From aeeca9ffb50203b56924ee3f1325deab4029f4d9 Mon Sep 17 00:00:00 2001 From: Chris R Date: Mon, 19 Oct 2026 22:17:10 +1100 Subject: [PATCH] Prove rounded trace transfer for QQ16 streamed recovery --- research/qq16-rounded-trace/PREDECESSORS.json | 34 + research/qq16-rounded-trace/PROOF.md | 224 + research/qq16-rounded-trace/README.md | 55 + research/qq16-rounded-trace/RESULT.json | 24085 ++++++++++++++++ research/qq16-rounded-trace/REVIEWS.json | 24 + research/qq16-rounded-trace/SOURCES.json | 30 + research/qq16-rounded-trace/TASK.json | 96 + research/qq16-rounded-trace/VERIFICATION.json | 38 + research/qq16-rounded-trace/VERIFY.json | 36 + research/qq16-rounded-trace/test_verify.py | 59 + .../qq16-rounded-trace/vendor/PR3652-PROOF.md | 147 + .../vendor/PR3985-WORD.json | 1 + .../vendor/PR4015-WORD.json | 1 + research/qq16-rounded-trace/verify.py | 233 + 14 files changed, 25063 insertions(+) create mode 100644 research/qq16-rounded-trace/PREDECESSORS.json create mode 100644 research/qq16-rounded-trace/PROOF.md create mode 100644 research/qq16-rounded-trace/README.md create mode 100644 research/qq16-rounded-trace/RESULT.json create mode 100644 research/qq16-rounded-trace/REVIEWS.json create mode 100644 research/qq16-rounded-trace/SOURCES.json create mode 100644 research/qq16-rounded-trace/TASK.json create mode 100644 research/qq16-rounded-trace/VERIFICATION.json create mode 100644 research/qq16-rounded-trace/VERIFY.json create mode 100644 research/qq16-rounded-trace/test_verify.py create mode 100644 research/qq16-rounded-trace/vendor/PR3652-PROOF.md create mode 100644 research/qq16-rounded-trace/vendor/PR3985-WORD.json create mode 100644 research/qq16-rounded-trace/vendor/PR4015-WORD.json create mode 100644 research/qq16-rounded-trace/verify.py diff --git a/research/qq16-rounded-trace/PREDECESSORS.json b/research/qq16-rounded-trace/PREDECESSORS.json new file mode 100644 index 0000000000..58eed19741 --- /dev/null +++ b/research/qq16-rounded-trace/PREDECESSORS.json @@ -0,0 +1,34 @@ +{ + "files": [ + { + "path": "vendor/PR3985-WORD.json", + "upstream_head": "400df7fca8f60c19bf163c77564fe3fbe9154b04", + "upstream_path": "research/qq16-recovery-fusion/WORD.json", + "sha256": "a854f516f1d80635fb3414734f9e1c6d1251a5d79ef12e137c143fc6b0b51722", + "git_blob": "1518ddc9b61aa6bede045d20f0d5e8cf664863fa", + "reuse": "Retained data/text only; no predecessor executable imported." + }, + { + "path": "vendor/PR4015-WORD.json", + "upstream_head": "0fff81d8997cef646538bcd4f60d7d455cf93b8e", + "upstream_path": "research/qq16-streaming-recovery/WORD.json", + "sha256": "272d8c1bd172c29044eb227ec6d67a882501250978234685e035158f4479aa58", + "git_blob": "9a57a6f9c2fd8cdc4e5934408d78ef54e5f266b6", + "reuse": "Retained data/text only; no predecessor executable imported." + }, + { + "path": "vendor/PR3652-PROOF.md", + "upstream_head": "35f38c8482e70129860cdb174615bc8f2251b01a", + "upstream_path": "research/qq16-polynomial-interface-audit/PROOF.md", + "sha256": "0edd900b2bf312c532f0e5067cb27a14495bf0c8a2ccddd25073ef4c592989e4", + "git_blob": "36b39daec5c2cdebdb659e1047058642e5e09617", + "reuse": "Retained data/text only; no predecessor executable imported." + } + ], + "credit": [ + "Chris R / Clear1nsight PR3985 and4015, ywz65 PR2707, Arham Tahir PR2681, Ali Romman and retained QQ16/native/geometry lineage", + "Nick Petalas PR3303/2965; ToikY PR3652 independent all-depth numeric audit", + "PR3932 first-caller range audit and native rounding components package are scoped adjacent evidence, not a decoder format certificate." + ], + "license": "Apache-2.0; original retained source texts unchanged." +} diff --git a/research/qq16-rounded-trace/PROOF.md b/research/qq16-rounded-trace/PROOF.md new file mode 100644 index 0000000000..f248745f5d --- /dev/null +++ b/research/qq16-rounded-trace/PROOF.md @@ -0,0 +1,224 @@ +# Relative rounded-trace transfer for streamed QQ16 recovery + +This proves a compiler-style relative statement about the complete retained +PR3985 and PR4015 words. It does not infer a numerical decoder certificate from +the producer certificate. Source identities and credit are in PREDECESSORS.json +and SOURCES.json. No predecessor executable is imported or rerun. + +## Result and concrete obligation removed + +The 3,935-event materialized word and 3,813-event hosted streaming word have +exactly the same 3,392 value-producing event expressions, including occurrence +multiplicity: 2,816 ordered scalar ADDs, 352 cover maps and 224 signed native +calls. All 224 final output expression roots match. The inverse-B1 checkpoint +matches at old event2852 / new event2730. The sequence of native labels, signs +and input expressions also matches in order. + +The comparison does not cancel inverses, commute cover maps, reassociate sums, +replace a rounded operation by exact arithmetic, or compare numerical samples. +It interns structural tuples by exact equality; hashes only record evidence. +The complete old-to-new event mapping is in RESULT.json. Thus the streaming +change does not create another set of arithmetic-error or intermediate-value +expressions. Under the contract below, a valid certificate for the materialized +word transfers to the streamed word without a new rescheduling-error term or +an additional range analysis of those same arithmetic expressions. + +This removes a *duplicate proof obligation*, not an arithmetic operation or an +already established error reserve. There are zero eliminated ADD/map/native +rounding sites. PR3985 itself explicitly leaves numerical defects open. +A valid finite-format/range/error certificate for that decoder is still needed. + +## Explicit finite-storage and primitive contract + +Let every logical field be an array on the actual common owner/payload domain; +the argument applies to every positive tensor depth and does not enumerate that +domain. Native and cover tags retain their actual port, stage and sign. Supply: + +1. A common finite value representation for all paired roles, including the + old private F accumulators, the old D copies, the new persistent Q roles and + reusable D, and the output banks that host them. One concrete permitted + representation has signed W-bit real/imaginary integers in a common binary + quantum q. Signed zero, exceptional values and overflow conventions must + also agree if the chosen format has them. +2. CLEAR writes the same exact zero bit pattern independently of prior dirt. + Plain loads, stores, copies within an arithmetic primitive, and retention + across native calls preserve those bits. Moving private F into persistent Q + must not introduce an extra store-round, narrowing conversion or rescaling. +3. For each scalar coefficient c in {1,-1,1/4,-1/4}, ADD is the *same ordered + deterministic function* of the prior destination and source in both words. + For example, it may separately round the product c*s, then add to d and + round/store the result, with one fixed signed division and overflow policy. + A fused multiply-add and a separately rounded product/add are different + contracts. Division by four is not silently made exact. +4. Each tagged cover map and signed native call is the same deterministic + whole-array function with the same internal arithmetic sequence, precision, + factor order, coefficients and wrapper recipe in the two executions. This + includes every native interior, coordinate permutation and signed operation; + it is not merely equality of the ideal unitary operator. +5. A native call's scratch is disjoint from live query/output banks. Its + entrance protocol removes dependence on disposable dirt, and its specified + zero-return state is restored. There is no unmodelled shared accumulator, + global random stream, sticky-state-dependent rounding, clock/address-dependent + result, or concurrent external reader of temporary output-bank contents. + Reordering independent calls/ADDs is allowed only under this isolation. + +These premises allow signed-floor, truncation, nearest rounding, deterministic +saturation or modular overflow, provided the paired operations use the same +rules. Bit equality under overflowing arithmetic is not an accuracy theorem. +For a trapping implementation, the matched dataflow expressions have the same +potential traps; the theorem below concerns executions where all required +operations are defined. The first trap in chronological order need not match. + +If a real kernel uses variable widths, it is enough to assign equal complete +primitive implementations to each paired event; a common W/q is a simple +sufficient condition. That assignment must also cover persistent stores and +native internal widths. The finite words do not supply it themselves. + +## Structural proof and storage safety + +Use an arena of terms. Initial borrowed inputs have distinct symbols X_p,Y_p. +An initialized zero field has the single common zero term. An ADD creates +`ADD(format,c,old_destination,source)`; a cover creates +`MAP(format,stage,p,inverse,input)`; a native creates +`LINE(format,p,sign,input)`. No algebraic identities are imposed on these +constructors. Each term denotes its entire array, including every owner and +coordinate. Identical constructor terms denote identical bits by induction +under the deterministic primitive contract, regardless of interleaving with +unrelated terms. The same argument applies to every internal instruction of a +paired native call because its input bits and complete kernel are identical. + +The new checker interprets both full words and validates the access discipline: +borrowed X/Y cannot be written or cleared; every arithmetic read has a live +initialized value; only owned fields or the active private scope can be written; +no native/map call occurs inside a private scope; every private scope returns +zero with an identity clear; all materialized D copies return zero/identity. +When a private scope ends its names cease to exist. Missing recycled-D clears, +premature query clears, missing deferred output copies and hidden private +workspace are rejecting controls. Thus matching roots does not assume that +aliased storage starts clean or that dead private fields survive implicitly. + +The source trace records numerical arrays, with control frame tags preserved in +the source words. Legal native/chart/frame identities were checked in the +predecessors and remain inherited. This relative audit does not repeat their +73-coordinate phase proof or claim a new physical owner-layout construction. + +For the future query, let t_p be the output of the source copy, map and negative +native call for p in the ordered 104-port U+T list. Both words compute, for each +k, the same left-associated chain starting at zero and visiting the same +nonzero coefficients R[k,p] in the same p order. The old outer loop is k; the +new outer loop is p. Different k chains have no dependencies on one another. +The eight response chains similarly retain k order and the same quarter ADDs, +positive native, inverse map and addition to W_A. Reusing D changes its storage +name, not the input or evaluation order of any term. + +The nine deferred Z_U definitions are independent initial CLEAR/X-copy pairs. +The streamed word first uses their storage for Q0..Q7,D, then performs the +same nine paid definitions at events2600..2617 before any preserved Z update +(first at2618). The full trace checks this by reads and output dependencies; +no equality is obtained by erasing an observable output value. The 120 removed +CLEARs and one removed begin/end pair have no value-producing counterpart to +match. Their effects are initialization/retirement of dead roles, not new +rounding events or a claim of physically free cleanup. + +Inductively evaluate the shared term arena. Every paired arithmetic expression +has equal arguments and equal output bits. The complete occurrence multiset +check supplies an event bijection even when two equal terms were recomputed. +All final output roots and the intermediate checkpoint agree. Initial borrowed +states are untouched. This proves the relative bit-equivalence theorem and +transfers every bound on matched intermediate arithmetic values or decoder +output error, once its actual finite-primitive premises are supplied. + +This is a dependency-trace equivalence, not equality of the global chronological +trace, wall-clock behavior, tape-head movements, simultaneous storage peaks, +physical addresses, or observable intermediate output-bank contents. + +## Discriminating finite-format controls + +The actual first two nonzero future F0-query contributions are + +``` +old2140: F0 += D2 new1716: Z1 += Z10 +old2141: F0 += D9 new1764: Z1 += Z10 +``` + +At this *query boundary*, choose the two aligned source components as3 and1, +with a four-bit old private accumulator and a three-bit new owned accumulator. +The first addition gives3 in both. The second gives4 in the old accumulator; +the new one traps, wraps to-4, or saturates to3 according to its policy. This is +an actual source-site format counterexample, not an asserted reachable full +producer trajectory or a failure of PR4015 under its missing format premise. + +At old2563 and its mapped new event, the literal instruction is the response +coefficient-1/4 applied to F0/Q0. With query component1 and initial response0, +signed floor gives-1 whereas truncation toward zero gives0. A common signed +floor policy agrees in both schedules; a storage-dependent change does not. +The test compares negative-quarter decisions and overflow handling against an +independent exact-rational/two's-complement oracle. Reordering the source loop +also fails the symbolic DAG check, even when exact commutative arithmetic +would permit that reordering. + +A second countermodel isolates hidden state: the second native call, port1 +with positive sign, occurs at old9/new7 after respectively4 and3 scalar ADDs. +A kernel adding the parity of that hidden global count returns different bits +on equal declared inputs. This is not an observed actual-kernel defect; it +demonstrates why even matching the native call sequence is insufficient +without declared-input determinism. + +Native scratch isolation is separately indispensable: a kernel that reads a +live query bank through shared scratch is not a function of its declared input. +The new schedule keeps owned queries alive across112 future native calls; +the old query-private scope begins after104 source natives. Hence old private +scratch permission cannot be reused for those new owned query slots. The +checker rejects a private scope spanning a native call, while the physical +non-alias proof is an actual caller obligation. + +## Binding the available precision results + +The authenticated canonical PR3303 proof, independently checked by ToikY's +retained PR3652 proof, gives for the *literal producer F0 then B1*: + +``` +q = h*2^(-71-19*(lambda-1)) +W = P+215+38*(lambda-1). +``` + +Its domain is all704 persistent entry fields in h Z with component magnitudes +strictly below2^P h; eight private fields begin zero. It bounds53,118 producer +events and native/product interiors. Every required division is exactly +divisible, so no rounding or overflow occurs for that producer reference. +It explicitly excludes F17 consumption. Neither its grid exponent nor its +width statement is a decoder-interior bound. The first absent format fact for +this transfer is the paired decoder primitive/retention assignment, especially +old private F_k versus persistent hosted Q_k. Even adopting its global q/W +would require proving the decoder intermediates fit and its divisions obey the +chosen finite lowering; the producer's completed output is only the input. + +PR3932's first F0-child audit shows why an unchanged coarse grid is unsafe and +why the finer PR3303 format conditionally repairs that *first producer child*. +It does not supply the new decoder format. The canonical concrete native-rounding +package likewise exhibits genuine producer rounding under its different +binary64 contract; that observation is adjacent, not rerun or transferred here. + +The authenticated PR2965 README states the completed-output implication +`49 epsF + 1923 epsB + epsD`. Its epsD must bound the implemented decoder against +the ideal inverse. Its use of the older PR2736 state-relative theorem concerns +the fixed PR2707 decoder, not an automatic certificate for PR3985's changed +rectangular word. The present result shows that once epsD is valid for a paired +finite implementation of PR3985, the same epsD is valid for PR4015. It does not +establish epsD, regenerate the old constants, or admit a supplied entry lattice. + +## Decision and remaining obligations + +Close the rescheduling-specific arithmetic-equivalence question under the +explicit contract. Do not optimize an isolated guard or claim a new kappa. +Next pin one actual paired finite decoder implementation: scalar product/add +rounding, native interior recipes/widths, persistent query-store representation +and scratch disjointness. Prove its range/error certificate once on the shared +DAG and transfer it. Caller entry format, owned output banks, physical movement, +helper return, recursion and productive-family coverage remain additional +obligations. Unknown costs are not zero. No physical tariff is altered here. + +Credit Chris R / Clear1nsight PR3985/4015; ywz65 PR2707; Arham Tahir PR2681; +Ali Romman and the retained QQ16/native/geometry lineage; Nick Petalas PR3303, +PR2965 and numerical predecessors; ToikY PR3652. Substantial OpenAI Codex +assistance, no independent human or formal-kernel review. Apache-2.0. diff --git a/research/qq16-rounded-trace/README.md b/research/qq16-rounded-trace/README.md new file mode 100644 index 0000000000..723e24cbe6 --- /dev/null +++ b/research/qq16-rounded-trace/README.md @@ -0,0 +1,55 @@ +# QQ16 rounded trace transfer across streaming storage reuse + +PR4015 changes where the future query lives and interleaves its scalar work with +native calls. It preserves all **3,392 value-producing operation dependencies** +of PR3985, their occurrence counts, all224 final output roots, the inverse-B1 +checkpoint, and the ordered224 native input/recipe sequence. + +Under explicitly identical deterministic finite primitives, formats and isolated +workspace, the two words therefore produce identical bits. A valid materialized +decoder range/error certificate transfers without a new rescheduling error term. +This is a relative result: PR3985 has no supplied numerical certificate, and +PR3303/3652's exact producer grid does not bound this decoder's interiors. +No new decoder precision constant, physical tariff, supplier or kappa is claimed. + +The new interpreter reads only authenticated source data/text, imports no +predecessor code and performs no arithmetic simplification. It compares exact +structural tuples, verifies access/initialization/zero-return discipline and +retains the full event bijection in RESULT.json. PROOF.md states the quantified +finite-primitive theorem and the first missing actual format premise. + +Two source-site fixtures separate the premise from a universal assertion: +old privateF0 at events2140/2141 and new hostedZ1 at1716/1764 diverge if width4 +becomes width3 on query values3,1; the actual-1/4 response at old2563/new2537 +separates signed floor from truncation. These are boundary fixtures, not claimed +reachable full-producer inputs. A wrong source order and eight other semantic +mutations are rejected. All tested uniform-format arithmetic decisions are +checked against exact rational/two's-complement conventions. + +Reproduce from the repository root, standard-library Python3.12: + +``` +python3 -I -O -Werror -B research/qq16-rounded-trace/verify.py +python3 -I -O -Werror -B research/qq16-rounded-trace/test_verify.py +python3 -B scripts/research_package.py --package research/qq16-rounded-trace +``` + +Default replay is read-only; --write exclusively creates an absent RESULT. +Runtime inputs are the two canonical scope sources in SOURCES/VERIFY and three +narrow retained data/text sources in PREDECESSORS. Pending Git history or +network fetches are not required. The actual native/cover semantics and original +frame proofs are inherited; this package does not reexecute producer payloads. + +## Open next questions + +Pin an actual decoder scalar/native/store implementation and prove the shared +DAG's range/error certificate once. The first missing assignment is matching +private F accumulators to persistent Q/output-bank widths, rounding and storage +semantics. Then bind disjoint native workspace and actual caller output ownership, +movement and numerical entry format. TASK.json gives the first step and blockers. +Global chronology and physical tape work are not preserved by this theorem. + +Credit Chris R/Clear1nsight PR3985/4015, ywz65 PR2707, Arham Tahir PR2681, +Ali Romman and retained QQ16/native/geometry lineage; Nick Petalas PR3303/2965; +ToikY PR3652. Original retained proof notice is unchanged. Substantial OpenAI +Codex assistance, no human or proof-kernel acceptance claimed. Apache-2.0. diff --git a/research/qq16-rounded-trace/RESULT.json b/research/qq16-rounded-trace/RESULT.json new file mode 100644 index 0000000000..412bbeaf6a --- /dev/null +++ b/research/qq16-rounded-trace/RESULT.json @@ -0,0 +1,24085 @@ +{ + "canonical_inputs": { + "research/qq16-all-depth-producer-grid/PROOF.md": "6dd878aa01807eecf4a37f7ce3fbc1105d79f6b1b06791b23d4deeef90b7d994", + "research/qq16-producer-defect-transfer/README.md": "30cf4389425f7704b1ed45af6cf4b5165e7b5c04af5077640ac96399c61cd703" + }, + "checkpoint_event_pairs": [ + [ + 2852, + 2730 + ] + ], + "event_mapping": [ + [ + 1, + 1, + "Z0", + "Z0", + 225 + ], + [ + 3, + 3, + "W0", + "W0", + 226 + ], + [ + 4, + 4, + "W0", + "W0", + 227 + ], + [ + 6, + 2601, + "Z1", + "Z1", + 228 + ], + [ + 8, + 6, + "W1", + "W1", + 229 + ], + [ + 9, + 7, + "W1", + "W1", + 230 + ], + [ + 11, + 2603, + "Z2", + "Z2", + 231 + ], + [ + 13, + 9, + "W2", + "W2", + 232 + ], + [ + 14, + 10, + "W2", + "W2", + 233 + ], + [ + 16, + 2605, + "Z3", + 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trajectory." + }, + "stateful_kernel_countermodel": { + "example_hidden_additive_offset_mod2": [ + 0, + 1 + ], + "native_port": 1, + "new_event": 7, + "new_prior_ADD_count": 3, + "old_event": 9, + "old_prior_ADD_count": 4, + "scope": "Countermodel only: a kernel consulting global scalar-count parity violates declared-input determinism; not an observed defect of the actual native kernel.", + "sign": 1 + }, + "uniform_policy_control_decisions": 29400, + "uniform_policy_control_sha256": "a5a1e624aad20a645d4914aea9d5638a9177c9dbc721a1a3eb98e3827bdde5dd" + }, + "format_binding": "PR3303/3652 certify only the literal F0/B1 producer. No retained3985 or4015 decoder width/range/interior certificate is supplied. Relative transfer only; PR2965 still needs epsD.", + "matched_value_events": 3392, + "native_call_sequence_equal": true, + "new_events": 3813, + "old_events": 3935, + "operation_counts": { + "new": { + "add": 2816, + "begin": 2, + "checkpoint": 1, + "clear": 416, + "end": 2, + "line": 224, + "map": 352 + }, + "old": { + "add": 2816, + "begin": 3, + "checkpoint": 1, + "clear": 536, + "end": 3, + "line": 224, + "map": 352 + } + }, + "output_roots": { + "W0": 3548, + "W1": 2568, + "W10": 2577, + "W100": 2667, + "W101": 2668, + "W102": 2669, + "W103": 2670, + "W104": 2671, + "W105": 2672, + "W106": 2673, + "W107": 2674, + "W108": 2675, + "W109": 2676, + "W11": 2578, + "W110": 3563, + "W111": 3555, + "W12": 2579, + "W13": 2580, + "W14": 2581, + "W15": 2582, + "W16": 2583, + "W17": 2584, + "W18": 2585, + "W19": 2586, + "W2": 2569, + "W20": 3550, + "W21": 3556, + "W22": 2589, + "W23": 2590, + "W24": 2591, + "W25": 2592, + "W26": 2593, + "W27": 3551, + "W28": 2595, + "W29": 2596, + "W3": 2570, + "W30": 2597, + "W31": 2598, + "W32": 2599, + "W33": 2600, + "W34": 2601, + "W35": 2602, + "W36": 3552, + "W37": 3557, + "W38": 2605, + "W39": 2606, + "W4": 2571, + "W40": 2607, + "W41": 2608, + "W42": 2609, + "W43": 2610, + "W44": 2611, + "W45": 2612, + "W46": 3553, + "W47": 3558, + "W48": 2615, + "W49": 2616, + "W5": 2572, + "W50": 2617, + "W51": 2618, + "W52": 2619, + "W53": 2620, + "W54": 2621, + "W55": 2622, + "W56": 2623, + "W57": 3554, + "W58": 2625, + "W59": 2626, + "W6": 2573, + "W60": 2627, + "W61": 2628, + "W62": 2629, + "W63": 2630, + "W64": 2631, + "W65": 2632, + "W66": 2633, + "W67": 2634, + "W68": 2635, + "W69": 2636, + "W7": 3549, + "W70": 2637, + "W71": 2638, + "W72": 2639, + "W73": 2640, + "W74": 2641, + "W75": 2642, + "W76": 3559, + "W77": 2644, + "W78": 2645, + "W79": 2646, + "W8": 2575, + "W80": 2647, + "W81": 3560, + "W82": 2649, + "W83": 2650, + "W84": 2651, + "W85": 2652, + "W86": 2653, + "W87": 3561, + "W88": 2655, + "W89": 2656, + "W9": 2576, + "W90": 2657, + "W91": 2658, + "W92": 3562, + "W93": 2660, + "W94": 2661, + "W95": 2662, + "W96": 2663, + "W97": 2664, + "W98": 2665, + "W99": 2666, + "Z0": 3507, + "Z1": 2731, + "Z10": 2763, + "Z100": 3075, + "Z101": 3079, + "Z102": 3083, + "Z103": 3087, + "Z104": 3091, + "Z105": 3095, + "Z106": 3099, + "Z107": 3103, + "Z108": 3107, + "Z109": 3111, + "Z11": 2767, + "Z110": 3547, + "Z111": 3525, + "Z12": 2771, + "Z13": 2775, + "Z14": 2779, + "Z15": 2783, + "Z16": 2787, + "Z17": 2791, + "Z18": 2795, + "Z19": 2799, + "Z2": 2735, + "Z20": 3514, + "Z21": 3529, + "Z22": 2803, + "Z23": 2807, + "Z24": 2811, + "Z25": 2815, + "Z26": 2819, + "Z27": 3516, + "Z28": 2823, + "Z29": 2827, + "Z3": 2739, + "Z30": 2831, + "Z31": 2835, + "Z32": 2839, + "Z33": 2843, + "Z34": 2847, + "Z35": 2851, + "Z36": 3519, + "Z37": 3532, + "Z38": 2855, + "Z39": 2859, + "Z4": 2743, + "Z40": 2863, + "Z41": 2867, + "Z42": 2871, + "Z43": 2875, + "Z44": 2879, + "Z45": 2883, + "Z46": 3521, + "Z47": 3534, + "Z48": 2887, + "Z49": 2891, + "Z5": 2747, + "Z50": 2895, + "Z51": 2899, + "Z52": 2903, + "Z53": 2907, + "Z54": 2911, + "Z55": 2915, + "Z56": 2919, + "Z57": 3523, + "Z58": 2923, + "Z59": 2927, + "Z6": 2751, + "Z60": 2931, + "Z61": 2935, + "Z62": 2939, + "Z63": 2943, + "Z64": 2947, + "Z65": 2951, + "Z66": 2955, + "Z67": 2959, + "Z68": 2963, + "Z69": 2967, + "Z7": 3510, + "Z70": 2971, + "Z71": 2975, + "Z72": 2979, + "Z73": 2983, + "Z74": 2987, + "Z75": 2991, + "Z76": 3538, + "Z77": 2995, + "Z78": 2999, + "Z79": 3003, + "Z8": 2755, + "Z80": 3007, + "Z81": 3541, + "Z82": 3011, + "Z83": 3015, + "Z84": 3019, + "Z85": 3023, + "Z86": 3027, + "Z87": 3543, + "Z88": 3031, + "Z89": 3035, + "Z9": 2759, + "Z90": 3039, + "Z91": 3043, + "Z92": 3545, + "Z93": 3047, + "Z94": 3051, + "Z95": 3055, + "Z96": 3059, + "Z97": 3063, + "Z98": 3067, + "Z99": 3071 + }, + "premise": "Common exact zero plus identical deterministic storage-independent ADD/map/native functions with identical argument order, widths, rounding/overflow policy and disjoint reset native workspace. No precision narrowing on persistent query stores. Whole-array primitives include actual ordered coordinate/native arithmetic.", + "removed_arithmetic_error_sites": 0, + "retained_inputs": { + "vendor/PR3652-PROOF.md": "0edd900b2bf312c532f0e5067cb27a14495bf0c8a2ccddd25073ef4c592989e4", + "vendor/PR3985-WORD.json": "a854f516f1d80635fb3414734f9e1c6d1251a5d79ef12e137c143fc6b0b51722", + "vendor/PR4015-WORD.json": "272d8c1bd172c29044eb227ec6d67a882501250978234685e035158f4479aa58" + }, + "scope": "Exact operation DAG/occurrence equivalence under stated finite-primitive contract; not global chronological trace equality, decoder accuracy certification, physical movement tariff or supplier/kappa result.", + "semantic_controls": [ + "missing first hosted query clear", + "missing recycled D clear", + "early query clear", + "borrowed input clear", + "missing deferred output copy", + "native hidden private overlap", + "wrong signed native", + "wrong quarter sign", + "source accumulation order" + ], + "separate_stream_rescheduling_error_analysis_required_under_contract": false, + "status": "PASS_QQ16_ROUNDED_TRACE_EQUIVALENCE", + "unique_structural_nodes": 3564 +} diff --git a/research/qq16-rounded-trace/REVIEWS.json b/research/qq16-rounded-trace/REVIEWS.json new file mode 100644 index 0000000000..b94a1fc657 --- /dev/null +++ b/research/qq16-rounded-trace/REVIEWS.json @@ -0,0 +1,24 @@ +{ + "status": "bounded independent AI reviews passed", + "science_files": { + "verify.py": "5ea49be0a44b4d0ac36901f936a70abbafc119cc181f8c09faf05d8f7d9262ce", + "PROOF.md": "40575dbc25d2bf88e982e5d5458b31cf1e345131a2a516756fa9161fb2da4969", + "RESULT.json": "7e0d42df97657dfa1085b73881f1a9f7f74dc9ab36ea1a1f3987884aa9ffad5a", + "test_verify.py": "5caeec72dc68d76e6753e1071bd328df8dd5b0d90f52c646dbb1fa03451c6b5a" + }, + "reviews": [ + { + "reviewer": "coordinating agent", + "checks": "Read proof and verifier, independently ran isolated optimized warning-strict primary", + "result": "PASS;3392 value events/3564 nodes/checkpoint2852\u21922730; no theorem blocker under explicit deterministic finite-primitive scope", + "limits": "Native/frame semantic premises inherited; no physical, human, formal-kernel or supplier admission." + }, + { + "reviewer": "parallel physical-transition agent", + "checks": "Read-only source/proof/access/format review and separate optimized primary replay", + "result": "PASS; accumulation order retained in destination/source DAG edges; alias reads initialized; private scopes die with zero/identity; numeric counterexamples correctly scoped; producer grid not a decoder certificate", + "limits": "Native scratch disjointness and storage determinism remain premises; no actual native/physical replay or human/formal review." + } + ], + "disclosure": "Separate OpenAI Codex agents, not human reviewers." +} diff --git a/research/qq16-rounded-trace/SOURCES.json b/research/qq16-rounded-trace/SOURCES.json new file mode 100644 index 0000000000..45eeb3f9d5 --- /dev/null +++ b/research/qq16-rounded-trace/SOURCES.json @@ -0,0 +1,30 @@ +{ + "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/qq16-all-depth-producer-grid/PROOF.md", + "usage": "input", + "git_blob": "9cf1ec57646fb760fd26f206d754e52c99c347e3", + "sha256": "6dd878aa01807eecf4a37f7ce3fbc1105d79f6b1b06791b23d4deeef90b7d994" + }, + { + "path": "research/qq16-producer-defect-transfer/README.md", + "usage": "input", + "git_blob": "16903a0090c020d033d24712cce11c633031e688", + "sha256": "30cf4389425f7704b1ed45af6cf4b5165e7b5c04af5077640ac96399c61cd703" + } + ] +} diff --git a/research/qq16-rounded-trace/TASK.json b/research/qq16-rounded-trace/TASK.json new file mode 100644 index 0000000000..b4c7e0a43c --- /dev/null +++ b/research/qq16-rounded-trace/TASK.json @@ -0,0 +1,96 @@ +{ + "schema_version": 1, + "task_id": "joint-query-controller", + "priority_revision": 6, + "base_commit": "20ecf2891d80b5acf18d980b2164fb44ea7faa90", + "original_card": { + "id": "joint-query-controller", + "question": "Can a literal QQ16 producer meet the proposed completed-output error budgets with dirty helpers and an affordable physical consumer?", + "starting_points": [ + "docs/research/research-family-status.md", + "research/joint-query/README.md", + "research/joint-query/evidence/QQ16-SELECTED-WITNESS.md", + "research/joint-query/evidence/JOINT-QUERY-TRANSFER.md", + "docs/research/community-efficient1000-review.md", + "research/qq16-producer-defect-transfer/README.md" + ], + "methods": [ + "Derive one literal producer's completed-output defects and intermediate dirty-helper bounds, with its physical bill.", + "Design or audit one consumer, retention or hosting boundary and its complete cost for the pinned producer/decoder." + ], + "acceptance_gate": "Name the changed premise of the fixed F0/B1 observation obstruction. Show exactly which query is recovered, legal native reads and restoration, and a full favorable budget including cover maps, helpers and endpoints. Local inverse identities alone do not close the global controller. 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 #2965 producer-defect transfer after the local QQ16 decoder contract. Its author-checked output-error estimate does not implement producer interiors, bound dirty helpers, or pay for the consumer; independently check the implication used.", + "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": "Pin one literal F0/B1 producer and its native-child contracts; derive the actual intermediate magnitude ledger and completed-output defects, including dirty helpers and correlations. Compare with #2965 budgets and price storage, movement, cleanup and F17 consumption. Stop with a precise missing bound if no producer contract supplies it; do not optimize another decoder precision constant in isolation.", + "bottleneck_link": "The native local words exist; retained query information and its physical access are the missing link to a composed recursive interface.", + "allowed_variations": [ + "One paid query, one changed first pair, or one precisely specified affine helper state.", + "A counterexample or lower bound for that exact proposed repair.", + "One unresolved obligation of a newer local decoder, with exact source heads and a distinct claim/domain." + ], + "scope_change_triggers": [ + "Retaining the fixed first pair and ordinary schedule while allowing only homogeneous selected-only control, already excluded by the witness.", + "Treating cover-map counts as zero-cost physical address operations.", + "Recreating the pending complete local decoder or early-record/output-bank coalescing already under investigation without a distinct audit or changed premise.", + "Treating a completed-output defect inequality as a producer-interior, dirty-range or physical-cost certificate." + ], + "overlap_terms": [ + "QQ16", + "joint-query", + "changing-chart controller", + "selected observation", + "1969", + "2540", + "early record", + "output-bank retention", + "complete native decoder", + "2965", + "producer defect", + "dirty-helper range", + "F17 consumer" + ] + }, + "scope_status": "refined", + "actual_scope": "Prove or refute finite-primitive arithmetic dependency-trace equivalence of PR3985 and PR4015, then bind the missing precision premise to actual producer/decoder sources.", + "scope_change_reason": "Explicit assigned new audit of the streamed output-hosting decoder. Relative trace equivalence can eliminate duplicate rescheduling error analysis; no isolated precision constant is optimized.", + "bottleneck_link": "Makes the new consumer storage schedule reusable under one validated decoder finite-format certificate while distinguishing missing actual precision and caller obligations.", + "budget_minutes": 60, + "stop_rule": "Close the exact relative DAG theorem and first missing format premise; stop before new guard constants or physical supplier construction.", + "outcome": "partial", + "evidence": "PROOF.md; full3392-event bijection and224 output roots in RESULT.json; signed overflow/quarter fixtures; nine semantic rejections and six boundary groups.", + "author": "Chris R / Clear1nsight with OpenAI Codex assistance", + "ai_assistance": "Substantial OpenAI Codex assistance; separate coordinating-agent source/proof review is requested; no human or formal-kernel review claimed.", + "open_questions": [ + { + "question": "Which actual decoder finite format covers the paired private and persistent query operations?", + "why_it_matters": "Relative bit equivalence transfers a certificate only after matching widths, rounding, store behavior and native scratch semantics are supplied.", + "first_step": "Pin the complete scalar/native lowering and assign formats to one materialized/streamed event pair, starting with oldF0/newZ1 query accumulation; prove common range/error bounds on the shared DAG.", + "blocked_by": "PR3303/3652 bound producer events only; PR3985/4015 do not provide decoder interior or persistent-store formats." + } + ], + "coordination": { + "assigned": true, + "canonical_main": "20ecf2891d80b5acf18d980b2164fb44ea7faa90", + "root_refresh": "2026-10-19T10:52Z; unchanged priority6/selected record", + "live_heads_checked": [ + "3652", + "3303", + "2965", + "3932", + "4030", + "4015", + "3985" + ], + "overlap": "Targeted live QQ16 rounding/trace/streaming PR search plus offline helper; remote Discussion coverage partial. Root coordinates canonical public thread.", + "canonical_claim": "https://github.com/CrocSwap/integer-mult-bounds/pull/3985#issuecomment-6263114494", + "prepublication_checkpoint": "Root canonical fetch11:15UTC:20ec unchanged, priority6/selected unchanged; baseline binding PASS; live targeted overlap partial." + } +} diff --git a/research/qq16-rounded-trace/VERIFICATION.json b/research/qq16-rounded-trace/VERIFICATION.json new file mode 100644 index 0000000000..ab2248e85f --- /dev/null +++ b/research/qq16-rounded-trace/VERIFICATION.json @@ -0,0 +1,38 @@ +{ + "status": "PASS_REGISTERED_RESEARCH_PACKAGE outcome=partial", + "environment": "Linux CPython3.12.3, standard library", + "commands": [ + { + "command": "python3 -I -Werror -B research/qq16-rounded-trace/verify.py --write", + "result": "PASS_QQ16_ROUNDED_TRACE_EQUIVALENCE; exclusive receipt generation" + }, + { + "command": "python3 -B scripts/research_package.py --package research/qq16-rounded-trace", + "result": "Primary PASS; all6 boundary groups PASS in33.439seconds; registered outcome=partial" + } + ], + "checks": [ + "Both complete pinned word DAGs and3392 occurrence bijection", + "All224 final roots and inverse-B1 checkpoint", + "Borrowed read-only, initialized owned reads, private zero/identity teardown, oldD zero return", + "Exact source loop ordering and native sequence", + "Signed floor/truncation and width/overflow boundary witnesses;29,400 exact-rational control decisions", + "Hidden-state kernel countermodel; nine semantic rejections", + "Normal/optimized read-only; Git-free read-only in both modes", + "Retained word/proof and canonical scope source integrity; full mapping/typed receipt and overwrite controls" + ], + "science_files": { + "verify.py": "5ea49be0a44b4d0ac36901f936a70abbafc119cc181f8c09faf05d8f7d9262ce", + "PROOF.md": "40575dbc25d2bf88e982e5d5458b31cf1e345131a2a516756fa9161fb2da4969", + "RESULT.json": "7e0d42df97657dfa1085b73881f1a9f7f74dc9ab36ea1a1f3987884aa9ffad5a", + "test_verify.py": "5caeec72dc68d76e6753e1071bd328df8dd5b0d90f52c646dbb1fa03451c6b5a" + }, + "not_run": [ + "Actual native/tape or enormous full-payload execution", + "New decoder range/grid or rounded error certificate", + "Caller format/ownership admission and whole physical invoice", + "Selected cold replay, Lean, independent human review" + ], + "baseline": "Own baseline binding command completedPASS; complex side binds and selected record hashbb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129 unchanged. Root independently completed the same coordinated checkpoint11:15UTC.", + "publication_preflight": "Final committed byte/source ancestry/export and hosted status are reported outside this commit receipt." +} diff --git a/research/qq16-rounded-trace/VERIFY.json b/research/qq16-rounded-trace/VERIFY.json new file mode 100644 index 0000000000..c9ccaf825a --- /dev/null +++ b/research/qq16-rounded-trace/VERIFY.json @@ -0,0 +1,36 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [ + "research/qq16-all-depth-producer-grid/PROOF.md", + "research/qq16-producer-defect-transfer/README.md" + ], + "commands": [ + { + "argv": [ + "{python}", + "-I", + "-O", + "-Werror", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 90, + "checks": "Complete arithmetic DAG/occurrence mapping, output/checkpoint/borrowed state, access and zero-return discipline, adversarial signed format controls." + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-Werror", + "-B", + "{package}/test_verify.py" + ], + "timeout_seconds": 180, + "checks": "Normal/optimized read-only, Git-free read-only, all retained/canonical source authentication, full mapping/typed receipt and overwrite controls." + } + ] +} diff --git a/research/qq16-rounded-trace/test_verify.py b/research/qq16-rounded-trace/test_verify.py new file mode 100644 index 0000000000..d0ba71785e --- /dev/null +++ b/research/qq16-rounded-trace/test_verify.py @@ -0,0 +1,59 @@ +#!/usr/bin/env python3 +"""Boundary, provenance and receipt controls for the rounded trace theorem.""" +import hashlib +import json +import os +from pathlib import Path +import shutil +import subprocess +import sys +import tempfile +import unittest + +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] + +def snapshot(root): + return {str(p.relative_to(root)):hashlib.sha256(p.read_bytes()).hexdigest() for p in root.rglob('*') if p.is_file()} + +def run(root,opt=True,extra=(),env=None): + argv=[sys.executable,'-I']+(['-O'] if opt else [])+['-Werror','-B',str(root/'research/qq16-rounded-trace/verify.py'),*extra] + return subprocess.run(argv,cwd=root,env=env,capture_output=True,text=True,timeout=60) + +class Boundary(unittest.TestCase): + def export(self): + td=tempfile.TemporaryDirectory();self.addCleanup(td.cleanup);root=Path(td.name) + shutil.copytree(HERE,root/'research/qq16-rounded-trace',ignore=shutil.ignore_patterns('__pycache__')) + for row in json.loads((HERE/'SOURCES.json').read_text())['files']: + if row['usage']=='input': + p=root/row['path'];p.parent.mkdir(parents=True,exist_ok=True);shutil.copyfile(ROOT/row['path'],p) + return root + def test_normal_optimized_readonly(self): + before=snapshot(HERE) + for opt in (False,True): + p=run(ROOT,opt);self.assertEqual(p.returncode,0,p.stdout+p.stderr);self.assertIn('PASS_QQ16_ROUNDED_TRACE_EQUIVALENCE',p.stdout) + self.assertEqual(before,snapshot(HERE)) + def test_git_free_readonly(self): + root=self.export();before=snapshot(root) + for p in root.rglob('*'): + if p.is_file():p.chmod(0o444) + for opt in (False,True): + p=run(root,opt,env=dict(os.environ,PATH='/nonexistent',PYTHONDONTWRITEBYTECODE='1'));self.assertEqual(p.returncode,0,p.stdout+p.stderr) + self.assertEqual(before,snapshot(root)) + def test_retained_words_and_proof_authenticated(self): + for name in ('PR3985-WORD.json','PR4015-WORD.json','PR3652-PROOF.md'): + root=self.export();p=root/'research/qq16-rounded-trace/vendor'/name;p.write_bytes(b'not valid JSON or source') + r=run(root);self.assertNotEqual(r.returncode,0);self.assertIn('retained source hash:',r.stderr);self.assertNotIn('JSONDecodeError',r.stderr) + def test_canonical_scope_source_authenticated(self): + root=self.export();p=root/'research/qq16-all-depth-producer-grid/PROOF.md';p.write_text('changed scope') + r=run(root);self.assertNotEqual(r.returncode,0);self.assertIn('source hash:',r.stderr) + def test_mapping_and_typed_receipt(self): + root=self.export();p=root/'research/qq16-rounded-trace/RESULT.json';original=json.loads(p.read_text()) + for mode in ('mapping','type'): + r=json.loads(json.dumps(original)) + if mode=='mapping':r['event_mapping'][0][1]+=1 + else:r['matched_value_events']=3392.0 + p.write_text(json.dumps(r));out=run(root);self.assertNotEqual(out.returncode,0);self.assertIn('whole typed receipt mismatch',out.stderr) + def test_refuse_overwrite(self): + before=snapshot(HERE);r=run(ROOT,extra=('--write',));self.assertNotEqual(r.returncode,0);self.assertIn('refuse overwrite',r.stderr);self.assertEqual(before,snapshot(HERE)) +if __name__=='__main__':unittest.main(verbosity=2) diff --git a/research/qq16-rounded-trace/vendor/PR3652-PROOF.md b/research/qq16-rounded-trace/vendor/PR3652-PROOF.md new file mode 100644 index 0000000000..36b39daec5 --- /dev/null +++ b/research/qq16-rounded-trace/vendor/PR3652-PROOF.md @@ -0,0 +1,147 @@ +# Independent polynomial and grid proof + +This checks the sufficient numerical theorem of Nick Petalas's PR3303, head +`f9031ff1412c9a4e62a38306009ae9c334cfc34e`. It does not introduce that theorem +as a new construction. The input, tensor-native, bridge, cover and endpoint +premises are those stated in the README and the pinned source proofs. + +## Independent representation + +Put `t=lambda-1 >= 0` and `z=2^t`. Associate to each field a nonnegative rational +polynomial p and a finite family of integer affine grid exponents `(b,g)`: + +```text +every real/imaginary component has magnitude <= 2^P h p(z), +every component is in h*2^(-max_(b,g)(g+b*t)) Z. +``` + +The known-zero field has an empty polynomial/grid family. Each of the 704 +persistent input fields starts with p=1 and exponent 0; the eight private +fields start zero. Polynomials retain individual degree coefficients. There +is no assumption that different input fields or errors are independent. + +Addition adds coefficient vectors and takes the union of grid families. +Deleting a line dominated in both slope and intercept by another line does +not change their maximum for t>=0. For a dyadic c=n/d in lowest terms, +multiply p by |c| and add `log2(d)-v2(n)` to every intercept. A zero result +has the canonical empty representation. This grid rule follows from exact +divisibility by powers of two, including negative coefficients and negative +intercepts. Owned CLEARs produce zero; no borrowed/data CLEAR is permitted. + +The constant-product lowering forms shifted copies of the original integer +components and sums them before division. Each partial has magnitude bounded +by `|n| p(z)` and retains the original grid. The audit observes that bound, +the final integer numerator (with its stronger divisibility), and the divided +result. It therefore includes intermediates that a completed-scalar-only +ledger would miss. + +## Native interiors at arbitrary depth + +For sign epsilon in {−1,1}, one Gaussian coordinate line on x=a+ib, y=c+id +forms the four pair sums/differences and then + +```text +(a+c-epsilon*(b-d), b+d+epsilon*(a-c), + a+c+epsilon*(b-d), b+d-epsilon*(a-c)) / 2. +``` + +If each entry component is bounded by L, pair components are bounded by 2L, +cross numerators by 4L and outputs by 2L. Pair/cross additions preserve the +incoming dyadic grid; output halves refine it by at most one bit. This +argument is sign-independent. It concerns component capacity, not the +sharper Hilbert norm of a completed unitary line. + +PR3303 PROOF.md's corresponding displayed second output is `(d+i*s)/2`. +The pinned source defines `C_q=(1+i)I/2+(1-i)T_q/2`, giving `(s-i*d)/2` +instead. Multiplication of that second output by i gives the displayed +variant. The distinction matters for the operator, but not for these +component magnitude/grid inequalities or operation counts. The source proof +file is pinned as provenance; exact sign-sensitive fixtures check the formula +used here. No predecessor source is edited. + +At tensor depth lambda, a rank-one active-axis factor executes lambda such +coordinate lines, one in each layer. Before line j, earlier outputs multiply +the component envelope by at most `2^(j-1)` and refine the grid by j−1. +Consequently the following polynomial observations bound every intermediate +line, and the last row bounds all completed outputs: + +| Observation | Polynomial | Grid family replacing `(b,g)` | +|---|---|---| +| Pair interiors | `2*z*p` | `(b+1,g)` | +| Cross interiors | `4*z*p` | `(b+1,g)` | +| Completed lambda-line factor | `2*z*p` | `(b+1,g+1)` | + +For example j−1<=t and j<=lambda give both the pair grid and its magnitude +bound. Apply this rule r times for a rank-r recipe. The exponent is not a +lambda-fold repetition of the entire producer, and scalar coefficients act +once at their literal source locations. + +Each authenticated nine-axis monomial has an exhaustively checked bijective +binary image and quarter-turn phase data, hence is a signed permutation of +real/imaginary components. Its tensor lift preserves the uniform grid and +magnitude. Each used full-cover action has an independently reconstructed +two-sided 73-axis owner inverse. Recover the old owner first, then undo the +owner-dependent XOR translation in every layer. Thus it is a bijection for +every lambda and preserves a bound uniform over owners. This does not +reprove the inherited native/bridge operator identities or cover closure. + +## Source induction and constants + +The new loader reads only pinned data files. It expands raw F0 and B1 program +records, visiting every retained core and sweep itself; original Python +loaders/expanders/dispatchers are not imported. The event hashes independently +agree with PR3303. Source-address hashes distinguish the actual program +locations. All 712 field representations survive the stage boundary intact. + +Induction over the literal operations and the preceding local rules proves +the invariant at all primitive observations. The independently derived +certificate gives: + +```text +53,118 events; 270,288 primitive observations; +maximum polynomial degree = 19; +global grid maximum = 71 + 19*t; +max_observation p(1) = 35714190970741142696015664337123072062513575/4 + < 2^143. +``` + +For z>=1, nonnegative coefficients imply `p(z)<=p(1)*z^degree(p)`. +Every observed component is therefore strictly below +`2^P h * 2^(143+19*t)` in magnitude. With quantum +`q=h*2^(-71-19*t)`, each is an integer number of q units of magnitude strictly +below `2^(P+214+38*t)`. Signed width `W=P+215+38*t` suffices. Integer-product +partials and native cross numerators are observations too. Every exact right +shift has the required divisibility. No rounding, overflow or underflow +relative to this exact reference is required on the stated input domain. + +These maxima describe the positive envelope, not sharp reachable amplitudes +or minimum grid widths. Small exact Gaussian tests corroborate the local +rules; the induction supplies the universal quantifier over lambda. + +## Numeric reference bill and limits + +The independent traversal prices every literal source event. Per N complex +coordinates, a scalar operation acts on 2N real components; a tensor monomial +pays 4N copies and at most 2N sign changes. A coordinate Gaussian line pays +4N real additions, 2N halves and 4N component copies. There are 11,076 active +axis factors, hence `110760*lambda*N` Gaussian operations. Only those factors +multiply by lambda. Literal scalar products, ADDs, private clears and +monomial counts do not. + +Summing the independent numeric counters, including `2N+12` final reusable +scratch clears, gives `483082*N+12` at lambda=1. Subtracting `110760*N` yields +the complete stated numeric-reference expression +`(372322+110760*lambda)*N+12`. The 528 covers separately pay 4N conceptual +real-component transfers each. At most 712 complex fields, one reusable +complex cover buffer and twelve scalar words give `1426*N+12` numeric words. +Every published counter key is compared; diagnostic labels are not counted +as arithmetic operations. + +For an actual recursive caller its cost must additionally include the cost +of each W-bit numeric operation, physical transfers and source access, +address/sign/control computation, instruction and layout preparation, +entry-format admission, owned/borrowed lifetimes and restoration, recursive +children and F17 consumption. Those functions are unknown here. This numeric +reference expression supplies neither their recurrence nor a favorable +complete supplier moment. Literal common-coordinate helper return and native +functional endpoint proofs remain inherited or outside the statement. diff --git a/research/qq16-rounded-trace/vendor/PR3985-WORD.json b/research/qq16-rounded-trace/vendor/PR3985-WORD.json new file mode 100644 index 0000000000..1518ddc9b6 --- /dev/null +++ b/research/qq16-rounded-trace/vendor/PR3985-WORD.json @@ -0,0 +1 @@ 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diff --git a/research/qq16-rounded-trace/verify.py b/research/qq16-rounded-trace/verify.py new file mode 100644 index 0000000000..6468d03da0 --- /dev/null +++ b/research/qq16-rounded-trace/verify.py @@ -0,0 +1,233 @@ +#!/usr/bin/env python3 +"""Exact rounded-operation DAG equivalence of PR3985 and PR4015. +Chris R / Clear1nsight, with OpenAI Codex assistance. Apache-2.0. +No inherited executable, native idealization, or reassociation is used. +""" +import argparse +from collections import Counter, defaultdict, deque +from fractions import Fraction +import hashlib +import json +from pathlib import Path + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +PINNED = { + 'vendor/PR3985-WORD.json': 'a854f516f1d80635fb3414734f9e1c6d1251a5d79ef12e137c143fc6b0b51722', + 'vendor/PR4015-WORD.json': '272d8c1bd172c29044eb227ec6d67a882501250978234685e035158f4479aa58', + 'vendor/PR3652-PROOF.md': '0edd900b2bf312c532f0e5067cb27a14495bf0c8a2ccddd25073ef4c592989e4', +} + +def need(ok, message): + if not ok: + raise ValueError(message) + +def canon(value): + return json.dumps(value, sort_keys=True, separators=(',', ':'), allow_nan=False).encode() + +def typed(value): + if isinstance(value, dict): + return ('dict', tuple((k, typed(v)) for k, v in sorted(value.items()))) + if isinstance(value, list): + return ('list', tuple(map(typed, value))) + return (type(value).__name__, value) + +def authenticate(): + records = json.loads((HERE/'SOURCES.json').read_text())['files'] + seen = {} + for row in records: + if row['usage'] != 'input': + continue + raw = (ROOT/row['path']).read_bytes() + need(hashlib.sha256(raw).hexdigest() == row['sha256'], 'source hash: '+row['path']) + need(hashlib.sha1(b'blob '+str(len(raw)).encode()+b'\0'+raw).hexdigest() == row['git_blob'], 'source blob') + seen[row['path']] = row['sha256'] + for name, expected in PINNED.items(): + raw = (HERE/name).read_bytes() + need(hashlib.sha256(raw).hexdigest() == expected, 'retained source hash: '+name) + return seen + +class Arena: + """Structural tuple equality, not digest equality, is the decision procedure.""" + def __init__(self): + self.nodes = [] + self.ids = {} + def make(self, key): + if key not in self.ids: + self.ids[key] = len(self.nodes) + self.nodes.append(key) + return self.ids[key] + +def trace(word, arena, format_tag='common-format'): + need(isinstance(word, list) and len(word) < 5000, 'word bounds') + borrowed = {s+str(p) for s in ('X','Y') for p in range(112)} + owned = {s+str(p) for s in ('Z','W','D') for p in range(112)} + state = {n: arena.make(('input', n)) for n in sorted(borrowed)} + original = dict(state) + active = set(); zero = arena.make(('zero', format_tag)) + frames = {}; events = []; reads = []; initialized = set(); cuts = [] + def read(n, i): + need(n in borrowed | owned | active, 'read ownership at '+str(i)) + need(n in state, 'read before CLEAR at '+str(i)+': '+n) + reads.append((i, n)) + return state[n] + for i, e in enumerate(word): + need(isinstance(e, list) and e, 'event schema') + op = e[0] + if op == 'begin': + need(len(e)==3 and not active and e[2] in (8,16), 'private begin') + active = {s+str(k) for s in (('F','G') if e[2]==16 else ('F',)) for k in range(8)} + for n in active: + state.pop(n, None); frames.pop(n, None) + elif op == 'end': + need(len(active)==e[2], 'private end') + need(all(state.get(n)==zero and frames.get(n)=='identity' for n in active), 'private zero/identity return') + for n in active: + state.pop(n); frames.pop(n) + active = set() + elif op == 'clear': + need(len(e)==3 and e[1] in owned | active, 'CLEAR ownership') + need(e[2] in ('current','wide','identity','query2') or e[2].startswith('hole'), 'CLEAR frame') + state[e[1]] = zero; frames[e[1]] = e[2]; initialized.add(e[1]) + elif op == 'add': + need(len(e)==4 and e[1] in owned | active and e[1]!=e[2], 'ADD ownership') + need(e[3] in ('1','-1','1/4','-1/4'), 'ADD coefficient') + state[e[1]] = arena.make(('add', format_tag, e[3], read(e[1],i), read(e[2],i))) + events.append((i, e[1], state[e[1]])) + elif op in ('line','map'): + need(not active and e[1] in owned, 'native/map workspace overlap') + if op=='line': + need(len(e)==4 and type(e[2]) is int and 0<=e[2]<112 and e[3] in (-1,1), 'line schema') + else: + need(len(e)==5 and e[2] in (1,2) and type(e[3]) is int and 0<=e[3]<112 and type(e[4]) is bool, 'map schema') + state[e[1]] = arena.make((op, format_tag, *e[2:], read(e[1],i))) + events.append((i,e[1],state[e[1]])) + elif op == 'checkpoint': + need(not active, 'checkpoint private leak') + cuts.append((i,{n:state[n] for n in sorted(owned) if n.startswith(('Z','W'))})) + else: + raise ValueError('unknown event '+str(e)) + need(not active, 'private leak') + need(all(state[n]==v for n,v in original.items()), 'borrowed write') + outputs = {s+str(p):state[s+str(p)] for s in ('Z','W') for p in range(112)} + for n in owned: + if n.startswith('D') and n in state: + need(state[n]==zero and frames[n]=='identity', 'old temporary zero/identity return') + return {'outputs':outputs,'events':events,'reads':reads,'cuts':cuts,'initialized':sorted(initialized)} + +def compare(old, new): + a = Arena(); left = trace(old,a); right = trace(new,a) + need(left['outputs']==right['outputs'], 'output DAG mismatch') + need([x[1] for x in left['cuts']]==[x[1] for x in right['cuts']], 'checkpoint DAG mismatch') + buckets = defaultdict(deque) + for i,d,n in right['events']: + buckets[n].append((i,d)) + mapping=[] + for i,d,n in left['events']: + need(bool(buckets[n]), 'value-event DAG multiset mismatch') + j,t=buckets[n].popleft();mapping.append([i,j,d,t,n]) + need(not any(buckets.values()), 'unmatched new value event') + need(len(mapping)==3392, 'value-event census') + # Complete instruction identities and occurrence multiplicity, not only roots. + native_left=[(old[i][2:],n) for i,_,n in left['events'] if old[i][0]=='line'] + native_right=[(new[i][2:],n) for i,_,n in right['events'] if new[i][0]=='line'] + need(native_left==native_right, 'native sequence mismatch') + return a,left,right,mapping + +def signed(value, width, mode='trap'): + lo,hi=-(1<<(width-1)),(1<<(width-1))-1 + if mode=='wrap': + return (value-lo)%(1<=0 else -1)*(abs(value)//4) + raise ValueError('rounding policy') + +def probes(old,new,mapping): + paired={i:j for i,j,*_ in mapping} + def stateful_signature(word): + count=0;rows=[] + for i,e in enumerate(word): + if e[0]=='add':count+=1 + if e[0]=='line':rows.append((i,e[2:],count)) + return rows + old_state,new_state=stateful_signature(old),stateful_signature(new) + first=next((a,b) for a,b in zip(old_state,new_state) if a[2]!=b[2]) + need(first[0][0]==9 and first[1][0]==7 and first[0][2]==4 and first[1][2]==3,'first hidden-state divergence') + stateful={'old_event':9,'new_event':7,'native_port':1,'sign':1,'old_prior_ADD_count':4,'new_prior_ADD_count':3,'example_hidden_additive_offset_mod2':[0,1],'scope':'Countermodel only: a kernel consulting global scalar-count parity violates declared-input determinism; not an observed defect of the actual native kernel.'} + query=[i for i,e in enumerate(old) if e[0]=='add' and e[1]=='F0' and e[2].startswith('D')] + need(old[query[0]]==['add','F0','D2','1'] and old[query[1]]==['add','F0','D9','1'], 'source-bound query fixture') + qevent=next(i for i,e in enumerate(old) if e==['add','D0','F0','-1/4']) + need(new[paired[qevent]][3]=='-1/4','paired quarter') + try:signed(3+1,3) + except ValueError:overflow=True + else:overflow=False + need(overflow and signed(3+1,4)==4,'overflow fixture') + decisions=[] + for x in range(-17,18): + for y in range(-17,18): + for c in (-1,1): + for mode in ('floor','trunc'): + product=quarter(c*y,mode) + for width in (3,4,6): + for overflow_mode in ('wrap','saturate'): + v=signed(x+product,width,overflow_mode) + # An independent exact-rational oracle checks signed rounding/overflow conventions. + exact=Fraction(c*y,4) + rounded=exact.numerator//exact.denominator if mode=='floor' else int(exact) + total=x+rounded;lo,hi=-(1<<(width-1)),(1<<(width-1))-1 + if overflow_mode=='saturate':expected=max(lo,min(total,hi)) + else: + bits=total & ((1<