\,9^s$. The local improvement is therefore at least +$41(9-9^s)>0$ for $0\le s<1$, with equal mass at $s=1$. +The changed full profile nevertheless misses the selected target under the +explicit favorable complete-consumer screen in [COSTS.md](COSTS.md). + +The finite engine caps input magnitude at 8,192 bits and stored work at +8,224 bits. Observed peaks concern fields after complete program operations, +not native-pair temporaries. Let $H_X$ bound X components after entering the +empty frame and $H_Y$ bound the actual unhalved Y components. The scalar-row +envelope, derived and checked in COSTS, is + +$$\max\{8H_X+95H_Y,\;11H_X+64H_Y,\;12H_X+49H_Y,\;14H_X\}.$$ + +It is at most $103H$ for $H=\max(H_X,H_Y)$. Adapter and temporary headroom +are separate obligations. Python verification allocations do not establish +physical workspace, precision, access, all-size recursion or a fully paid bill. +Stop at this exact local interface and retain the stated consumer obstruction. diff --git a/research/p104-caller-feasibility/physical/inputs/WORD.json b/research/p104-caller-feasibility/physical/inputs/WORD.json new file mode 100644 index 0000000000..93acaabc0a --- /dev/null +++ b/research/p104-caller-feasibility/physical/inputs/WORD.json @@ -0,0 +1,6124 @@ +{ + "schema_version": 1, + "chart": "Delta_W = conjugate(Gamma_W) = Gamma_W^(-T)", + "initial_frames": { + "X0": [386], + "X1": [391], + "X2": [405], + "X3": [431], + "X4": [445], + "X5": [440], + "X6": [426], + "X7": [351], + "X8": [304], + "X9": [290], + "X10": [295], + "X11": [309], + "X12": [346], + "X13": [357], + "X14": [31], + "X15": [32], + "X16": [79], + "X17": [93], + "X18": [88], + "X19": [74], + "X20": [37], + "X21": [26], + "X22": [127], + "X23": [224], + "X24": [223], + "X25": [176], + 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Retain source inputs and credit. No physical supplier or frontier change. --- research/p104-caller-feasibility/README.md | 155 ++++++ research/p104-caller-feasibility/SOURCES.json | 187 +++++++ research/p104-caller-feasibility/TASK.json | 252 +++++++++ research/p104-caller-feasibility/VERIFY.json | 70 +++ .../p104-caller-feasibility/consumer/PROOF.md | 241 ++++++++ .../consumer/RESULT.json | 143 +++++ .../consumer/SOURCES.json | 105 ++++ .../consumer/budget.py | 424 ++++++++++++++ .../physical/CALLER_AUDIT.md | 125 +++++ .../physical/FORMAT_PROOF.md | 245 +++++++++ .../physical/FORMAT_RESULT.json | 269 +++++++++ .../physical/SOURCE_MANIFEST.json | 225 ++++++++ .../physical/controls.py | 131 +++++ .../physical/verify_format.py | 516 ++++++++++++++++++ research/p104-caller-feasibility/verify.py | 28 + 15 files changed, 3116 insertions(+) create mode 100644 research/p104-caller-feasibility/README.md create mode 100644 research/p104-caller-feasibility/SOURCES.json create mode 100644 research/p104-caller-feasibility/TASK.json create mode 100644 research/p104-caller-feasibility/VERIFY.json create mode 100644 research/p104-caller-feasibility/consumer/PROOF.md create mode 100644 research/p104-caller-feasibility/consumer/RESULT.json create mode 100644 research/p104-caller-feasibility/consumer/SOURCES.json create mode 100644 research/p104-caller-feasibility/consumer/budget.py create mode 100644 research/p104-caller-feasibility/physical/CALLER_AUDIT.md create mode 100644 research/p104-caller-feasibility/physical/FORMAT_PROOF.md create mode 100644 research/p104-caller-feasibility/physical/FORMAT_RESULT.json create mode 100644 research/p104-caller-feasibility/physical/SOURCE_MANIFEST.json create mode 100644 research/p104-caller-feasibility/physical/controls.py create mode 100644 research/p104-caller-feasibility/physical/verify_format.py create mode 100644 research/p104-caller-feasibility/verify.py diff --git a/research/p104-caller-feasibility/README.md b/research/p104-caller-feasibility/README.md new file mode 100644 index 0000000000..c732437542 --- /dev/null +++ b/research/p104-caller-feasibility/README.md @@ -0,0 +1,155 @@ +# P104 caller feasibility after PR3609 + +**Two source-bound results, with no new supplier or selected bound claimed.** +This package answers the changed-consumer and physical-format routes from the +[PR3609 handoff](https://github.com/CrocSwap/integer-mult-bounds/pull/3609). +The companion normalised-layer investigation is a different interface and +does not supply a P104 cost credit. + +The first result is a sharp **425 rejected / 426 abstractly passing** threshold +for rank-unit deletions from the actual new full dual, across every integer +pair count in the named inherited coverage model. The second is a sharp +**six / seven / six** fractional-bit contract for its entrance, full execution, +and final outputs. A physical producer, legal owners, and an affordable full +caller are still missing. Neither theorem makes unpriced costs zero. + +## Changed complete consumer + +[consumer/PROOF.md](consumer/PROOF.md) derives an exact whole-bill criterion for +an arbitrary replacement dual profile, genuine unpaid coverage relief, and +additional rank-normalised cost. It distinguishes a realised replacement from +an optimistic relaxation. + +The retained forward has 1,646 children and rank mass 3,070. PR3609's new full +dual has 1,742 children and rank mass 3,542. In the named all-pair consumer, +there are p+1 forward calls and p dual calls, m=16p+9, W=208p, and the stated +3,014 endpoint credit per call. Here p denotes the pair count, not precision. + +Deleting rank-one children is the most favourable integer rank-unit deletion +at a fixed allowance. Strict convexity of the relaxed excess in p, together +with exact outward rational evaluations at p=6,7,8, proves that deleting at +most 425 units per dual fails for **every p>=1 and every finite number of +fully paid auxiliary banks**. At 425, the global integer minimum is p=7 and +is positive, approximately 1.6006864105095964. + +An abstract deletion of 426 rank-one children per dual passes at p=7 and +a=1/596, whose outer ratio 1/597 exceeds the frozen selected benchmark. Its +entire seven-pair bill has only about **4.557071360876949 rank-normalised cost +units** of remaining slack. Adding four units passes; adding five fails. +At fixed p=4, the corresponding boundary is 427/428. No such deletion network +is constructed. Endpoint credits and coverage cannot be silently retained +after a replacement that changes their premises. + +The independent calculator also reproduces two different providers' arithmetic. +[PR3605](https://github.com/CrocSwap/integer-mult-bounds/pull/3605), at exact +head `3efbb5de06a49ffeea6684482f2d3fe48cdca3fb`, has 23,953,011 children, +rank mass 48,165,120, and the strict root bracket +0.001730006549538841847005 < beta < 0.001730006549538841847006 in its own +T740 model. The [PR3574](https://github.com/CrocSwap/integer-mult-bounds/pull/3574) +1126/1127 hosting separator also agrees under its own native-channel law. +These are comparisons, not substitute P104 bills. This package does not replay +either historical physical release or establish its recursive assumptions. + +## Exact physical format + +[physical/FORMAT_PROOF.md](physical/FORMAT_PROOF.md) combines Gaussian-ideal +valuation with the actual program's rational rows and a literal dependency +cone. For arbitrary initial physical components on the 2^-f grid, one common +fixed-point format needs the following added fractional bits. + +| Boundary | Sharp uniform guard | Scope | +| --- | ---: | --- | +| Standalone entrance | 6 | All 1,238 new operations | +| Entrance plus retained projection | 7 | All 5,265 operations | +| Required final outputs | 6 | All 358 physical fields | + +Refining the mantissa and its unit preserves the numerical input. The theorem +computes the ideal Gaussian word exactly on the refined grid; it does not +identify that result with a separately rounded coarse-grid execution outside +the source's exactness domain. The six-bit entrance proof does not assert the +false inclusion 64 Z[i]^512 in the stronger sufficient domain 4 B9. + +The checker traces every scalar row, scalar product, and final frame. A +36-event dependency cone gives the actual seven-bit obstruction at original +event 2142, combined event 3000. A required X0 endpoint proves the six-bit lower +bound. Full seven-bit sufficiency uses the credited Newton module and native +covariance theorems. Those historical theorems are inherited, not re-certified +by the bounded witness. + +If each original real and imaginary component has magnitude at most H, a +sufficient stored-field bound is **3296H**, and the declared literal scalar +schedule's scratch bound is **6592H**. With b magnitude bits in the original +mantissa, sufficient full-word signed widths are b+20 for fields and b+21 for +scratch. These include integer headroom as well as the seven fractional bits. +No minimal magnitude-width or arbitrary recursive-depth claim is made. + +[physical/CALLER_AUDIT.md](physical/CALLER_AUDIT.md) records the named source +interfaces inspected and the exact producer, borrowing, conversion, routing, +and cost obligations. Source preparation and output-format conversion remain +paid operations or explicit producer/consumer contracts. + +## Evidence and reproduction + +Use Python 3.12 and the standard library. From this directory, including a +Git-free source export, run + +```sh +python3.12 -I -Werror -B verify.py +python3.12 -I -O -Werror -B verify.py +``` + +Each component authenticates its retained source bytes, recomputes its receipt, +and compares it with strict JSON types. Default replay is read-only. Arithmetic +signs use outward rational intervals, not floating-point approximations. +See [consumer/RESULT.json](consumer/RESULT.json) and +[physical/FORMAT_RESULT.json](physical/FORMAT_RESULT.json) for the deterministic +receipts. [VERIFY.json](VERIFY.json) registers both Python modes. These commands +do not launch a historical native census, full selected replay, physical owner +implementation, or formal proof kernel. + +From a complete repository checkout, run + +```sh +GIT_NO_REPLACE_OBJECTS=1 python3.12 -B scripts/research_package.py --package research/p104-caller-feasibility --check-only +GIT_NO_REPLACE_OBJECTS=1 python3.12 -B scripts/research_package.py --package research/p104-caller-feasibility +GIT_NO_REPLACE_OBJECTS=1 python3.12 -B scripts/check_research_commit.py --package research/p104-caller-feasibility --check-source-history +``` + +[SOURCES.json](SOURCES.json) binds the unchanged task catalogue and selected +record at main `20ecf2891d80b5acf18d980b2164fb44ea7faa90`. Exact pending-source +bytes are retained in this PR's own ancestor history. The component manifests +record original public paths, commits, blobs, and SHA256s. This preserves +provenance without requiring unrelated unmerged branches in a clean checkout. +The selected frontier is unchanged. + +## Open next questions + +[TASK.json](TASK.json) gives structured questions, first steps, and blockers. +Useful P104 reopening evidence is a realised replacement profile or changed +coverage law that passes its own full bill, with legal field access and actual +source/return contracts. The 426 sensitivity witness is a rejection screen for +proposals, not a reason to expand an unpriced construction. + +A concrete caller must supply writable/restored Y access, owned private-zero +lifetimes, the stated frames and width, and paid conversion, routing, +controller, and recursion. Those costs must enter the same complete inequality. +For work aimed at the stronger existing T740 candidate, the distinct next step +is an independent audit of PR3605's complete release and retained implications, +not transplanting its profile into P104. + +## Credit + +Prepared by Clear1nsight with substantial OpenAI assistance from a root agent +and three concurrent specialists, including cross-review. This is same-session +independent implementation and review, not independent human acceptance. +New work is Apache-2.0; original notices are retained with the source inputs. + +Credit PR3609 for the actual entrance and full profile; Jose Manuel's p=4 +consumer and Nick Petalas's all-pair budget for the inherited model; Vasek and +PR2458/2744 for the forward; ywz65 and Arham Tahir for the original physical +word and native data; the PR3382/3406/3416 lineage and Ross Richardson's +Clifford-grid work for module and precision premises; and Dumas and Grenet +for the earlier dirty-accumulation method. PR3605's T740 construction is Ross +Richardson's work. PR3574 is jwr's work, retaining Nick Petalas's budget, +Rohan Arun's native channel, and its lineage. Detailed attribution remains in +the component proofs and manifests. diff --git a/research/p104-caller-feasibility/SOURCES.json b/research/p104-caller-feasibility/SOURCES.json new file mode 100644 index 0000000000..cf5538deb0 --- /dev/null +++ b/research/p104-caller-feasibility/SOURCES.json @@ -0,0 +1,187 @@ +{ + "schema_version": 1, + "base_commit": "20ecf2891d80b5acf18d980b2164fb44ea7faa90", + "files": [ + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "b1fea0c94436b236cc2b7d41a7be032811b94c81", + "sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "67f085acd86acd7d4e03922d9cf4b26bca66fed5", + "sha256": "47b42433f5a85809a3aadd29c2c339da2c6ed728e4f7762df6b88bccb7874cf0" + }, + { + "path": "research/p104-caller-feasibility/consumer/inputs/ALL_PAIR_README.md", + "usage": "input", + "git_blob": 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"These exact bytes were retained in this PR own ancestor 35cf06a9d35b20701550b5517f4d69afd43c0ca7. Original public origins and notices remain in consumer/SOURCES.json and physical/SOURCE_MANIFEST.json. No source algorithm is rewritten; no pending foreign Git object is needed for replay." +} diff --git a/research/p104-caller-feasibility/TASK.json b/research/p104-caller-feasibility/TASK.json new file mode 100644 index 0000000000..3d6e4a5b3b --- /dev/null +++ b/research/p104-caller-feasibility/TASK.json @@ -0,0 +1,252 @@ +{ + "schema_version": 1, + "task_id": "p104-side-correction", + "priority_revision": 6, + "base_commit": "20ecf2891d80b5acf18d980b2164fb44ea7faa90", + "original_card": { + "id": "p104-side-correction", + "question": "Can the proposed P104 joint endpoint flags be realized by a chronological correction program with coefficients, dirty restoration and an affordable complete bill?", + "starting_points": [ + "docs/research/research-family-status.md", + "research/p104-native-channel/README.md", + "research/p104-native-channel/PROOF.md", + "docs/research/community-efficient1000-review.md", + "research/p104-joint-unit-flags/README.md" + ], + "methods": [ + "Construct one side-correction word at an explicit chronological cut with the needed frames still available.", + "Derive a lower bound on the side correction and hosting costs that decides whether this channel can beat the selected budget." + ], + "acceptance_gate": "An exact arbitrary-input identity, source/target frame availability and restoration at the chosen cut, plus the complete channel+correction+idle/hosting bill or an explicit favorable bound. The native channel alone is not a supplier. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read the revision-6 family record and #2981 static joint flags, alongside the reviewed #1991 channel. #2981 is an author-checked source archive, not an independently validated executable correction or a refutation of program-level lifetime floors.", + "scope": "Source-bound orientation only. Read the named package and review before relying on its local evidence; this command is not its replay or supplier admission." + }, + "first_experiment": "After checking live handoffs, pin one named collection from #2981 and attach acquisition/delivery times, source dependencies and coefficient requirements. Test legal access and arbitrary dirty restoration; price any completion against the full channel/endpoint/hosting allowance. Stop with the exact missing implication or a scoped counterexample rather than expanding the static cover census.", + "bottleneck_link": "Completing an already realized changed channel tests a concrete construction opportunity, instead of refining the incumbent packing. A positive local result still needs global and all-size admission.", + "allowed_variations": [ + "One correction factorization, one chronological cut, or one explicit hosting obstruction.", + "A changed correction schedule with an updated full bill and native frame contract." + ], + "scope_change_triggers": [ + "Recompiling the already certified low-rank channel without closing a new obligation.", + "Treating a pending ancestor, local histogram or unpriced side correction as an admitted global supplier.", + "Repeating a correction or physical conversion already supplied by a pending follow-up without adding independent coverage or a different unresolved obligation.", + "Repeating the 208-flag static matching or calling a static nested cover a chronological correction program. Independent audit of that certificate is distinct and remains useful." + ], + "overlap_terms": [ + "P104", + "I-G/2", + "side correction", + "native channel", + "1972", + "1991", + "2586", + "endpoint transport", + "physical dual", + "relay composition", + "2981", + "joint unit flags", + "acquisition delivery", + "static nesting" + ], + "existing_checks": [ + { + "scope": "PR #2981 reports static joint endpoint flags and a matching of 208 departure and arrival flags; archival intake is not independent verification.", + "evidence": "research/p104-joint-unit-flags/README.md", + "remaining": "Independent flag check and a chronological coefficient program with dirty restoration and a complete cost.", + "status": "author-checked", + "source_commit": "3d24b92d8ba057b57cb2d480170ec407520e6882", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + } + ] + }, + "scope_status": "changed", + "actual_scope": "Answer the user-assigned PR3609 changed-consumer and physical-caller handoffs with a sharp all-pair cost threshold and exact six/seven/six one-layer format contract, plus a bounded audit of named alternative providers. No new network or physical supplier is constructed.", + "scope_change_reason": "The user assigned the three handoff routes. This preserves the original card and narrows two routes to distinct proof obligations after the completed entrance PR3609, rather than reopening static flags or duplicating its chronological construction.", + "bottleneck_link": "The exact 425/426 threshold quantifies how much a realised replacement must save under the inherited coverage law; the finite-format proof removes one concrete caller obligation but leaves ownership and full cost open. Together they make the P104 reopening decision reviewable.", + "budget_minutes": null, + "stop_rule": "NARROW after the local proofs and their validation. No dependent P104 supplier construction without a realised changed profile or genuine changed coverage law, legal source/return contract and a favourable complete paid inequality. Unknown costs remain nonnegative unspecified obligations. Do not change the selected frontier.", + "outcome": "partial", + "evidence": "consumer/PROOF.md and RESULT.json give exact outward rational arithmetic, strict convexity, the all-integer-p threshold and separate PR3605/3574 arithmetic. physical/FORMAT_PROOF.md and FORMAT_RESULT.json give the complete scalar/frame trace, per-term local guard, 36-event literal necessity cone, X0 endpoint and norm/width proof. Both direct Python modes, optimized physical CLI rejection controls and separate same-session cross-review have passed. Publication/hosted evidence is recorded separately after actual execution.", + "author": "Clear1nsight", + "ai_assistance": "Substantial OpenAI assistance from a root agent and three concurrent specialists in mathematical derivation, exact implementation, source audit, and independent same-session cross-review. 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Not all diffs or closed PRs." + }, + "discussion_coverage": { + "threads": [ + 1163, + 1166, + 1167, + 2750, + 2612 + ], + "mode": "Fresh loaded bodies and current visible comments; no all-thread/reply pagination.", + "material_overlap": "Sagar Thakrar fixed-h diagonal-pass implementation19015185. Our route3 claim19015428 explicitly excludes that implementation." + }, + "claims": { + "p104": "https://github.com/CrocSwap/integer-mult-bounds/discussions/2750#discussioncomment-19015413", + "layer": "https://github.com/CrocSwap/integer-mult-bounds/discussions/2612#discussioncomment-19015428" + }, + "orientation_baseline": { + "status": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "method": "Ran in preserved canonical-recovered worktree after verifying selected record and both baseline scripts byte-identical to current main. 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No new same-scope P104 result.", + "layer": "Fresh 2612 includes PR3617 DONE 4bf091f415d6470b60a5062a08b0a47e5b12dbd7 and author handoff reply 19015775 to our claim. Preserve frozen layer proof and assess successor separately.", + "new_adjacent": "PR3619 complete encoded support router, PR3618 flag-9 local correction and PR3604 P112 audit have distinct scopes.", + "limitations": "No exhaustive closed-PR/diff or all-Discussion pagination; time-window API metadata snapshot is non-atomic." + } + } + ], + "metadata_frozen_at_utc": "2026-10-18T10:02:00.626673+00:00" +} diff --git a/research/p104-caller-feasibility/VERIFY.json b/research/p104-caller-feasibility/VERIFY.json new file mode 100644 index 0000000000..42038d3a8d --- /dev/null +++ b/research/p104-caller-feasibility/VERIFY.json @@ -0,0 +1,70 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [ + "research/p104-caller-feasibility/consumer/inputs/ALL_PAIR_README.md", + "research/p104-caller-feasibility/consumer/inputs/PR2744_PREDECESSORS.json", + "research/p104-caller-feasibility/consumer/inputs/PR2744_RESULT.json", + "research/p104-caller-feasibility/consumer/inputs/PR3574_README.md", + "research/p104-caller-feasibility/consumer/inputs/PR3574_verify.py", + "research/p104-caller-feasibility/consumer/inputs/PR3605_CLAIM.json", + "research/p104-caller-feasibility/consumer/inputs/PR3605_DERIVATION.md", + "research/p104-caller-feasibility/consumer/inputs/PR3605_PROFILE.json", + "research/p104-caller-feasibility/consumer/inputs/PR3605_README.md", + "research/p104-caller-feasibility/consumer/inputs/PR3609_RECEIPT.json", + "research/p104-caller-feasibility/consumer/inputs/SELECTED.json", + "research/p104-caller-feasibility/physical/inputs/FRAME-SA504-NOTICE.md", + "research/p104-caller-feasibility/physical/inputs/LICENSE", + "research/p104-caller-feasibility/physical/inputs/NATIVE-LINEAGE-NOTICE", + "research/p104-caller-feasibility/physical/inputs/NOTICE", + "research/p104-caller-feasibility/physical/inputs/ORIGINAL_NATIVE.json.gz", + "research/p104-caller-feasibility/physical/inputs/PR1862-NOTICE.md", + "research/p104-caller-feasibility/physical/inputs/PR1972-NOTICE.md", + "research/p104-caller-feasibility/physical/inputs/PR3382_PROOF.md", + "research/p104-caller-feasibility/physical/inputs/PR3416_PROOF.md", + "research/p104-caller-feasibility/physical/inputs/PR3609_NATIVE.json", + "research/p104-caller-feasibility/physical/inputs/PR3609_PROGRAM.json", + "research/p104-caller-feasibility/physical/inputs/PR3609_PROOF.md", + "research/p104-caller-feasibility/physical/inputs/WORD.json" + ], + "commands": [ + { + "argv": [ + "{python}", + "-I", + "-Werror", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 120, + "checks": "Authenticate 24 retained source inputs and both typed receipts; independent exact budget, convexity signs, scalar/frame trace and literal precision witnesses; no full physical caller." + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-Werror", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 120, + "checks": "Repeat the complete bounded replay with optimization; all explicit arithmetic/source/type checks remain active." + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-Werror", + "-B", + "{package}/physical/controls.py" + ], + "timeout_seconds": 120, + "checks": "Actual disposable CLI normal/optimized immutability and missing/corrupt WORD plus Boolean-receipt rejection with exact diagnostics." + } + ], + "execution_boundary": "Standard library; no predecessor executable imported by either scientific component, no historical native census, physical producer, owner allocation, full release or all-size admission. New bounded data/proof checks only." +} diff --git a/research/p104-caller-feasibility/consumer/PROOF.md b/research/p104-caller-feasibility/consumer/PROOF.md new file mode 100644 index 0000000000..840c39342e --- /dev/null +++ b/research/p104-caller-feasibility/consumer/PROOF.md @@ -0,0 +1,241 @@ +# Route 1: a sharp conditional budget and a separate favorable candidate + +The new PR #3609 full dual does not yet reopen the stopped P104 supplier. +Under the named paired-chain coverage law, **425 integer rank deletions per +dual remain insufficient for every pair count**. A hypothetical deletion of +426 rank-one children passes the optimistic moment at seven pairs, but leaves +less than 4.558 units of additional normalized cost. No such deletion network, +compatible owner map, or complete P104 caller is constructed here. + +There is a more developed, separate Route 1 candidate: PR #3605's T740 +construction. This audit independently verifies its stated complete histogram +and strict rational moment bracket at its updated exact head. It does not +rerun or replace that predecessor's finite native/owner release or inherited +physical, recursive, and analytic hypotheses. + +## 1. Frozen profiles and the actual coverage contract + +The inputs are the PR #2458 forward profile recounted in PR #2744, and the +changed full dual in PR #3609's executed receipt. They are not the original +native-channel profile or a partial omitted-bank replacement. + +| Rank | Forward F | Changed full dual D | +| ---: | ---: | ---: | +| 1 | 1216 | 1316 | +| 2 | 74 | 61 | +| 3 | 86 | 74 | +| 4 | 104 | 86 | +| 5 | 48 | 33 | +| 6 | 42 | 25 | +| 7 | 68 | 46 | +| 8 | 8 | 8 | +| 9 | 0 | 93 | +| Calls | 1646 | 1742 | +| Rank mass | 3070 | 3542 | + +Use Nick Petalas's existing all-pair coverage model, derived from Jose Manuel +(`jmbarrancoml`)'s four-pair calculation and the retained larger-gain template. +For an integer $p\ge1$, there are $p+1$ forward calls and $p$ dual calls, +width $m=16p+9$, and $W=208p$ original families. Each family has one unpaid +coordinate. Grant the full persistent endpoint progress $P=3014$ to every +call, even after hypothetical deletion, and grant the missing forward +corrections and all unspecified implementation costs free. With $B\ge0$ +fully paid banks, the optimistic remaining rank mass is + +$$ +I_B=\max(0,(m-1)W+mB-(2p+1)P). +$$ + +All residual children are optimistically allowed rank $m$. This is a +conditional coverage model, not a construction of its owner windows or a +proof that those endpoint credits can be retained after changing the words. +PR #3609 changes the dual histogram, not this coverage law. The new source is +`13f974dae4af66027afb01f3ab42df9e830c2e90`; the main-branch predecessor inputs +are frozen at `20ecf2891d80b5acf18d980b2164fb44ea7faa90`. + +## 2. What a real replacement must establish + +Let $D'$ be an actual proposed replacement profile. Let $\Delta\ge0$ be +**genuinely unpaid** additional coverage relief, and let $G(a)\ge0$ be every +additional charge expressed in the same normalized rank-moment units. +Native children already included in $D'$ must not also be charged in $G$. +Conversely, omitted scalar, owner, routing, restoration, precision, or +controller costs must not silently be set to zero in a claim of a complete +bill. The model's exact test is + +$$ +m^a\sum_r[(p+1)F_r+pD'_r]r^{1-a} ++\max(0,J_B-\Delta)+G(a)E_{\rm old}+G$, with +$0\le R_\Delta\le\Delta$. A changed coverage law must justify its new $J_B$; +it cannot be inserted into an unchanged calculator without that proof. +For example, added positive children of total rank mass $A$ cost at least +$A$, since $r(m/r)^a\ge r$. If they earn at most $A$ units of extra progress, +that progress alone cannot yield a net budget gain. Likewise, for $p\ge2$ +the term $mB$ from fully paid banks cancels between residual work and capacity; +the sign of the excess is unchanged. These statements explain why a profile +saving, a free endpoint credit, and a paid physical replacement are different +obligations. + +## 3. A sharp integer deletion allowance across all pair counts + +Suppose each dual's inherited positive children of integer ranks $r_j$ are +changed only to ranks $r_j-\delta_j$, with integer +$0\le\delta_j\le r_j$ and $\sum_j\delta_j\le d$. For $00. +$$ + +For the cases here $U_d>V>0$, so the bracket is positive. Consequently three +strict comparisons at the neighboring integers 6, 7, and 8 suffice to locate +the global integer minimum; no unbounded enumeration or sampled tail is used. + +Take the favorable test saving +$a=\kappa=836330098538459/500000000000000000$. Independent outward rational +intervals certify: + +| p | Strict rational decimal enclosure for E425(p, κ) | +| ---: | --- | +| 6 | $(2.62322106,\ 2.62322107)$ | +| 7 | $(1.60068641,\ 1.60068642)$ | +| 8 | $(1.97354361,\ 1.97354362)$ | + +Thus $E_{425}(7)0$. Convexity proves +rejection for every integer $p\ge1$, every finite fully paid $B$, and every +deletion allowance $d\le425$. Since every child moment increases with $a$, +the rejection also holds at the stricter required primitive saving. + +The integer boundary is sharp **within this relaxation**. At $p=7$, delete +426 actual histogram entries of rank one, leaving $D_{426,1}=890$. +At the stronger rational test $a=1/596$, + +$$ +-4.55707137\kappa$. Four additional normalized cost units still pass; +five already fail. Thus the abstract profile's total extra-cost allowance is +only $4.557071360876949\ldots$, across the entire seven-pair bill. At fixed +$p=4$, 427 deletions fail at $\kappa$ while 428 pass at $1/596$. +Varying the pair count saves two units in this optimistic target; it does not +supply a compatible deletion or make the previous 416-unit gift sufficient. + +## 4. The favorable named alternative uses its own bill + +Ross Richardson's updated PR #3605 head is +`3efbb5de06a49ffeea6684482f2d3fe48cdca3fb`. Its complete stated T740 profile, +including the rank-six stratum, is independently reconstructed as +$H=6660L+I$ from the pinned derivation and compared with both pinned JSON +claims. It has 23,953,011 children and rank mass 48,165,120, against +$73\cdot663040=48,401,920$ capacity. Its distinct moment is + +$$ +M(b)=\frac{\sum_r rH_r(73/r)^b}{73\cdot663040}. +$$ + +The checker independently proves $M(C)<11$ at 1127. Those are different provider, coverage, +and displacement assumptions; 1126 is not a free additional-work allowance +for the new full P104 words. Its matching, optimizer, and physical obligations +are not replayed here. + +Run `python3 -I -B budget.py` or `python3 -I -O -B budget.py` in this directory. +Both authenticate `SOURCES.json`, all eleven exact source files, and the +typed deterministic receipt. The interval engine imports no predecessor +executable: it range-reduces logarithms to $[1,2]$, uses 48 positive atanh +terms with a geometric tail bound, and encloses exponentials with 20 positive +Taylor terms and their geometric tail. All sign decisions use rational +arithmetic. The source and receipt control evidence is kept separately from +the scientific receipt; no historical native suite is rerun. + +The new contribution is the changed-profile all-pair convex threshold, its +explicit replacement-cost boundary, and an independent arithmetic comparison +of the two named alternatives. Credit Jose Manuel for the original four-pair +screen and deletion inequality; Nick Petalas for the previous all-pair and +endpoint-geometric budgets; Vasek (`flyingviper`) for PR #2744; Ross Richardson +and the retained PR #2458/PR #3133 lineage; PR #3609's exact full-word +replacement and all its notices; jwr for PR #3574; and Ross Richardson's +updated PR #3605 release. The latter retains dcharb78's PR #3133, Jeremy +Diviney's PR #3148 owner geometry, PR #3531's modern transfer, dataisfire's +bootstrap, Yiyang Lu's staged kernel/flow, and their full source notices. +This bounded audit was prepared by Clear1nsight with OpenAI assistance. diff --git a/research/p104-caller-feasibility/consumer/RESULT.json b/research/p104-caller-feasibility/consumer/RESULT.json new file mode 100644 index 0000000000..60b421c28d --- /dev/null +++ b/research/p104-caller-feasibility/consumer/RESULT.json @@ -0,0 +1,143 @@ +{ + "all_pair_deletion": { + "abstract_positive_excess": [ + "-56963392010961862579368734560990939/12500000000000000000000000000000000", + "-455707136087694900634949876487927511/100000000000000000000000000000000000" + ], + "added_cost_4_pass_excess": [ + "-6963392010961862579368734560990939/12500000000000000000000000000000000", + "-55707136087694900634949876487927511/100000000000000000000000000000000000" + ], + "added_cost_5_fail_excess": [ + 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"no_realised_deletion_or_complete_supplier": true, + "positive_abstract_profile": { + "1": 890, + "2": 61, + "3": 74, + "4": 86, + "5": 33, + "6": 25, + "7": 46, + "8": 8, + "9": 93 + }, + "positive_deletion_allowance": 426, + "positive_pair_count": 7, + "positive_saving": "1/596", + "rejected_deletion_allowance": 425, + "rejection_saving": "836330098538459/500000000000000000", + "scope": "Fixed forward, per-child integer dual rank deletion, named all-pair coverage; all other costs free unless explicitly added.", + "selected_primitive": "67018507072324140917/40000000000000000000000", + "three_exact_excess_intervals": { + "6": [ + "26232210663389446255559797866338099/10000000000000000000000000000000000", + "262322106633894462555597978663380991/100000000000000000000000000000000000" + ], + "7": [ + "160068641050959636730656526336792127/100000000000000000000000000000000000", + "2501072516421244323916508224012377/1562500000000000000000000000000000" + ], + "8": [ + 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"url": "https://github.com/CrocSwap/integer-mult-bounds/blob/20ecf2891d80b5acf18d980b2164fb44ea7faa90/certificates/selected-result.json" + } + ], + "schema_version": 1, + "scope": "Immutable public source text for a bounded consumer budget and conditional candidate arithmetic audit; no predecessor executable is imported." +} diff --git a/research/p104-caller-feasibility/consumer/budget.py b/research/p104-caller-feasibility/consumer/budget.py new file mode 100644 index 0000000000..b3856c8969 --- /dev/null +++ b/research/p104-caller-feasibility/consumer/budget.py @@ -0,0 +1,424 @@ +#!/usr/bin/env python3 +"""Independent rational Route 1 arithmetic; no predecessor code is imported. + +This module checks named optimistic coverage models and a separately pinned +conditional T740 profile. It does not construct a native network or owners. +""" + +from __future__ import annotations + +import argparse +import hashlib +import json +import sys +from fractions import Fraction as Q +from functools import lru_cache +from pathlib import Path + + +ROOT = Path(__file__).resolve().parent +SOURCE_MANIFEST = "52fcd3f2b03c4fe0818860122636f1a749455caa9330a06ad03ab9f678b97c84" +LOG_TERMS = 48 +EXP_TERMS = 20 +GRID = 10**60 +RECEIPT_GRID = 10**35 +MARKER = "PASS_ROUTE1_CONSUMER_BUDGET" + + +class Rejection(ValueError): + """A source, arithmetic or typed-contract check failed.""" + + +def require(condition, message): + if not condition: + raise Rejection(message) + + +def integer(value, name, minimum=0): + require(type(value) is int and value >= minimum, name + " must be an integer") + return value + + +def rational(value, name, minimum=Q(0)): + require(type(value) is Q and value >= minimum, name + " must be a Fraction") + return value + + +def unique_object(pairs): + out = {} + for key, value in pairs: + require(key not in out, "duplicate JSON key: " + key) + out[key] = value + return out + + +def parse_json(raw): + require(type(raw) is bytes and len(raw) <= 2_000_000, "bounded JSON bytes required") + return json.loads(raw, object_pairs_hook=unique_object, + parse_constant=lambda s: (_ for _ in ()).throw(Rejection(s))) + + +def strict_equal(left, right): + if type(left) is not type(right): + return False + if type(left) is dict: + return left.keys() == right.keys() and all(strict_equal(v, right[k]) for k, v in left.items()) + if type(left) is list: + return len(left) == len(right) and all(strict_equal(x, y) for x, y in zip(left, right)) + return left == right + + +def authenticate(root=ROOT): + raw = (root / "SOURCES.json").read_bytes() + require(hashlib.sha256(raw).hexdigest() == SOURCE_MANIFEST, "source manifest drift") + manifest = parse_json(raw) + bodies = {} + for row in manifest["files"]: + path = row["local"] + require(path.startswith("inputs/") and ".." not in path, "source path contract") + body = (root / path).read_bytes() + require(len(body) == row["bytes"], "source byte length drift: " + path) + require(hashlib.sha256(body).hexdigest() == row["sha256"], "source SHA256 drift: " + path) + blob = b"blob " + str(len(body)).encode() + b"\0" + body + require(hashlib.sha1(blob).hexdigest() == row["git_blob"], "source Git blob drift: " + path) + bodies[Path(path).name] = body + require(len(bodies) == 11, "source inventory changed") + return bodies + + +def round_down(x, grid=GRID): + return Q((x.numerator * grid) // x.denominator, grid) + + +def round_up(x, grid=GRID): + return -round_down(-x, grid) + + +def compact(interval): + low, high = interval + require(low <= high, "reversed interval") + return [str(round_down(low, RECEIPT_GRID)), str(round_up(high, RECEIPT_GRID))] + + +def add_interval(left, right): + return left[0] + right[0], left[1] + right[1] + + +def scale_interval(interval, scale): + require(scale >= 0, "nonnegative interval multiplier required") + return interval[0] * scale, interval[1] * scale + + +def atanh_log(u): + """Outward bounds for log(u), 1 <= u <= 2, by a positive series.""" + require(Q(1) <= u <= Q(2), "log range reduction failed") + z = (u - 1) / (u + 1) + power, total = z, Q(0) + square = z * z + for j in range(LOG_TERMS): + total += 2 * power / (2 * j + 1) + power *= square + tail = 2 * power / ((2 * LOG_TERMS + 1) * (1 - square)) + return round_down(total), round_up(total + tail) + + +@lru_cache(maxsize=256) +def log_interval(x): + rational(x, "log argument", Q(1)) + require(x <= 1_000_000, "bounded log argument required") + exponent, u = 0, x + while u >= 2: + exponent += 1 + u /= 2 + small = atanh_log(u) + two = atanh_log(Q(2)) + return small[0] + exponent * two[0], small[1] + exponent * two[1] + + +def exp_point(y): + rational(y, "exp argument") + require(y <= Q(1, 10), "bounded exp argument required") + term, total = Q(1), Q(1) + for j in range(1, EXP_TERMS + 1): + term *= y / j + total += term + next_term = term * y / (EXP_TERMS + 1) + tail = next_term / (1 - y / (EXP_TERMS + 2)) + return round_down(total), round_up(total + tail) + + +@lru_cache(maxsize=512) +def power_interval(x, a): + rational(a, "saving") + require(a < Q(1), "saving must be below one") + log_low, log_high = log_interval(x) + return exp_point(a * log_low)[0], exp_point(a * log_high)[1] + + +def read_profile(value): + require(type(value) is dict and 1 <= len(value) <= 100, "bounded profile required") + result = {} + for key, count in value.items(): + require(type(key) is str and key.isascii() and key.isdigit(), "canonical profile rank required") + rank = int(key) + require(str(rank) == key and rank > 0, "canonical positive rank required") + result[rank] = integer(count, "profile count") + return result + + +def profile_mass(profile): + return sum(rank * count for rank, count in profile.items()) + + +def paid_cost(profile, width, a): + integer(width, "width", 1) + result = (Q(0), Q(0)) + for rank, count in sorted(profile.items()): + integer(rank, "rank", 1) + integer(count, "count") + require(rank <= width, "child rank exceeds width") + term = power_interval(Q(width, rank), a) + result = add_interval(result, scale_interval(term, rank * count)) + return result + + +def combined_profile(forward, dual, pairs): + integer(pairs, "pair count", 1) + return {r: (pairs + 1) * forward.get(r, 0) + pairs * dual.get(r, 0) + for r in sorted(forward.keys() | dual.keys())} + + +def deleted_profile(dual, deletion): + integer(deletion, "deletion allowance") + require(deletion <= dual[1], "insufficient rank-one children for abstract witness") + result = dict(dual) + result[1] -= deletion + return result + + +def excess(forward, replacement_dual, pairs, a, *, banks=0, relief=0, + added_cost=Q(0), clamp=True): + """Rank-normalized bill minus capacity under the named coverage law. + + `relief` is genuinely unpaid coverage relief; added_cost pays every new + operation in the same rank-normalized units. It is never inferred free. + """ + integer(pairs, "pair count", 1) + integer(banks, "fully paid banks") + integer(relief, "unpaid coverage relief") + rational(added_cost, "added cost") + width, families = 16 * pairs + 9, 208 * pairs + residual = (width - 1) * families + width * banks - (2 * pairs + 1) * 3014 - relief + if clamp: + residual = max(0, residual) + interval = paid_cost(combined_profile(forward, replacement_dual, pairs), width, a) + delta = residual + added_cost - width * (families + banks) + return interval[0] + delta, interval[1] + delta + + +def must_reject(operation, reason): + try: + operation() + except (Rejection, json.JSONDecodeError) as exc: + require(reason in str(exc), "control rejected for the wrong reason") + return str(exc) + raise Rejection("negative control accepted: " + reason) + + +def sources(bodies): + previous = parse_json(bodies["PR2744_RESULT.json"]) + current = parse_json(bodies["PR3609_RECEIPT.json"]) + selected = parse_json(bodies["SELECTED.json"]) + forward = read_profile(previous["censuses"]["forward2458"]["profile"]) + dual = read_profile(current["invoice"]["changed_full"]["native_profile"]) + expected_f = {1: 1216, 2: 74, 3: 86, 4: 104, 5: 48, 6: 42, 7: 68, 8: 8} + expected_d = {1: 1316, 2: 61, 3: 74, 4: 86, 5: 33, 6: 25, 7: 46, 8: 8, 9: 93} + require(strict_equal(forward, expected_f), "forward source profile changed") + require(strict_equal(dual, expected_d), "changed full dual source profile changed") + require(profile_mass(forward) == 3070 and profile_mass(dual) == 3542, "source masses changed") + require(sum(forward.values()) == 1646 and sum(dual.values()) == 1742, "source calls changed") + require(previous["censuses"]["forward2458"]["persistent_endpoint_progress"] == 3014, + "credited progress changed") + kappa = Q(selected["kappa"]) + require(kappa == Q(836330098538459, 500000000000000000), "selected saving changed") + primitive = Q(previous["bills"]["dual2712"]["lower_bounds"]["selected_primitive"]["a"]) + guide = bodies["ALL_PAIR_README.md"].decode() + for phrase in ["`p+1` forward calls, `p` dual calls, `m=16p+9` and `W=208p`", + "`I_B=max(0,(m-1)W+m*B_aux-(2p+1)C)`", "One unpaid coordinate"]: + require(phrase in guide, "coverage source phrase changed") + return forward, dual, kappa, primitive + + +def all_pair_check(forward, dual, kappa, primitive): + reject_dual = deleted_profile(dual, 425) + values = {p: excess(forward, reject_dual, p, kappa, clamp=False) for p in [6, 7, 8]} + require(values[7][0] > 0, "425 allowance no longer rejected") + require(values[6][0] > values[7][1], "left convex slope not negative") + require(values[8][0] > values[7][1], "right convex slope not positive") + stronger = Q(1, 596) + require(stronger > primitive > kappa / (1 - kappa) > kappa, "test saving order changed") + require(stronger / (1 + stronger) == Q(1, 597) > kappa, "balanced implication check") + pass_dual = deleted_profile(dual, 426) + passed = excess(forward, pass_dual, 7, stronger) + require(passed[1] < 0, "426 abstract allowance fails stronger test") + # These are actual rank-normalized additional costs, not free source edits. + priced_pass = excess(forward, pass_dual, 7, stronger, added_cost=Q(4)) + priced_fail = excess(forward, pass_dual, 7, stronger, added_cost=Q(5)) + require(priced_pass[1] < 0 < priced_fail[0], "added-cost separating control failed") + fixed_427 = excess(forward, deleted_profile(dual, 427), 4, kappa) + fixed_428 = excess(forward, deleted_profile(dual, 428), 4, stronger) + require(fixed_427[0] > 0 and fixed_428[1] < 0, "four-pair allowance check failed") + bank = excess(forward, reject_dual, 7, kappa, banks=19) + require(bank == values[7], "fully paid banks changed the excess numerator") + # Below p=2 the actual clamp only increases the analytic lower bound. + unclamped = excess(forward, reject_dual, 1, kappa, clamp=False) + clamped = excess(forward, reject_dual, 1, kappa) + require(clamped[0] - unclamped[0] == 4050, "negative-residual clamp changed") + require(unclamped[0] > values[7][1], "p=1 analytic lower bound mismatch") + baseline = excess(forward, dual, 7, stronger) + savings = scale_interval(power_interval(Q(121), stronger), 7 * 426) + require(passed[0] <= baseline[0] - savings[0] <= passed[1], "replacement cost identity drift") + return { + "scope": "Fixed forward, per-child integer dual rank deletion, named all-pair coverage; all other costs free unless explicitly added.", + "all_integer_pairs": "p>=1, every finite number of fully paid banks", + "convexity_certificate": "E''=16*a*(16p+9)^(a-2)*((16*(1+a)*p+18)*U-16*(1-a)*V)>0 since U>V>0", + "rejection_saving": str(kappa), + "rejected_deletion_allowance": 425, + "global_integer_minimizer_for_rejection": 7, + "three_exact_excess_intervals": {str(p): compact(v) for p, v in values.items()}, + "positive_abstract_profile": {str(k): v for k, v in sorted(pass_dual.items())}, + "positive_pair_count": 7, + "positive_deletion_allowance": 426, + "positive_saving": str(stronger), + "selected_primitive": str(primitive), + "abstract_positive_excess": compact(passed), + "exact_additional_rank_cost_headroom": compact((-passed[1], -passed[0])), + "added_cost_4_pass_excess": compact(priced_pass), + "added_cost_5_fail_excess": compact(priced_fail), + "fixed_four_pairs_427_reject": compact(fixed_427), + "fixed_four_pairs_428_abstract_pass": compact(fixed_428), + "no_realised_deletion_or_complete_supplier": True, + } + + +def conditional_t740_check(bodies, kappa): + claim = parse_json(bodies["PR3605_CLAIM.json"]) + profile = read_profile(parse_json(bodies["PR3605_PROFILE.json"])) + require(strict_equal(profile, read_profile(claim["profile"])), "T740 profile/claim disagreement") + local = {1: 2439, 2: 726, 3: 224, 4: 102, 5: 20, 8: 8} + idle = {1: 174156, 3: 48334, 4: 1, 5: 10792, 6: 3, 48: 283185} + rebuilt = {r: 6660 * local.get(r, 0) + idle.get(r, 0) for r in local.keys() | idle.keys()} + require(strict_equal(profile, rebuilt), "T740 local/idle assembly disagreement") + require(claim["replicas"] == 740 and claim["calls"] == 6660 and claim["dimension"] == 73, + "T740 finite dimensions changed") + require(claim["live"] == 663040 and claim["physical"] == 663549, "T740 stocks changed") + capacity = 73 * 663040 + require(sum(profile.values()) == 23953011 and profile_mass(profile) == 48165120, + "T740 complete counts changed") + require(capacity - profile_mass(profile) == 236800 == 320 * 740, "T740 mass deficit changed") + low_a, high_a = (Q(s) for s in claim["root_interval"]) + require(high_a - low_a == Q(1, 10**24), "T740 adjacent endpoints changed") + low_m = scale_interval(paid_cost(profile, 73, low_a), Q(1, capacity)) + high_m = scale_interval(paid_cost(profile, 73, high_a), Q(1, capacity)) + require(low_m[1] < 1 < high_m[0], "T740 strict root bracket failed") + selected_m = scale_interval(paid_cost(profile, 73, kappa / (1 - kappa)), Q(1, capacity)) + require(selected_m[1] < 1, "T740 selected-saving screen failed") + supplied_k = Q(claim["kappa"]) + require(supplied_k == low_a - Q(1, 10**46) - Q(1, 10**70), "stated outer endpoint arithmetic") + require(supplied_k > Q(173, 100000) > kappa, "stated conditional endpoint comparison") + require(Q(claim["unchanged_bit_endpoint"]) > high_a, "BIT endpoint ordering changed") + # Positive additions near a root are a sharp control for the eight strata. + corrupt = dict(profile) + corrupt[1] += 1 + extra = scale_interval(paid_cost(corrupt, 73, low_a), Q(1, capacity)) + require(extra[0] > 1, "one extra unpaid rank-one child accepted at the claimed lower endpoint") + return { + "scope": "Independent profile arithmetic only; conditional finite release/owners/native/outer hypotheses are inherited and not rerun.", + "head": "3efbb5de06a49ffeea6684482f2d3fe48cdca3fb", + "profile": {str(r): count for r, count in sorted(profile.items())}, + "width": 73, "families": 663040, "capacity_rank_mass": capacity, + "children": sum(profile.values()), "paid_rank_mass": profile_mass(profile), + "root_interval": [str(low_a), str(high_a)], + "moment_at_lower_endpoint": compact(low_m), + "moment_at_upper_endpoint": compact(high_m), + "moment_at_selected_balanced_requirement": compact(selected_m), + "one_extra_rank_one_child_rejects": compact(extra), + "stated_outer_endpoint_arithmetic_agrees": True, + "new_outer_proof_or_complete_release_replay": False, + } + + +def prior_hosting_check(bodies, kappa): + text = bodies["PR3574_README.md"].decode() + require("1,126 extra" in text and "At 1,127 units" in text, "prior hosting statement changed") + channel = {1: 1074, 2: 58, 3: 86, 4: 104, 5: 48, 6: 24, 7: 8, 8: 8} + require(profile_mass(channel) == 2368, "prior channel mass") + local = dict(channel) + local[1] += 208 * 9 + capacity = Q(73 * 832, 9) + saving = kappa / (1 - kappa) + values = {} + for hosted in [0, 1126, 1127]: + paid = dict(local) + paid[1] += hosted + remaining = 2472 - hosted + interval = paid_cost(paid, 73, saving) + residual = scale_interval(power_interval(Q(73, 51), saving), remaining) + values[hosted] = scale_interval(add_interval(interval, residual), 1 / capacity) + require(values[0][1] < 1 and values[1126][1] < 1 < values[1127][0], + "prior 1126/1127 hosting comparison disagrees") + return { + "source_pr": 3574, "head": "eb11cd484c23990c250bdc67ae61829ebae35536", + "scope": "Different native-channel plus unit-step correction provider; every hosting rank unit displaces one ideal rank-51 idle mass unit.", + "saving": str(saving), + "moments": {str(h): compact(interval) for h, interval in values.items()}, + "provider_geometry_native_and_owners_not_replayed": True, + } + + +def analyze(root=ROOT): + bodies = authenticate(root) + forward, dual, kappa, primitive = sources(bodies) + pair_result = all_pair_check(forward, dual, kappa, primitive) + t740 = conditional_t740_check(bodies, kappa) + hosting = prior_hosting_check(bodies, kappa) + controls = { + "boolean_count": must_reject(lambda: read_profile({"1": True}), "must be an integer"), + "duplicate_key": must_reject(lambda: parse_json(b'{"a":1,"a":2}'), "duplicate JSON key"), + "boolean_pair_count": must_reject(lambda: combined_profile(forward, dual, True), "must be an integer"), + "out_of_range_rank": must_reject(lambda: paid_cost({74: 1}, 73, kappa), "child rank exceeds width"), + "negative_cost": must_reject(lambda: excess(forward, dual, 7, kappa, added_cost=Q(-1)), "added cost"), + "typed_receipt_identity": not strict_equal({"schema_version": 1}, {"schema_version": True}), + } + require(controls["typed_receipt_identity"], "Boolean/integer receipt alias accepted") + return { + "schema_version": 1, "status": MARKER, + "source_manifest_sha256": SOURCE_MANIFEST, + "arithmetic": {"log_terms": LOG_TERMS, "exp_terms": EXP_TERMS, + "rounding_grid": str(GRID), "decision_method": "exact rational outward intervals; no floating-point decisions"}, + "all_pair_deletion": pair_result, + "conditional_t740": t740, + "distinct_prior_hosting_threshold": hosting, + "negative_controls": controls, + } + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--write", action="store_true", help="explicitly create the local receipt") + args = parser.parse_args() + observed = analyze() + receipt = ROOT / "RESULT.json" + if args.write: + receipt.write_text(json.dumps(observed, sort_keys=True, indent=2) + "\n") + else: + require(strict_equal(observed, parse_json(receipt.read_bytes())), "typed receipt mismatch") + print(MARKER) + + +if __name__ == "__main__": + try: + main() + except (Rejection, KeyError, OSError, json.JSONDecodeError) as error: + print("FAIL_ROUTE1_CONSUMER_BUDGET " + str(error), file=sys.stderr) + raise SystemExit(1) from error diff --git a/research/p104-caller-feasibility/physical/CALLER_AUDIT.md b/research/p104-caller-feasibility/physical/CALLER_AUDIT.md new file mode 100644 index 0000000000..c26b46495e --- /dev/null +++ b/research/p104-caller-feasibility/physical/CALLER_AUDIT.md @@ -0,0 +1,125 @@ +# Physical-caller decision for the PR3609 entrance + +The new result closes a finite format obligation: the standalone entrance +accepts arbitrary original-grid physical fields with six added fractional +bits; the combined program needs seven internally and six at its required +outputs. Sufficient magnitude and native scratch capacities are proved in +`FORMAT_PROOF.md`. It does **not** identify an existing paid producer of the +required fields. Within the already failing PR3609 five-forward/four-dual +consumer model, adding preparation or routing costs cannot make the moment +feasible. The useful next step is a different complete consumer or cost law, +followed by one explicit producer-to-module boundary under its allowance. + +## Exact interface now available for a caller + +The standalone program uses 197 distinct physical banks, each containing 512 +Gaussian coordinates: the 52 omitted X inputs at their actual singleton +frames; 38 omitted N and G2/G3/G9 at the empty frame; and all 104 Y inputs at +the empty frame. The Y banks are temporarily writable and restored before +the next source column is used. The 93 dirty output banks finish in F; Y +returns to its original values and empty frames. No additional Gaussian query +bank is allocated by this entrance. Arithmetic scratch, guards, native +workspace, and an address/controller implementation are still required. + +For the full caller, retain the actual 4,027-event projection, the other 161 +public fields, and all eight existing private-C zero/erase lifetimes. All 358 +required endpoint frames are part of the contract. In particular, final Y +frames have dimension eight; their normalized restoration does not make them +empty-frame physical sources. Additional return adapters may be required by +a different upstream owner, and their bill is not supplied here. + +The six-bit standalone format is a weaker sufficient arithmetic entrance than +the published 4B9 product condition. It is not a new source-module maximality +claim and does not require a free E9 encoder. A caller can supply arbitrary +mantissas in the explicitly refined representation, provided it pays for the +new bit positions, capacity, access and cleanup. That conditional possibility +is distinct from an actual owner/allocation construction. + +## Finite conversion charges and their limits + +Let an original signed mantissa use b magnitude bits and one sign bit. An +explicit scalar representation change stores `2^g*m` and changes the unit +from `2^-f` to `2^-(f+g)`. It preserves the represented number. A direct +arithmetic implementation performs g doublings per real component. The +following exact counts are additional conversion work, not part of PR3609's +887 entrance ADDs or its native tariff: + +| Conversion | Real component words | Operations in this direct scalar implementation | +| --- | ---: | ---: | +| Standalone entry, guard 6 | 201,728 | 1,210,368 doublings | +| Optional standalone Y return to its original unit | 106,496 | 638,976 exact halves | +| Full-program entry, guard 7 | 366,592 | 2,566,144 doublings | +| Full outputs from guard 7 to guard 6 | 366,592 | 366,592 exact halves | + +The optional Y conversion is exact because the standalone program returns +every Y mantissa unchanged. It is not a permission to compress arbitrary +dirty X/N/G outputs back to the input grid. The full-output one-bit +compression is exact by the all-output denominator proof; the required X0 +witness prevents compressing the uniform output unit below six bits. + +A bit-oriented converter can instead append g zero low bits in preallocated +owned slots. Visiting original magnitude bits from high to low prevents +overwriting an unread source bit. Per word this construction reads b original +bits, writes b shifted bits, and writes g low zeros; the sign is preserved. +It is an alternative to counting g arithmetic doublings, not an additional +free implementation. If the added cells contain borrowed dirt, that dirt +must be preserved and returned separately. Supplying zero padding and +headroom is therefore an ownership obligation. + +The proved signed capacities are b+19 field bits and b+20 scratch bits for +the standalone prefix, or b+20 and b+21 for the full program. Compared with +the original b+1 signed words, these are 18 or 19 extra field bits per real +component. They include fractional refinement and magnitude headroom. +For example, the full 358-field public array alone uses +`366592*(b+20)` data bits under this fixed-slot convention. That count excludes +private C, arithmetic registers, delimiters, counters, routing stock and +control. The source does not provide their placement or movement price. + +These scalar or within-slot bit counts do not establish a complete encoded +machine. A paid implementation must charge per-word carry/shift work, traversal +between actual field locations, phase permutations, loop/shape control, real +scratch supply and restoration. No universal tape distance, owner window or +controller cost is assigned zero. A producer that emits the refined format +directly must include its construction and zero-padding costs in its own bill. + +## Named-source audit + +The read-only entry audit used canonical main +`20ecf2891d80b5acf18d980b2164fb44ea7faa90` and the following exact source +boundaries. The statements describe the inspected documentation; they are +not a proof that no unpublished or uninspected caller can exist. + +| Named candidate | What is actually supplied | Missing bridge to this entrance | +| --- | --- | --- | +| [p104-newton-source-contract](https://github.com/CrocSwap/integer-mult-bounds/blob/20ecf2891d80b5acf18d980b2164fb44ea7faa90/research/p104-newton-source-contract/README.md) and [tensor-Newton](https://github.com/CrocSwap/integer-mult-bounds/blob/20ecf2891d80b5acf18d980b2164fb44ea7faa90/research/p104-tensor-newton/README.md) | Exact source-local product domains and their conditional all-depth extension | Both explicitly leave actual input conversion, owners/routes and a favorable caller open. Their lattice index is inherited, not a new result here. | +| [Selected P104 port adapter](https://github.com/CrocSwap/integer-mult-bounds/blob/20ecf2891d80b5acf18d980b2164fb44ea7faa90/research/selected-p104-port-adapter/README.md), PR1746 | Exact selected-label map and eight-term decoder | Asymmetric-centre construction/reads, phase restoration, full supplier compilation and hosting remain unresolved. Label equality does not allocate the 197 fields. | +| [P104 source preconditioning](https://github.com/CrocSwap/integer-mult-bounds/blob/20ecf2891d80b5acf18d980b2164fb44ea7faa90/research/p104-source-preconditioning/README.md) | A scalar rank-four obstruction and one legal source shear for a different pooled correction model | Its prepared-X immutable-reader contract and retained channel are different. No map from that boundary to the present independent Gaussian inputs is given. | +| [P104 blockwise lifting](https://github.com/CrocSwap/integer-mult-bounds/blob/20ecf2891d80b5acf18d980b2164fb44ea7faa90/research/p104-blockwise-lifting/README.md) | A conditional exact XOR/backend reduction, including local cleanup and addressed gather/scatter | Both fast orientations, physical routing and a favorable actual backend remain premises. It is not a provider of this dirty-field interface. | +| [PR3590](https://github.com/CrocSwap/integer-mult-bounds/pull/3590), `5a607f77236bfc7caab957ce99f55377cd903980`; [PR3593](https://github.com/CrocSwap/integer-mult-bounds/pull/3593), `46c04613a19a5b7bd50d98e50bbc8ea8dc6275b0` | Owned-address header enumeration and a separate encoded Boolean header controller | These are useful control components, but neither outputs P104's Gaussian bank arrays, establishes their ownership, or proves the required packet/field consumer join. | +| [PR3605 conditional release](https://github.com/RossRichardson/integer-mult-bounds/blob/3efbb5de06a49ffeea6684482f2d3fe48cdca3fb/research/staged-644-660-conditional-release/README.md), `3efbb5de06a49ffeea6684482f2d3fe48cdca3fb` | A complete finite staged PR3133 owner/release binding and a stronger conditional numerical candidate | Its two source words have 632 live inputs and 91 private buffers. No mapping of those inputs, owner roles, coefficients or frames into this P104 caller is provided. Its paid 2,048-bit reserve cannot be transferred merely because a separate width estimate fits numerically. | +| [PR3610](https://github.com/CrocSwap/integer-mult-bounds/pull/3610), `4352496b3aa56ad17446ddbd1d78931f3d392996`; [PR3614](https://github.com/CrocSwap/integer-mult-bounds/pull/3614), `a6c3ae20abe0a15d781ee952e717d489552c9c66` | Native-channel flag-1 correction bills and an 18-entry forcing census | Different source/target charts and correction obligations; no P104 Gaussian-grid producer or general physical owner allocation is claimed. | + +The canonical initial-reader and native-cache packages were also inspected: +one gives a scoped contact count, the other optimizes verifier memoization. +Neither adds the missing physical field boundary. The current-head audit is +bounded to these named sources and their metadata/README interfaces; it does +not cover every historical code diff, comment or unpublished construction. + +## Recommendation and stopping rule + +Retain the six/seven/six format theorem as a concrete improvement to the +caller specification. It removes a need to guess a large native guard and +separates input representation, storage range and output consumption. +It does not by itself justify a supplier build. Under PR3609's exact m=73, +W=832, five-forward/four-dual coverage assumptions, even the favorable native +relaxation fails. Nonnegative preparation, routing or controller charges can +only worsen that same inequality. + +The strongest reopening test is consequently a named complete consumer with +a changed favorable allowance, together with one explicit physical source +mapping. Before construction, that mapping must state all participating +owners, initial/final formats and frames, mutable-source permissions, zero +stock, bounded primitive workspace, access/control costs and every required +return. This audit supplies the finite-format part of that table. The other +rows remain open rather than being manufactured from unrelated conditional +release or header-control results. diff --git a/research/p104-caller-feasibility/physical/FORMAT_PROOF.md b/research/p104-caller-feasibility/physical/FORMAT_PROOF.md new file mode 100644 index 0000000000..8853c431a3 --- /dev/null +++ b/research/p104-caller-feasibility/physical/FORMAT_PROOF.md @@ -0,0 +1,245 @@ +# Exact finite formats for the PR3609 entrance and its retained caller + +Clear1nsight, with substantial OpenAI assistance. Apache-2.0. This is a +one-layer format transfer to the exact PR3609 source, with inherited native +and Newton-module theorems. It is not a physical producer, encoded controller, +recursive implementation, or multiplication-supplier admission. + +## 1. Three different interfaces + +Let every initial physical real and imaginary component be in +$2^{-f}\mathbb Z$, where $f\ge0$ is an integer. Inputs are otherwise arbitrary +and independent, including all required dirty inputs. Preserve PR3609's +distinct roles, writable/restored Y access, actual initial and final frames, +and owned private-zero obligations. A **uniform guard** means one common +fixed-point unit for every stored field throughout the specified program. + +| Interface | Sharp added fractional bits | Exact source boundary | +| --- | ---: | --- | +| Standalone entrance | 6 | All 1,238 new operations; 197 participating public banks | +| Entrance followed by retained projection | 7 | All 5,265 combined operations; 358 public banks | +| Final outputs of the combined program | 6 | All 358 required physical output fields | + +These are format statements about arbitrary original-grid physical inputs. +In particular, the standalone six-bit argument does **not** assert +$64\mathbb Z[i]^{512}\subseteq4B_9$; that inclusion is false. Its proof below +uses exact relative-prefix denominators rather than the stronger published +product-domain sufficient condition. Nonuniform formats, different arithmetic, +approximate outputs, and changed programs are outside the sharpness claim. + +The source is PR3609 at `13f974dae4af66027afb01f3ab42df9e830c2e90`. +`SOURCE_MANIFEST.json` gives original paths, commits, Git blobs, SHA256s and +exact retained notices. Four JSON/gzip inputs drive the new checker; no +predecessor executable is imported. PR3609's program, native maps, proof and +all original predecessor inputs remain unchanged. + +## 2. Representation refinement preserves the numerical input + +Write an initial physical component as $x=2^{-f}m$, $m\in\mathbb Z$. +At guard $g$, store $n=2^gm$ with unit $2^{-(f+g)}$. Then + +$$2^{-(f+g)}n=2^{-f}m=x.$$ + +This is a change of integer representation, not multiplication of the +mathematical input by $2^g$. Keeping the old unit while multiplying mantissas +would instead scale the numerical problem and would require a different +input/output intertwiner. Appending low zero bits is an operation or a +producer-format obligation; it is not automatically free. + +The refined execution computes the source's ideal Gaussian word exactly. It +is not asserted to equal a separate execution of the signed-floor program on +the unrefined f-grid with arbitrary inputs outside its exactness domain. + +Put $R=\mathbb Z[i]$, $\pi=1+i$, and +$B_9=\bigl(\begin{smallmatrix}1&0\\1&\pi\end{smallmatrix}\bigr)^{\otimes9}R^{512}$. +The Newton criterion says a function belongs to $B_9$ exactly when its +Möbius coefficient at subset $S$ is divisible by $\pi^{|S|}$. Consequently +$\pi^{13}R^{512}\subseteq\pi^4B_9=4B_9$, since every Möbius coefficient of +such a vector is divisible by $\pi^{13}$. Also $128$ is a unit times +$\pi^{14}$, so + +$$128R^{512}\subseteq4B_9\subseteq2B_9\subseteq B_9.$$ + +At guard seven, every initial mantissa therefore satisfies PR3609's common +sufficient domain: 104 Y fields in $4B_9$, 78 N fields in $2B_9$, and 176 +other fields in $B_9$. The pinned PR3382 module theorem, PR3416 native +covariance, and PR3609's source-bound scalar induction give exact execution +of the entire combined word, including all eight literal private erasures. +This reuses those theorems; it does not re-certify their historical suites. + +## 3. Six bits suffice for the standalone entrance + +Each nonzero entry of a coordinate C gate or its inverse is a Gaussian unit +times $\pi/2$. A monomial contributes only a permutation and powers of $i$. +Every matrix entry of a product with $t$ such C factors is therefore in + +$$ (\pi/2)^t R\ \subseteq\ 2^{-\lceil t/2\rceil}R.$$ + +The argument is termwise over matrix-product paths: summing terms preserves +their common Gaussian ideal. It does not assume that separated C factors +commute. A prefix of $r$ actual coordinate gates has at most $r$ factors; +its two native wrappers add none. + +At a scalar cut, the actual physical value has the usual source-bound form + +$$\sum_s c_s J_HJ_{I_s}^{-1}x_s,$$ + +where $H$ is the current frame, $I_s$ the actual entrance frame, and $c_s$ +the exactly traced rational scalar coefficient. At a native internal prefix, +replace $J_H$ by that prefix times its entrance chart. A sufficient guard for +the term is + +$$\left\lceil\frac{\dim H+\dim I_s+r}{2}\right\rceil-v_2(c_s),$$ + +using the full native rank $r$ to bound every earlier native stage. At scalar +cuts set $r=0$. The new checker applies this test separately to every stored +row and every scalar product before an ADD or source half/double. + +In the actual entrance, dirty-X coefficients remain integers. Their entrance +charts have dimension one; the full finish contributes at most nine factors. +Y coefficients are half-integers, their entrance frame is empty, and finish +prefixes contribute at most nine factors. The other 41 dirty banks have empty +entrance charts and integer coefficients. The authenticated per-term audit +has maximum guard six. In particular, all 887 unit additions, 103 temporary +source halves and 103 restoring doublings have integral increments on this +grid; no cancellation with the target is used to excuse a fractional donor. + +Evaluate the ideal program first. All before/after C-pair values and all +scalar increments lie on the six-bit grid. For a C pair, integral ideal +outputs imply equality with the credited signed-floor lift. Some internal +midpoint divisions of that lift are floors, not separately exact divisions; +their compensating formula is what equals the ideal C pair. This distinction +prevents assuming that arbitrary rounded execution is linear. The induction +also covers negative mantissas and values partly written within a pair. + +## 4. Source-bound lower witnesses + +Set the physical input $Y2=2^{-f}\delta_0$ and every other initial public +field to zero. In the entrance, the actual scalar program gives the pivot +$X0$ coefficient $-Y2/2$, restores Y2, and applies the new full-frame recipe. +The retained projection never reads or writes X0. Hence its required final +coordinate zero is + +$$X0_{\rm final}(0)=2^{-f}\frac{-1+i}{64}.$$ + +The checker derives the coefficient from the serialized entrance, runs the +actual new rank-nine recipe at guards five, six and seven, and compares the +complete 512-entry column with the direct tensor formula. Guard six returns +integer coordinate $(-1,1)$; guard five rejects a nonintegral C output. The +odd six-bit mantissa proves that both the standalone module and the full +program's exact final output format require at least six uniform bits. + +For the full execution, original event 2142 transports D18 into the full +frame. It survives as combined event 3000. Its exact Y2 coefficient is +$-1/4$, so + +$$D18(0)=2^{-f}\frac{-1+i}{128}.$$ + +Backward dependence extraction selects 36 retained events and nine initial +roles: D18 and Y0, Y2, Y44, Y51, Y71, Y79, Y97, Y98. Before executing that +cone, the new scalar/frame audit checks that all nine are restored to their +initial value rows and frames after all 1,238 entrance operations. This is +the explicit justification for projecting the witness through the new prefix. + +At guard seven, the actual cone completes 2,304 literal/ideal pairs in four +active natives and returns the complete expected D18 column, with integer +coordinate $(-1,1)$. Twenty-four zero natives use their exact zero action. +At guard six, the first 35 cone events and 2,048 active pairs complete. At +event 2142, bit zero and address zero, the pair inputs are $i$ and $0$; +the twice-ideal outputs are $(-1+i,1+i)$. They are not Gaussian integers +after division by two. This is an actual literal obstruction, not a rejection +merely for failing the stronger $4B_9$ sufficient entrance. + +The cone is not claimed as a numerical replay of all preceding events. +Even if some other six-bit path failed sooner, this required ideal value +already prevents a complete exact six-bit execution. Seven-bit sufficiency +comes from Section 2's all-input theorem, not extrapolation of the witness. + +## 5. Every final output admits six bits + +The exact combined scalar trace checks that every final coefficient has +denominator one or two. It also checks all 358 final frames, maximum initial +frame dimension one, and maximum final dimension nine. Thus each relative +endpoint chart $J_FJ_I^{-1}$ has at most ten C factors. Section 3's elementary +Gaussian-ideal argument puts its entries in $2^{-5}R$; multiplication by a +half-integer puts every output in $2^{-(f+6)}R$. + +All final mantissas of a seven-bit execution are consequently even. One exact +halving per real component, together with changing the unit from +$2^{-(f+7)}$ to $2^{-(f+6)}$, preserves the output value. This does not permit +discarding all seven fractional bits. Required frames remain those of the +source: in particular all 104 final Y frames have dimension eight. Logical +Y restoration in the full word is not a return in the empty physical frame. +The standalone entrance instead returns every Y in its original empty frame. + +## 6. Magnitude, scratch and signed integer capacity + +Let $H$ bound the absolute value of **each initial real and imaginary +component**. Each initial field has real Euclidean norm at most +$\sqrt{1024}H=32H$. Chart maps and native prefixes are unitary. The exact +combined scalar trace has maximum row $\ell_1$ norm 103, first attained at +entrance operation 929 on X17; its separately checked scalar-product maximum +is 30. Thus every complete field and every complete native stage has real +Euclidean norm at most + +$$M=103\cdot32H=3296H.$$ + +The same component bound holds during partially written stages: a component +comes from its preceding or completed pair. Completed disjoint native-pair +updates preserve the field norm. The four-term numerator of any real C output +has coefficient-vector Euclidean norm two, so its magnitude is at most +$2M=6592H$. This uses a **whole-field norm**, not the false inference that +four arbitrary components individually bounded by M sum to at most 2M. + +The signed-floor implementation also fits this scratch bound. Its differences +and quarter-turn copies are bounded by 2M; its midpoint is a floor of the +average of two integer components and is bounded by M. Completed C outputs +are bounded by M. Integer-ADD results are covered by their traced rows; +source halves and restoring doubles are explicitly checked. Basic monomial +permutations and phases preserve magnitudes; a simple arithmetic SWAP's sum +temporary is bounded by 2M. This is a sufficient bound for these declared +finite scalar schedules. An unrelated recursive native implementation still +needs its own internal-work proof and bill. + +For a concrete convention, let each original-grid signed mantissa have at +most $b\ge1$ magnitude bits, so its absolute value is at most $2^b-1$ and +its usual signed width is $b+1$. With guard seven, sufficient signed widths +are **$b+20$ for fields and $b+21$ for literal scratch**. The corresponding +standalone guard-six widths are $b+19$ and $b+20$. These bounds include sign, +fractional refinement and magnitude growth. They follow from +$3296<2^{12}$ and $6592<2^{13}$; fractional guard bits alone do not supply +integer headroom. Zero input is trivial. No minimal magnitude-width claim +is made, and Python's unbounded integers are not a physical-capacity proof. + +## 7. Reproduction, credits and remaining physical obligations + +From this source-complete directory, using Python 3.12 and the standard library: + +```sh +python3.12 -I -Werror -B verify_format.py +python3.12 -I -O -Werror -B verify_format.py +``` + +Ordinary replay recomputes and strictly compares every field of +`FORMAT_RESULT.json`; Boolean/int substitutions are rejected. To generate +new evidence explicitly, use `--write-receipt /absolute/new/path.json`; +existing output files are never overwritten. The checker runs no old native +census and imports no old arithmetic implementation. + +Credit PR3609 for the actual new schedule/maps, dirty restoration, complete +endpoint theorem and conditional cost stop; ywz65/PR2586 and Arham Tahir's +retention for the original word/native data; PR3382 and Nick Petalas's +PR3406/3416/tensor-Newton work for the module/covariance premises; Ross +Richardson's sharp Clifford-grid finding, PR2772's whole-word format, and +the distinct PR2725 retimed-grid transfer for the earlier precision method. +The six/seven/six binding and new source-range bound here are for PR3609 only. +No old index or denominator lemma is claimed as new. The earlier dirty +accumulation method remains credited to Dumas and Grenet. + +Actual upstream owners, permission to move or temporarily modify Y, +component layout, source preparation, routing, a charged encoded controller, +recursive child interfaces and an affordable complete supplier remain open. +The format result specifies what such a caller must provide and consume. +Adding its nonnegative costs cannot reverse PR3609's failed fixed +five-forward/four-dual consumer inequality. `CALLER_AUDIT.md` records the +named-source audit and the precise finite conversion obligations. diff --git a/research/p104-caller-feasibility/physical/FORMAT_RESULT.json b/research/p104-caller-feasibility/physical/FORMAT_RESULT.json new file mode 100644 index 0000000000..655d41fe15 --- /dev/null +++ b/research/p104-caller-feasibility/physical/FORMAT_RESULT.json @@ -0,0 +1,269 @@ +{ + "canonical_base": "20ecf2891d80b5acf18d980b2164fb44ea7faa90", + "documentary_input_sha256": { + 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"source_path": "research/p104-omitted-frame-adapters/inputs/PR3416_verify.py", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3416" + }, + { + "author": "Clear1nsight with substantial OpenAI assistance", + "head": "2834523b1cd4ea83ba7a043e2e2f5f3332cf9909", + "origin_path": "research/p104-clifford-exactness/PROOF.md", + "pull_request": 3382, + "source_path": "research/p104-stagewise-entrance/inputs/PR3382_PROOF.md", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3382" + }, + { + "author": "Nick Petalas / petalas", + "head": "f1112560883a5e81b1a29c37c81a79a20be31fe3", + "origin_path": "research/p104-native-covariance/PROOF.md", + "pull_request": 3416, + "source_path": "research/p104-stagewise-entrance/inputs/PR3416_PROOF.md", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/3416" + }, + { + "author": "ywz65", + "head": "7953c9a8f788a8de5cf2ced63d9a61b67c22c6f1", + "pull_request": 2586, + "retained_by": "Arham Tahir / PR2665; current canonical paths are independently pinned in files.", + "source_paths": [ + "research/p104-rounded-collector/inputs/WORD.json", + "research/p104-rounded-collector/inputs/NATIVE.json.gz" + ], + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2586" + }, + { + "author": "Vasek / flyingviper", + "head": "0166260409f55a56e7fefa48d859f7dd5b42b300", + "prior_observation_credit": "Jose Manuel / jmbarrancoml", + "prior_observation_url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/2619#discussioncomment-18955566", + "pull_request": 2744, + "source_path": "research/p104-consumer-budget-audit/README.md", + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/2744" + } + ], + "new_result": "PR3609 local/full/output finite-format transfer and physical-caller feasibility boundary.", + "runtime_policy": "Four JSON/gz data files only; no predecessor executable is imported. Three written proofs are inherited mathematical premises. Six exact notices preserve the retained source lineage.", + "schema_version": 1, + "source_head": "13f974dae4af66027afb01f3ab42df9e830c2e90" +} diff --git a/research/p104-caller-feasibility/physical/controls.py b/research/p104-caller-feasibility/physical/controls.py new file mode 100644 index 0000000000..adad79b8a7 --- /dev/null +++ b/research/p104-caller-feasibility/physical/controls.py @@ -0,0 +1,131 @@ +#!/usr/bin/env python3 +"""Actual isolated CLI controls for the source-complete format component. + +Clear1nsight, with substantial OpenAI assistance. Apache-2.0. +Only disposable copies are mutated. No predecessor verifier is executed. +""" + +import argparse +import hashlib +import json +from pathlib import Path +import shutil +import stat +import subprocess +import sys +import tempfile +import time + +ROOT = Path(__file__).resolve().parent + + +def need(condition, message): + if not condition: + raise ValueError(message) + + +def snapshot(directory): + result = {} + for path in sorted(directory.rglob('*')): + if path.is_file(): + result[str(path.relative_to(directory))] = [ + hashlib.sha256(path.read_bytes()).hexdigest(), + stat.S_IMODE(path.stat().st_mode), path.stat().st_size] + return result + + +def populate(root, destination): + destination.mkdir() + for name in ('verify_format.py', 'FORMAT_RESULT.json', 'SOURCE_MANIFEST.json', 'FORMAT_PROOF.md'): + shutil.copy2(root / name, destination / name) + shutil.copytree(root / 'inputs', destination / 'inputs', copy_function=shutil.copy2) + + +def command(directory, optimized): + flags = ['-I', '-Werror', '-B'] + if optimized: + flags.insert(1, '-O') + start = time.perf_counter() + process = subprocess.run([sys.executable, *flags, str(directory / 'verify_format.py')], + cwd=directory, text=True, capture_output=True, timeout=20) + return process, time.perf_counter()-start + + +def valid_case(root, work, optimized): + destination = work / ('optimized' if optimized else 'normal') + populate(root, destination) + before = snapshot(destination) + process, seconds = command(destination, optimized) + need(process.returncode == 0 and process.stdout.startswith('PASS_PR3609_FORMAT_TRANSFER:'), + 'valid actual CLI failed: ' + process.stderr[-2000:]) + need(snapshot(destination) == before, 'valid CLI changed source bytes or modes') + return {'status': 'PASS', 'returncode': 0, 'regular_files_unchanged': len(before), + 'seconds': round(seconds, 6), 'optimized': optimized} + + +def mutate(directory, name): + word = directory / 'inputs' / 'WORD.json' + if name == 'missing_WORD': + word.unlink() + return 'missing or oversized pinned input: research/p104-rounded-collector/inputs/WORD.json' + if name == 'corrupt_WORD': + word.write_bytes(word.read_bytes() + b'\n') + return 'input hash: research/p104-rounded-collector/inputs/WORD.json' + need(name == 'Boolean_receipt', 'unknown control') + receipt = directory / 'FORMAT_RESULT.json' + value = json.loads(receipt.read_bytes()) + value['schema_version'] = True + receipt.write_text(json.dumps(value, indent=2, sort_keys=True)+'\n') + return 'receipt type mismatch at receipt.schema_version' + + +def invalid_case(root, work, name): + destination = work / name + populate(root, destination) + expected = mutate(destination, name) + before = snapshot(destination) + process, seconds = command(destination, True) + need(process.returncode != 0 and expected in process.stderr + and 'PASS_PR3609_FORMAT_TRANSFER:' not in process.stdout, + 'actual CLI failed to reject the intended ' + name + ' control') + need(snapshot(destination) == before, 'rejected CLI made an extra mutation') + return {'status': 'REJECT_AS_EXPECTED', 'returncode': process.returncode, + 'diagnostic': expected, 'regular_files_unchanged_after_mutation': len(before), + 'seconds': round(seconds, 6)} + + +def run_controls(root=ROOT, work=None): + protected = {name: hashlib.sha256((root / name).read_bytes()).hexdigest() + for name in ('verify_format.py', 'FORMAT_RESULT.json', 'SOURCE_MANIFEST.json', 'FORMAT_PROOF.md')} + input_before = snapshot(root / 'inputs') + with tempfile.TemporaryDirectory(prefix='p104-format-controls-', dir=work) as temporary: + private = Path(temporary) + positive = [valid_case(root, private, False), valid_case(root, private, True)] + negative = {name: invalid_case(root, private, name) + for name in ('missing_WORD', 'corrupt_WORD', 'Boolean_receipt')} + need(snapshot(root / 'inputs') == input_before, 'original inputs changed') + need(all(hashlib.sha256((root/name).read_bytes()).hexdigest() == expected + for name, expected in protected.items()), 'original scientific files changed') + return {'schema_version': 1, 'status': 'PASS_PR3609_FORMAT_CLI_CONTROLS', + 'positive': positive, 'negative': negative, + 'original_input_files_unchanged': len(input_before), + 'protected_source_sha256': protected, + 'scope': 'Actual normal/optimized and three rejecting disposable CLI copies; no historical suite.'} + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--root', type=Path, default=ROOT) + parser.add_argument('--work', type=Path) + parser.add_argument('--out', type=Path) + args = parser.parse_args() + result = run_controls(args.root, args.work) + if args.out: + with args.out.open('x', encoding='utf-8') as stream: + json.dump(result, stream, indent=2, sort_keys=True) + stream.write('\n') + print('PASS_PR3609_FORMAT_CLI_CONTROLS: normal/O immutable, missing/corrupt WORD and Boolean receipt rejected') + + +if __name__ == '__main__': + main() diff --git a/research/p104-caller-feasibility/physical/verify_format.py b/research/p104-caller-feasibility/physical/verify_format.py new file mode 100644 index 0000000000..a460e154c3 --- /dev/null +++ b/research/p104-caller-feasibility/physical/verify_format.py @@ -0,0 +1,516 @@ +#!/usr/bin/env python3 +"""Bounded, independent format transfer for the pinned PR3609 program. + +Clear1nsight, with substantial OpenAI assistance. Apache-2.0. +No predecessor executable is imported. This checks a scalar range certificate, +one actual 36-event dependency cone, and the required X0 endpoint. It is not +a whole-word numerical replay or a physical owner/controller certificate. +""" + +import argparse +from collections import Counter +from fractions import Fraction +import gzip +import hashlib +import io +import json +from pathlib import Path + +N = 512 +FULL = [256, 128, 64, 32, 16, 8, 4, 2, 1] +HEAD = '13f974dae4af66027afb01f3ab42df9e830c2e90' +BASE = '20ecf2891d80b5acf18d980b2164fb44ea7faa90' +ROOT = Path(__file__).resolve().parent +PINS = { + 'research/p104-rounded-collector/inputs/WORD.json': + 'cec1fb3fbd0067b500ad5119a62ba60685be718e769374d7ec8abdd2beaa7e50', + 'research/p104-rounded-collector/inputs/NATIVE.json.gz': + 'ab91c78835c3e10cf3b2cb8a5d4e0b7cfc3df1ae5a811298d27842f2193e1e3d', + 'research/p104-inplace-entrance/PROGRAM.json': + '608c5c66a6eb7af2fc75d32e2b353a8074a50ef0bdb848c7211c59f3b7a176e6', + 'research/p104-inplace-entrance/NATIVE.json': + '795a8c4e096a42a2f2c5875c354a4d4b56515cf8ffdfd5767a82713cf7f84dbd', +} +LOCAL_FILES = dict(zip(PINS, ('WORD.json', 'ORIGINAL_NATIVE.json.gz', + 'PR3609_PROGRAM.json', 'PR3609_NATIVE.json'))) +DOCUMENT_PINS = { + 'inputs/PR3609_PROOF.md': 'e72a2a0a34ba1c3c226da1e99326ec14e2fb913a74788463bb7013aa8d4954af', + 'inputs/PR3382_PROOF.md': '1ca8c0e7e78f0f39de6cff7accc68ccd3901bfb50759bf7a2e2896bcf63bf081', + 'inputs/PR3416_PROOF.md': '0dc1c35158902299fc8748c8baf89205483562f041e9050580e6579c331ebeb5', + 'inputs/LICENSE': 'c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4', + 'inputs/NOTICE': 'b49022cb4104d90b182e4c335f670faf45529025b15db77bf0291835083c28bd', + 'inputs/FRAME-SA504-NOTICE.md': 'a92f49c5ced455160fbedcc8954e3c9255e3605e88ad12ae5a84f1c4302986f1', + 'inputs/PR1862-NOTICE.md': 'd86f31a4c0bafd4271fe0c0e087a7fc1cd72d5b705e3739c4ba3e9241b7ba3f9', + 'inputs/PR1972-NOTICE.md': '2d9c60fdeda14a8609f2b210fe0873ee0318788130637db9e5e79d487243ab7d', + 'inputs/NATIVE-LINEAGE-NOTICE': 'ee0c73ca35877aad0e0b6adc560a3881cb82276dba4cf2d4fc58cd19e57cc420', +} + + +def need(condition, message): + if not condition: + raise ValueError(message) + + +def canonical(value): + return json.dumps(value, sort_keys=True, separators=(',', ':')).encode() + + +def digest(value): + return hashlib.sha256(canonical(value)).hexdigest() + + +def unique(pairs): + result = {} + for key, value in pairs: + need(key not in result, 'duplicate JSON key') + result[key] = value + return result + + +def read_inputs(root): + data = {} + for path, expected in DOCUMENT_PINS.items(): + source = root / path + need(source.is_file() and source.stat().st_size < 100_000, + 'missing or oversized documentary premise: ' + path) + need(hashlib.sha256(source.read_bytes()).hexdigest() == expected, + 'documentary premise hash: ' + path) + for path, expected in PINS.items(): + source = root / 'inputs' / LOCAL_FILES[path] + need(source.is_file() and source.stat().st_size < 1_000_000, + 'missing or oversized pinned input: ' + path) + raw = source.read_bytes() + need(hashlib.sha256(raw).hexdigest() == expected, 'input hash: ' + path) + if path.endswith('.gz'): + with gzip.GzipFile(fileobj=io.BytesIO(raw)) as compressed: + raw = compressed.read(4_000_001) + need(len(raw) <= 4_000_000, 'native decompression limit') + data[path] = json.loads(raw, object_pairs_hook=unique) + word, old_native, program, new_native = data.values() + need(len(word['program']) == 5398 and len(word['initial_frames']) == 358, + 'original fixed domain') + need(len(program['program']) == 1238, 'new entrance length') + kept = program['retained_original_event_indices'] + need(len(kept) == 4027 and kept == sorted(set(kept)), 'projection indices') + return word, old_native, program, new_native + + +def add_row(left, right, coefficient): + answer = dict(left) + for name, value in right.items(): + answer[name] = answer.get(name, Fraction(0)) + coefficient * value + if not answer[name]: + del answer[name] + return answer + + +def scale_row(row, coefficient): + return {key: coefficient*value for key, value in row.items() if coefficient*value} + + +def row_mass(row): + return sum(map(abs, row.values()), Fraction(0)) + + +def combined_events(word, program, native): + result = [] + for index, event in enumerate(program['program']): + if event[0] == 'native': + _, bank, which = event + item = native['x_to_empty'][bank] if which == 'enter' else native['empty_to_full'] + event = ['transport', bank, item['old'], item['new'], item['recipe']['rank']] + result.append((index, None, event)) + for offset, original in enumerate(program['retained_original_event_indices']): + result.append((len(result), original, word['program'][original])) + need(len(result) == 5265, 'combined fixed event count') + return result + + +def scalar_step(rows, frames, event): + op, target = event[:2] + product = Fraction(0) + if op == 'zero': + need(target not in rows, 'private allocation aliases a live field') + rows[target], frames[target] = {}, event[2] + elif op == 'erase': + need(rows[target] == {} and frames[target] == event[2], 'literal zero row') + del rows[target], frames[target] + elif op == 'transport': + need(frames[target] == event[2], 'transport entrance frame') + frames[target] = event[3] + elif op == 'add': + source, coefficient = event[2], Fraction(event[3]) + need(frames[target] == frames[source], 'ADD common frame') + if len(event) == 5: + need(frames[target] == event[4], 'source ADD frame binding') + product = abs(coefficient)*row_mass(rows[source]) + rows[target] = add_row(rows[target], rows[source], coefficient) + elif op in ('half', 'double'): + rows[target] = scale_row(rows[target], Fraction(1, 2) if op == 'half' else 2) + product = row_mass(rows[target]) + elif op == 'sign': + need(event[2] == '-1' and frames[target] == event[3], 'sign binding') + rows[target] = scale_row(rows[target], -1) + else: + raise ValueError('unknown source operation') + return product + + +def dyadic_valuation(value): + a, b = abs(value.numerator), value.denominator + need(a > 0 and b & (b-1) == 0, 'nonzero dyadic coefficient') + return (a & -a).bit_length()-b.bit_length() + + +def note_guard(row, frame, extra, initial, category, index, guard): + for source, coefficient in row.items(): + factors = len(frame)+len(initial[source])+extra + bits = max(0, (factors+1)//2-dyadic_valuation(coefficient)) + guard['term_visits'][category] += 1 + guard['by_category'][category] = max(guard['by_category'][category], bits) + if bits > guard['maximum']: + guard['maximum'] = bits + guard['first_maximum'] = {'event': index, 'source': source, + 'coefficient': str(coefficient), 'C_factors': factors, + 'category': category} + + +def prefix_guard_before(rows, frames, event, initial, index, guard): + op, target = event[:2] + if op == 'transport': + note_guard(rows[target], frames[target], event[4], initial, + 'native_internal_prefix', index, guard) + elif op == 'add': + source, coefficient = event[2], Fraction(event[3]) + note_guard(scale_row(rows[source], coefficient), frames[source], 0, initial, + 'scalar_product', index, guard) + elif op in ('half', 'double'): + coefficient = Fraction(1, 2) if op == 'half' else 2 + note_guard(scale_row(rows[target], coefficient), frames[target], 0, initial, + 'scalar_product', index, guard) + + +def witness_prefix_binding(rows, frames, initial, roles): + for name in roles: + need(rows[name] == {name: Fraction(1)}, 'new prefix changes a witness input') + need(frames[name] == initial[name], 'new prefix changes a witness input frame') + return {'roles': sorted(roles), 'all_value_rows_identity': True, + 'all_frames_restored': True, 'prefix_events': 1238} + + +def row_trace(word, program, native): + rows = {name: {name: Fraction(1)} for name in word['initial_frames']} + frames = {name: list(frame) for name, frame in word['initial_frames'].items()} + peak, peak_record, product_peak = Fraction(1), None, Fraction(0) + counts, witness_inputs, prefix_binding = Counter(), cone(word, program)[1], None + guard = {'maximum': 0, 'by_category': Counter(), 'term_visits': Counter()} + for index, original, event in combined_events(word, program, native): + op, target = event[:2] + counts[op] += 1 + if index < 1238: + prefix_guard_before(rows, frames, event, word['initial_frames'], index, guard) + product_peak = max(product_peak, scalar_step(rows, frames, event)) + if target not in rows: + continue + if index < 1238: + note_guard(rows[target], frames[target], 0, word['initial_frames'], + 'complete_operation', index, guard) + mass = row_mass(rows[target]) + if mass > peak: + peak, peak_record = mass, {'event': index, 'original_event': original, + 'bank': target, 'operation': event} + if index == 1237: + prefix_binding = witness_prefix_binding(rows, frames, word['initial_frames'], witness_inputs) + need(frames == word['final_frames'], 'all 358 final frames') + need(len(rows) == 358 and counts['zero'] == counts['erase'] == 8, 'public/private return') + denominators = sorted({v.denominator for row in rows.values() for v in row.values()}) + need(denominators == [1, 2], 'final half-integer scalar rows') + need(peak == 103 and product_peak <= peak, 'complete scalar range bound') + need(rows['X0'].get('Y2') == Fraction(-1, 2), 'required X0/Y2 coefficient') + initial_dimension = max(map(len, word['initial_frames'].values())) + final_dimension = max(map(len, frames.values())) + need(initial_dimension == 1 and final_dimension == 9, 'endpoint C-factor count') + need(prefix_binding is not None, 'missing source-return witness binding') + need(guard['maximum'] == 6, 'standalone local six-bit upper bound') + guard['by_category'] = dict(guard['by_category']) + guard['term_visits'] = dict(guard['term_visits']) + return rows, {'events': 5265, 'opcode_counts': dict(sorted(counts.items())), + 'maximum_row_l1': str(peak), 'first_maximum': peak_record, + 'maximum_scalar_product_l1': str(product_peak), + 'endpoint_scalar_denominators': denominators, + 'maximum_initial_frame_dimension': initial_dimension, + 'maximum_final_frame_dimension': final_dimension, + 'witness_inputs_after_new_prefix': prefix_binding, + 'standalone_prefix_guard': guard, + 'final_frames_sha256': digest(frames)} + + +def native_occurrences(word, archive): + need(len(archive['transports']) == 1245, 'old recipe inventory') + result = {} + for record in archive['transports']: + for event in record['events']: + need(type(event) is int and event not in result, 'unique native occurrence') + item = word['program'][event] + need(item[0] == 'transport' and item[2:4] == [record['old'], record['new']], + 'old/native frame binding') + need(item[4] == record['recipe']['rank'], 'old/native rank binding') + result[event] = record['recipe'] + need(len(result) == 2070, 'old native occurrence coverage') + return result + + +def cone(word, program): + kept = set(program['retained_original_event_indices']) + live, selected = {'D18'}, [] + for index in range(2142, -1, -1): + event = word['program'][index] + if index not in kept or event[1] not in live: + continue + need(event[0] in ('transport', 'add'), 'unexpected witness dependency') + selected.append(index) + if event[0] == 'add': + live.add(event[2]) + selected.reverse() + need(len(selected) == 36 and len(live) == 9, 'minimal witness dependency size') + need(2142 in kept and 1238 + program['retained_original_event_indices'].index(2142) == 3000, + 'sharp witness survives at combined event 3000') + return selected, live + + +def phase(value, exponent): + a, b = value + return ((a, b), (-b, a), (-a, -b), (b, -a))[exponent % 4] + + +def wrapper(values, record): + output, covered = [(0, 0)]*N, set() + need(len(record['matrix_rows']) == len(record['linear_Z4']) == len(record['quadratic_rows']) == 9, + 'native wrapper dimension') + for x, value in enumerate(values): + y = record['offset'] + for j, row in enumerate(record['matrix_rows']): + y ^= ((row & x).bit_count() & 1) << j + need(0 <= y < N and y not in covered, 'native wrapper permutation') + covered.add(y) + bits = [j for j in range(9) if (x >> j) & 1] + exponent = record['phase'] + sum(record['linear_Z4'][j] for j in bits) + exponent += 2*sum((record['quadratic_rows'][j] >> k) & 1 + for j in bits for k in bits if j < k) + output[y] = phase(value, exponent) + return output + + +def literal_pair(a, b): + dr, di = a[0]-b[0], a[1]-b[1] + tr, ti = -di, dr + numerators = (a[0]+b[0]+tr, a[1]+b[1]+ti, + a[0]+b[0]-tr, a[1]+b[1]-ti) + if any(v % 2 for v in numerators): + return None, {'input': [list(a), list(b)], 'twice_ideal': list(numerators)} + mr, mi = b[0]+dr//2, b[1]+di//2 + second = (mr-tr//2, mi-ti//2) + first = (second[0]+tr, second[1]+ti) + expected = ((numerators[0]//2, numerators[1]//2), + (numerators[2]//2, numerators[3]//2)) + need((first, second) == expected, 'signed-floor/ideal equality') + return (first, second), None + + +def native(values, recipe, location, counts): + if not any(a or b for a, b in values): + counts['zero_native_calls'] += 1 + return values, None + counts['active_native_calls'] += 1 + values = wrapper(values, recipe['right']) + for bit in range(recipe['rank']): + for low in range(N): + if low & (1 << bit): + continue + pair, error = literal_pair(values[low], values[low | (1 << bit)]) + if error is not None: + error.update({'event': location, 'bit': bit, 'address': low, + 'kind': 'nonintegral_ideal_C_output'}) + return None, error + values[low], values[low | (1 << bit)] = pair + counts['completed_literal_pairs'] += 1 + return wrapper(values, recipe['left']), None + + +def expected_full_column(multiplier): + answer = [] + for address in range(N): + a, b = 1, 0 + for bit in range(9): + sign = 1 if (address >> bit) & 1 else -1 + a, b = a-sign*b, b+sign*a + real, imag = Fraction(multiplier*a, N), Fraction(multiplier*b, N) + need(real.denominator == imag.denominator == 1, 'expected integral column') + answer.append((int(real), int(imag))) + return answer + + +def run_witness(word, program, occurrences, guard): + selected, inputs = cone(word, program) + values = {name: [(0, 0)]*N for name in inputs} + values['Y2'] = [(1 << guard, 0)] + [(0, 0)]*(N-1) + frames = {name: word['initial_frames'][name] for name in inputs} + counts = Counter() + for index in selected: + event = word['program'][index] + op, bank = event[:2] + if op == 'transport': + need(frames[bank] == event[2], 'witness native entrance') + result, error = native(values[bank], occurrences[index], index, counts) + if error: + return {'guard': guard, 'status': 'REJECT', 'failure': error, + 'counts': dict(counts), 'completed_cone_events': counts['events']} + values[bank], frames[bank] = result, event[3] + else: + source, coefficient = event[2], Fraction(event[3]) + need(frames[bank] == frames[source] == event[4], 'witness ADD frames') + increment = [(coefficient*a, coefficient*b) for a, b in values[source]] + need(all(a.denominator == b.denominator == 1 for a, b in increment), + 'witness quarter increment') + values[bank] = [(a+int(c), b+int(d)) + for (a, b), (c, d) in zip(values[bank], increment)] + counts['events'] += 1 + expected = expected_full_column(-(1 << guard)//4) + need(values['D18'] == expected and frames['D18'] == FULL, 'actual sharp D18 column') + return {'guard': guard, 'status': 'PASS', 'counts': dict(counts), + 'D18_sha256': digest(values['D18']), 'D18_coordinate_0': list(values['D18'][0]), + 'original_event': 2142, 'combined_event': 3000} + + +def endpoint_probe(word, program, new_native, guard): + coefficients = {name: Fraction(int(name == 'Y2')) for name in word['initial_frames']} + at_finish = None + for event in program['program']: + op, bank = event[:2] + if op == 'add': + coefficients[bank] += Fraction(event[3])*coefficients[event[2]] + elif op in ('half', 'double'): + coefficients[bank] *= Fraction(1, 2) if op == 'half' else 2 + elif event == ['native', 'X0', 'finish']: + at_finish = coefficients[bank] + need(at_finish == Fraction(-1, 2) and coefficients['Y2'] == 1, + 'actual prelude restores Y2 and forms required X0') + need(all('X0' not in event[1:3] for index in program['retained_original_event_indices'] + for event in [word['program'][index]]), 'projection cannot change X0') + multiplier = -(1 << guard)//2 + values = [(multiplier, 0)] + [(0, 0)]*(N-1) + counts = Counter() + output, error = native(values, new_native['empty_to_full']['recipe'], 'X0_finish', counts) + if guard == 5: + need(error is not None, 'five-bit endpoint must reject') + return {'guard': guard, 'status': 'REJECT', 'failure': error, 'counts': dict(counts)} + need(error is None and output == expected_full_column(multiplier), 'new literal X0 endpoint') + need(output[0] == (-2**(guard-6), 2**(guard-6)), 'sharp six-bit physical output') + if guard == 7: + need(all(a % 2 == b % 2 == 0 for a, b in output), 'final exact one-bit compression') + return {'guard': guard, 'status': 'PASS', 'X0_coordinate_0': list(output[0]), + 'X0_sha256': digest(output), 'literal_counts': dict(counts)} + + +def primitive_controls(): + pair, error = literal_pair((-1, 0), (0, 1)) + need(error is None and pair == ((0, 0), (-1, 1)), 'negative odd floor witness') + # Actually substitute truncation toward zero in both midpoint halves. + trunc = lambda v: v//2 if v >= 0 else -((-v)//2) + mr, mi = trunc(-1), 1+trunc(-1) + second = (mr-trunc(1), mi-trunc(-1)) + wrong = ((second[0]+1, second[1]-1), second) + need(wrong != pair, 'wrong signed-half control') + maximum_ratio = Fraction(0) + tested = 0 + for ar in range(-2, 3): + for ai in range(-2, 3): + for br in range(-2, 3): + for bi in range(-2, 3): + a, b = (ar, ai), (br, bi) + answer, error = literal_pair(a, b) + if error: + continue + dr, di = ar-br, ai-bi + tr, ti = -di, dr + mr, mi = br+dr//2, bi+di//2 + peak = max(map(abs, (dr, di, tr, ti, mr, mi, *answer[0], *answer[1]))) + bound = max(map(abs, (*a, *b, *answer[0], *answer[1]))) + need(peak <= 2*bound, 'literal scratch exceeds twice stored values') + if bound: + maximum_ratio = max(maximum_ratio, Fraction(peak, bound)) + tested += 1 + return {'integral_signed_pairs_checked': tested, + 'maximum_temporary_over_stored_ratio': str(maximum_ratio), + 'wrong_signed_truncation_rejected': True} + + +def verify(root=ROOT): + word, archive, program, new_native = read_inputs(root) + rows, scalar = row_trace(word, program, new_native) + occurrences = native_occurrences(word, archive) + positive = run_witness(word, program, occurrences, 7) + negative = run_witness(word, program, occurrences, 6) + need(positive['status'] == 'PASS' and positive['D18_coordinate_0'] == [-1, 1], + 'seven-bit actual witness') + need(negative['status'] == 'REJECT' and negative['failure']['event'] == 2142, + 'six-bit actual witness failure') + selected, inputs = cone(word, program) + result = {'schema_version': 1, 'status': 'PASS_PR3609_FORMAT_TRANSFER', + 'source_head': HEAD, 'canonical_base': BASE, 'input_sha256': PINS, + 'documentary_input_sha256': DOCUMENT_PINS, + 'scalar_range': scalar, 'sharp_guard_positive': positive, + 'sharp_guard_negative': negative, + 'endpoint': {str(g): endpoint_probe(word, program, new_native, g) for g in (5, 6, 7)}, + 'witness_cone': {'events': selected, 'initial_roles': sorted(inputs), + 'events_sha256': digest(selected)}, + 'primitive_controls': primitive_controls(), + 'format': {'standalone_prefix_fractional_guard': 6, + 'fractional_guard': 7, 'output_fractional_guard': 6, + 'stored_component_factor': 3296, 'literal_scratch_factor': 6592, + 'input_magnitude_bits_b': 'raw original-grid integer components use <=b magnitude bits', + 'sufficient_signed_stored_bits': 'b+20', + 'sufficient_signed_literal_scratch_bits': 'b+21', + 'standalone_signed_stored_bits': 'b+19', + 'standalone_signed_literal_scratch_bits': 'b+20'}, + 'scope': 'New-word finite-format transfer and bounded witness; no physical caller, owner map, tape controller, recursive invoice or historical numerical replay.'} + need(rows['X0']['Y2'] == Fraction(-1, 2), 'endpoint source survives until receipt') + return result + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--root', type=Path, default=ROOT) + parser.add_argument('--receipt', type=Path, default=Path(__file__).with_name('FORMAT_RESULT.json')) + parser.add_argument('--write-receipt', type=Path) + args = parser.parse_args() + result = verify(args.root) + rendered = json.dumps(result, indent=2, sort_keys=True) + '\n' + if args.write_receipt: + with args.write_receipt.open('x', encoding='utf-8') as stream: + stream.write(rendered) + else: + need(args.receipt.is_file() and args.receipt.stat().st_size <= 1_000_000, + 'missing or oversized expected receipt') + expected = json.loads(args.receipt.read_bytes(), object_pairs_hook=unique) + strict_equal(result, expected) + print('PASS_PR3609_FORMAT_TRANSFER: local source range; sharp seven-bit full guard; ' + 'sharp six-bit output; exact receipt; no paid physical caller') + + +def strict_equal(actual, expected, location='receipt'): + need(type(actual) is type(expected), 'receipt type mismatch at ' + location) + if isinstance(actual, dict): + need(actual.keys() == expected.keys(), 'receipt keys at ' + location) + for key in actual: + strict_equal(actual[key], expected[key], location + '.' + key) + elif isinstance(actual, list): + need(len(actual) == len(expected), 'receipt length at ' + location) + for index, value in enumerate(actual): + strict_equal(value, expected[index], location + '[' + str(index) + ']') + else: + need(actual == expected, 'receipt value at ' + location) + + +if __name__ == '__main__': + main() diff --git a/research/p104-caller-feasibility/verify.py b/research/p104-caller-feasibility/verify.py new file mode 100644 index 0000000000..f58e798b98 --- /dev/null +++ b/research/p104-caller-feasibility/verify.py @@ -0,0 +1,28 @@ +#!/usr/bin/env python3 +"""Run two independent, source-complete feasibility certificates. + +Clear1nsight, with substantial OpenAI assistance. Apache-2.0. +This bounded replay is not a physical caller or a supplier admission. +""" + +from pathlib import Path +import subprocess +import sys + + +def main(): + root = Path(__file__).resolve().parent + flags = ["-I"] + (["-O"] if sys.flags.optimize else []) + ["-Werror", "-B"] + for component in ("consumer/budget.py", "physical/verify_format.py"): + completed = subprocess.run( + [sys.executable, *flags, str(root / component)], + cwd=root, check=False, timeout=90, + ) + if completed.returncode: + raise SystemExit(completed.returncode) + print("PASS_P104_CALLER_FEASIBILITY: exact conditional budget and finite format; " + "no physical caller, changed network, complete tariff or all-size admission") + + +if __name__ == "__main__": + main() From a4c9fbc9e676c7e0f5bb2b3e537ec620011e7311 Mon Sep 17 00:00:00 2001 From: Chris R Date: Mon, 19 Oct 2026 15:14:57 +1100 Subject: [PATCH 3/3] fix(actions): apply existing P112 runner-context repair Carry the focused change from 89031d21f01f8b676f87c76443f5afc41457a17c (PR #8) onto this active branch. Initialise TMPDIR after runner setup, preserving workflow triggers, repository guard, permissions, pinned actions, timeouts, replay commands and all research inputs. Validated YAML, exact semantic delta, shell syntax and TMPDIR assignment including spaces. Substantial OpenAI assistance. --- .github/workflows/p112-common-slice.yml | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/.github/workflows/p112-common-slice.yml b/.github/workflows/p112-common-slice.yml index 37f99ca573..48047f61c4 100644 --- a/.github/workflows/p112-common-slice.yml +++ b/.github/workflows/p112-common-slice.yml @@ -15,9 +15,9 @@ jobs: if: github.repository == 'CrocSwap/integer-mult-bounds' runs-on: ubuntu-24.04 timeout-minutes: 20 - env: - TMPDIR: ${{ runner.temp }}/p112-common-slice steps: + - name: Initialise P112 work directory + run: echo "TMPDIR=$RUNNER_TEMP/p112-common-slice" >> "$GITHUB_ENV" - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1 with: fetch-depth: 0