diff --git a/research/native-rank8-helper-provider/ATTRIBUTION.md b/research/native-rank8-helper-provider/ATTRIBUTION.md new file mode 100644 index 0000000000..efe3acb566 --- /dev/null +++ b/research/native-rank8-helper-provider/ATTRIBUTION.md @@ -0,0 +1,50 @@ +# Predecessors and exact scope + +Ali Romman's [PR5383](https://github.com/CrocSwap/integer-mult-bounds/pull/5383), +head `4bd6efa51a495a7c7b7754915cf0244e7e60969e`, supplies the exact eight +cached-center candidate rows and sites. Its WITNESS is retained verbatim as +package-local candidate data. The byte hash is checked, and all used +relations, chronology and zero-call claims are independently recomputed from +the pinned main native source. The PR head is provenance, not a required Git +object or an assumed accepted theorem. We do not claim priority for the +cached-center relation or for center deletion. + +Cao Yifan / intqwq supplies `kappa-round3-warp-20261022`'s canonical native +helper/map/contact source and the PR4610 lineage. Its exact payload is +retained by main's `native-center-free-code/SOURCE-WORD.json.gz`. +Dugongue / mdumitrean supplies [PR4929](https://github.com/CrocSwap/integer-mult-bounds/pull/4929)'s +center-free code, eight-mode factorization, source construction and analytic +interpretation. Cinna Davis / 1337isnot1337 supplies the +[PR4694](https://github.com/CrocSwap/integer-mult-bounds/pull/4694) retained-center +interface, [PR4698](https://github.com/CrocSwap/integer-mult-bounds/pull/4698) +common-chart helper basis and conditional consumer, and +[PR4470](https://github.com/CrocSwap/integer-mult-bounds/pull/4470) controller. +A retained cache or eight-dimensional defect is not newly discovered here. + +The pinned `coded-native-caller` supplies the physical main normalizers, +corrected conjugated backward convention, compiled wrapper recipes, contact +matrix M, and exact Clifford evaluator. Its Clifford source traces through +`t74-native-fast/vendor/native/new/code/borrow/vendor/clifford`; retain zxv's +native/productive/compiler work and the original license. Retain Jacob Alan +Sussman's mixed-target recursion, Ryanson Jonathan's controller checks, +Dugongue's transported-frame lemma and the cumulative helper/native lineage +identified by the predecessor packages. The exact shared bytes are pinned in +SOURCES.json rather than duplicated under new authorship. + +Within this continuation, coordinated OpenAI Codex agents constructed the +unrestricted retained-cache source, independently replayed all 641 columns, +derived the dual retraction and physical rank-eight normalization, and +reviewed the basis costs. This package combines that work into one fresh +registered replay with an explicit all-owner boundary recipe, verbatim +candidate provenance, local bill and every-positive-width proof. New work is +the fully owned **coupled** provider with all 632 originals preserved and all +nine owned outputs cleared. It is not a caller, an autonomous H8 donor, an +exponent improvement, a formal-kernel proof or independent human review. + +The broader investigation and priority/overlap checkpoints remain in the +campaign's [Discussion4930](https://github.com/CrocSwap/integer-mult-bounds/discussions/4930) +and TASK.json. This package preserves the same frozen native payload while +binding its publication task metadata to main at +`1ec1119972c9aefe42525172d07b332fcff81cb4`. It does not claim an exhaustive +novelty search or alter the selected result. Prepared for Dillon with +substantial OpenAI Codex assistance. Apache-2.0. diff --git a/research/native-rank8-helper-provider/PROOF.md b/research/native-rank8-helper-provider/PROOF.md new file mode 100644 index 0000000000..5cbfc4fd02 --- /dev/null +++ b/research/native-rank8-helper-provider/PROOF.md @@ -0,0 +1,236 @@ +# A source-bound backward provider with eight coupled rank-eight outputs + +The construction has 632 arbitrary original inputs and nine arbitrary owned +inputs. Its paid native profile is +`{1:2193,2:412,3:510,4:127,5:40}`. It returns 400 unchanged native helper jobs +and a coupled block on the 224 main and eight remaining helper owners: + +\[ + X=Dx-Ry+RW h,\qquad Y=Dy,\qquad H=D(h-Zy). \tag{1} +\] + +Here `R=DQ` is the full native rank-nine Gaussian, `D` acts on the eight +noncentral axes, and `Q` acts on the central axis. The eight `H` outputs remain +coupled; they are **not eight autonomous H8 targets**. No complete caller or +new multiplication exponent follows. All nine owned outputs are zero. + +## 1. Exact source and the changed word + +`SOURCES.json` pins the main-branch source, code, normalizers and Clifford +compiler. The native source's decompressed SHA256 is +`cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd`. +`WITNESS.json` retains Ali Romman's PR5383 candidate verbatim, with SHA256 +`24599011da06325e1012619b2b84a4dd3aceb90ab42d3caaf6414879e7d16591`. +It supplies candidate sites and rational rows; it is not a proof oracle or a +pending Git-object dependency. Every used identity is checked again against +the pinned main source. + +For witness row `i`, after the indicated original `cached_event`, CLEAR owned +`C[i+1]` and COPY the indicated persistent row into it at its actual chart. +Every cache precedes every removed center. At the original center event, +replace the H8 call by CLEAR `C0`, then COPY `C[i+1]` into `C0` at that same +rank-eight chart. At the indicated later H1 call, replace the call by a +`zero_retag`: this is physical identity on the **exactly zero** field, with +its bookkeeping chart changed to the old call's output chart. All other +instructions, including inherited physical metadata, remain unchanged. +`WORD.json.gz` emits the complete resulting backward native word; the verifier +regenerates it from the canonical source and compares its parsed content. + +The replay begins with one independent formal column per field, including +all nine owned fields. It tracks exact rational coefficients in the free +group on the source's native warp symbols, their inverses, and actual chart +tags. Every ordinary operation is checked at its true chart. COPY fills only +owned zero; CLEAR acts only on owned fields. Before each of the eight retags, +every one of the 641 input coefficients is zero. All initial owned dirt is +cleared before use and is absent from every endpoint. + +The source's ten `phase` records are named stage annotations, not scalar +Clifford phase gates; its 448 `adapter` records retain the predecessor's +physical entrance/exit bindings (there are no `residual_adapter` records in +this backward word). As in the pinned predecessor normalized-row semantics, +these do not update formal rows. They are preserved in the emitted word, +not deleted or priced away. Their physical interpretation and native cost +are inherited; this package separately verifies every new physical boundary +identity including absolute phase. + +The same interpreter replays the original source, obtaining its full +632-row normalized backward endpoint `(x-y,y,h)` and clean original temporary. +It separately replays center deletion to derive the native coupling below. +The changed word has eight fewer H8 and eight fewer H1 calls than the original +source, with no additional Gaussian call. It has 16 extra COPYs and 16 extra +CLEARs. This is a changed source construction, not a constraint such as +`Delta h=0` on otherwise independent inputs. + +## 2. Source-derived coupling and an ordinary helper basis + +Use the inherited 112-by-8 matrix `M`, stored transposed as `mode_columns`. +The verifier checks all entries of + +\[ + M^T M=56I_8,\qquad A=I-MM^T/4. +\] + +Fresh replay of the center-deleted source gives + +\[ + X=x-A^Ty,\qquad Y=y,\qquad H=h-B^TM^Ty. +\] + +The verifier derives every entry of `B` by projecting the actual 408-by-112 +helper-to-Y coefficient matrix onto `M/56`; it then checks the entire +factorization and all 632 endpoints. The eight candidate rows `Delta` satisfy +`Delta B^T = S`, an exactly checked signed permutation. Put `E=S^-1 Delta`. +Thus `E B^T=I8`. Fresh original-prefix replay also binds the candidate cache +rows, their chronology and their actual rank-eight charts. + +In these coordinates the changed word has normalized endpoint + +\[ + X=x-y+(M/4)Eh,\quad Y=y,\quad H=(I-B^TE)h, \tag{2} +\] + +and its canonical mode-`k` cache is + +\[ + f_i(E_kh-M_k^Ty),\qquad f_i=\texttt{zero_factor}_i\,S_{ik}. \tag{3} +\] + +The registered check composes all changed endpoint rows with the following +basis, rather than accepting (2) or (3) from a saved endpoint registry. + +The union of supports of `B` and `E` comprises 122 actual cold H9 owners: each +has ground entrance chart and full-R exit chart. Choose the eight original +mode owners `[224,225,227,229,240,241,256,257]`. Define `L` on these 122 owners: +its mode columns are `B^T`; its other columns are `(I-B^TE)e_j`. Exact +Gauss-Jordan reduction constructs `L^-1` and verifies both inverse products, +`EL` selecting precisely the eight mode coordinates, and `L^-1B^T` embedding +precisely those coordinates. Every coefficient is dyadic. The emitted +`input_basis_program` and `output_basis_program` execute these two maps in +place, without extra owned basis storage. + +Both bases mix only fields sharing the appropriate physical chart, so scalar +owner operations implement them ordinarily. After entrance `L` and exit +`L^-1`, every one of the 632 persistent rows is checked: the eight selected +helper rows are zero, the other 400 helper rows are unchanged, `Y=y`, and +`X=x-y+(M/4)h_mode`. Each cache is exactly +`f_i(h_mode,k-M_k^T y)`. Thus the cache fills a vacated original direction; +it supplies no additional productive input or job credit. + +## 3. Literal physical boundary maps and ownership + +Backward frames use complex conjugation of the native frames, as in the +pinned source convention; they are not silently replaced by adjoints. Let +`Kp` be the 112 inherited main normalizers. For each actual cache frame `F8`, +the verifier constructs an orthogonal, phase-correct monomial `Km` from its +unique missing odd noncharacteristic line, and compiles a monomial `N` with + +\[ + N\overline{F8}K_m=D,\qquad K_mR=RK_m. +\] + +`PROVIDER.json` contains all eight literal `Km` and `N` words, signed tableaux +and nonzero zero-column phase anchors. The compiler's output is checked +explicitly even under Python `-O`. All `Kp` commute with `R`, including +absolute phase. Every boundary word contains only monomial gates. + +Apply `2Km` to the eight original mode inputs before `L`. At the exit, apply +`N/(2f_i)` to each cache. Use the inherited **fused compiled** backward main +input/output wrappers. The verifier checks 336 main diagonal/shear blocks, +896 nonzero main/helper coupling blocks and eight helper diagonal blocks, +for 1,240 exact physical equations. Comparison includes the signed tableau +and exact zero-state vector, so an undetected global phase is impossible +within this Clifford model. These equations yield (1), with + +\[ + W=\operatorname{diag}(K_p^{-1})M\operatorname{diag}(K_m)/2, + \quad + Z=\operatorname{diag}(K_m^{-1})M^T\operatorname{diag}(K_p)/2. +\] + +The main code is the predecessor's `C=diag(Kp^-1) A diag(Kp)`. Exact word +cancellation and the scalar factorization give +`ZW=14I8`, `WZ=I-C`; `W` and `Z` intertwine `R` on their respective banks. +No commutation with `D` or `Q` is assumed. These are finite ordinary code +maps with exterior scalar coefficients, not additional Gaussian calls. + +After normalization, SWAP each cache's **whole physical field and chart tag** +with its identically zero original mode output. The original owner now holds +the normalized coupled output; the owned slot holds zero and can be CLEARed. +There is no persistent erasure and no attempted free chart conversion of a +nonzero field. `C0` is already zero, so all nine owned outputs are zero. +Ordering the coupled input/output banks as `(y,h,x)` makes (1) triangular +with invertible diagonal `D`. Together with the 400 unchanged native jobs, +this proves preservation of all 632 original input directions. It does not +emit an inverse schedule or establish a same-cost inverse/transpose. + +## 4. Exact local bill + +Relative to the original raw backward source, the selected schedule adds: + +| Ordinary operation | Added field operations | +| --- | ---: | +| ADD | 1,644 | +| SCALE | 40 | +| COPY | 16 | +| CLEAR | 24 | +| Whole-field SWAP, with chart tag | 8 | +| Monomial field map | 464 | + +Each basis direction uses 822 ADD and 12 SCALE: its three elimination swaps +are expanded into three ADDs and one SCALE each. Eight input scalings and +eight cache scalings give the remaining 16 SCALEs. The source rewrite adds +16 COPY and 16 CLEAR; final cache consumption adds eight CLEAR. The 464 +monomial maps are 448 fused inherited main standardizers, eight `Km` and +eight `N`. This counts the newly installed boundary schedule; all unchanged +source warp/phase/adapter traffic and native child implementations remain in +the emitted word and retain their inherited costs. In particular, this table +does not assert that a field monomial map is zero machine work. + +The original source has 16,273 ADD, 1,164 SCALE and 16 CLEAR. Including the +new boundary scalars, the schedule therefore has 17,917 ADD, 1,204 SCALE, +16 COPY, 40 CLEAR and eight whole-field SWAP, plus the explicitly described +monomial boundary maps and inherited native operations. Nine owned fields +suffice: the original center temporary and eight retained caches. Their +initial values are arbitrary; their final values are zero. The autonomous +helper profile is `{4:28,7:7,8:47,9:318}`. The physical implementations of +those unchanged native helper jobs are inherited from the pinned source; +scalar identity rows alone are not a new proof of those implementations. + +For an explicit local stability bound, use the maximum of field Euclidean +norms. ADD by `a` has norm at most `1+|a|`, SCALE has norm at most +`max(1,|a|)`, and unitary Gaussian/monomial maps, COPY, CLEAR and SWAP have +norm at most one. The verifier sums upward-rounded base-two logarithms for +every scalar operation in this finite schedule, obtaining **18,996**. Hence +every suffix amplifies an injected field error by at most `2^18996`; at most +`m` injections of norm `epsilon` give the conservative bound +`m*2^18996*epsilon`. All dyadic constants and word lengths are fixed. This +establishes local bounded amplification, not a complete coordinate rounding, +tape movement, recursive precision or outer multiplier budget. + +## 5. Every positive fiber width and verification boundary + +A free-group identity evaluates in any assignment of invertible native warp +operators. Therefore the exact rational row equalities and zero-retag +premises hold uniformly when native operations act on any positive fiber +width `f`. The scalar owner coefficients and scalar `L/L^-1` programs stay +outside the tensor product; in particular `ZW=14I`, not `14^f I`. Each +compiled monomial word uses the inherited prescription: `P` and `X` act +columnwise, `D` sums its Z4 polynomial over the columns, and a `phase` gate +contributes its phase once per column. Each address-operator identity is lifted +columnwise; an absolute phase `i^gamma` lifts to `i^(f gamma)`, rather than +being confused with an exterior scalar sign. Exact one-column operator +identities, word cancellation and rational matrix identities then prove the +same physical boundary composition for every `f`. The inherited native +uniform implementation hypotheses remain inherited. + +The registered verifier performs complete 641-column native row replay, +exact scalar endpoint composition, and the 1,240 physical boundary checks. +It does not claim a separately flattened 641-column physical-matrix replay, +a formal-kernel proof, independent human approval, hosted CI, or a complete +caller. It rejects a nonzero zero-retag, a single changed basis ADD +coefficient, a changed saved-cache coefficient and a phase-only error with +the correct tableau. Normal and optimized runs use explicit checks for the +new claims. The caller must close all 224 main and eight coupled helper +outputs, preserve the other 400 jobs, charge every added child and ordinary +operation, and discharge precision, storage and outer-budget obligations +before any new target credit or exponent is admitted. diff --git a/research/native-rank8-helper-provider/PROVIDER.json b/research/native-rank8-helper-provider/PROVIDER.json new file mode 100644 index 0000000000..0afd30ed01 --- /dev/null +++ b/research/native-rank8-helper-provider/PROVIDER.json @@ -0,0 +1,13105 @@ +{ + "schema_version": 1, + "source_payload_sha256": "cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd", + "candidate_witness_sha256": "24599011da06325e1012619b2b84a4dd3aceb90ab42d3caaf6414879e7d16591", + "word_payload_sha256": "05490717144b3e6c69c0cc9e5c5df5c69d841ca13bf29aabd1b0db180628f038", + "basis_roles": [ + 224, + 225, + 227, + 229, + 230, + 231, + 232, + 233, + 234, + 235, + 236, + 237, + 238, + 239, + 240, + 241, + 242, + 243, + 245, + 246, + 247, + 250, + 252, + 253, + 254, + 255, + 256, + 257, + 258, + 259, + 261, + 262, + 263, + 266, + 268, + 269, + 270, + 271, + 272, + 276, + 280, + 283, + 286, + 287, + 288, + 294, + 296, + 297, + 300, + 302, + 303, + 306, + 308, + 312, + 315, + 318, + 319, + 324, + 326, + 328, + 332, + 333, + 334, + 335, + 336, + 340, + 347, + 350, + 351, + 352, + 356, + 366, + 367, + 368, + 372, + 379, + 382, + 383, + 384, + 388, + 390, + 391, + 392, + 397, + 398, + 399, + 400, + 401, + 402, + 403, + 405, + 406, + 409, + 410, + 411, + 413, + 414, + 415, + 416, + 417, + 418, + 419, + 421, + 422, + 425, + 426, + 427, + 429, + 430, + 431, + 432, + 433, + 434, + 435, + 437, + 438, + 441, + 442, + 443, + 445, + 446, + 447 + ], + "mode_owners": [ + 224, + 225, + 227, + 229, + 240, + 241, + 256, + 257 + ], + "candidate_mode_permutation": [ + 2, + 0, + 1, + 3, + 5, + 7, + 6, + 4 + ], + "candidate_mode_signs": [ + "1", + "1", + "1", + "-1", + "-1", + "1", + "1", + "-1" + ], + "canonical_retraction_E": [ + [ + [ + 1, + "1" + ], + [ + 160, + "-1" + ], + [ + 164, + "-1" + ], + [ + 166, + "1" + ], + [ + 167, + "1" + ], + [ + 168, + "1" + ], + [ + 173, + "-1" + ] + ], + [ + [ + 1, + "1" + ], + [ + 3, + "-1" + ], + [ + 5, + "1" + ], + [ + 7, + "-2" + ], + [ + 8, + "1" + ], + [ + 10, + "-1" + ], + [ + 11, + "-1" + ], + [ + 12, + "-1" + ], + [ + 13, + "-1" + ], + [ + 14, + "2" + ], + [ + 15, + "1" + ], + [ + 160, + "-1" + ], + [ + 164, + "-1" + ], + [ + 166, + "1" + ], + [ + 167, + "1" + ], + [ + 168, + "1" + ], + [ + 173, + "-1" + ] + ], + [ + [ + 6, + "1" + ], + [ + 100, + "-1" + ], + [ + 102, + "1" + ], + [ + 104, + "1" + ], + [ + 109, + "-1" + ] + ], + [ + [ + 3, + "-1" + ], + [ + 5, + "-1" + ], + [ + 8, + "1" + ], + [ + 10, + "-1" + ], + [ + 11, + "-1" + ], + [ + 12, + "1" + ], + [ + 13, + "-1" + ], + [ + 15, + "1" + ], + [ + 100, + "1" + ], + [ + 102, + "-1" + ], + [ + 104, + "-1" + ], + [ + 109, + "1" + ] + ], + [ + [ + 64, + "-1" + ], + [ + 70, + "1" + ], + [ + 72, + "1" + ], + [ + 73, + "1" + ], + [ + 76, + "-1" + ], + [ + 79, + "-1" + ] + ], + [ + [ + 17, + "-1" + ], + [ + 19, + "1" + ], + [ + 21, + "-1" + ], + [ + 23, + "1" + ], + [ + 28, + "1" + ], + [ + 29, + "1" + ], + [ + 30, + "-1" + ], + [ + 31, + "-1" + ] + ], + [ + [ + 33, + "1" + ], + [ + 35, + "-1" + ], + [ + 37, + "1" + ], + [ + 39, + "-1" + ], + [ + 44, + "-1" + ], + [ + 45, + "-1" + ], + [ + 46, + "1" + ], + [ + 47, + "1" + ] + ], + [ + [ + 1, + "1" + ], + [ + 17, + "-1" + ], + [ + 19, + "1" + ], + [ + 21, + "1" + ], + [ + 23, + "-1" + ], + [ + 28, + "-1" + ], + [ + 29, + "1" + ], + [ + 30, + "1" + ], + [ + 31, + "-1" + ], + [ + 100, + "-1" + ], + [ + 102, + "1" + ], + [ + 104, + "1" + ], + [ + 109, + "-1" + ], + [ + 160, + "-1" + ], + [ + 164, + "-1" + ], + [ + 166, + "1" + ], + [ + 167, + "1" + ], + [ + 168, + "1" + ], + [ + 173, + "-1" + ] + ] + ], + "input_basis_program": [ + [ + "add", + 257, + 397, + "1" + ], + [ + "add", + 225, + 397, + "1" + ], + [ + "add", + 224, + 397, + "1" + ], + [ + "add", + 257, + 392, + "-1" + ], + [ + "add", + 225, + 392, + "-1" + ], + [ + "add", + 224, + 392, + "-1" + ], + [ + "add", + 257, + 391, + "-1" + ], + [ + "add", + 225, + 391, + "-1" + ], + [ + "add", + 224, + 391, + "-1" + ], + [ + "add", + 257, + 390, + "-1" + ], + [ + "add", + 225, + 390, + "-1" + ], + [ + "add", + 224, + 390, + "-1" + ], + [ + "add", + 257, + 388, + "1" + ], + [ + "add", + 225, + 388, + "1" + ], + [ + "add", + 224, + 388, + "1" + ], + [ + "add", + 257, + 384, + "1" + ], + [ + "add", + 225, + 384, + "1" + ], + [ + "add", + 224, + 384, + "1" + ], + [ + "add", + 257, + 333, + "1" + ], + [ + "add", + 229, + 333, + "-1" + ], + [ + "add", + 227, + 333, + "1" + ], + [ + "add", + 257, + 328, + "-1" + ], + [ + "add", + 229, + 328, + "1" + ], + [ + "add", + 227, + 328, + "-1" + ], + [ + "add", + 257, + 326, + "-1" + ], + [ + "add", + 229, + 326, + "1" + ], + [ + "add", + 227, + 326, + "-1" + ], + [ + "add", + 257, + 324, + "1" + ], + [ + "add", + 229, + 324, + "-1" + ], + [ + "add", + 227, + 324, + "1" + ], + [ + "add", + 240, + 303, + "1" + ], + [ + "add", + 240, + 300, + "1" + ], + [ + "add", + 240, + 297, + "-1" + ], + [ + "add", + 240, + 296, + "-1" + ], + [ + "add", + 240, + 294, + "-1" + ], + [ + "add", + 240, + 288, + "1" + ], + [ + "add", + 256, + 271, + "-1" + ], + [ + "add", + 256, + 270, + "-1" + ], + [ + "add", + 256, + 269, + "1" + ], + [ + "add", + 256, + 268, + "1" + ], + [ + "add", + 256, + 263, + "1" + ], + [ + "add", + 256, + 261, + "-1" + ], + [ + "add", + 256, + 259, + "1" + ], + [ + "add", + 255, + 257, + "1" + ], + [ + "add", + 241, + 257, + "-1" + ], + [ + "scale", + 257, + "-1" + ], + [ + "add", + 447, + 256, + "-1/2" + ], + [ + "add", + 446, + 256, + "1/2" + ], + [ + "add", + 445, + 256, + "1/2" + ], + [ + "add", + 443, + 256, + "-1/2" + ], + [ + "add", + 437, + 256, + "1/2" + ], + [ + "add", + 435, + 256, + "-1/2" + ], + [ + "add", + 433, + 256, + "1/2" + ], + [ + "add", + 432, + 256, + "-1/2" + ], + [ + "add", + 431, + 256, + "-1/2" + ], + [ + "add", + 430, + 256, + "1/2" + ], + [ + "add", + 429, + 256, + "1/2" + ], + [ + "add", + 427, + 256, + "-1/2" + ], + [ + "add", + 421, + 256, + "1/2" + ], + [ + "add", + 419, + 256, + "-1/2" + ], + [ + "add", + 417, + 256, + "1/2" + ], + [ + "add", + 399, + 256, + "-3/4" + ], + [ + "add", + 398, + 256, + "1/4" + ], + [ + "add", + 388, + 256, + "1/4" + ], + [ + "add", + 384, + 256, + "-1/4" + ], + [ + "add", + 383, + 256, + "3/4" + ], + [ + "add", + 382, + 256, + "-1/4" + ], + [ + "add", + 372, + 256, + "-1/4" + ], + [ + "add", + 368, + 256, + "1/4" + ], + [ + "add", + 367, + 256, + "3/4" + ], + [ + "add", + 366, + 256, + "-1/4" + ], + [ + "add", + 356, + 256, + "-1/4" + ], + [ + "add", + 352, + 256, + "1/4" + ], + [ + "add", + 351, + 256, + "-3/4" + ], + [ + "add", + 350, + 256, + "1/4" + ], + [ + "add", + 340, + 256, + "1/4" + ], + [ + "add", + 336, + 256, + "-1/4" + ], + [ + "add", + 334, + 256, + "-1/2" + ], + [ + "add", + 332, + 256, + "1/2" + ], + [ + "add", + 328, + 256, + "-1" + ], + [ + "add", + 326, + 256, + "1/2" + ], + [ + "add", + 324, + 256, + "-1/2" + ], + [ + "add", + 319, + 256, + "-1/2" + ], + [ + "add", + 318, + 256, + "1/4" + ], + [ + "add", + 312, + 256, + "1/4" + ], + [ + "add", + 308, + 256, + "1/4" + ], + [ + "add", + 306, + 256, + "-1/4" + ], + [ + "add", + 303, + 256, + "-1/2" + ], + [ + "add", + 302, + 256, + "1/4" + ], + [ + "add", + 296, + 256, + "1/4" + ], + [ + "add", + 288, + 256, + "-1/4" + ], + [ + "add", + 287, + 256, + "1/2" + ], + [ + "add", + 286, + 256, + "-1/4" + ], + [ + "add", + 280, + 256, + "-1/4" + ], + [ + "add", + 272, + 256, + "1/4" + ], + [ + "add", + 271, + 256, + "-1/2" + ], + [ + "add", + 270, + 256, + "1/2" + ], + [ + "add", + 269, + 256, + "1/2" + ], + [ + "add", + 261, + 256, + "1/2" + ], + [ + "add", + 259, + 256, + "-1/2" + ], + [ + "add", + 258, + 256, + "-1/2" + ], + [ + "add", + 240, + 256, + "-1" + ], + [ + "scale", + 256, + "1/2" + ], + [ + "add", + 256, + 257, + "1" + ], + [ + "add", + 257, + 256, + "-1" + ], + [ + "add", + 256, + 257, + "1" + ], + [ + "scale", + 257, + "-1" + ], + [ + "add", + 447, + 255, + "-1" + ], + [ + "add", + 446, + 255, + "1" + ], + [ + "add", + 443, + 255, + "1" + ], + [ + "add", + 442, + 255, + "-1" + ], + [ + "add", + 438, + 255, + "1" + ], + [ + "add", + 437, + 255, + "1" + ], + [ + "add", + 435, + 255, + "1" + ], + [ + "add", + 432, + 255, + "1" + ], + [ + "add", + 415, + 255, + "-1" + ], + [ + "add", + 411, + 255, + "-1" + ], + [ + "add", + 410, + 255, + "1" + ], + [ + "add", + 409, + 255, + "1" + ], + [ + "add", + 406, + 255, + "-1" + ], + [ + "add", + 403, + 255, + "1" + ], + [ + "add", + 402, + 255, + "-1" + ], + [ + "add", + 400, + 255, + "1" + ], + [ + "add", + 399, + 255, + "-1/2" + ], + [ + "add", + 398, + 255, + "-1/2" + ], + [ + "add", + 388, + 255, + "-1/2" + ], + [ + "add", + 384, + 255, + "1/2" + ], + [ + "add", + 383, + 255, + "-1/2" + ], + [ + "add", + 382, + 255, + "-1/2" + ], + [ + "add", + 372, + 255, + "-1/2" + ], + [ + "add", + 368, + 255, + "1/2" + ], + [ + "add", + 367, + 255, + "-1/2" + ], + [ + "add", + 366, + 255, + "-1/2" + ], + [ + "add", + 356, + 255, + "-1/2" + ], + [ + "add", + 352, + 255, + "1/2" + ], + [ + "add", + 351, + 255, + "-1/2" + ], + [ + "add", + 350, + 255, + "-1/2" + ], + [ + "add", + 340, + 255, + "-1/2" + ], + [ + "add", + 336, + 255, + "1/2" + ], + [ + "add", + 335, + 255, + "-2" + ], + [ + "add", + 334, + 255, + "-1" + ], + [ + "add", + 332, + 255, + "1" + ], + [ + "add", + 328, + 255, + "-2" + ], + [ + "add", + 326, + 255, + "1" + ], + [ + "add", + 324, + 255, + "-1" + ], + [ + "add", + 319, + 255, + "-1" + ], + [ + "add", + 318, + 255, + "-1/2" + ], + [ + "add", + 312, + 255, + "-1/2" + ], + [ + "add", + 308, + 255, + "-1/2" + ], + [ + "add", + 306, + 255, + "1/2" + ], + [ + "add", + 303, + 255, + "-1" + ], + [ + "add", + 302, + 255, + "-1/2" + ], + [ + "add", + 296, + 255, + "-1/2" + ], + [ + "add", + 288, + 255, + "1/2" + ], + [ + "add", + 287, + 255, + "-1" + ], + [ + "add", + 286, + 255, + "-1/2" + ], + [ + "add", + 280, + 255, + "-1/2" + ], + [ + "add", + 272, + 255, + "1/2" + ], + [ + "add", + 250, + 255, + "1" + ], + [ + "add", + 246, + 255, + "-1" + ], + [ + "add", + 243, + 255, + "1" + ], + [ + "add", + 255, + 256, + "1" + ], + [ + "add", + 256, + 255, + "-1" + ], + [ + "add", + 255, + 256, + "1" + ], + [ + "scale", + 256, + "-1" + ], + [ + "add", + 447, + 254, + "1" + ], + [ + "add", + 446, + 254, + "-1" + ], + [ + "add", + 443, + 254, + "-1" + ], + [ + "add", + 442, + 254, + "1" + ], + [ + "add", + 438, + 254, + "-1" + ], + [ + "add", + 437, + 254, + "-1" + ], + [ + "add", + 435, + 254, + "-1" + ], + [ + "add", + 432, + 254, + "-1" + ], + [ + "add", + 415, + 254, + "1" + ], + [ + "add", + 411, + 254, + "1" + ], + [ + "add", + 410, + 254, + "-1" + ], + [ + "add", + 409, + 254, + "-1" + ], + [ + "add", + 406, + 254, + "1" + ], + [ + "add", + 403, + 254, + "-1" + ], + [ + "add", + 402, + 254, + "1" + ], + [ + "add", + 400, + 254, + "-1" + ], + [ + "add", + 399, + 254, + "1/2" + ], + [ + "add", + 398, + 254, + "1/2" + ], + [ + "add", + 388, + 254, + "1/2" + ], + [ + "add", + 384, + 254, + "-1/2" + ], + [ + "add", + 383, + 254, + "1/2" + ], + [ + "add", + 382, + 254, + "1/2" + ], + [ + "add", + 372, + 254, + "1/2" + ], + [ + "add", + 368, + 254, + "-1/2" + ], + [ + "add", + 367, + 254, + "1/2" + ], + [ + "add", + 366, + 254, + "1/2" + ], + [ + "add", + 356, + 254, + "1/2" + ], + [ + "add", + 352, + 254, + "-1/2" + ], + [ + "add", + 351, + 254, + "1/2" + ], + [ + "add", + 350, + 254, + "1/2" + ], + [ + "add", + 340, + 254, + "1/2" + ], + [ + "add", + 336, + 254, + "-1/2" + ], + [ + "add", + 335, + 254, + "2" + ], + [ + "add", + 334, + 254, + "1" + ], + [ + "add", + 332, + 254, + "-1" + ], + [ + "add", + 328, + 254, + "2" + ], + [ + "add", + 326, + 254, + "-1" + ], + [ + "add", + 324, + 254, + "1" + ], + [ + "add", + 319, + 254, + "1" + ], + [ + "add", + 318, + 254, + "1/2" + ], + [ + "add", + 312, + 254, + "1/2" + ], + [ + "add", + 308, + 254, + "1/2" + ], + [ + "add", + 306, + 254, + "-1/2" + ], + [ + "add", + 303, + 254, + "1" + ], + [ + "add", + 302, + 254, + "1/2" + ], + [ + "add", + 296, + 254, + "1/2" + ], + [ + "add", + 288, + 254, + "-1/2" + ], + [ + "add", + 287, + 254, + "1" + ], + [ + "add", + 286, + 254, + "1/2" + ], + [ + "add", + 280, + 254, + "1/2" + ], + [ + "add", + 272, + 254, + "-1/2" + ], + [ + "add", + 256, + 254, + "-1" + ], + [ + "add", + 255, + 254, + "1" + ], + [ + "add", + 250, + 254, + "-1" + ], + [ + "add", + 246, + 254, + "1" + ], + [ + "add", + 243, + 254, + "-1" + ], + [ + "add", + 241, + 254, + "2" + ], + [ + "add", + 447, + 253, + "1" + ], + [ + "add", + 446, + 253, + "-1" + ], + [ + "add", + 443, + 253, + "-1" + ], + [ + "add", + 442, + 253, + "1" + ], + [ + "add", + 438, + 253, + "-1" + ], + [ + "add", + 437, + 253, + "-1" + ], + [ + "add", + 435, + 253, + "-1" + ], + [ + "add", + 432, + 253, + "-1" + ], + [ + "add", + 415, + 253, + "1" + ], + [ + "add", + 411, + 253, + "1" + ], + [ + "add", + 410, + 253, + "-1" + ], + [ + "add", + 409, + 253, + "-1" + ], + [ + "add", + 406, + 253, + "1" + ], + [ + "add", + 403, + 253, + "-1" + ], + [ + "add", + 402, + 253, + "1" + ], + [ + "add", + 400, + 253, + "-1" + ], + [ + "add", + 399, + 253, + "1/2" + ], + [ + "add", + 398, + 253, + "1/2" + ], + [ + "add", + 388, + 253, + "1/2" + ], + [ + "add", + 384, + 253, + "-1/2" + ], + [ + "add", + 383, + 253, + "1/2" + ], + [ + "add", + 382, + 253, + "1/2" + ], + [ + "add", + 372, + 253, + "1/2" + ], + [ + "add", + 368, + 253, + "-1/2" + ], + [ + "add", + 367, + 253, + "1/2" + ], + [ + "add", + 366, + 253, + "1/2" + ], + [ + "add", + 356, + 253, + "1/2" + ], + [ + "add", + 352, + 253, + "-1/2" + ], + [ + "add", + 351, + 253, + "1/2" + ], + [ + "add", + 350, + 253, + "1/2" + ], + [ + "add", + 340, + 253, + "1/2" + ], + [ + "add", + 336, + 253, + "-1/2" + ], + [ + "add", + 335, + 253, + "2" + ], + [ + "add", + 334, + 253, + "1" + ], + [ + "add", + 332, + 253, + "-1" + ], + [ + "add", + 328, + 253, + "2" + ], + [ + "add", + 326, + 253, + "-1" + ], + [ + "add", + 324, + 253, + "1" + ], + [ + "add", + 319, + 253, + "1" + ], + [ + "add", + 318, + 253, + "1/2" + ], + [ + "add", + 312, + 253, + "1/2" + ], + [ + "add", + 308, + 253, + "1/2" + ], + [ + "add", + 306, + 253, + "-1/2" + ], + [ + "add", + 303, + 253, + "1" + ], + [ + "add", + 302, + 253, + "1/2" + ], + [ + "add", + 296, + 253, + "1/2" + ], + [ + "add", + 288, + 253, + "-1/2" + ], + [ + "add", + 287, + 253, + "1" + ], + [ + "add", + 286, + 253, + "1/2" + ], + [ + "add", + 280, + 253, + "1/2" + ], + [ + "add", + 272, + 253, + "-1/2" + ], + [ + "add", + 256, + 253, + "-1" + ], + [ + "add", + 255, + 253, + "1" + ], + [ + "add", + 250, + 253, + "-1" + ], + [ + "add", + 246, + 253, + "1" + ], + [ + "add", + 243, + 253, + "-1" + ], + [ + "add", + 447, + 252, + "-1" + ], + [ + "add", + 446, + 252, + "1" + ], + [ + "add", + 443, + 252, + "1" + ], + [ + "add", + 442, + 252, + "-1" + ], + [ + "add", + 438, + 252, + "1" + ], + [ + "add", + 437, + 252, + "1" + ], + [ + "add", + 435, + 252, + "1" + ], + [ + "add", + 432, + 252, + "1" + ], + [ + "add", + 415, + 252, + "-1" + ], + [ + "add", + 411, + 252, + "-1" + ], + [ + "add", + 410, + 252, + "1" + ], + [ + "add", + 409, + 252, + "1" + ], + [ + "add", + 406, + 252, + "-1" + ], + [ + "add", + 403, + 252, + "1" + ], + [ + "add", + 402, + 252, + "-1" + ], + [ + "add", + 400, + 252, + "1" + ], + [ + "add", + 399, + 252, + "-1/2" + ], + [ + "add", + 398, + 252, + "-1/2" + ], + [ + "add", + 388, + 252, + "-1/2" + ], + [ + "add", + 384, + 252, + "1/2" + ], + [ + "add", + 383, + 252, + "-1/2" + ], + [ + "add", + 382, + 252, + "-1/2" + ], + [ + "add", + 372, + 252, + "-1/2" + ], + [ + "add", + 368, + 252, + "1/2" + ], + [ + "add", + 367, + 252, + "-1/2" + ], + [ + "add", + 366, + 252, + "-1/2" + ], + [ + "add", + 356, + 252, + "-1/2" + ], + [ + "add", + 352, + 252, + "1/2" + ], + [ + "add", + 351, + 252, + "-1/2" + ], + [ + "add", + 350, + 252, + "-1/2" + ], + [ + "add", + 340, + 252, + "-1/2" + ], + [ + "add", + 336, + 252, + "1/2" + ], + [ + "add", + 335, + 252, + "-2" + ], + [ + "add", + 334, + 252, + "-1" + ], + [ + "add", + 332, + 252, + "1" + ], + [ + "add", + 328, + 252, + "-2" + ], + [ + "add", + 326, + 252, + "1" + ], + [ + "add", + 324, + 252, + "-1" + ], + [ + "add", + 319, + 252, + "-1" + ], + [ + "add", + 318, + 252, + "-1/2" + ], + [ + "add", + 312, + 252, + "-1/2" + ], + [ + "add", + 308, + 252, + "-1/2" + ], + [ + "add", + 306, + 252, + "1/2" + ], + [ + "add", + 303, + 252, + "-1" + ], + [ + "add", + 302, + 252, + "-1/2" + ], + [ + "add", + 296, + 252, + "-1/2" + ], + [ + "add", + 288, + 252, + "1/2" + ], + [ + "add", + 287, + 252, + "-1" + ], + [ + "add", + 286, + 252, + "-1/2" + ], + [ + "add", + 280, + 252, + "-1/2" + ], + [ + "add", + 272, + 252, + "1/2" + ], + [ + "add", + 256, + 252, + "1" + ], + [ + "add", + 255, + 252, + "-1" + ], + [ + "add", + 250, + 252, + "1" + ], + [ + "add", + 246, + 252, + "-1" + ], + [ + "add", + 243, + 252, + "1" + ], + [ + "add", + 241, + 252, + "-2" + ], + [ + "add", + 447, + 247, + "-1" + ], + [ + "add", + 446, + 247, + "1" + ], + [ + "add", + 443, + 247, + "1" + ], + [ + "add", + 442, + 247, + "-1" + ], + [ + "add", + 438, + 247, + "1" + ], + [ + "add", + 437, + 247, + "1" + ], + [ + "add", + 435, + 247, + "1" + ], + [ + "add", + 432, + 247, + "1" + ], + [ + "add", + 415, + 247, + "-1" + ], + [ + "add", + 411, + 247, + "-1" + ], + [ + "add", + 410, + 247, + "1" + ], + [ + "add", + 409, + 247, + "1" + ], + [ + "add", + 406, + 247, + "-1" + ], + [ + "add", + 403, + 247, + "1" + ], + [ + "add", + 402, + 247, + "-1" + ], + [ + "add", + 400, + 247, + "1" + ], + [ + "add", + 399, + 247, + "-1/2" + ], + [ + "add", + 398, + 247, + "-1/2" + ], + [ + "add", + 388, + 247, + "-1/2" + ], + [ + "add", + 384, + 247, + "1/2" + ], + [ + "add", + 383, + 247, + "-1/2" + ], + [ + "add", + 382, + 247, + "-1/2" + ], + [ + "add", + 372, + 247, + "-1/2" + ], + [ + "add", + 368, + 247, + "1/2" + ], + [ + "add", + 367, + 247, + "-1/2" + ], + [ + "add", + 366, + 247, + "-1/2" + ], + [ + "add", + 356, + 247, + "-1/2" + ], + [ + "add", + 352, + 247, + "1/2" + ], + [ + "add", + 351, + 247, + "-1/2" + ], + [ + "add", + 350, + 247, + "-1/2" + ], + [ + "add", + 340, + 247, + "-1/2" + ], + [ + "add", + 336, + 247, + "1/2" + ], + [ + "add", + 335, + 247, + "-2" + ], + [ + "add", + 334, + 247, + "-1" + ], + [ + "add", + 332, + 247, + "1" + ], + [ + "add", + 328, + 247, + "-2" + ], + [ + "add", + 326, + 247, + "1" + ], + [ + "add", + 324, + 247, + "-1" + ], + [ + "add", + 319, + 247, + "-1" + ], + [ + "add", + 318, + 247, + "-1/2" + ], + [ + "add", + 312, + 247, + "-1/2" + ], + [ + "add", + 308, + 247, + "-1/2" + ], + [ + "add", + 306, + 247, + "1/2" + ], + [ + "add", + 303, + 247, + "-1" + ], + [ + "add", + 302, + 247, + "-1/2" + ], + [ + "add", + 296, + 247, + "-1/2" + ], + [ + "add", + 288, + 247, + "1/2" + ], + [ + "add", + 287, + 247, + "-1" + ], + [ + "add", + 286, + 247, + "-1/2" + ], + [ + "add", + 280, + 247, + "-1/2" + ], + [ + "add", + 272, + 247, + "1/2" + ], + [ + "add", + 256, + 247, + "1" + ], + [ + "add", + 255, + 247, + "-1" + ], + [ + "add", + 250, + 247, + "1" + ], + [ + "add", + 246, + 247, + "-1" + ], + [ + "add", + 243, + 247, + "1" + ], + [ + "add", + 241, + 247, + "-2" + ], + [ + "add", + 447, + 245, + "1" + ], + [ + "add", + 446, + 245, + "-1" + ], + [ + "add", + 443, + 245, + "-1" + ], + [ + "add", + 442, + 245, + "1" + ], + [ + "add", + 438, + 245, + "-1" + ], + [ + "add", + 437, + 245, + "-1" + ], + [ + "add", + 435, + 245, + "-1" + ], + [ + "add", + 432, + 245, + "-1" + ], + [ + "add", + 415, + 245, + "1" + ], + [ + "add", + 411, + 245, + "1" + ], + [ + "add", + 410, + 245, + "-1" + ], + [ + "add", + 409, + 245, + "-1" + ], + [ + "add", + 406, + 245, + "1" + ], + [ + "add", + 403, + 245, + "-1" + ], + [ + "add", + 402, + 245, + "1" + ], + [ + "add", + 400, + 245, + "-1" + ], + [ + "add", + 399, + 245, + "1/2" + ], + [ + "add", + 398, + 245, + "1/2" + ], + [ + "add", + 388, + 245, + "1/2" + ], + [ + "add", + 384, + 245, + "-1/2" + ], + [ + "add", + 383, + 245, + "1/2" + ], + [ + "add", + 382, + 245, + "1/2" + ], + [ + "add", + 372, + 245, + "1/2" + ], + [ + "add", + 368, + 245, + "-1/2" + ], + [ + "add", + 367, + 245, + "1/2" + ], + [ + "add", + 366, + 245, + "1/2" + ], + [ + "add", + 356, + 245, + "1/2" + ], + [ + "add", + 352, + 245, + "-1/2" + ], + [ + "add", + 351, + 245, + "1/2" + ], + [ + "add", + 350, + 245, + "1/2" + ], + [ + "add", + 340, + 245, + "1/2" + ], + [ + "add", + 336, + 245, + "-1/2" + ], + [ + "add", + 335, + 245, + "2" + ], + [ + "add", + 334, + 245, + "1" + ], + [ + "add", + 332, + 245, + "-1" + ], + [ + "add", + 328, + 245, + "2" + ], + [ + "add", + 326, + 245, + "-1" + ], + [ + "add", + 324, + 245, + "1" + ], + [ + "add", + 319, + 245, + "1" + ], + [ + "add", + 318, + 245, + "1/2" + ], + [ + "add", + 312, + 245, + "1/2" + ], + [ + "add", + 308, + 245, + "1/2" + ], + [ + "add", + 306, + 245, + "-1/2" + ], + [ + "add", + 303, + 245, + "1" + ], + [ + "add", + 302, + 245, + "1/2" + ], + [ + "add", + 296, + 245, + "1/2" + ], + [ + "add", + 288, + 245, + "-1/2" + ], + [ + "add", + 287, + 245, + "1" + ], + [ + "add", + 286, + 245, + "1/2" + ], + [ + "add", + 280, + 245, + "1/2" + ], + [ + "add", + 272, + 245, + "-1/2" + ], + [ + "add", + 256, + 245, + "-1" + ], + [ + "add", + 255, + 245, + "1" + ], + [ + "add", + 250, + 245, + "-1" + ], + [ + "add", + 246, + 245, + "1" + ], + [ + "add", + 243, + 245, + "-1" + ], + [ + "add", + 241, + 245, + "2" + ], + [ + "add", + 447, + 243, + "1/2" + ], + [ + "add", + 446, + 243, + "-1/2" + ], + [ + "add", + 443, + 243, + "-1/2" + ], + [ + "add", + 442, + 243, + "1/2" + ], + [ + "add", + 438, + 243, + "-1/2" + ], + [ + "add", + 437, + 243, + "-1/2" + ], + [ + "add", + 435, + 243, + "-1/2" + ], + [ + "add", + 432, + 243, + "-1/2" + ], + [ + "add", + 415, + 243, + "1/2" + ], + [ + "add", + 411, + 243, + "1/2" + ], + [ + "add", + 410, + 243, + "-1/2" + ], + [ + "add", + 409, + 243, + "-1/2" + ], + [ + "add", + 406, + 243, + "1/2" + ], + [ + "add", + 403, + 243, + "-1/2" + ], + [ + "add", + 402, + 243, + "1/2" + ], + [ + "add", + 400, + 243, + "-1/2" + ], + [ + "add", + 399, + 243, + "1/4" + ], + [ + "add", + 398, + 243, + "1/4" + ], + [ + "add", + 388, + 243, + "1/4" + ], + [ + "add", + 384, + 243, + "-1/4" + ], + [ + "add", + 383, + 243, + "1/4" + ], + [ + "add", + 382, + 243, + "1/4" + ], + [ + "add", + 372, + 243, + "1/4" + ], + [ + "add", + 368, + 243, + "-1/4" + ], + [ + "add", + 367, + 243, + "1/4" + ], + [ + "add", + 366, + 243, + "1/4" + ], + [ + "add", + 356, + 243, + "1/4" + ], + [ + "add", + 352, + 243, + "-1/4" + ], + [ + "add", + 351, + 243, + "1/4" + ], + [ + "add", + 350, + 243, + "1/4" + ], + [ + "add", + 340, + 243, + "1/4" + ], + [ + "add", + 336, + 243, + "-1/4" + ], + [ + "add", + 335, + 243, + "1" + ], + [ + "add", + 334, + 243, + "1/2" + ], + [ + "add", + 332, + 243, + "-1/2" + ], + [ + "add", + 328, + 243, + "1" + ], + [ + "add", + 326, + 243, + "-1/2" + ], + [ + "add", + 324, + 243, + "1/2" + ], + [ + "add", + 319, + 243, + "1/2" + ], + [ + "add", + 318, + 243, + "1/4" + ], + [ + "add", + 312, + 243, + "1/4" + ], + [ + "add", + 308, + 243, + "1/4" + ], + [ + "add", + 306, + 243, + "-1/4" + ], + [ + "add", + 303, + 243, + "1/2" + ], + [ + "add", + 302, + 243, + "1/4" + ], + [ + "add", + 296, + 243, + "1/4" + ], + [ + "add", + 288, + 243, + "-1/4" + ], + [ + "add", + 287, + 243, + "1/2" + ], + [ + "add", + 286, + 243, + "1/4" + ], + [ + "add", + 280, + 243, + "1/4" + ], + [ + "add", + 272, + 243, + "-1/4" + ], + [ + "add", + 256, + 243, + "-1/2" + ], + [ + "add", + 255, + 243, + "1/2" + ], + [ + "add", + 250, + 243, + "-1/2" + ], + [ + "add", + 246, + 243, + "1/2" + ], + [ + "scale", + 243, + "1/2" + ], + [ + "add", + 446, + 241, + "1/4" + ], + [ + "add", + 445, + 241, + "1/4" + ], + [ + "add", + 443, + 241, + "1/2" + ], + [ + "add", + 442, + 241, + "-1/4" + ], + [ + "add", + 441, + 241, + "1/4" + ], + [ + "add", + 438, + 241, + "1/4" + ], + [ + "add", + 437, + 241, + "1/4" + ], + [ + "add", + 435, + 241, + "1/2" + ], + [ + "add", + 434, + 241, + "-1/4" + ], + [ + "add", + 433, + 241, + "1/4" + ], + [ + "add", + 414, + 241, + "-1/4" + ], + [ + "add", + 413, + 241, + "-1/4" + ], + [ + "add", + 410, + 241, + "1/4" + ], + [ + "add", + 409, + 241, + "1/4" + ], + [ + "add", + 406, + 241, + "-1/4" + ], + [ + "add", + 405, + 241, + "-1/4" + ], + [ + "add", + 403, + 241, + "1/2" + ], + [ + "add", + 402, + 241, + "-1/4" + ], + [ + "add", + 401, + 241, + "-1/4" + ], + [ + "add", + 400, + 241, + "1/4" + ], + [ + "add", + 383, + 241, + "-1/4" + ], + [ + "add", + 382, + 241, + "-1/4" + ], + [ + "add", + 372, + 241, + "-1/4" + ], + [ + "add", + 368, + 241, + "1/4" + ], + [ + "add", + 351, + 241, + "-1/4" + ], + [ + "add", + 350, + 241, + "-1/4" + ], + [ + "add", + 340, + 241, + "-1/4" + ], + [ + "add", + 336, + 241, + "1/4" + ], + [ + "add", + 319, + 241, + "-1/2" + ], + [ + "add", + 318, + 241, + "-1/4" + ], + [ + "add", + 312, + 241, + "-1/4" + ], + [ + "add", + 308, + 241, + "-1/4" + ], + [ + "add", + 306, + 241, + "1/4" + ], + [ + "add", + 287, + 241, + "-1/2" + ], + [ + "add", + 286, + 241, + "-1/4" + ], + [ + "add", + 280, + 241, + "-1/4" + ], + [ + "add", + 272, + 241, + "1/4" + ], + [ + "add", + 256, + 241, + "1/4" + ], + [ + "add", + 254, + 241, + "-1/4" + ], + [ + "add", + 253, + 241, + "-1/4" + ], + [ + "add", + 250, + 241, + "1/4" + ], + [ + "add", + 246, + 241, + "-1/4" + ], + [ + "add", + 245, + 241, + "-1/4" + ], + [ + "add", + 243, + 241, + "1/2" + ], + [ + "add", + 242, + 241, + "1/4" + ], + [ + "scale", + 241, + "-1/4" + ], + [ + "add", + 447, + 240, + "-1/2" + ], + [ + "add", + 446, + 240, + "1/4" + ], + [ + "add", + 445, + 240, + "1/4" + ], + [ + "add", + 443, + 240, + "-1/2" + ], + [ + "add", + 442, + 240, + "1/4" + ], + [ + "add", + 441, + 240, + "1/4" + ], + [ + "add", + 438, + 240, + "-1/4" + ], + [ + "add", + 437, + 240, + "1/4" + ], + [ + "add", + 434, + 240, + "-1/4" + ], + [ + "add", + 433, + 240, + "1/4" + ], + [ + "add", + 431, + 240, + "-1/2" + ], + [ + "add", + 430, + 240, + "1/4" + ], + [ + "add", + 429, + 240, + "1/4" + ], + [ + "add", + 427, + 240, + "-1/2" + ], + [ + "add", + 426, + 240, + "1/4" + ], + [ + "add", + 425, + 240, + "1/4" + ], + [ + "add", + 422, + 240, + "-1/4" + ], + [ + "add", + 421, + 240, + "1/4" + ], + [ + "add", + 418, + 240, + "-1/4" + ], + [ + "add", + 417, + 240, + "1/4" + ], + [ + "add", + 416, + 240, + "1/4" + ], + [ + "add", + 399, + 240, + "-3/4" + ], + [ + "add", + 398, + 240, + "1/4" + ], + [ + "add", + 388, + 240, + "1/4" + ], + [ + "add", + 384, + 240, + "-1/4" + ], + [ + "add", + 351, + 240, + "-3/4" + ], + [ + "add", + 350, + 240, + "1/4" + ], + [ + "add", + 340, + 240, + "1/4" + ], + [ + "add", + 336, + 240, + "-1/4" + ], + [ + "add", + 319, + 240, + "-1/2" + ], + [ + "add", + 318, + 240, + "1/4" + ], + [ + "add", + 312, + 240, + "1/4" + ], + [ + "add", + 308, + 240, + "1/4" + ], + [ + "add", + 306, + 240, + "-1/4" + ], + [ + "add", + 303, + 240, + "-1/2" + ], + [ + "add", + 302, + 240, + "1/4" + ], + [ + "add", + 296, + 240, + "1/4" + ], + [ + "add", + 288, + 240, + "-1/4" + ], + [ + "add", + 271, + 240, + "-1/2" + ], + [ + "add", + 270, + 240, + "1/4" + ], + [ + "add", + 269, + 240, + "1/4" + ], + [ + "add", + 266, + 240, + "1/4" + ], + [ + "add", + 262, + 240, + "-1/4" + ], + [ + "add", + 261, + 240, + "1/4" + ], + [ + "add", + 258, + 240, + "-1/4" + ], + [ + "add", + 257, + 240, + "1/4" + ], + [ + "scale", + 240, + "1/4" + ], + [ + "add", + 240, + 256, + "1" + ], + [ + "add", + 256, + 240, + "-1" + ], + [ + "add", + 240, + 256, + "1" + ], + [ + "scale", + 256, + "-1" + ], + [ + "add", + 229, + 239, + "-1" + ], + [ + "add", + 225, + 239, + "-1" + ], + [ + "add", + 225, + 238, + "-2" + ], + [ + "add", + 229, + 237, + "1" + ], + [ + "add", + 225, + 237, + "1" + ], + [ + "add", + 229, + 236, + "-1" + ], + [ + "add", + 225, + 236, + "1" + ], + [ + "add", + 229, + 235, + "1" + ], + [ + "add", + 225, + 235, + "1" + ], + [ + "add", + 229, + 234, + "1" + ], + [ + "add", + 225, + 234, + "1" + ], + [ + "add", + 229, + 232, + "-1" + ], + [ + "add", + 225, + 232, + "-1" + ], + [ + "add", + 225, + 231, + "2" + ], + [ + "add", + 227, + 230, + "-1" + ], + [ + "add", + 431, + 229, + "1/2" + ], + [ + "add", + 429, + 229, + "1/2" + ], + [ + "add", + 427, + 229, + "1/2" + ], + [ + "add", + 425, + 229, + "1/2" + ], + [ + "add", + 419, + 229, + "1/2" + ], + [ + "add", + 418, + 229, + "-1/2" + ], + [ + "add", + 417, + 229, + "1/2" + ], + [ + "add", + 415, + 229, + "1/2" + ], + [ + "add", + 413, + 229, + "1/2" + ], + [ + "add", + 411, + 229, + "1/2" + ], + [ + "add", + 409, + 229, + "1/2" + ], + [ + "add", + 403, + 229, + "1/2" + ], + [ + "add", + 402, + 229, + "-1/2" + ], + [ + "add", + 401, + 229, + "1/2" + ], + [ + "add", + 399, + 229, + "1/2" + ], + [ + "add", + 398, + 229, + "-1/2" + ], + [ + "add", + 388, + 229, + "-1/2" + ], + [ + "add", + 384, + 229, + "-1/2" + ], + [ + "add", + 383, + 229, + "1/2" + ], + [ + "add", + 382, + 229, + "-1/2" + ], + [ + "add", + 372, + 229, + "-1/2" + ], + [ + "add", + 368, + 229, + "-1/2" + ], + [ + "add", + 347, + 229, + "-1" + ], + [ + "add", + 335, + 229, + "2" + ], + [ + "add", + 332, + 229, + "-1" + ], + [ + "add", + 328, + 229, + "2" + ], + [ + "add", + 326, + 229, + "-1" + ], + [ + "add", + 319, + 229, + "1" + ], + [ + "add", + 318, + 229, + "-1/2" + ], + [ + "add", + 312, + 229, + "1/2" + ], + [ + "add", + 308, + 229, + "-1/2" + ], + [ + "add", + 306, + 229, + "-1/2" + ], + [ + "add", + 303, + 229, + "1" + ], + [ + "add", + 302, + 229, + "-1/2" + ], + [ + "add", + 296, + 229, + "1/2" + ], + [ + "add", + 288, + 229, + "-1/2" + ], + [ + "add", + 283, + 229, + "-1" + ], + [ + "add", + 276, + 229, + "1/2" + ], + [ + "add", + 271, + 229, + "1/2" + ], + [ + "add", + 270, + 229, + "-1/2" + ], + [ + "add", + 266, + 229, + "1/2" + ], + [ + "add", + 262, + 229, + "-1/2" + ], + [ + "add", + 261, + 229, + "-1/2" + ], + [ + "add", + 259, + 229, + "-1/2" + ], + [ + "add", + 258, + 229, + "-1/2" + ], + [ + "add", + 256, + 229, + "-1/2" + ], + [ + "add", + 255, + 229, + "1/2" + ], + [ + "add", + 254, + 229, + "-1/2" + ], + [ + "add", + 250, + 229, + "1/2" + ], + [ + "add", + 246, + 229, + "-1/2" + ], + [ + "add", + 245, + 229, + "-1/2" + ], + [ + "add", + 243, + 229, + "-1/2" + ], + [ + "add", + 242, + 229, + "-1/2" + ], + [ + "add", + 240, + 229, + "-1/2" + ], + [ + "add", + 239, + 229, + "1" + ], + [ + "add", + 238, + 229, + "-1" + ], + [ + "add", + 237, + 229, + "-1/2" + ], + [ + "add", + 234, + 229, + "1/2" + ], + [ + "add", + 227, + 229, + "-1" + ], + [ + "add", + 225, + 229, + "1" + ], + [ + "add", + 224, + 229, + "-1" + ], + [ + "scale", + 229, + "-1" + ], + [ + "add", + 335, + 227, + "2" + ], + [ + "add", + 332, + 227, + "-1" + ], + [ + "add", + 328, + 227, + "2" + ], + [ + "add", + 326, + 227, + "-1" + ], + [ + "add", + 319, + 227, + "1/2" + ], + [ + "add", + 318, + 227, + "-1/4" + ], + [ + "add", + 315, + 227, + "-1/2" + ], + [ + "add", + 312, + 227, + "1/4" + ], + [ + "add", + 308, + 227, + "-1/4" + ], + [ + "add", + 306, + 227, + "-1/4" + ], + [ + "add", + 303, + 227, + "1" + ], + [ + "add", + 302, + 227, + "-1/2" + ], + [ + "add", + 296, + 227, + "1/2" + ], + [ + "add", + 288, + 227, + "-1/2" + ], + [ + "add", + 287, + 227, + "1/2" + ], + [ + "add", + 286, + 227, + "-1/4" + ], + [ + "add", + 283, + 227, + "-1/2" + ], + [ + "add", + 280, + 227, + "1/4" + ], + [ + "add", + 276, + 227, + "1/4" + ], + [ + "add", + 272, + 227, + "-1/4" + ], + [ + "add", + 270, + 227, + "-1/4" + ], + [ + "add", + 269, + 227, + "-1/4" + ], + [ + "add", + 266, + 227, + "1/4" + ], + [ + "add", + 262, + 227, + "-1/4" + ], + [ + "add", + 261, + 227, + "-1/4" + ], + [ + "add", + 259, + 227, + "-1/2" + ], + [ + "add", + 258, + 227, + "-1/4" + ], + [ + "add", + 257, + 227, + "-1/4" + ], + [ + "add", + 256, + 227, + "-1/4" + ], + [ + "add", + 254, + 227, + "-1/4" + ], + [ + "add", + 253, + 227, + "-1/4" + ], + [ + "add", + 250, + 227, + "1/4" + ], + [ + "add", + 246, + 227, + "-1/4" + ], + [ + "add", + 245, + 227, + "-1/4" + ], + [ + "add", + 243, + 227, + "-1/2" + ], + [ + "add", + 242, + 227, + "-1/4" + ], + [ + "add", + 241, + 227, + "-1/4" + ], + [ + "add", + 240, + 227, + "-1/4" + ], + [ + "add", + 238, + 227, + "-1/4" + ], + [ + "add", + 237, + 227, + "-1/4" + ], + [ + "add", + 235, + 227, + "-1/2" + ], + [ + "add", + 234, + 227, + "1/4" + ], + [ + "add", + 233, + 227, + "-1/4" + ], + [ + "add", + 229, + 227, + "-1/4" + ], + [ + "scale", + 227, + "-1/4" + ], + [ + "add", + 430, + 225, + "-1/4" + ], + [ + "add", + 429, + 225, + "-1/4" + ], + [ + "add", + 427, + 225, + "-1/2" + ], + [ + "add", + 426, + 225, + "1/4" + ], + [ + "add", + 425, + 225, + "-1/4" + ], + [ + "add", + 422, + 225, + "-1/4" + ], + [ + "add", + 421, + 225, + "-1/4" + ], + [ + "add", + 419, + 225, + "-1/2" + ], + [ + "add", + 418, + 225, + "1/4" + ], + [ + "add", + 417, + 225, + "-1/4" + ], + [ + "add", + 416, + 225, + "-1/4" + ], + [ + "add", + 414, + 225, + "-1/4" + ], + [ + "add", + 413, + 225, + "-1/4" + ], + [ + "add", + 411, + 225, + "-1/2" + ], + [ + "add", + 410, + 225, + "1/4" + ], + [ + "add", + 409, + 225, + "-1/4" + ], + [ + "add", + 406, + 225, + "-1/4" + ], + [ + "add", + 405, + 225, + "-1/4" + ], + [ + "add", + 403, + 225, + "-1/2" + ], + [ + "add", + 402, + 225, + "1/4" + ], + [ + "add", + 401, + 225, + "-1/4" + ], + [ + "add", + 400, + 225, + "-1/4" + ], + [ + "add", + 399, + 225, + "-1/4" + ], + [ + "add", + 398, + 225, + "1/4" + ], + [ + "add", + 388, + 225, + "1/4" + ], + [ + "add", + 384, + 225, + "1/4" + ], + [ + "add", + 383, + 225, + "-1/4" + ], + [ + "add", + 382, + 225, + "1/4" + ], + [ + "add", + 379, + 225, + "1/2" + ], + [ + "add", + 372, + 225, + "1/4" + ], + [ + "add", + 368, + 225, + "1/4" + ], + [ + "add", + 347, + 225, + "1" + ], + [ + "add", + 287, + 225, + "1/2" + ], + [ + "add", + 286, + 225, + "-1/4" + ], + [ + "add", + 283, + 225, + "1/2" + ], + [ + "add", + 280, + 225, + "1/4" + ], + [ + "add", + 276, + 225, + "-1/2" + ], + [ + "add", + 272, + 225, + "-1/4" + ], + [ + "add", + 271, + 225, + "-1/2" + ], + [ + "add", + 270, + 225, + "1/4" + ], + [ + "add", + 269, + 225, + "-1/4" + ], + [ + "add", + 266, + 225, + "-1/4" + ], + [ + "add", + 262, + 225, + "1/4" + ], + [ + "add", + 261, + 225, + "1/4" + ], + [ + "add", + 258, + 225, + "1/4" + ], + [ + "add", + 257, + 225, + "-1/4" + ], + [ + "add", + 256, + 225, + "1/4" + ], + [ + "add", + 255, + 225, + "-1/2" + ], + [ + "add", + 254, + 225, + "1/4" + ], + [ + "add", + 253, + 225, + "-1/4" + ], + [ + "add", + 250, + 225, + "-1/4" + ], + [ + "add", + 246, + 225, + "1/4" + ], + [ + "add", + 245, + 225, + "1/4" + ], + [ + "add", + 242, + 225, + "1/4" + ], + [ + "add", + 241, + 225, + "-1/4" + ], + [ + "add", + 240, + 225, + "1/4" + ], + [ + "add", + 239, + 225, + "-1/2" + ], + [ + "add", + 238, + 225, + "1/2" + ], + [ + "add", + 234, + 225, + "-1/2" + ], + [ + "add", + 233, + 225, + "-1/2" + ], + [ + "add", + 229, + 225, + "1/2" + ], + [ + "add", + 227, + 225, + "-1/2" + ], + [ + "add", + 224, + 225, + "1" + ], + [ + "scale", + 225, + "-1/2" + ], + [ + "add", + 399, + 224, + "1/4" + ], + [ + "add", + 398, + 224, + "-1/4" + ], + [ + "add", + 388, + 224, + "-1/4" + ], + [ + "add", + 384, + 224, + "-1/4" + ], + [ + "add", + 383, + 224, + "1/4" + ], + [ + "add", + 382, + 224, + "-1/4" + ], + [ + "add", + 379, + 224, + "-1/2" + ], + [ + "add", + 372, + 224, + "-1/4" + ], + [ + "add", + 368, + 224, + "-1/4" + ], + [ + "add", + 367, + 224, + "1/4" + ], + [ + "add", + 366, + 224, + "-1/4" + ], + [ + "add", + 356, + 224, + "-1/4" + ], + [ + "add", + 352, + 224, + "-1/4" + ], + [ + "add", + 351, + 224, + "1/4" + ], + [ + "add", + 350, + 224, + "-1/4" + ], + [ + "add", + 347, + 224, + "-1/2" + ], + [ + "add", + 340, + 224, + "-1/4" + ], + [ + "add", + 336, + 224, + "-1/4" + ], + [ + "add", + 276, + 224, + "1/4" + ], + [ + "add", + 271, + 224, + "1/2" + ], + [ + "add", + 270, + 224, + "-1/4" + ], + [ + "add", + 269, + 224, + "1/4" + ], + [ + "add", + 266, + 224, + "1/4" + ], + [ + "add", + 262, + 224, + "-1/4" + ], + [ + "add", + 261, + 224, + "-1/4" + ], + [ + "add", + 258, + 224, + "-1/4" + ], + [ + "add", + 257, + 224, + "1/4" + ], + [ + "add", + 256, + 224, + "-1/4" + ], + [ + "add", + 255, + 224, + "1/2" + ], + [ + "add", + 254, + 224, + "-1/4" + ], + [ + "add", + 253, + 224, + "1/4" + ], + [ + "add", + 250, + 224, + "1/4" + ], + [ + "add", + 246, + 224, + "-1/4" + ], + [ + "add", + 245, + 224, + "-1/4" + ], + [ + "add", + 242, + 224, + "-1/4" + ], + [ + "add", + 241, + 224, + "1/4" + ], + [ + "add", + 240, + 224, + "-1/4" + ], + [ + "add", + 239, + 224, + "1/2" + ], + [ + "add", + 238, + 224, + "-1/4" + ], + [ + "add", + 237, + 224, + "1/4" + ], + [ + "add", + 234, + 224, + "1/4" + ], + [ + "add", + 233, + 224, + "1/4" + ], + [ + "add", + 229, + 224, + "-1/4" + ], + [ + "add", + 227, + 224, + "1/4" + ], + [ + "add", + 225, + 224, + "1/2" + ], + [ + "scale", + 224, + "-1/2" + ] + ], + "output_basis_program": [ + [ + "scale", + 224, + "-2" + ], + [ + "add", + 225, + 224, + "-1/2" + ], + [ + "add", + 227, + 224, + "-1/4" + ], + [ + "add", + 229, + 224, + "1/4" + ], + [ + "add", + 233, + 224, + "-1/4" + ], + [ + "add", + 234, + 224, + "-1/4" + ], + [ + "add", + 237, + 224, + "-1/4" + ], + [ + "add", + 238, + 224, + "1/4" + ], + [ + "add", + 239, + 224, + "-1/2" + ], + [ + "add", + 240, + 224, + "1/4" + ], + [ + "add", + 241, + 224, + "-1/4" + ], + [ + "add", + 242, + 224, + "1/4" + ], + [ + "add", + 245, + 224, + "1/4" + ], + [ + "add", + 246, + 224, + "1/4" + ], + [ + "add", + 250, + 224, + "-1/4" + ], + [ + "add", + 253, + 224, + "-1/4" + ], + [ + "add", + 254, + 224, + "1/4" + ], + [ + "add", + 255, + 224, + "-1/2" + ], + [ + "add", + 256, + 224, + "1/4" + ], + [ + "add", + 257, + 224, + "-1/4" + ], + [ + "add", + 258, + 224, + "1/4" + ], + [ + "add", + 261, + 224, + "1/4" + ], + [ + "add", + 262, + 224, + "1/4" + ], + [ + "add", + 266, + 224, + "-1/4" + ], + [ + "add", + 269, + 224, + "-1/4" + ], + [ + "add", + 270, + 224, + "1/4" + ], + [ + "add", + 271, + 224, + "-1/2" + ], + [ + "add", + 276, + 224, + "-1/4" + ], + [ + "add", + 336, + 224, + "1/4" + ], + [ + "add", + 340, + 224, + "1/4" + ], + [ + "add", + 347, + 224, + "1/2" + ], + [ + "add", + 350, + 224, + "1/4" + ], + [ + "add", + 351, + 224, + "-1/4" + ], + [ + "add", + 352, + 224, + "1/4" + ], + [ + "add", + 356, + 224, + "1/4" + ], + [ + "add", + 366, + 224, + "1/4" + ], + [ + "add", + 367, + 224, + "-1/4" + ], + [ + "add", + 368, + 224, + "1/4" + ], + [ + "add", + 372, + 224, + "1/4" + ], + [ + "add", + 379, + 224, + "1/2" + ], + [ + "add", + 382, + 224, + "1/4" + ], + [ + "add", + 383, + 224, + "-1/4" + ], + [ + "add", + 384, + 224, + "1/4" + ], + [ + "add", + 388, + 224, + "1/4" + ], + [ + "add", + 398, + 224, + "1/4" + ], + [ + "add", + 399, + 224, + "-1/4" + ], + [ + "scale", + 225, + "-2" + ], + [ + "add", + 224, + 225, + "-1" + ], + [ + "add", + 227, + 225, + "1/2" + ], + [ + "add", + 229, + 225, + "-1/2" + ], + [ + "add", + 233, + 225, + "1/2" + ], + [ + "add", + 234, + 225, + "1/2" + ], + [ + "add", + 238, + 225, + "-1/2" + ], + [ + "add", + 239, + 225, + "1/2" + ], + [ + "add", + 240, + 225, + "-1/4" + ], + [ + "add", + 241, + 225, + "1/4" + ], + [ + "add", + 242, + 225, + "-1/4" + ], + [ + "add", + 245, + 225, + "-1/4" + ], + [ + "add", + 246, + 225, + "-1/4" + ], + [ + "add", + 250, + 225, + "1/4" + ], + [ + "add", + 253, + 225, + "1/4" + ], + [ + "add", + 254, + 225, + "-1/4" + ], + [ + "add", + 255, + 225, + "1/2" + ], + [ + "add", + 256, + 225, + "-1/4" + ], + [ + "add", + 257, + 225, + "1/4" + ], + [ + "add", + 258, + 225, + "-1/4" + ], + [ + "add", + 261, + 225, + "-1/4" + ], + [ + "add", + 262, + 225, + "-1/4" + ], + [ + "add", + 266, + 225, + "1/4" + ], + [ + "add", + 269, + 225, + "1/4" + ], + [ + "add", + 270, + 225, + "-1/4" + ], + [ + "add", + 271, + 225, + "1/2" + ], + [ + "add", + 272, + 225, + "1/4" + ], + [ + "add", + 276, + 225, + "1/2" + ], + [ + "add", + 280, + 225, + "-1/4" + ], + [ + "add", + 283, + 225, + "-1/2" + ], + [ + "add", + 286, + 225, + "1/4" + ], + [ + "add", + 287, + 225, + "-1/2" + ], + [ + "add", + 347, + 225, + "-1" + ], + [ + "add", + 368, + 225, + "-1/4" + ], + [ + "add", + 372, + 225, + "-1/4" + ], + [ + "add", + 379, + 225, + "-1/2" + ], + [ + "add", + 382, + 225, + "-1/4" + ], + [ + "add", + 383, + 225, + "1/4" + ], + [ + "add", + 384, + 225, + "-1/4" + ], + [ + "add", + 388, + 225, + "-1/4" + ], + [ + "add", + 398, + 225, + "-1/4" + ], + [ + "add", + 399, + 225, + "1/4" + ], + [ + "add", + 400, + 225, + "1/4" + ], + [ + "add", + 401, + 225, + "1/4" + ], + [ + "add", + 402, + 225, + "-1/4" + ], + [ + "add", + 403, + 225, + "1/2" + ], + [ + "add", + 405, + 225, + "1/4" + ], + [ + "add", + 406, + 225, + "1/4" + ], + [ + "add", + 409, + 225, + "1/4" + ], + [ + "add", + 410, + 225, + "-1/4" + ], + [ + "add", + 411, + 225, + "1/2" + ], + [ + "add", + 413, + 225, + "1/4" + ], + [ + "add", + 414, + 225, + "1/4" + ], + [ + "add", + 416, + 225, + "1/4" + ], + [ + "add", + 417, + 225, + "1/4" + ], + [ + "add", + 418, + 225, + "-1/4" + ], + [ + "add", + 419, + 225, + "1/2" + ], + [ + "add", + 421, + 225, + "1/4" + ], + [ + "add", + 422, + 225, + "1/4" + ], + [ + "add", + 425, + 225, + "1/4" + ], + [ + "add", + 426, + 225, + "-1/4" + ], + [ + "add", + 427, + 225, + "1/2" + ], + [ + "add", + 429, + 225, + "1/4" + ], + [ + "add", + 430, + 225, + "1/4" + ], + [ + "scale", + 227, + "-4" + ], + [ + "add", + 229, + 227, + "1/4" + ], + [ + "add", + 233, + 227, + "1/4" + ], + [ + "add", + 234, + 227, + "-1/4" + ], + [ + "add", + 235, + 227, + "1/2" + ], + [ + "add", + 237, + 227, + "1/4" + ], + [ + "add", + 238, + 227, + "1/4" + ], + [ + "add", + 240, + 227, + "1/4" + ], + [ + "add", + 241, + 227, + "1/4" + ], + [ + "add", + 242, + 227, + "1/4" + ], + [ + "add", + 243, + 227, + "1/2" + ], + [ + "add", + 245, + 227, + "1/4" + ], + [ + "add", + 246, + 227, + "1/4" + ], + [ + "add", + 250, + 227, + "-1/4" + ], + [ + "add", + 253, + 227, + "1/4" + ], + [ + "add", + 254, + 227, + "1/4" + ], + [ + "add", + 256, + 227, + "1/4" + ], + [ + "add", + 257, + 227, + "1/4" + ], + [ + "add", + 258, + 227, + "1/4" + ], + [ + "add", + 259, + 227, + "1/2" + ], + [ + "add", + 261, + 227, + "1/4" + ], + [ + "add", + 262, + 227, + "1/4" + ], + [ + "add", + 266, + 227, + "-1/4" + ], + [ + "add", + 269, + 227, + "1/4" + ], + [ + "add", + 270, + 227, + "1/4" + ], + [ + "add", + 272, + 227, + "1/4" + ], + [ + "add", + 276, + 227, + "-1/4" + ], + [ + "add", + 280, + 227, + "-1/4" + ], + [ + "add", + 283, + 227, + "1/2" + ], + [ + "add", + 286, + 227, + "1/4" + ], + [ + "add", + 287, + 227, + "-1/2" + ], + [ + "add", + 288, + 227, + "1/2" + ], + [ + "add", + 296, + 227, + "-1/2" + ], + [ + "add", + 302, + 227, + "1/2" + ], + [ + "add", + 303, + 227, + "-1" + ], + [ + "add", + 306, + 227, + "1/4" + ], + [ + "add", + 308, + 227, + "1/4" + ], + [ + "add", + 312, + 227, + "-1/4" + ], + [ + "add", + 315, + 227, + "1/2" + ], + [ + "add", + 318, + 227, + "1/4" + ], + [ + "add", + 319, + 227, + "-1/2" + ], + [ + "add", + 326, + 227, + "1" + ], + [ + "add", + 328, + 227, + "-2" + ], + [ + "add", + 332, + 227, + "1" + ], + [ + "add", + 335, + 227, + "-2" + ], + [ + "scale", + 229, + "-1" + ], + [ + "add", + 224, + 229, + "1" + ], + [ + "add", + 225, + 229, + "-1" + ], + [ + "add", + 227, + 229, + "1" + ], + [ + "add", + 234, + 229, + "-1/2" + ], + [ + "add", + 237, + 229, + "1/2" + ], + [ + "add", + 238, + 229, + "1" + ], + [ + "add", + 239, + 229, + "-1" + ], + [ + "add", + 240, + 229, + "1/2" + ], + [ + "add", + 242, + 229, + "1/2" + ], + [ + "add", + 243, + 229, + "1/2" + ], + [ + "add", + 245, + 229, + "1/2" + ], + [ + "add", + 246, + 229, + "1/2" + ], + [ + "add", + 250, + 229, + "-1/2" + ], + [ + "add", + 254, + 229, + "1/2" + ], + [ + "add", + 255, + 229, + "-1/2" + ], + [ + "add", + 256, + 229, + "1/2" + ], + [ + "add", + 258, + 229, + "1/2" + ], + [ + "add", + 259, + 229, + "1/2" + ], + [ + "add", + 261, + 229, + "1/2" + ], + [ + "add", + 262, + 229, + "1/2" + ], + [ + "add", + 266, + 229, + "-1/2" + ], + [ + "add", + 270, + 229, + "1/2" + ], + [ + "add", + 271, + 229, + "-1/2" + ], + [ + "add", + 276, + 229, + "-1/2" + ], + [ + "add", + 283, + 229, + "1" + ], + [ + "add", + 288, + 229, + "1/2" + ], + [ + "add", + 296, + 229, + "-1/2" + ], + [ + "add", + 302, + 229, + "1/2" + ], + [ + "add", + 303, + 229, + "-1" + ], + [ + "add", + 306, + 229, + "1/2" + ], + [ + "add", + 308, + 229, + "1/2" + ], + [ + "add", + 312, + 229, + "-1/2" + ], + [ + "add", + 318, + 229, + "1/2" + ], + [ + "add", + 319, + 229, + "-1" + ], + [ + "add", + 326, + 229, + "1" + ], + [ + "add", + 328, + 229, + "-2" + ], + [ + "add", + 332, + 229, + "1" + ], + [ + "add", + 335, + 229, + "-2" + ], + [ + "add", + 347, + 229, + "1" + ], + [ + "add", + 368, + 229, + "1/2" + ], + [ + "add", + 372, + 229, + "1/2" + ], + [ + "add", + 382, + 229, + "1/2" + ], + [ + "add", + 383, + 229, + "-1/2" + ], + [ + "add", + 384, + 229, + "1/2" + ], + [ + "add", + 388, + 229, + "1/2" + ], + [ + "add", + 398, + 229, + "1/2" + ], + [ + "add", + 399, + 229, + "-1/2" + ], + [ + "add", + 401, + 229, + "-1/2" + ], + [ + "add", + 402, + 229, + "1/2" + ], + [ + "add", + 403, + 229, + "-1/2" + ], + [ + "add", + 409, + 229, + "-1/2" + ], + [ + "add", + 411, + 229, + "-1/2" + ], + [ + "add", + 413, + 229, + "-1/2" + ], + [ + "add", + 415, + 229, + "-1/2" + ], + [ + "add", + 417, + 229, + "-1/2" + ], + [ + "add", + 418, + 229, + "1/2" + ], + [ + "add", + 419, + 229, + "-1/2" + ], + [ + "add", + 425, + 229, + "-1/2" + ], + [ + "add", + 427, + 229, + "-1/2" + ], + [ + "add", + 429, + 229, + "-1/2" + ], + [ + "add", + 431, + 229, + "-1/2" + ], + [ + "add", + 227, + 230, + "1" + ], + [ + "add", + 225, + 231, + "-2" + ], + [ + "add", + 225, + 232, + "1" + ], + [ + "add", + 229, + 232, + "1" + ], + [ + "add", + 225, + 234, + "-1" + ], + [ + "add", + 229, + 234, + "-1" + ], + [ + "add", + 225, + 235, + "-1" + ], + [ + "add", + 229, + 235, + "-1" + ], + [ + "add", + 225, + 236, + "-1" + ], + [ + "add", + 229, + 236, + "1" + ], + [ + "add", + 225, + 237, + "-1" + ], + [ + "add", + 229, + 237, + "-1" + ], + [ + "add", + 225, + 238, + "2" + ], + [ + "add", + 225, + 239, + "1" + ], + [ + "add", + 229, + 239, + "1" + ], + [ + "add", + 240, + 256, + "1" + ], + [ + "add", + 256, + 240, + "-1" + ], + [ + "add", + 240, + 256, + "1" + ], + [ + "scale", + 256, + "-1" + ], + [ + "scale", + 240, + "4" + ], + [ + "add", + 257, + 240, + "-1/4" + ], + [ + "add", + 258, + 240, + "1/4" + ], + [ + "add", + 261, + 240, + "-1/4" + ], + [ + "add", + 262, + 240, + "1/4" + ], + [ + "add", + 266, + 240, + "-1/4" + ], + [ + "add", + 269, + 240, + "-1/4" + ], + [ + "add", + 270, + 240, + "-1/4" + ], + [ + "add", + 271, + 240, + "1/2" + ], + [ + "add", + 288, + 240, + "1/4" + ], + [ + "add", + 296, + 240, + "-1/4" + ], + [ + "add", + 302, + 240, + "-1/4" + ], + [ + "add", + 303, + 240, + "1/2" + ], + [ + "add", + 306, + 240, + "1/4" + ], + [ + "add", + 308, + 240, + "-1/4" + ], + [ + "add", + 312, + 240, + "-1/4" + ], + [ + "add", + 318, + 240, + "-1/4" + ], + [ + "add", + 319, + 240, + "1/2" + ], + [ + "add", + 336, + 240, + "1/4" + ], + [ + "add", + 340, + 240, + "-1/4" + ], + [ + "add", + 350, + 240, + "-1/4" + ], + [ + "add", + 351, + 240, + "3/4" + ], + [ + "add", + 384, + 240, + "1/4" + ], + [ + "add", + 388, + 240, + "-1/4" + ], + [ + "add", + 398, + 240, + "-1/4" + ], + [ + "add", + 399, + 240, + "3/4" + ], + [ + "add", + 416, + 240, + "-1/4" + ], + [ + "add", + 417, + 240, + "-1/4" + ], + [ + "add", + 418, + 240, + "1/4" + ], + [ + "add", + 421, + 240, + "-1/4" + ], + [ + "add", + 422, + 240, + "1/4" + ], + [ + "add", + 425, + 240, + "-1/4" + ], + [ + "add", + 426, + 240, + "-1/4" + ], + [ + "add", + 427, + 240, + "1/2" + ], + [ + "add", + 429, + 240, + "-1/4" + ], + [ + "add", + 430, + 240, + "-1/4" + ], + [ + "add", + 431, + 240, + "1/2" + ], + [ + "add", + 433, + 240, + "-1/4" + ], + [ + "add", + 434, + 240, + "1/4" + ], + [ + "add", + 437, + 240, + "-1/4" + ], + [ + "add", + 438, + 240, + "1/4" + ], + [ + "add", + 441, + 240, + "-1/4" + ], + [ + "add", + 442, + 240, + "-1/4" + ], + [ + "add", + 443, + 240, + "1/2" + ], + [ + "add", + 445, + 240, + "-1/4" + ], + [ + "add", + 446, + 240, + "-1/4" + ], + [ + "add", + 447, + 240, + "1/2" + ], + [ + "scale", + 241, + "-4" + ], + [ + "add", + 242, + 241, + "-1/4" + ], + [ + "add", + 243, + 241, + "-1/2" + ], + [ + "add", + 245, + 241, + "1/4" + ], + [ + "add", + 246, + 241, + "1/4" + ], + [ + "add", + 250, + 241, + "-1/4" + ], + [ + "add", + 253, + 241, + "1/4" + ], + [ + "add", + 254, + 241, + "1/4" + ], + [ + "add", + 256, + 241, + "-1/4" + ], + [ + "add", + 272, + 241, + "-1/4" + ], + [ + "add", + 280, + 241, + "1/4" + ], + [ + "add", + 286, + 241, + "1/4" + ], + [ + "add", + 287, + 241, + "1/2" + ], + [ + "add", + 306, + 241, + "-1/4" + ], + [ + "add", + 308, + 241, + "1/4" + ], + [ + "add", + 312, + 241, + "1/4" + ], + [ + "add", + 318, + 241, + "1/4" + ], + [ + "add", + 319, + 241, + "1/2" + ], + [ + "add", + 336, + 241, + "-1/4" + ], + [ + "add", + 340, + 241, + "1/4" + ], + [ + "add", + 350, + 241, + "1/4" + ], + [ + "add", + 351, + 241, + "1/4" + ], + [ + "add", + 368, + 241, + "-1/4" + ], + [ + "add", + 372, + 241, + "1/4" + ], + [ + "add", + 382, + 241, + "1/4" + ], + [ + "add", + 383, + 241, + "1/4" + ], + [ + "add", + 400, + 241, + "-1/4" + ], + [ + "add", + 401, + 241, + "1/4" + ], + [ + "add", + 402, + 241, + "1/4" + ], + [ + "add", + 403, + 241, + "-1/2" + ], + [ + "add", + 405, + 241, + "1/4" + ], + [ + "add", + 406, + 241, + "1/4" + ], + [ + "add", + 409, + 241, + "-1/4" + ], + [ + "add", + 410, + 241, + "-1/4" + ], + [ + "add", + 413, + 241, + "1/4" + ], + [ + "add", + 414, + 241, + "1/4" + ], + [ + "add", + 433, + 241, + "-1/4" + ], + [ + "add", + 434, + 241, + "1/4" + ], + [ + "add", + 435, + 241, + "-1/2" + ], + [ + "add", + 437, + 241, + "-1/4" + ], + [ + "add", + 438, + 241, + "-1/4" + ], + [ + "add", + 441, + 241, + "-1/4" + ], + [ + "add", + 442, + 241, + "1/4" + ], + [ + "add", + 443, + 241, + "-1/2" + ], + [ + "add", + 445, + 241, + "-1/4" + ], + [ + "add", + 446, + 241, + "-1/4" + ], + [ + "scale", + 243, + "2" + ], + [ + "add", + 246, + 243, + "-1/2" + ], + [ + "add", + 250, + 243, + "1/2" + ], + [ + "add", + 255, + 243, + "-1/2" + ], + [ + "add", + 256, + 243, + "1/2" + ], + [ + "add", + 272, + 243, + "1/4" + ], + [ + "add", + 280, + 243, + "-1/4" + ], + [ + "add", + 286, + 243, + "-1/4" + ], + [ + "add", + 287, + 243, + "-1/2" + ], + [ + "add", + 288, + 243, + "1/4" + ], + [ + "add", + 296, + 243, + "-1/4" + ], + [ + "add", + 302, + 243, + "-1/4" + ], + [ + "add", + 303, + 243, + "-1/2" + ], + [ + "add", + 306, + 243, + "1/4" + ], + [ + "add", + 308, + 243, + "-1/4" + ], + [ + "add", + 312, + 243, + "-1/4" + ], + [ + "add", + 318, + 243, + "-1/4" + ], + [ + "add", + 319, + 243, + "-1/2" + ], + [ + "add", + 324, + 243, + "-1/2" + ], + [ + "add", + 326, + 243, + "1/2" + ], + [ + "add", + 328, + 243, + "-1" + ], + [ + "add", + 332, + 243, + "1/2" + ], + [ + "add", + 334, + 243, + "-1/2" + ], + [ + "add", + 335, + 243, + "-1" + ], + [ + "add", + 336, + 243, + "1/4" + ], + [ + "add", + 340, + 243, + "-1/4" + ], + [ + "add", + 350, + 243, + "-1/4" + ], + [ + "add", + 351, + 243, + "-1/4" + ], + [ + "add", + 352, + 243, + "1/4" + ], + [ + "add", + 356, + 243, + "-1/4" + ], + [ + "add", + 366, + 243, + "-1/4" + ], + [ + "add", + 367, + 243, + "-1/4" + ], + [ + "add", + 368, + 243, + "1/4" + ], + [ + "add", + 372, + 243, + "-1/4" + ], + [ + "add", + 382, + 243, + "-1/4" + ], + [ + "add", + 383, + 243, + "-1/4" + ], + [ + "add", + 384, + 243, + "1/4" + ], + [ + "add", + 388, + 243, + "-1/4" + ], + [ + "add", + 398, + 243, + "-1/4" + ], + [ + "add", + 399, + 243, + "-1/4" + ], + [ + "add", + 400, + 243, + "1/2" + ], + [ + "add", + 402, + 243, + "-1/2" + ], + [ + "add", + 403, + 243, + "1/2" + ], + [ + "add", + 406, + 243, + "-1/2" + ], + [ + "add", + 409, + 243, + "1/2" + ], + [ + "add", + 410, + 243, + "1/2" + ], + [ + "add", + 411, + 243, + "-1/2" + ], + [ + "add", + 415, + 243, + "-1/2" + ], + [ + "add", + 432, + 243, + "1/2" + ], + [ + "add", + 435, + 243, + "1/2" + ], + [ + "add", + 437, + 243, + "1/2" + ], + [ + "add", + 438, + 243, + "1/2" + ], + [ + "add", + 442, + 243, + "-1/2" + ], + [ + "add", + 443, + 243, + "1/2" + ], + [ + "add", + 446, + 243, + "1/2" + ], + [ + "add", + 447, + 243, + "-1/2" + ], + [ + "add", + 241, + 245, + "-2" + ], + [ + "add", + 243, + 245, + "1" + ], + [ + "add", + 246, + 245, + "-1" + ], + [ + "add", + 250, + 245, + "1" + ], + [ + "add", + 255, + 245, + "-1" + ], + [ + "add", + 256, + 245, + "1" + ], + [ + "add", + 272, + 245, + "1/2" + ], + [ + "add", + 280, + 245, + "-1/2" + ], + [ + "add", + 286, + 245, + "-1/2" + ], + [ + "add", + 287, + 245, + "-1" + ], + [ + "add", + 288, + 245, + "1/2" + ], + [ + "add", + 296, + 245, + "-1/2" + ], + [ + "add", + 302, + 245, + "-1/2" + ], + [ + "add", + 303, + 245, + "-1" + ], + [ + "add", + 306, + 245, + "1/2" + ], + [ + "add", + 308, + 245, + "-1/2" + ], + [ + "add", + 312, + 245, + "-1/2" + ], + [ + "add", + 318, + 245, + "-1/2" + ], + [ + "add", + 319, + 245, + "-1" + ], + [ + "add", + 324, + 245, + "-1" + ], + [ + "add", + 326, + 245, + "1" + ], + [ + "add", + 328, + 245, + "-2" + ], + [ + "add", + 332, + 245, + "1" + ], + [ + "add", + 334, + 245, + "-1" + ], + [ + "add", + 335, + 245, + "-2" + ], + [ + "add", + 336, + 245, + "1/2" + ], + [ + "add", + 340, + 245, + "-1/2" + ], + [ + "add", + 350, + 245, + "-1/2" + ], + [ + "add", + 351, + 245, + "-1/2" + ], + [ + "add", + 352, + 245, + "1/2" + ], + [ + "add", + 356, + 245, + "-1/2" + ], + [ + "add", + 366, + 245, + "-1/2" + ], + [ + "add", + 367, + 245, + "-1/2" + ], + [ + "add", + 368, + 245, + "1/2" + ], + [ + "add", + 372, + 245, + "-1/2" + ], + [ + "add", + 382, + 245, + "-1/2" + ], + [ + "add", + 383, + 245, + "-1/2" + ], + [ + "add", + 384, + 245, + "1/2" + ], + [ + "add", + 388, + 245, + "-1/2" + ], + [ + "add", + 398, + 245, + "-1/2" + ], + [ + "add", + 399, + 245, + "-1/2" + ], + [ + "add", + 400, + 245, + "1" + ], + [ + "add", + 402, + 245, + "-1" + ], + [ + "add", + 403, + 245, + "1" + ], + [ + "add", + 406, + 245, + "-1" + ], + [ + "add", + 409, + 245, + "1" + ], + [ + "add", + 410, + 245, + "1" + ], + [ + "add", + 411, + 245, + "-1" + ], + [ + "add", + 415, + 245, + "-1" + ], + [ + "add", + 432, + 245, + "1" + ], + [ + "add", + 435, + 245, + "1" + ], + [ + "add", + 437, + 245, + "1" + ], + [ + "add", + 438, + 245, + "1" + ], + [ + "add", + 442, + 245, + "-1" + ], + [ + "add", + 443, + 245, + "1" + ], + [ + "add", + 446, + 245, + "1" + ], + [ + "add", + 447, + 245, + "-1" + ], + [ + "add", + 241, + 247, + "2" + ], + [ + "add", + 243, + 247, + "-1" + ], + [ + "add", + 246, + 247, + "1" + ], + [ + "add", + 250, + 247, + "-1" + ], + [ + "add", + 255, + 247, + "1" + ], + [ + "add", + 256, + 247, + "-1" + ], + [ + "add", + 272, + 247, + "-1/2" + ], + [ + "add", + 280, + 247, + "1/2" + ], + [ + "add", + 286, + 247, + "1/2" + ], + [ + "add", + 287, + 247, + "1" + ], + [ + "add", + 288, + 247, + "-1/2" + ], + [ + "add", + 296, + 247, + "1/2" + ], + [ + "add", + 302, + 247, + "1/2" + ], + [ + "add", + 303, + 247, + "1" + ], + [ + "add", + 306, + 247, + "-1/2" + ], + [ + "add", + 308, + 247, + "1/2" + ], + [ + "add", + 312, + 247, + "1/2" + ], + [ + "add", + 318, + 247, + "1/2" + ], + [ + "add", + 319, + 247, + "1" + ], + [ + "add", + 324, + 247, + "1" + ], + [ + "add", + 326, + 247, + "-1" + ], + [ + "add", + 328, + 247, + "2" + ], + [ + "add", + 332, + 247, + "-1" + ], + [ + "add", + 334, + 247, + "1" + ], + [ + "add", + 335, + 247, + "2" + ], + [ + "add", + 336, + 247, + "-1/2" + ], + [ + "add", + 340, + 247, + "1/2" + ], + [ + "add", + 350, + 247, + "1/2" + ], + [ + "add", + 351, + 247, + "1/2" + ], + [ + "add", + 352, + 247, + "-1/2" + ], + [ + "add", + 356, + 247, + "1/2" + ], + [ + "add", + 366, + 247, + "1/2" + ], + [ + "add", + 367, + 247, + "1/2" + ], + [ + "add", + 368, + 247, + "-1/2" + ], + [ + "add", + 372, + 247, + "1/2" + ], + [ + "add", + 382, + 247, + "1/2" + ], + [ + "add", + 383, + 247, + "1/2" + ], + [ + "add", + 384, + 247, + "-1/2" + ], + [ + "add", + 388, + 247, + "1/2" + ], + [ + "add", + 398, + 247, + "1/2" + ], + [ + "add", + 399, + 247, + "1/2" + ], + [ + "add", + 400, + 247, + "-1" + ], + [ + "add", + 402, + 247, + "1" + ], + [ + "add", + 403, + 247, + "-1" + ], + [ + "add", + 406, + 247, + "1" + ], + [ + "add", + 409, + 247, + "-1" + ], + [ + "add", + 410, + 247, + "-1" + ], + [ + "add", + 411, + 247, + "1" + ], + [ + "add", + 415, + 247, + "1" + ], + [ + "add", + 432, + 247, + "-1" + ], + [ + "add", + 435, + 247, + "-1" + ], + [ + "add", + 437, + 247, + "-1" + ], + [ + "add", + 438, + 247, + "-1" + ], + [ + "add", + 442, + 247, + "1" + ], + [ + "add", + 443, + 247, + "-1" + ], + [ + "add", + 446, + 247, + "-1" + ], + [ + "add", + 447, + 247, + "1" + ], + [ + "add", + 241, + 252, + "2" + ], + [ + "add", + 243, + 252, + "-1" + ], + [ + "add", + 246, + 252, + "1" + ], + [ + "add", + 250, + 252, + "-1" + ], + [ + "add", + 255, + 252, + "1" + ], + [ + "add", + 256, + 252, + "-1" + ], + [ + "add", + 272, + 252, + "-1/2" + ], + [ + "add", + 280, + 252, + "1/2" + ], + [ + "add", + 286, + 252, + "1/2" + ], + [ + "add", + 287, + 252, + "1" + ], + [ + "add", + 288, + 252, + "-1/2" + ], + [ + "add", + 296, + 252, + "1/2" + ], + [ + "add", + 302, + 252, + "1/2" + ], + [ + "add", + 303, + 252, + "1" + ], + [ + "add", + 306, + 252, + "-1/2" + ], + [ + "add", + 308, + 252, + "1/2" + ], + [ + "add", + 312, + 252, + "1/2" + ], + [ + "add", + 318, + 252, + "1/2" + ], + [ + "add", + 319, + 252, + "1" + ], + [ + "add", + 324, + 252, + "1" + ], + [ + "add", + 326, + 252, + "-1" + ], + [ + "add", + 328, + 252, + "2" + ], + [ + "add", + 332, + 252, + "-1" + ], + [ + "add", + 334, + 252, + "1" + ], + [ + "add", + 335, + 252, + "2" + ], + [ + "add", + 336, + 252, + "-1/2" + ], + [ + "add", + 340, + 252, + "1/2" + ], + [ + "add", + 350, + 252, + "1/2" + ], + [ + "add", + 351, + 252, + "1/2" + ], + [ + "add", + 352, + 252, + "-1/2" + ], + [ + "add", + 356, + 252, + "1/2" + ], + [ + "add", + 366, + 252, + "1/2" + ], + [ + "add", + 367, + 252, + "1/2" + ], + [ + "add", + 368, + 252, + "-1/2" + ], + [ + "add", + 372, + 252, + "1/2" + ], + [ + "add", + 382, + 252, + "1/2" + ], + [ + "add", + 383, + 252, + "1/2" + ], + [ + "add", + 384, + 252, + "-1/2" + ], + [ + "add", + 388, + 252, + "1/2" + ], + [ + "add", + 398, + 252, + "1/2" + ], + [ + "add", + 399, + 252, + "1/2" + ], + [ + "add", + 400, + 252, + "-1" + ], + [ + "add", + 402, + 252, + "1" + ], + [ + "add", + 403, + 252, + "-1" + ], + [ + "add", + 406, + 252, + "1" + ], + [ + "add", + 409, + 252, + "-1" + ], + [ + "add", + 410, + 252, + "-1" + ], + [ + "add", + 411, + 252, + "1" + ], + [ + "add", + 415, + 252, + "1" + ], + [ + "add", + 432, + 252, + "-1" + ], + [ + "add", + 435, + 252, + "-1" + ], + [ + "add", + 437, + 252, + "-1" + ], + [ + "add", + 438, + 252, + "-1" + ], + [ + "add", + 442, + 252, + "1" + ], + [ + "add", + 443, + 252, + "-1" + ], + [ + "add", + 446, + 252, + "-1" + ], + [ + "add", + 447, + 252, + "1" + ], + [ + "add", + 243, + 253, + "1" + ], + [ + "add", + 246, + 253, + "-1" + ], + [ + "add", + 250, + 253, + "1" + ], + [ + "add", + 255, + 253, + "-1" + ], + [ + "add", + 256, + 253, + "1" + ], + [ + "add", + 272, + 253, + "1/2" + ], + [ + "add", + 280, + 253, + "-1/2" + ], + [ + "add", + 286, + 253, + "-1/2" + ], + [ + "add", + 287, + 253, + "-1" + ], + [ + "add", + 288, + 253, + "1/2" + ], + [ + "add", + 296, + 253, + "-1/2" + ], + [ + "add", + 302, + 253, + "-1/2" + ], + [ + "add", + 303, + 253, + "-1" + ], + [ + "add", + 306, + 253, + "1/2" + ], + [ + "add", + 308, + 253, + "-1/2" + ], + [ + "add", + 312, + 253, + "-1/2" + ], + [ + "add", + 318, + 253, + "-1/2" + ], + [ + "add", + 319, + 253, + "-1" + ], + [ + "add", + 324, + 253, + "-1" + ], + [ + "add", + 326, + 253, + "1" + ], + [ + "add", + 328, + 253, + "-2" + ], + [ + "add", + 332, + 253, + "1" + ], + [ + "add", + 334, + 253, + "-1" + ], + [ + "add", + 335, + 253, + "-2" + ], + [ + "add", + 336, + 253, + "1/2" + ], + [ + "add", + 340, + 253, + "-1/2" + ], + [ + "add", + 350, + 253, + "-1/2" + ], + [ + "add", + 351, + 253, + "-1/2" + ], + [ + "add", + 352, + 253, + "1/2" + ], + [ + "add", + 356, + 253, + "-1/2" + ], + [ + "add", + 366, + 253, + "-1/2" + ], + [ + "add", + 367, + 253, + "-1/2" + ], + [ + "add", + 368, + 253, + "1/2" + ], + [ + "add", + 372, + 253, + "-1/2" + ], + [ + "add", + 382, + 253, + "-1/2" + ], + [ + "add", + 383, + 253, + "-1/2" + ], + [ + "add", + 384, + 253, + "1/2" + ], + [ + "add", + 388, + 253, + "-1/2" + ], + [ + "add", + 398, + 253, + "-1/2" + ], + [ + "add", + 399, + 253, + "-1/2" + ], + [ + "add", + 400, + 253, + "1" + ], + [ + "add", + 402, + 253, + "-1" + ], + [ + "add", + 403, + 253, + "1" + ], + [ + "add", + 406, + 253, + "-1" + ], + [ + "add", + 409, + 253, + "1" + ], + [ + "add", + 410, + 253, + "1" + ], + [ + "add", + 411, + 253, + "-1" + ], + [ + "add", + 415, + 253, + "-1" + ], + [ + "add", + 432, + 253, + "1" + ], + [ + "add", + 435, + 253, + "1" + ], + [ + "add", + 437, + 253, + "1" + ], + [ + "add", + 438, + 253, + "1" + ], + [ + "add", + 442, + 253, + "-1" + ], + [ + "add", + 443, + 253, + "1" + ], + [ + "add", + 446, + 253, + "1" + ], + [ + "add", + 447, + 253, + "-1" + ], + [ + "add", + 241, + 254, + "-2" + ], + [ + "add", + 243, + 254, + "1" + ], + [ + "add", + 246, + 254, + "-1" + ], + [ + "add", + 250, + 254, + "1" + ], + [ + "add", + 255, + 254, + "-1" + ], + [ + "add", + 256, + 254, + "1" + ], + [ + "add", + 272, + 254, + "1/2" + ], + [ + "add", + 280, + 254, + "-1/2" + ], + [ + "add", + 286, + 254, + "-1/2" + ], + [ + "add", + 287, + 254, + "-1" + ], + [ + "add", + 288, + 254, + "1/2" + ], + [ + "add", + 296, + 254, + "-1/2" + ], + [ + "add", + 302, + 254, + "-1/2" + ], + [ + "add", + 303, + 254, + "-1" + ], + [ + "add", + 306, + 254, + "1/2" + ], + [ + "add", + 308, + 254, + "-1/2" + ], + [ + "add", + 312, + 254, + "-1/2" + ], + [ + "add", + 318, + 254, + "-1/2" + ], + [ + "add", + 319, + 254, + "-1" + ], + [ + "add", + 324, + 254, + "-1" + ], + [ + "add", + 326, + 254, + "1" + ], + [ + "add", + 328, + 254, + "-2" + ], + [ + "add", + 332, + 254, + "1" + ], + [ + "add", + 334, + 254, + "-1" + ], + [ + "add", + 335, + 254, + "-2" + ], + [ + "add", + 336, + 254, + "1/2" + ], + [ + "add", + 340, + 254, + "-1/2" + ], + [ + "add", + 350, + 254, + "-1/2" + ], + [ + "add", + 351, + 254, + "-1/2" + ], + [ + "add", + 352, + 254, + "1/2" + ], + [ + "add", + 356, + 254, + "-1/2" + ], + [ + "add", + 366, + 254, + "-1/2" + ], + [ + "add", + 367, + 254, + "-1/2" + ], + [ + "add", + 368, + 254, + "1/2" + ], + [ + "add", + 372, + 254, + "-1/2" + ], + [ + "add", + 382, + 254, + "-1/2" + ], + [ + "add", + 383, + 254, + "-1/2" + ], + [ + "add", + 384, + 254, + "1/2" + ], + [ + "add", + 388, + 254, + "-1/2" + ], + [ + "add", + 398, + 254, + "-1/2" + ], + [ + "add", + 399, + 254, + "-1/2" + ], + [ + "add", + 400, + 254, + "1" + ], + [ + "add", + 402, + 254, + "-1" + ], + [ + "add", + 403, + 254, + "1" + ], + [ + "add", + 406, + 254, + "-1" + ], + [ + "add", + 409, + 254, + "1" + ], + [ + "add", + 410, + 254, + "1" + ], + [ + "add", + 411, + 254, + "-1" + ], + [ + "add", + 415, + 254, + "-1" + ], + [ + "add", + 432, + 254, + "1" + ], + [ + "add", + 435, + 254, + "1" + ], + [ + "add", + 437, + 254, + "1" + ], + [ + "add", + 438, + 254, + "1" + ], + [ + "add", + 442, + 254, + "-1" + ], + [ + "add", + 443, + 254, + "1" + ], + [ + "add", + 446, + 254, + "1" + ], + [ + "add", + 447, + 254, + "-1" + ], + [ + "add", + 255, + 256, + "1" + ], + [ + "add", + 256, + 255, + "-1" + ], + [ + "add", + 255, + 256, + "1" + ], + [ + "scale", + 256, + "-1" + ], + [ + "add", + 243, + 255, + "-1" + ], + [ + "add", + 246, + 255, + "1" + ], + [ + "add", + 250, + 255, + "-1" + ], + [ + "add", + 272, + 255, + "-1/2" + ], + [ + "add", + 280, + 255, + "1/2" + ], + [ + "add", + 286, + 255, + "1/2" + ], + [ + "add", + 287, + 255, + "1" + ], + [ + "add", + 288, + 255, + "-1/2" + ], + [ + "add", + 296, + 255, + "1/2" + ], + [ + "add", + 302, + 255, + "1/2" + ], + [ + "add", + 303, + 255, + "1" + ], + [ + "add", + 306, + 255, + "-1/2" + ], + [ + "add", + 308, + 255, + "1/2" + ], + [ + "add", + 312, + 255, + "1/2" + ], + [ + "add", + 318, + 255, + "1/2" + ], + [ + "add", + 319, + 255, + "1" + ], + [ + "add", + 324, + 255, + "1" + ], + [ + "add", + 326, + 255, + "-1" + ], + [ + "add", + 328, + 255, + "2" + ], + [ + "add", + 332, + 255, + "-1" + ], + [ + "add", + 334, + 255, + "1" + ], + [ + "add", + 335, + 255, + "2" + ], + [ + "add", + 336, + 255, + "-1/2" + ], + [ + "add", + 340, + 255, + "1/2" + ], + [ + "add", + 350, + 255, + "1/2" + ], + [ + "add", + 351, + 255, + "1/2" + ], + [ + "add", + 352, + 255, + "-1/2" + ], + [ + "add", + 356, + 255, + "1/2" + ], + [ + "add", + 366, + 255, + "1/2" + ], + [ + "add", + 367, + 255, + "1/2" + ], + [ + "add", + 368, + 255, + "-1/2" + ], + [ + "add", + 372, + 255, + "1/2" + ], + [ + "add", + 382, + 255, + "1/2" + ], + [ + "add", + 383, + 255, + "1/2" + ], + [ + "add", + 384, + 255, + "-1/2" + ], + [ + "add", + 388, + 255, + "1/2" + ], + [ + "add", + 398, + 255, + "1/2" + ], + [ + "add", + 399, + 255, + "1/2" + ], + [ + "add", + 400, + 255, + "-1" + ], + [ + "add", + 402, + 255, + "1" + ], + [ + "add", + 403, + 255, + "-1" + ], + [ + "add", + 406, + 255, + "1" + ], + [ + "add", + 409, + 255, + "-1" + ], + [ + "add", + 410, + 255, + "-1" + ], + [ + "add", + 411, + 255, + "1" + ], + [ + "add", + 415, + 255, + "1" + ], + [ + "add", + 432, + 255, + "-1" + ], + [ + "add", + 435, + 255, + "-1" + ], + [ + "add", + 437, + 255, + "-1" + ], + [ + "add", + 438, + 255, + "-1" + ], + [ + "add", + 442, + 255, + "1" + ], + [ + "add", + 443, + 255, + "-1" + ], + [ + "add", + 446, + 255, + "-1" + ], + [ + "add", + 447, + 255, + "1" + ], + [ + "add", + 256, + 257, + "1" + ], + [ + "add", + 257, + 256, + "-1" + ], + [ + "add", + 256, + 257, + "1" + ], + [ + "scale", + 257, + "-1" + ], + [ + "scale", + 256, + "2" + ], + [ + "add", + 240, + 256, + "1" + ], + [ + "add", + 258, + 256, + "1/2" + ], + [ + "add", + 259, + 256, + "1/2" + ], + [ + "add", + 261, + 256, + "-1/2" + ], + [ + "add", + 269, + 256, + "-1/2" + ], + [ + "add", + 270, + 256, + "-1/2" + ], + [ + "add", + 271, + 256, + "1/2" + ], + [ + "add", + 272, + 256, + "-1/4" + ], + [ + "add", + 280, + 256, + "1/4" + ], + [ + "add", + 286, + 256, + "1/4" + ], + [ + "add", + 287, + 256, + "-1/2" + ], + [ + "add", + 288, + 256, + "1/4" + ], + [ + "add", + 296, + 256, + "-1/4" + ], + [ + "add", + 302, + 256, + "-1/4" + ], + [ + "add", + 303, + 256, + "1/2" + ], + [ + "add", + 306, + 256, + "1/4" + ], + [ + "add", + 308, + 256, + "-1/4" + ], + [ + "add", + 312, + 256, + "-1/4" + ], + [ + "add", + 318, + 256, + "-1/4" + ], + [ + "add", + 319, + 256, + "1/2" + ], + [ + "add", + 324, + 256, + "1/2" + ], + [ + "add", + 326, + 256, + "-1/2" + ], + [ + "add", + 328, + 256, + "1" + ], + [ + "add", + 332, + 256, + "-1/2" + ], + [ + "add", + 334, + 256, + "1/2" + ], + [ + "add", + 336, + 256, + "1/4" + ], + [ + "add", + 340, + 256, + "-1/4" + ], + [ + "add", + 350, + 256, + "-1/4" + ], + [ + "add", + 351, + 256, + "3/4" + ], + [ + "add", + 352, + 256, + "-1/4" + ], + [ + "add", + 356, + 256, + "1/4" + ], + [ + "add", + 366, + 256, + "1/4" + ], + [ + "add", + 367, + 256, + "-3/4" + ], + [ + "add", + 368, + 256, + "-1/4" + ], + [ + "add", + 372, + 256, + "1/4" + ], + [ + "add", + 382, + 256, + "1/4" + ], + [ + "add", + 383, + 256, + "-3/4" + ], + [ + "add", + 384, + 256, + "1/4" + ], + [ + "add", + 388, + 256, + "-1/4" + ], + [ + "add", + 398, + 256, + "-1/4" + ], + [ + "add", + 399, + 256, + "3/4" + ], + [ + "add", + 417, + 256, + "-1/2" + ], + [ + "add", + 419, + 256, + "1/2" + ], + [ + "add", + 421, + 256, + "-1/2" + ], + [ + "add", + 427, + 256, + "1/2" + ], + [ + "add", + 429, + 256, + "-1/2" + ], + [ + "add", + 430, + 256, + "-1/2" + ], + [ + "add", + 431, + 256, + "1/2" + ], + [ + "add", + 432, + 256, + "1/2" + ], + [ + "add", + 433, + 256, + "-1/2" + ], + [ + "add", + 435, + 256, + "1/2" + ], + [ + "add", + 437, + 256, + "-1/2" + ], + [ + "add", + 443, + 256, + "1/2" + ], + [ + "add", + 445, + 256, + "-1/2" + ], + [ + "add", + 446, + 256, + "-1/2" + ], + [ + "add", + 447, + 256, + "1/2" + ], + [ + "scale", + 257, + "-1" + ], + [ + "add", + 241, + 257, + "1" + ], + [ + "add", + 255, + 257, + "-1" + ], + [ + "add", + 256, + 259, + "-1" + ], + [ + "add", + 256, + 261, + "1" + ], + [ + "add", + 256, + 263, + "-1" + ], + [ + "add", + 256, + 268, + "-1" + ], + [ + "add", + 256, + 269, + "-1" + ], + [ + "add", + 256, + 270, + "1" + ], + [ + "add", + 256, + 271, + "1" + ], + [ + "add", + 240, + 288, + "-1" + ], + [ + "add", + 240, + 294, + "1" + ], + [ + "add", + 240, + 296, + "1" + ], + [ + "add", + 240, + 297, + "1" + ], + [ + "add", + 240, + 300, + "-1" + ], + [ + "add", + 240, + 303, + "-1" + ], + [ + "add", + 227, + 324, + "-1" + ], + [ + "add", + 229, + 324, + "1" + ], + [ + "add", + 257, + 324, + "-1" + ], + [ + "add", + 227, + 326, + "1" + ], + [ + "add", + 229, + 326, + "-1" + ], + [ + "add", + 257, + 326, + "1" + ], + [ + "add", + 227, + 328, + "1" + ], + [ + "add", + 229, + 328, + "-1" + ], + [ + "add", + 257, + 328, + "1" + ], + [ + "add", + 227, + 333, + "-1" + ], + [ + "add", + 229, + 333, + "1" + ], + [ + "add", + 257, + 333, + "-1" + ], + [ + "add", + 224, + 384, + "-1" + ], + [ + "add", + 225, + 384, + "-1" + ], + [ + "add", + 257, + 384, + "-1" + ], + [ + "add", + 224, + 388, + "-1" + ], + [ + "add", + 225, + 388, + "-1" + ], + [ + "add", + 257, + 388, + "-1" + ], + [ + "add", + 224, + 390, + "1" + ], + [ + "add", + 225, + 390, + "1" + ], + [ + "add", + 257, + 390, + "1" + ], + [ + "add", + 224, + 391, + "1" + ], + [ + "add", + 225, + 391, + "1" + ], + [ + "add", + 257, + 391, + "1" + ], + [ + "add", + 224, + 392, + "1" + ], + [ + "add", + 225, + 392, + "1" + ], + [ + "add", + 257, + 392, + "1" + ], + [ + "add", + 224, + 397, + "-1" + ], + [ + "add", + 225, + 397, + "-1" + ], + [ + "add", + 257, + 397, + "-1" + ] + ], + "mode_boundaries": [ + { + "mode": 0, + "owner": 224, + "cache_slot": 634, + "witness_row": 1, + "frame": 274, + "missing_line": 7, + "cache_scalar": "-2", + "input_K": { + "literal_word": [ + [ + "D", + [ + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 2, + 2, + 2, + 2, + 0, + 0, + 0, + 0, + 0 + ] + ], + [ + "P", + [ + 7, + 13, + 11, + 14, + 16, + 32, + 64, + 128, + 256 + ] + ], + [ + "X", + 0 + ], + [ + "phase", + 0 + ] + ], + "signed_tableau": [ + [ + 7, + 0, + 2 + ], + [ + 13, + 0, + 2 + ], + [ + 11, + 0, + 2 + ], + [ + 14, + 0, + 2 + ], + [ + 16, + 0, + 0 + ], + [ + 32, + 0, + 0 + ], + [ + 64, + 0, + 0 + ], + [ + 128, + 0, + 0 + ], + [ + 256, + 0, + 0 + ], + [ + 0, + 7, + 0 + ], + [ + 0, + 13, + 0 + ], + [ + 0, + 11, + 0 + ], + [ + 0, + 14, + 0 + ], + [ + 0, + 16, + 0 + ], + [ + 0, + 32, + 0 + ], + [ + 0, + 64, + 0 + ], + [ + 0, + 128, + 0 + ], + [ + 0, + 256, + 0 + ] + ], + "zero_column_anchor": { + "index": 0, + "gaussian_numerator": [ + 1, + 0 + ], + "denominator_power2": 0 + } + }, + "output_N": { + "literal_word": [ + [ + "D", + [ + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 0, + 2, + 2, + 2, + 0, + 0, + 0, + 0, + 0 + ] + ], + [ + "P", + [ + 7, + 12, + 10, + 14, + 16, + 32, + 64, + 128, + 256 + ] + ], + [ + "X", + 504 + ], + [ + "phase", + 2 + ] + ], + "signed_tableau": [ + [ + 1, + 0, + 0 + ], + [ + 13, + 0, + 2 + ], + [ + 11, + 0, + 2 + ], + [ + 14, + 0, + 2 + ], + [ + 16, + 0, + 0 + ], + [ + 32, + 0, + 0 + ], + [ + 64, + 0, + 0 + ], + [ + 128, + 0, + 0 + ], + [ + 256, + 0, + 0 + ], + [ + 0, + 7, + 0 + ], + [ + 0, + 10, + 2 + ], + [ + 0, + 12, + 2 + ], + [ + 0, + 14, + 2 + ], + [ + 0, + 16, + 2 + ], + [ + 0, + 32, + 2 + ], + [ + 0, + 64, + 2 + ], + [ + 0, + 128, + 2 + ], + [ + 0, + 256, + 2 + ] + ], + "zero_column_anchor": { + "index": 504, + "gaussian_numerator": [ + -1, + 0 + ], + "denominator_power2": 0 + } + } + }, + { + "mode": 1, + "owner": 225, + "cache_slot": 635, + "witness_row": 2, + "frame": 619, + "missing_line": 25, + "cache_scalar": "-2", + "input_K": { + "literal_word": [ + [ + "D", + [ + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 2, + 2, + 0, + 2, + 2, + 0, + 0, + 0, + 0 + ] + ], + [ + "P", + [ + 25, + 26, + 4, + 19, + 11, + 32, + 64, + 128, + 256 + ] + ], + [ + "X", + 0 + ], + [ + "phase", + 0 + ] + ], + "signed_tableau": [ + [ + 25, + 0, + 2 + ], + [ + 26, + 0, + 2 + ], + [ + 4, + 0, + 0 + ], + [ + 19, + 0, + 2 + ], + [ + 11, + 0, + 2 + ], + [ + 32, + 0, + 0 + ], + [ + 64, + 0, + 0 + ], + [ + 128, + 0, + 0 + ], + [ + 256, + 0, + 0 + ], + [ + 0, + 25, + 0 + ], + [ + 0, + 26, + 0 + ], + [ + 0, + 4, + 0 + ], + [ + 0, + 19, + 0 + ], + [ + 0, + 11, + 0 + ], + [ + 0, + 32, + 0 + ], + [ + 0, + 64, + 0 + ], + [ + 0, + 128, + 0 + ], + [ + 0, + 256, + 0 + ] + ], + "zero_column_anchor": { + "index": 0, + "gaussian_numerator": [ + 1, + 0 + ], + "denominator_power2": 0 + } + }, + "output_N": { + "literal_word": [ + [ + "D", + [ + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 0, + 2, + 0, + 2, + 2, + 0, + 0, + 0, + 0 + ] + ], + [ + "P", + [ + 25, + 26, + 4, + 18, + 10, + 32, + 64, + 128, + 256 + ] + ], + [ + "X", + 486 + ], + [ + "phase", + 2 + ] + ], + "signed_tableau": [ + [ + 1, + 0, + 0 + ], + [ + 26, + 0, + 2 + ], + [ + 4, + 0, + 0 + ], + [ + 19, + 0, + 2 + ], + [ + 11, + 0, + 2 + ], + [ + 32, + 0, + 0 + ], + [ + 64, + 0, + 0 + ], + [ + 128, + 0, + 0 + ], + [ + 256, + 0, + 0 + ], + [ + 0, + 25, + 0 + ], + [ + 0, + 26, + 2 + ], + [ + 0, + 4, + 2 + ], + [ + 0, + 10, + 2 + ], + [ + 0, + 18, + 2 + ], + [ + 0, + 32, + 2 + ], + [ + 0, + 64, + 2 + ], + [ + 0, + 128, + 2 + ], + [ + 0, + 256, + 2 + ] + ], + "zero_column_anchor": { + "index": 486, + "gaussian_numerator": [ + -1, + 0 + ], + "denominator_power2": 0 + } + } + }, + { + "mode": 2, + "owner": 227, + "cache_slot": 633, + "witness_row": 0, + "frame": 254, + "missing_line": 42, + "cache_scalar": "-2", + "input_K": { + "literal_word": [ + [ + "D", + [ + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 2, + 2, + 0, + 2, + 0, + 2, + 0, + 0, + 0 + ] + ], + [ + "P", + [ + 42, + 41, + 4, + 35, + 16, + 11, + 64, + 128, + 256 + ] + ], + [ + "X", + 0 + ], + [ + "phase", + 0 + ] + ], + "signed_tableau": [ + [ + 42, + 0, + 2 + ], + [ + 41, + 0, + 2 + ], + [ + 4, + 0, + 0 + ], + [ + 35, + 0, + 2 + ], + [ + 16, + 0, + 0 + ], + [ + 11, + 0, + 2 + ], + [ + 64, + 0, + 0 + ], + [ + 128, + 0, + 0 + ], + [ + 256, + 0, + 0 + ], + [ + 0, + 42, + 0 + ], + [ + 0, + 41, + 0 + ], + [ + 0, + 4, + 0 + ], + [ + 0, + 35, + 0 + ], + [ + 0, + 16, + 0 + ], + [ + 0, + 11, + 0 + ], + [ + 0, + 64, + 0 + ], + [ + 0, + 128, + 0 + ], + [ + 0, + 256, + 0 + ] + ], + "zero_column_anchor": { + "index": 0, + "gaussian_numerator": [ + 1, + 0 + ], + "denominator_power2": 0 + } + }, + "output_N": { + "literal_word": [ + [ + "D", + [ + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 2, + 0, + 0, + 2, + 0, + 2, + 0, + 0, + 0 + ] + ], + [ + "P", + [ + 42, + 41, + 4, + 33, + 16, + 9, + 64, + 128, + 256 + ] + ], + [ + "X", + 470 + ], + [ + "phase", + 2 + ] + ], + "signed_tableau": [ + [ + 42, + 0, + 2 + ], + [ + 1, + 0, + 0 + ], + [ + 4, + 0, + 0 + ], + [ + 35, + 0, + 2 + ], + [ + 16, + 0, + 0 + ], + [ + 11, + 0, + 2 + ], + [ + 64, + 0, + 0 + ], + [ + 128, + 0, + 0 + ], + [ + 256, + 0, + 0 + ], + [ + 0, + 42, + 2 + ], + [ + 0, + 41, + 0 + ], + [ + 0, + 4, + 2 + ], + [ + 0, + 10, + 2 + ], + [ + 0, + 16, + 2 + ], + [ + 0, + 34, + 2 + ], + [ + 0, + 64, + 2 + ], + [ + 0, + 128, + 2 + ], + [ + 0, + 256, + 2 + ] + ], + "zero_column_anchor": { + "index": 470, + "gaussian_numerator": [ + -1, + 0 + ], + "denominator_power2": 0 + } + } + }, + { + "mode": 3, + "owner": 229, + "cache_slot": 636, + "witness_row": 3, + "frame": 279, + "missing_line": 52, + "cache_scalar": "-2", + "input_K": { + "literal_word": [ + [ + "D", + [ + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 2, + 0, + 2, + 0, + 2, + 2, + 0, + 0, + 0 + ] + ], + [ + "P", + [ + 52, + 2, + 49, + 8, + 37, + 21, + 64, + 128, + 256 + ] + ], + [ + "X", + 0 + ], + [ + "phase", + 0 + ] + ], + "signed_tableau": [ + [ + 52, + 0, + 2 + ], + [ + 2, + 0, + 0 + ], + [ + 49, + 0, + 2 + ], + [ + 8, + 0, + 0 + ], + [ + 37, + 0, + 2 + ], + [ + 21, + 0, + 2 + ], + [ + 64, + 0, + 0 + ], + [ + 128, + 0, + 0 + ], + [ + 256, + 0, + 0 + ], + [ + 0, + 52, + 0 + ], + [ + 0, + 2, + 0 + ], + [ + 0, + 49, + 0 + ], + [ + 0, + 8, + 0 + ], + [ + 0, + 37, + 0 + ], + [ + 0, + 21, + 0 + ], + [ + 0, + 64, + 0 + ], + [ + 0, + 128, + 0 + ], + [ + 0, + 256, + 0 + ] + ], + "zero_column_anchor": { + "index": 0, + "gaussian_numerator": [ + 1, + 0 + ], + "denominator_power2": 0 + } + }, + "output_N": { + "literal_word": [ + [ + "D", + [ + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 2, + 0, + 0, + 0, + 2, + 2, + 0, + 0, + 0 + ] + ], + [ + "P", + [ + 52, + 2, + 49, + 8, + 33, + 17, + 64, + 128, + 256 + ] + ], + [ + "X", + 462 + ], + [ + "phase", + 2 + ] + ], + "signed_tableau": [ + [ + 52, + 0, + 2 + ], + [ + 2, + 0, + 0 + ], + [ + 1, + 0, + 0 + ], + [ + 8, + 0, + 0 + ], + [ + 37, + 0, + 2 + ], + [ + 21, + 0, + 2 + ], + [ + 64, + 0, + 0 + ], + [ + 128, + 0, + 0 + ], + [ + 256, + 0, + 0 + ], + [ + 0, + 52, + 2 + ], + [ + 0, + 2, + 2 + ], + [ + 0, + 49, + 0 + ], + [ + 0, + 8, + 2 + ], + [ + 0, + 20, + 2 + ], + [ + 0, + 36, + 2 + ], + [ + 0, + 64, + 2 + ], + [ + 0, + 128, + 2 + ], + [ + 0, + 256, + 2 + ] + ], + "zero_column_anchor": { + "index": 462, + "gaussian_numerator": [ + -1, + 0 + ], + "denominator_power2": 0 + } + } + }, + { + "mode": 4, + "owner": 240, + "cache_slot": 640, + "witness_row": 7, + "frame": 281, + "missing_line": 76, + "cache_scalar": "2", + "input_K": { + "literal_word": [ + [ + "D", + [ + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 2, + 0, + 2, + 2, + 0, + 0, + 2, + 0, + 0 + ] + ], + [ + "P", + [ + 76, + 2, + 73, + 69, + 16, + 32, + 13, + 128, + 256 + ] + ], + [ + "X", + 0 + ], + [ + "phase", + 0 + ] + ], + "signed_tableau": [ + [ + 76, + 0, + 2 + ], + [ + 2, + 0, + 0 + ], + [ + 73, + 0, + 2 + ], + [ + 69, + 0, + 2 + ], + [ + 16, + 0, + 0 + ], + [ + 32, + 0, + 0 + ], + [ + 13, + 0, + 2 + ], + [ + 128, + 0, + 0 + ], + [ + 256, + 0, + 0 + ], + [ + 0, + 76, + 0 + ], + [ + 0, + 2, + 0 + ], + [ + 0, + 73, + 0 + ], + [ + 0, + 69, + 0 + ], + [ + 0, + 16, + 0 + ], + [ + 0, + 32, + 0 + ], + [ + 0, + 13, + 0 + ], + [ + 0, + 128, + 0 + ], + [ + 0, + 256, + 0 + ] + ], + "zero_column_anchor": { + "index": 0, + "gaussian_numerator": [ + 1, + 0 + ], + "denominator_power2": 0 + } + }, + "output_N": { + "literal_word": [ + [ + "D", + [ + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 2, + 0, + 0, + 2, + 0, + 0, + 2, + 0, + 0 + ] + ], + [ + "P", + [ + 76, + 2, + 73, + 65, + 16, + 32, + 9, + 128, + 256 + ] + ], + [ + "X", + 438 + ], + [ + "phase", + 2 + ] + ], + "signed_tableau": [ + [ + 76, + 0, + 2 + ], + [ + 2, + 0, + 0 + ], + [ + 1, + 0, + 0 + ], + [ + 69, + 0, + 2 + ], + [ + 16, + 0, + 0 + ], + [ + 32, + 0, + 0 + ], + [ + 13, + 0, + 2 + ], + [ + 128, + 0, + 0 + ], + [ + 256, + 0, + 0 + ], + [ + 0, + 76, + 2 + ], + [ + 0, + 2, + 2 + ], + [ + 0, + 73, + 0 + ], + [ + 0, + 12, + 2 + ], + [ + 0, + 16, + 2 + ], + [ + 0, + 32, + 2 + ], + [ + 0, + 68, + 2 + ], + [ + 0, + 128, + 2 + ], + [ + 0, + 256, + 2 + ] + ], + "zero_column_anchor": { + "index": 438, + "gaussian_numerator": [ + -1, + 0 + ], + "denominator_power2": 0 + } + } + }, + { + "mode": 5, + "owner": 241, + "cache_slot": 637, + "witness_row": 4, + "frame": 621, + "missing_line": 82, + "cache_scalar": "2", + "input_K": { + "literal_word": [ + [ + "D", + [ + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 2, + 2, + 0, + 0, + 2, + 0, + 2, + 0, + 0 + ] + ], + [ + "P", + [ + 82, + 81, + 4, + 8, + 67, + 32, + 19, + 128, + 256 + ] + ], + [ + "X", + 0 + ], + [ + "phase", + 0 + ] + ], + "signed_tableau": [ + [ + 82, + 0, + 2 + ], + [ + 81, + 0, + 2 + ], + [ + 4, + 0, + 0 + ], + [ + 8, + 0, + 0 + ], + [ + 67, + 0, + 2 + ], + [ + 32, + 0, + 0 + ], + [ + 19, + 0, + 2 + ], + [ + 128, + 0, + 0 + ], + [ + 256, + 0, + 0 + ], + [ + 0, + 82, + 0 + ], + [ + 0, + 81, + 0 + ], + [ + 0, + 4, + 0 + ], + [ + 0, + 8, + 0 + ], + [ + 0, + 67, + 0 + ], + [ + 0, + 32, + 0 + ], + [ + 0, + 19, + 0 + ], + [ + 0, + 128, + 0 + ], + [ + 0, + 256, + 0 + ] + ], + "zero_column_anchor": { + "index": 0, + "gaussian_numerator": [ + 1, + 0 + ], + "denominator_power2": 0 + } + }, + "output_N": { + "literal_word": [ + [ + "D", + [ + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 2, + 0, + 0, + 0, + 2, + 0, + 2, + 0, + 0 + ] + ], + [ + "P", + [ + 82, + 81, + 4, + 8, + 65, + 32, + 17, + 128, + 256 + ] + ], + [ + "X", + 430 + ], + [ + "phase", + 2 + ] + ], + "signed_tableau": [ + [ + 82, + 0, + 2 + ], + [ + 1, + 0, + 0 + ], + [ + 4, + 0, + 0 + ], + [ + 8, + 0, + 0 + ], + [ + 67, + 0, + 2 + ], + [ + 32, + 0, + 0 + ], + [ + 19, + 0, + 2 + ], + [ + 128, + 0, + 0 + ], + [ + 256, + 0, + 0 + ], + [ + 0, + 82, + 2 + ], + [ + 0, + 81, + 0 + ], + [ + 0, + 4, + 2 + ], + [ + 0, + 8, + 2 + ], + [ + 0, + 18, + 2 + ], + [ + 0, + 32, + 2 + ], + [ + 0, + 66, + 2 + ], + [ + 0, + 128, + 2 + ], + [ + 0, + 256, + 2 + ] + ], + "zero_column_anchor": { + "index": 430, + "gaussian_numerator": [ + -1, + 0 + ], + "denominator_power2": 0 + } + } + }, + { + "mode": 6, + "owner": 256, + "cache_slot": 639, + "witness_row": 6, + "frame": 624, + "missing_line": 97, + "cache_scalar": "-2", + "input_K": { + "literal_word": [ + [ + "D", + [ + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 2, + 2, + 0, + 0, + 0, + 2, + 2, + 0, + 0 + ] + ], + [ + "P", + [ + 97, + 98, + 4, + 8, + 16, + 67, + 35, + 128, + 256 + ] + ], + [ + "X", + 0 + ], + [ + "phase", + 0 + ] + ], + "signed_tableau": [ + [ + 97, + 0, + 2 + ], + [ + 98, + 0, + 2 + ], + [ + 4, + 0, + 0 + ], + [ + 8, + 0, + 0 + ], + [ + 16, + 0, + 0 + ], + [ + 67, + 0, + 2 + ], + [ + 35, + 0, + 2 + ], + [ + 128, + 0, + 0 + ], + [ + 256, + 0, + 0 + ], + [ + 0, + 97, + 0 + ], + [ + 0, + 98, + 0 + ], + [ + 0, + 4, + 0 + ], + [ + 0, + 8, + 0 + ], + [ + 0, + 16, + 0 + ], + [ + 0, + 67, + 0 + ], + [ + 0, + 35, + 0 + ], + [ + 0, + 128, + 0 + ], + [ + 0, + 256, + 0 + ] + ], + "zero_column_anchor": { + "index": 0, + "gaussian_numerator": [ + 1, + 0 + ], + "denominator_power2": 0 + } + }, + "output_N": { + "literal_word": [ + [ + "D", + [ + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 0, + 2, + 0, + 0, + 0, + 2, + 2, + 0, + 0 + ] + ], + [ + "P", + [ + 97, + 98, + 4, + 8, + 16, + 66, + 34, + 128, + 256 + ] + ], + [ + "X", + 414 + ], + [ + "phase", + 2 + ] + ], + "signed_tableau": [ + [ + 1, + 0, + 0 + ], + [ + 98, + 0, + 2 + ], + [ + 4, + 0, + 0 + ], + [ + 8, + 0, + 0 + ], + [ + 16, + 0, + 0 + ], + [ + 67, + 0, + 2 + ], + [ + 35, + 0, + 2 + ], + [ + 128, + 0, + 0 + ], + [ + 256, + 0, + 0 + ], + [ + 0, + 97, + 0 + ], + [ + 0, + 98, + 2 + ], + [ + 0, + 4, + 2 + ], + [ + 0, + 8, + 2 + ], + [ + 0, + 16, + 2 + ], + [ + 0, + 34, + 2 + ], + [ + 0, + 66, + 2 + ], + [ + 0, + 128, + 2 + ], + [ + 0, + 256, + 2 + ] + ], + "zero_column_anchor": { + "index": 414, + "gaussian_numerator": [ + -1, + 0 + ], + "denominator_power2": 0 + } + } + }, + { + "mode": 7, + "owner": 257, + "cache_slot": 638, + "witness_row": 5, + "frame": 280, + "missing_line": 127, + "cache_scalar": "2", + "input_K": { + "literal_word": [ + [ + "D", + [ + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 2, + 2, + 2, + 2, + 2, + 2, + 2, + 2, + 0 + ] + ], + [ + "P", + [ + 127, + 253, + 251, + 247, + 239, + 223, + 191, + 254, + 256 + ] + ], + [ + "X", + 0 + ], + [ + "phase", + 0 + ] + ], + "signed_tableau": [ + [ + 127, + 0, + 2 + ], + [ + 253, + 0, + 2 + ], + [ + 251, + 0, + 2 + ], + [ + 247, + 0, + 2 + ], + [ + 239, + 0, + 2 + ], + [ + 223, + 0, + 2 + ], + [ + 191, + 0, + 2 + ], + [ + 254, + 0, + 2 + ], + [ + 256, + 0, + 0 + ], + [ + 0, + 127, + 0 + ], + [ + 0, + 253, + 0 + ], + [ + 0, + 251, + 0 + ], + [ + 0, + 247, + 0 + ], + [ + 0, + 239, + 0 + ], + [ + 0, + 223, + 0 + ], + [ + 0, + 191, + 0 + ], + [ + 0, + 254, + 0 + ], + [ + 0, + 256, + 0 + ] + ], + "zero_column_anchor": { + "index": 0, + "gaussian_numerator": [ + 1, + 0 + ], + "denominator_power2": 0 + } + }, + "output_N": { + "literal_word": [ + [ + "D", + [ + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0, + 0 + ], + [ + 0, + 2, + 2, + 2, + 2, + 2, + 2, + 2, + 0 + ] + ], + [ + "P", + [ + 127, + 252, + 250, + 246, + 238, + 222, + 190, + 254, + 256 + ] + ], + [ + "X", + 384 + ], + [ + "phase", + 2 + ] + ], + "signed_tableau": [ + [ + 1, + 0, + 0 + ], + [ + 253, + 0, + 2 + ], + [ + 251, + 0, + 2 + ], + [ + 247, + 0, + 2 + ], + [ + 239, + 0, + 2 + ], + [ + 223, + 0, + 2 + ], + [ + 191, + 0, + 2 + ], + [ + 254, + 0, + 2 + ], + [ + 256, + 0, + 0 + ], + [ + 0, + 127, + 0 + ], + [ + 0, + 130, + 2 + ], + [ + 0, + 132, + 2 + ], + [ + 0, + 136, + 2 + ], + [ + 0, + 144, + 2 + ], + [ + 0, + 160, + 2 + ], + [ + 0, + 192, + 2 + ], + [ + 0, + 254, + 2 + ], + [ + 0, + 256, + 2 + ] + ], + "zero_column_anchor": { + "index": 384, + "gaussian_numerator": [ + -1, + 0 + ], + "denominator_power2": 0 + } + } + } + ], + "ordered_schedule": [ + "Main input wrappers: NORMALIZERS.ports[j].compiled_wrappers.backward_input_X/Y.", + "On each mode owner apply input_K and scalar 2; run input_basis_program.", + "Run every instruction of WORD.json.gz; C0..C8 initially arbitrary.", + "Run output_basis_program on the 122 persistent common-chart helpers.", + "For each mode apply cache_scalar and output_N to its owned cache; SWAP the whole field and chart with its zero original owner; CLEAR the owned zero.", + "Main output wrappers: NORMALIZERS.ports[j].compiled_wrappers.backward_output_X/Y." + ], + "paid": { + "1": 2193, + "2": 412, + "3": 510, + "4": 127, + "5": 40 + }, + "autonomous_native_helpers": { + "4": 28, + "7": 7, + "8": 47, + "9": 318 + }, + "owned_fields": { + "count": 9, + "initial_values": "arbitrary", + "final_values": "zero", + "productive_credit": 0 + }, + "added_ordinary_work_vs_original_raw_source": { + "ADD": 1644, + "SCALE": 40, + "COPY": 16, + "CLEAR": 24, + "whole_field_SWAP": 8, + "monomial_field_maps": 464, + "monomial_breakdown": { + "fused_inherited_main_standardizers": 448, + "mode_inputs": 8, + "cache_outputs": 8 + } + }, + "local_error_amplification_power2_bound": 18996, + "source_original_scalar_counts": { + "add": 16273, + "clear": 16, + "scale": 1164 + }, + "source_changed_scalar_counts": { + "add": 16273, + "clear": 32, + "copy": 16, + "scale": 1164 + }, + "physical_phase_bindings": { + "main_diagonal_and_shear": 336, + "two_coupling_directions": 896, + "helper_diagonal": 8 + }, + "exact_zero_retags": [ + [ + 15608, + 92, + 254, + 1 + ], + [ + 15894, + 9, + 624, + 1 + ], + [ + 15900, + 11, + 621, + 1 + ], + [ + 17269, + 240, + 280, + 1 + ], + [ + 17280, + 81, + 619, + 1 + ], + [ + 17288, + 57, + 274, + 1 + ], + [ + 17604, + 288, + 281, + 1 + ], + [ + 17746, + 224, + 279, + 1 + ] + ], + "formula": { + "X": "D x - R y + R W h", + "Y": "D y", + "H": "D (h - Z y)", + "W": "diag(K_port^-1) M diag(K_mode)/2", + "Z": "diag(K_mode^-1) M^T diag(K_port)/2" + }, + "failure_controls": [ + "nonzero zero-retag rejected", + "one altered basis ADD coefficient rejected", + "same-tableau phase-only cache error rejected", + "one altered saved-cache coefficient rejected" + ], + "scope": "Changed coupled backward provider. No autonomous credit for eight coupled outputs; no completed caller, inverse/transpose implementation, new kappa or selected-result change." +} diff --git a/research/native-rank8-helper-provider/README.md b/research/native-rank8-helper-provider/README.md new file mode 100644 index 0000000000..92d0d7e523 --- /dev/null +++ b/research/native-rank8-helper-provider/README.md @@ -0,0 +1,83 @@ +# Eight coupled helper outputs from the retained-center native word + +This package constructs and replays an exact changed backward native provider +on all 632 original owners. It replaces eight rank-eight center calls by +retained earlier same-frame caches; eight later H1 inputs become identically +zero and their calls disappear. The resulting paid profile is +`{1:2193,2:412,3:510,4:127,5:40}`: the center-free profile minus eight H1 calls. + +After explicit ordinary basis and boundary operations, the coupled outputs are + +```text +X = D x - R y + R W h +Y = D y +H = D(h - Z y) +``` + +Here `R=DQ`, `D` is the native rank-eight Gaussian, `ZW=14I8`, and `WZ=I-C` +for the existing physical code `C`. The 400 other original helpers retain +their native jobs, with profile `{4:28,7:7,8:47,9:318}`. All nine owned fields +start arbitrary and finish zero. **The eight H outputs remain coupled; no +new autonomous Gaussian targets, complete caller or improved κ are claimed.** + +[PROOF.md](PROOF.md) gives the every-positive-width argument, ownership rule, +exact local bill and precision boundary. [WORD.json.gz](WORD.json.gz) is the +complete changed native word. [PROVIDER.json](PROVIDER.json) is its ordered +boundary recipe, including explicit dyadic basis programs and phase-bound +monomial words; its references to the pinned source main normalizers are part +of that recipe. The verifier recomputes the word and recipe from authenticated +main inputs, with no scratch paths or network access. + +The new schedule adds 1,644 ADD, 40 SCALE, 16 COPY, 24 CLEAR, eight physical +SWAPs and 464 monomial maps relative to the original raw source. The 464 maps +include 448 fused inherited main wrappers. Unchanged native internal traffic +and implementations remain inherited. These are ordinary work, not free +machine operations. Nine owned fields suffice without basis scratch storage. + +## Reproduce + +From the repository root, using only Python 3.12 and its standard library: + +```sh +python3.12 -B scripts/research_package.py --package research/native-rank8-helper-provider +python3.12 -I -Werror -B research/native-rank8-helper-provider/verify.py +python3.12 -I -Werror -O -B research/native-rank8-helper-provider/verify.py +``` + +The registered normal and optimized commands check all 641 native input +columns, every original endpoint, all nine owned outputs and 1,240 physical +phase bindings. Mutation controls reject a changed basis ADD coefficient, a +changed cache coefficient, nonzero zero-retag input and a same-tableau phase +error. A direct run takes about 13 seconds on the preparation machine; the +registered pair is bounded separately in [VERIFY.json](VERIFY.json). +`--emit` regenerates only the package-local `PROVIDER.json`; normal replay is +read-only. Frozen scientific source inputs are never regenerated or modified. + +[WITNESS.json](WITNESS.json) retains Ali Romman's PR5383 candidate verbatim, +from head `4bd6efa51a495a7c7b7754915cf0244e7e60969e`, SHA256 +`24599011da06325e1012619b2b84a4dd3aceb90ab42d3caaf6414879e7d16591`. +The candidate is package-local data; every used relation is reproved against +main's native source. No pending PR Git object is required. The phase engine, +existing code and native implementation retain their predecessor proof +boundaries; this is author-side exact replay, not formal or human acceptance. + +## Open next questions + +The complete structured obligations are in [TASK.json](TASK.json). A caller +must close the 224 main and eight coupled helper outputs while retaining the +400 autonomous helpers per call, price all additional children and ordinary +work, then prove its final Gaussian ranks, chronology, finite precision and +outer budget. Begin with one fully owned caller identity; a field becoming +available at rank eight is insufficient for autonomous target credit. The +selected frontier is unchanged. + +## Credit + +Ali Romman supplies PR5383's exact cached-center relations. Cao Yifan supplies +the native round-three helper/map word; Dugongue supplies the center-free code +and its factorization; Cinna Davis supplies the earlier retained-center, +helper-basis and controller work. Retain zxv's Clifford/native/compiler work, +Jacob Alan Sussman's recursion, Ryanson Jonathan's controller checks, and the +full source lineage. See [ATTRIBUTION.md](ATTRIBUTION.md). Prepared for Dillon +with substantial OpenAI Codex assistance from coordinated construction, +mechanism and review agents. Apache-2.0. diff --git a/research/native-rank8-helper-provider/SOURCES.json b/research/native-rank8-helper-provider/SOURCES.json new file mode 100644 index 0000000000..dd77397ca5 --- /dev/null +++ b/research/native-rank8-helper-provider/SOURCES.json @@ -0,0 +1,54 @@ +{ + "schema_version": 1, + "base_commit": "1ec1119972c9aefe42525172d07b332fcff81cb4", + "files": [ + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "b288ae44032fd84dd5564243422836cbcd29835e", + "sha256": "f9ed52bb642cd1e1486cf2743557ac5fa23cf1514a3277d786a644e39a565038" + }, + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "f126dd2e2dad2b669e75d1d0d0bd05c600725602", + "sha256": "f7a48bfa2659b88378282a8eee7d9fe52cdf505594124c4d1686b58510fffd72" + }, + { + "path": "research/coded-native-caller/NORMALIZERS.json", + "usage": "input", + "git_blob": "bca92c222c395d3d75c047fbb678f3cd0947c60f", + "sha256": "ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da" + }, + { + "path": "research/coded-native-caller/PHYSICAL.md", + "usage": "input", + "git_blob": "da8837ba67423ef08ef1afb8e8297a8032aafe9f", + "sha256": "4321b159ff8d3fe705419adaaa1beef75606e869e34341bda553f17d598a6078" + }, + { + "path": "research/coded-native-caller/clifford_exact.py", + "usage": "input", + "git_blob": "166841a037f069249f6f7f6dedb89248812f59e2", + "sha256": "2982ead07721e83358dc67c6f49c2b4c16a236a6bebdfd72f58221be1f5d0962" + }, + { + "path": "research/native-center-free-code/CODE.json", + "usage": "input", + "git_blob": "03170f4a31f7a8a3db7228f1cd5a6fdcb32720ae", + "sha256": "8be7f3f073b7981ec91c6af43edff0ac8a89f4824ef6026ae758c287dd6c03d0" + }, + { + "path": "research/native-center-free-code/CODED-PROOF.md", + "usage": "input", + "git_blob": "1f28d33884ec99b34f8366d022d8f7b9b7653ae2", + "sha256": "acd904af677718da8cdaf81d205d29866a6855efd393047e7128320a46753b01" + }, + { + "path": "research/native-center-free-code/SOURCE-WORD.json.gz", + "usage": "input", + "git_blob": "46d929df83817b85a5387bcdb9745e0627d6366e", + "sha256": "7679daa4ec6a40f56fc7f0202379a6f454310e94945aba4f48beaaaafb838d05" + } + ] +} diff --git a/research/native-rank8-helper-provider/TASK.json b/research/native-rank8-helper-provider/TASK.json new file mode 100644 index 0000000000..e82da0445c --- /dev/null +++ b/research/native-rank8-helper-provider/TASK.json @@ -0,0 +1,88 @@ +{ + "schema_version": 1, + "task_id": "centre-path-sharing", + "priority_revision": 7, + "base_commit": "1ec1119972c9aefe42525172d07b332fcff81cb4", + "original_card": { + "id": "centre-path-sharing", + "question": "Can the 64-per-call centre path (eight rank-8 COPY/ERASE totals through the private temporary) be shared across calls or shrunk?", + "starting_points": [ + "docs/research/research-family-status.md", + "research/complex-local-word-ceiling/README.md", + "research/split-centres-global/proofs/PR386-BIT-GEOMETRY.txt", + "certificates/selected-result.json" + ], + "methods": [ + "Derive a fully charged favorable relaxation for sharing one centre path across k calls, including restoration, hosting and precision.", + "Prove a lower bound on copied information per call for the selected decoder contract." + ], + "acceptance_gate": "Show the changed centre charge and copy profile per call with every added restoration or hosting cost charged, and its ceiling via ceiling.ceiling(centre=...). 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", + "research/complex-local-word-ceiling/verify.py" + ], + "expected": "PASS_COMPLEX_LOCAL_WORD_CEILING", + "inspect": "Read the selected word's per-call local profile, its packing ceiling and the lever table; run levers.py for the ideal budget of the lever you target.", + "scope": "Positive control and planning budget only; this is not a new construction or full cold replay." + }, + "first_experiment": "Write the per-call centre charge and copy children for sharing across k = 2 calls, charge the sharing overhead, and screen it; stop this route if even the ideal sharing gains under 10%. Ideal budgets: free 2.80x, shared by two 1.90x (levers.py).", + "bottleneck_link": "The centre path consumes 64 of about 99.6 unpaid coordinates per call, i.e. about 64% of the raw deficit.", + "allowed_variations": [ + "One sharing pattern across a fixed number of calls.", + "One reduced copied-total contract for the existing decoder.", + "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope." + ], + "scope_change_triggers": [ + "Removing copies without a replacement contract for the decoder's copied totals.", + "Continuing a partial cost improvement while leaving the same unpriced consumer, restoration or central-readout obligation unresolved; refresh the family expansion decision first. Local product-retiming evidence has a narrow scope and is not a ban on changed graphs or contracts." + ], + "overlap_terms": [ + "centre path", + "copied totals", + "private temporary", + "shared centre", + "batching" + ] + }, + "scope_status": "refined", + "actual_scope": "Emit a source-bound backward provider using retained center caches and an invertible cold-helper basis, with eight coupled rank-eight helper outputs, all 632 original owners retained and all 9 owned outputs zero.", + "scope_change_reason": "The user explicitly authorized ambitious changed-source research and removed the hour limit. This focused result replaces the copied-center path using source-proved early observations, while preserving every original direction; it does not claim an autonomous supplier or complete caller.", + "bottleneck_link": "Deletes all eight native H8 center calls and eight later H1 calls. The new bottleneck is closing eight main/helper couplings under a paid, fully owned caller rather than treating them as autonomous H8 targets.", + "budget_minutes": null, + "stop_rule": "Freeze this focused provider once original/changed all-owner replay, explicit ordinary basis programs, exact physical boundaries, owned cleanup, operation counts and every-positive-width proof pass. Further caller work is separate and must close all original outputs before admitting target credit.", + "outcome": "partial", + "evidence": "Registered Python3.12 normal and optimized replay derives B from main source, reproves the verbatim Ali candidate, checks 641 native input columns and 1240 exact physical phase bindings, executes both 122-owner basis programs, clears all 9 owned outputs and rejects coefficient/phase/zero-retag mutations.", + "author": "Dillon / dillona", + "ai_assistance": "Substantial OpenAI Codex assistance from coordinated construction, mechanism, packaging and independent author-side review agents; no independent human or kernel acceptance claimed.", + "open_questions": [ + { + "question": "Can a complete chronological caller close all 224 main and eight coupled helper outputs while retaining 400 autonomous native helper jobs per provider?", + "why_it_matters": "The eight D outputs depend on main inputs and earn no autonomous target credit. The paid savings alone do not imply a recursive multiplier or improved kappa.", + "first_step": "Emit one fully owned caller word using the exact W/Z physical maps; replay every original input and output, price all added Gaussian calls and keep all helper outputs.", + "blocked_by": "No accepted closure with final Gaussian ranks, complete query invoice and owner chronology is supplied by this provider package." + }, + { + "question": "What finite-precision and machine-work budget supports any successful complete caller?", + "why_it_matters": "The local finite schedule has bounded amplification and exact dyadic coefficients, but those facts do not supply recursive rounding, indexed movement or the outer multiplication recurrence.", + "first_step": "Use the emitted ordinary counts and local 2^18996 suffix amplification bound to assign coordinate precision and movement costs to the proposed complete caller.", + "blocked_by": "Depends on a complete caller and its recursion/packing contract; this package claims only the source-bound local primitive." + } + ], + "checkpoint": { + "canonical_main": "1ec1119972c9aefe42525172d07b332fcff81cb4", + "priority_revision": 7, + "selected_kappa": "0.0030217758", + "frozen_source_payload_sha256": "cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd", + "overlap": [ + "Ali Romman PR5383 retained-center candidate at 4bd6efa51a495a7c7b7754915cf0244e7e60969e", + "Cinna Davis PR4694 retained-center and PR4698 common-chart helper basis", + "Dugongue PR4929 center-free code and coded-native-caller physical normalizers", + "PR5397 scoped owned-exchange ceiling, PR5398 direct backward conjugation and independent PR5399/5400 reviews; these do not supply this unrestricted coupled-output contract." + ], + "campaign_thread": "https://github.com/CrocSwap/integer-mult-bounds/discussions/4930", + "frontier_changed": false, + "checked_at_utc": "2026-10-23T22:26:00Z" + } +} diff --git a/research/native-rank8-helper-provider/VERIFY.json b/research/native-rank8-helper-provider/VERIFY.json new file mode 100644 index 0000000000..6e831dff03 --- /dev/null +++ b/research/native-rank8-helper-provider/VERIFY.json @@ -0,0 +1,39 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [ + "research/coded-native-caller/NORMALIZERS.json", + "research/coded-native-caller/PHYSICAL.md", + "research/coded-native-caller/clifford_exact.py", + "research/native-center-free-code/CODE.json", + "research/native-center-free-code/CODED-PROOF.md", + "research/native-center-free-code/SOURCE-WORD.json.gz" + ], + "commands": [ + { + "argv": [ + "{python}", + "-I", + "-Werror", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 180, + "checks": "Fresh canonical original/center-free/changed native replay on 641 columns; candidate relation, literal dyadic basis, all 632 endpoint and 9 owned-zero checks; 1240 signed-tableau/absolute-phase bindings; exact recipe equality and altered basis/cache coefficient, phase-only and nonzero zero-retag rejection controls." + }, + { + "argv": [ + "{python}", + "-I", + "-Werror", + "-O", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 180, + "checks": "Fresh canonical original/center-free/changed native replay on 641 columns; candidate relation, literal dyadic basis, all 632 endpoint and 9 owned-zero checks; 1240 signed-tableau/absolute-phase bindings; exact recipe equality and altered basis/cache coefficient, phase-only and nonzero zero-retag rejection controls." + } + ] +} diff --git a/research/native-rank8-helper-provider/WITNESS.json b/research/native-rank8-helper-provider/WITNESS.json new file mode 100644 index 0000000000..19665f9eac --- /dev/null +++ b/research/native-rank8-helper-provider/WITNESS.json @@ -0,0 +1,434 @@ +[ + { + "relation": [ + [ + 230, + "1" + ], + [ + 324, + "-1" + ], + [ + 326, + "1" + ], + [ + 328, + "1" + ], + [ + 333, + "-1" + ] + ], + "event": 11332, + "frame": 254, + "cached_event": 11205, + "cached_role": 92, + "zero_event": 15584, + "zero_role": 92, + "copy_factor": "1", + "difference_factor": "1/4", + "zero_factor": "-1/4" + }, + { + "relation": [ + [ + 225, + "1" + ], + [ + 384, + "-1" + ], + [ + 388, + "-1" + ], + [ + 390, + "1" + ], + [ + 391, + "1" + ], + [ + 392, + "1" + ], + [ + 397, + "-1" + ] + ], + "event": 11358, + "frame": 274, + "cached_event": 11218, + "cached_role": 57, + "zero_event": 17264, + "zero_role": 57, + "copy_factor": "1", + "difference_factor": "1/4", + "zero_factor": "-1/4" + }, + { + "relation": [ + [ + 225, + "1" + ], + [ + 227, + "-1" + ], + [ + 229, + "1" + ], + [ + 231, + "-2" + ], + [ + 232, + "1" + ], + [ + 234, + "-1" + ], + [ + 235, + "-1" + ], + [ + 236, + "-1" + ], + [ + 237, + "-1" + ], + [ + 238, + "2" + ], + [ + 239, + "1" + ], + [ + 384, + "-1" + ], + [ + 388, + "-1" + ], + [ + 390, + "1" + ], + [ + 391, + "1" + ], + [ + 392, + "1" + ], + [ + 397, + "-1" + ] + ], + "event": 11384, + "frame": 619, + "cached_event": 11231, + "cached_role": 81, + "zero_event": 17256, + "zero_role": 81, + "copy_factor": "1", + "difference_factor": "1/4", + "zero_factor": "-1/4" + }, + { + "relation": [ + [ + 227, + "1" + ], + [ + 229, + "1" + ], + [ + 232, + "-1" + ], + [ + 234, + "1" + ], + [ + 235, + "1" + ], + [ + 236, + "-1" + ], + [ + 237, + "1" + ], + [ + 239, + "-1" + ], + [ + 324, + "-1" + ], + [ + 326, + "1" + ], + [ + 328, + "1" + ], + [ + 333, + "-1" + ] + ], + "event": 11410, + "frame": 279, + "cached_event": 11244, + "cached_role": 224, + "zero_event": 17722, + "zero_role": 224, + "copy_factor": "1", + "difference_factor": "-1/4", + "zero_factor": "1/4" + }, + { + "relation": [ + [ + 241, + "1" + ], + [ + 243, + "-1" + ], + [ + 245, + "1" + ], + [ + 247, + "-1" + ], + [ + 252, + "-1" + ], + [ + 253, + "-1" + ], + [ + 254, + "1" + ], + [ + 255, + "1" + ] + ], + "event": 11436, + "frame": 621, + "cached_event": 11257, + "cached_role": 11, + "zero_event": 15876, + "zero_role": 11, + "copy_factor": "1", + "difference_factor": "1/4", + "zero_factor": "-1/4" + }, + { + "relation": [ + [ + 225, + "1" + ], + [ + 241, + "-1" + ], + [ + 243, + "1" + ], + [ + 245, + "1" + ], + [ + 247, + "-1" + ], + [ + 252, + "-1" + ], + [ + 253, + "1" + ], + [ + 254, + "1" + ], + [ + 255, + "-1" + ], + [ + 324, + "-1" + ], + [ + 326, + "1" + ], + [ + 328, + "1" + ], + [ + 333, + "-1" + ], + [ + 384, + "-1" + ], + [ + 388, + "-1" + ], + [ + 390, + "1" + ], + [ + 391, + "1" + ], + [ + 392, + "1" + ], + [ + 397, + "-1" + ] + ], + "event": 11462, + "frame": 280, + "cached_event": 11270, + "cached_role": 240, + "zero_event": 17245, + "zero_role": 240, + "copy_factor": "1", + "difference_factor": "-1/4", + "zero_factor": "1/4" + }, + { + "relation": [ + [ + 257, + "1" + ], + [ + 259, + "-1" + ], + [ + 261, + "1" + ], + [ + 263, + "-1" + ], + [ + 268, + "-1" + ], + [ + 269, + "-1" + ], + [ + 270, + "1" + ], + [ + 271, + "1" + ] + ], + "event": 11488, + "frame": 624, + "cached_event": 11283, + "cached_role": 9, + "zero_event": 15870, + "zero_role": 9, + "copy_factor": "1", + "difference_factor": "1/4", + "zero_factor": "-1/4" + }, + { + "relation": [ + [ + 288, + "1" + ], + [ + 294, + "-1" + ], + [ + 296, + "-1" + ], + [ + 297, + "-1" + ], + [ + 300, + "1" + ], + [ + 303, + "1" + ] + ], + "event": 11514, + "frame": 281, + "cached_event": 11306, + "cached_role": 288, + "zero_event": 17580, + "zero_role": 288, + "copy_factor": "1", + "difference_factor": "1/4", + "zero_factor": "-1/4" + } +] diff --git a/research/native-rank8-helper-provider/WORD.json.gz b/research/native-rank8-helper-provider/WORD.json.gz new file mode 100644 index 0000000000..f3111b47e8 Binary files /dev/null and b/research/native-rank8-helper-provider/WORD.json.gz differ diff --git a/research/native-rank8-helper-provider/verify.py b/research/native-rank8-helper-provider/verify.py new file mode 100644 index 0000000000..b62af49c87 --- /dev/null +++ b/research/native-rank8-helper-provider/verify.py @@ -0,0 +1,602 @@ +#!/usr/bin/env python3 +"""Source-bound coupled provider, exact rational rows and absolute phases. + +No scratch registry, pending Git object, network access or third-party package. +The authenticated predecessor Clifford evaluator is the only imported module. +""" +from collections import Counter +from fractions import Fraction as F +from functools import lru_cache +from hashlib import sha256 +from pathlib import Path +import argparse +import gzip +import importlib.util +import json +import sys +import time + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parent.parent +SOURCE_HASH = 'cfcd36b40326d7a5815e1db5313444379b3fb756b27d5201c561574c085cc0dd' +WITNESS_HASH = '24599011da06325e1012619b2b84a4dd3aceb90ab42d3caaf6414879e7d16591' +MODE = [224, 225, 227, 229, 240, 241, 256, 257] +PAID = Counter({1: 2193, 2: 412, 3: 510, 4: 127, 5: 40}) + + +def need(condition, message): + if not condition: + raise ValueError(message) + + +def enc(row): + return [[j, str(a)] for j, a in sorted(row.items()) if a] + + +def add(target, source, factor=1): + for key, value in tuple(source.items()): + value = target.get(key, F(0)) + factor * value + if value: + target[key] = value + else: + target.pop(key, None) + + +def addr(ref): + need(ref[0] in ('L', 'C'), 'unknown field kind') + return ref[1] + (632 if ref[0] == 'C' else 0) + + +def replay(program, c, owners, snapshots=()): + """Every owner is an independent free-group column, including dirty C fields.""" + rows = [{(j, ()): F(1)} for j in range(owners)] + charts = c['start'][:] + [None] * (owners - 632) + paid, scalar = Counter(), Counter() + zeros, dirt_clears, saved = [], [], {} + for event, e in enumerate(program): + kind = e[0] + if kind == 'scalar': + op, chart = e[1:] + dst = addr(op[1]) + scalar[op[0]] += 1 + if op[0] == 'clear': + need(dst >= 632, 'persistent CLEAR forbidden') + dirt = {k: v for k, v in rows[dst].items() if k[0] >= 632} + if dirt: + dirt_clears.append((dst, dirt)) + rows[dst], charts[dst] = {}, chart + else: + need(charts[dst] == chart, 'destination chart') + if op[0] in ('copy', 'add'): + src = addr(op[2]) + need(charts[src] == chart, 'source chart') + if op[0] == 'copy': + need(dst >= 632 and not rows[dst], 'COPY must fill owned zero') + rows[dst] = dict(rows[src]) + else: + need(dst != src, 'ADD self alias') + add(rows[dst], rows[src], F(op[3], op[4])) + else: + need(op[0] == 'scale', 'unknown scalar operation') + factor = F(op[2], op[3]) + rows[dst] = {k: v * factor for k, v in rows[dst].items() if v * factor} + elif kind == 'warp': + _, ref, warp, old, new = e + dst = addr(ref) + need(charts[dst] == old, 'warp chart') + symbol = (1 if warp > 0 else -1) * (abs(warp) + 1000000) + after = {} + for (owner, word), value in rows[dst].items(): + word = word[1:] if word and word[0] == -symbol else (symbol,) + word + add(after, {(owner, word): value}) + rows[dst], charts[dst] = after, new + elif kind in ('climb', 'center'): + if kind == 'climb': + _, _, dst, old, new, rank = e + expected = len(c['frames'][new]) - len(c['frames'][old]) + else: + _, dst, old, new, rank = e + dst += 632 + expected = abs(len(c['frames'][new]) - len(c['frames'][old])) + need(charts[dst] == old and rank == expected and rank > 0, + 'paid child chart/rank') + charts[dst] = new + paid[rank] += 1 + elif kind == 'zero_retag': + _, dst, old, new = e + need(charts[dst] == old and not rows[dst], 'zero retag has nonzero input') + zeros.append([event, dst, old, new]) + charts[dst] = new + else: + # Inherited source annotations / physical boundary bindings. The + # predecessor's normalized-row convention treats these as no row + # update; they remain byte-for-byte records in the emitted word. + # New physical boundaries are checked separately below, with phase. + need(kind in ('phase', 'adapter', 'residual_adapter'), 'unknown source record') + for at, owner in snapshots: + if event == at: + saved[(at, owner)] = (charts[owner], dict(rows[owner])) + return rows, charts, paid, scalar, zeros, dirt_clears, saved + + +def scalar(row): + need(all(not word for _, word in row), 'endpoint has unreduced native word') + return {j: a for (j, _), a in row.items()} + + +def rewrite(source, witness): + centers = {r['event']: i for i, r in enumerate(witness)} + late = {r['zero_event']: i for i, r in enumerate(witness)} + caches = {r['cached_event']: i for i, r in enumerate(witness)} + need(len(centers) == len(late) == len(caches) == 8, 'distinct eight sites') + need(max(caches) < min(centers), 'caches must precede all replacements') + word = [] + for event, op in enumerate(source['programs']['backward']): + if event in centers: + i = centers[event] + frame = witness[i]['frame'] + need(op == ['center', 0, 0, frame, 8], 'center source binding') + word += [['scalar', ['clear', ['C', 0]], frame], + ['scalar', ['copy', ['C', 0], ['C', i + 1]], frame]] + elif event in late: + r = witness[late[event]] + need(op == ['climb', 'warp_retimed', r['zero_role'], r['frame'], 1, 1], + 'late H1 source binding') + word.append(['zero_retag', r['zero_role'], r['frame'], 1]) + else: + word.append(op) + if event in caches: + i = caches[event] + r = witness[i] + word += [['scalar', ['clear', ['C', i + 1]], r['frame']], + ['scalar', ['copy', ['C', i + 1], ['L', r['cached_role']]], r['frame']]] + return {'source_sha256': SOURCE_HASH, 'direction': 'backward', 'word': word} + + +def inverse(matrix): + n = len(matrix) + a, b, ops = [dict(r) for r in matrix], [{j: F(1)} for j in range(n)], [] + for j in range(n): + k = next((i for i in range(j, n) if a[i].get(j)), None) + need(k is not None, 'singular basis') + if k != j: + a[j], a[k], b[j], b[k] = a[k], a[j], b[k], b[j] + ops.append(['swap', j, k]) + factor = 1 / a[j][j] + if factor != 1: + a[j] = {k: factor * v for k, v in a[j].items()} + b[j] = {k: factor * v for k, v in b[j].items()} + ops.append(['scale', j, str(factor)]) + for i in range(n): + if i == j or not a[i].get(j): + continue + factor = -a[i][j] + add(a[i], a[j], factor) + add(b[i], b[j], factor) + ops.append(['add', i, j, str(factor)]) + need(a == [{j: F(1)} for j in range(n)], 'basis reduction') + return b, ops + + +def ordinary(ops, roles, reverse=False): + out = [] + for e in reversed(ops) if reverse else ops: + if e[0] == 'swap': + a, b = roles[e[1]], roles[e[2]] + out += [['add', a, b, '1'], ['add', b, a, '-1'], + ['add', a, b, '1'], ['scale', b, '-1']] + elif e[0] == 'scale': + v = F(e[2]) + out.append(['scale', roles[e[1]], str(1 / v if reverse else v)]) + else: + v = F(e[3]) + out.append(['add', roles[e[1]], roles[e[2]], str(-v if reverse else v)]) + return out + + +def apply_ordinary(program, rows): + rows = [dict(r) for r in rows] + for e in program: + if e[0] == 'add': + need(e[1] != e[2], 'ordinary ADD alias') + add(rows[e[1]], rows[e[2]], F(e[3])) + else: + need(e[0] == 'scale', 'ordinary operation') + rows[e[1]] = {j: a * F(e[2]) for j, a in rows[e[1]].items() if a * F(e[2])} + return rows + + +def authenticate(): + pins = json.loads((HERE / 'SOURCES.json').read_text()) + for r in pins['files']: + if r['usage'] == 'input': + need(sha256((ROOT / r['path']).read_bytes()).hexdigest() == r['sha256'], + 'changed scientific input: ' + r['path']) + raw = gzip.decompress((ROOT / 'research/native-center-free-code/SOURCE-WORD.json.gz').read_bytes()) + need(sha256(raw).hexdigest() == SOURCE_HASH, 'native payload') + need(sha256((HERE / 'WITNESS.json').read_bytes()).hexdigest() == WITNESS_HASH, + 'Ali verbatim candidate provenance') + cp = ROOT / 'research/coded-native-caller/clifford_exact.py' + spec = importlib.util.spec_from_file_location('rank8_provider_clifford', cp) + ce = importlib.util.module_from_spec(spec) + sys.modules[spec.name] = ce + spec.loader.exec_module(ce) + return json.loads(raw), json.loads((HERE / 'WITNESS.json').read_text()), ce + + +def main(emit=False): + started = time.monotonic() + source, witness, ce = authenticate() + c = source['canonical'] + normal = json.loads((ROOT / 'research/coded-native-caller/NORMALIZERS.json').read_text()) + M = normal['mode_columns'] + A = [[F(a) for a in r] for r in json.loads((ROOT / 'research/native-center-free-code/CODE.json').read_text())['A']] + need(c['start'][112:224] == [0] * 112, 'main Y inputs have ground chart') + need(len(M) == 8 and all(len(r) == 112 for r in M), 'M dimensions') + need(all(sum(M[k][i] * M[l][i] for i in range(112)) == 56 * int(k == l) + for k in range(8) for l in range(8)), 'M Gram') + need(all(A[i][j] == F(i == j) - sum(F(M[k][i] * M[k][j], 4) for k in range(8)) + for i in range(112) for j in range(112)), 'A factorization') + original = replay(source['programs']['backward'], c, 633, + [(r['cached_event'], r['cached_role']) for r in witness]) + oldrows, oldcharts, oldpaid, oldscalar = original[:4] + expected = [{(j, ()): F(1)} for j in range(632)] + for j in range(112): + expected[j][(j + 112, ())] = F(-1) + need(oldrows[:632] == expected and not oldrows[632], 'original 632-row endpoint') + need(oldcharts[:632] == c['final'], 'original exit charts') + + centerfree = [['scalar', ['clear', ['C', e[1]]], e[3]] if e[0] == 'center' else e + for e in source['programs']['backward']] + cf = replay(centerfree, c, 633) + cfrows = [scalar(r) for r in cf[0]] + need(cf[1][:632] == c['final'] and not cfrows[632], 'center-free charts/owned') + P = [[-cfrows[j + 224].get(i + 112, F(0)) for i in range(112)] for j in range(408)] + B = [[sum(P[j][i] * M[k][i] for i in range(112)) / 56 for j in range(408)] for k in range(8)] + need(all(P[j][i] == sum(B[k][j] * M[k][i] for k in range(8)) + for j in range(408) for i in range(112)), 'full native coupling factorization') + for j in range(632): + row = {j: F(1)} + if j < 112: + for i in range(112): + if A[i][j]: + row[i + 112] = -A[i][j] + elif j >= 224: + for i, a in enumerate(P[j - 224]): + if a: + row[i + 112] = -a + need(cfrows[j] == row, 'center-free complete scalar endpoint') + + delta = [{j - 224: F(a) for j, a in r['relation']} for r in witness] + coupling = [[sum(a * B[k][j] for j, a in d.items()) for k in range(8)] for d in delta] + need(all(sum(bool(a) for a in r) == 1 and set(r) <= {F(0), F(1), F(-1)} + for r in coupling), 'candidate is not a signed retraction') + perm = [next(k for k, a in enumerate(r) if a) for r in coupling] + sign = [coupling[i][perm[i]] for i in range(8)] + need(sorted(perm) == list(range(8)), 'retraction permutation') + E = [{} for _ in range(8)] + for i, k in enumerate(perm): + E[k] = {j: sign[i] * a for j, a in delta[i].items()} + row = {(j + 224, ()): F(witness[i]['zero_factor']) * a for j, a in delta[i].items()} + for j in range(112): + a = -F(witness[i]['zero_factor']) * sign[i] * M[k][j] + if a: + row[(j + 112, ())] = a + need(original[6][(witness[i]['cached_event'], witness[i]['cached_role'])] + == (witness[i]['frame'], row), 'fresh original cached row binding') + need(all(sum(a * B[l][j] for j, a in E[k].items()) == int(k == l) + for k in range(8) for l in range(8)), 'E B^T identity') + active = sorted(set(j for r in B for j, a in enumerate(r) if a) | set(j for r in E for j in r)) + roles, index = [224 + j for j in active], {j: i for i, j in enumerate(active)} + need(len(active) == 122 and all(c['start'][j] == 0 and c['final'][j] == 1 for j in roles), + 'basis requires 122 actual cold H9 owners') + J = [j - 224 for j in MODE] + L = [{} for _ in active] + for k, j in enumerate(J): + for r in active: + if B[k][r]: + L[index[r]][index[j]] = B[k][r] + for j in active: + if j in J: + continue + for r in active: + a = F(r == j) - sum(B[k][r] * E[k].get(j, F(0)) for k in range(8)) + if a: + L[index[r]][index[j]] = a + Li, ops = inverse(L) + for left, right in ((L, Li), (Li, L)): + for i, row in enumerate(left): + product = {} + for j, a in row.items(): + add(product, right[j], a) + need(product == {i: F(1)}, 'two-sided basis inverse') + for k, row in enumerate(E): + product = {} + for j, a in row.items(): + add(product, L[index[j]], a) + need(product == {index[J[k]]: F(1)}, 'E L mode selection') + need(all(sum(a * B[k][active[j]] for j, a in row.items()) == int(i == index[J[k]]) + for i, row in enumerate(Li) for k in range(8)), 'Li B mode embedding') + need(all(a.denominator & (a.denominator - 1) == 0 + for matrix in (L, Li) for row in matrix for a in row.values()), 'dyadic basis') + entrance, exitword = ordinary(ops, roles, True), ordinary(ops, roles) + identity = [{j: F(1)} for j in range(632)] + entered = apply_ordinary(entrance, identity) + def check_basis(rows): + for i, j in enumerate(roles): + need(rows[j] == {roles[k]: a for k, a in L[i].items()}, 'literal L program') + check_basis(entered) + need(apply_ordinary(exitword, entered) == identity, 'literal Li program') + need(Counter(e[0] for e in entrance) == Counter(add=822, scale=12), 'basis program bill') + need(Counter(e[0] for e in exitword) == Counter(add=822, scale=12), 'inverse program bill') + + changed = rewrite(source, witness) + frozen_word = json.loads(gzip.decompress((HERE / 'WORD.json.gz').read_bytes())) + need(changed == frozen_word, 'committed exact word differs from source rewrite') + result = replay(changed['word'], c, 641) + rawrows, charts, paid, scalars, zeros, dirt = result[:6] + need(charts[:632] == c['final'] and not rawrows[632], 'changed persistent charts/C0') + need(paid == PAID and oldpaid == paid + Counter({1: 8, 8: 8}), 'paid children') + need(scalars == oldscalar + Counter(clear=16, copy=16), 'source ordinary delta') + need(len(zeros) == 8, 'eight exact zero retags') + need(len(dirt) == 9 and {j for j, _ in dirt} == set(range(632, 641)) + and all(d == {(j, ()): F(1)} for j, d in dirt), 'all arbitrary owned dirt cleared') + need(not any(j >= 632 for row in rawrows for j, _ in row), 'owned dirt leaked') + need(sum(rawrows[j] != oldrows[j] for j in range(632)) == 218, 'changed endpoint count') + endpoint = [] + for row in rawrows: + out = {} + for j, a in scalar(row).items(): + add(out, entered[j], a) + endpoint.append(out) + endpoint = apply_ordinary(exitword, endpoint) + for j in range(632): + expected = {} if j in MODE else {j: F(1)} + if j < 112: + expected[j + 112] = F(-1) + for k in range(8): + if M[k][j]: + expected[MODE[k]] = F(M[k][j], 4) + need(endpoint[j] == expected, 'composed all-owner endpoint at ' + str(j)) + def check_cache(i, row): + r, k = witness[i], perm[i] + factor = F(r['zero_factor']) * sign[i] + expected = {MODE[k]: factor} + for j in range(112): + if M[k][j]: + expected[j + 112] = -factor * M[k][j] + need(row == expected and charts[633 + i] == r['frame'], 'composed retained cache') + for i in range(8): + check_cache(i, endpoint[633 + i]) + first_cache = dict(endpoint[633]) + + def conjugate(op): + circuit = [] + for e in op.circuit: + if e[0] == 'D': + circuit.append(('D', e[1], tuple((-x) % 4 for x in e[2]))) + elif e[0] == 'C': + circuit.append(('C', e[1], -e[2])) + elif e[0] == 'phase': + circuit.append(('phase', (-e[1]) % 4)) + else: + circuit.append(e) + return ce.Op(9, tuple((x, z, -p % 4) for x, z, p in op.tab), circuit) + + @lru_cache(None) + def frame(j, back=False): + op = ce.canonical_frame(9, c['frames'][j]) + return conjugate(op) if back else op + + def literal(word): + op = ce.ident(9) + for e in word: + if e[0] == 'P': + part = ce.perm(9, tuple(e[1])) + elif e[0] == 'D': + part = ce.diag(9, tuple(e[1]), tuple(e[2])) + elif e[0] == 'X': + part = ce.xgate(9, e[1]) + elif e[0] == 'phase': + part = ce.Op(9, ce.identity(9), [('phase', e[1])]) + else: + raise ValueError('boundary contains a Gaussian gate') + op = op.then(part) + return op + + def equal(a, b): + return a.tab == b.tab and a.zero_state() == b.zero_state() + + def rank(op): + return ce.rank([x for x, _, _ in op.tab[9:]]) + + def receipt(op): + vec, den = op.zero_state() + j = next(j for j, a in enumerate(vec) if a != (0, 0)) + return {'literal_word': op.circuit, 'signed_tableau': op.tab, + 'zero_column_anchor': {'index': j, 'gaussian_numerator': vec[j], + 'denominator_power2': den}} + + def compile_monomial(op): + need(rank(op) == 0, 'nonmonomial boundary map') + compiled, _ = ce.monomial(op) + need(equal(compiled, op) and equal(literal(compiled.circuit), op), + 'literal phase-correct monomial compilation') + return compiled + + R, D = frame(1), ce.fourier(9, range(1, 9)) + Km, N = [None] * 8, [None] * 8 + records = [None] * 8 + for i, r in enumerate(witness): + k = perm[i] + candidates = [q for q in range(1, 512) + if all(ce.parity(q & v) == 0 for v in c['frames'][r['frame']])] + need(len(candidates) == 1, 'rank-eight missing line') + q = candidates[0] + need(q.bit_count() % 2 == 1 and q != 511, 'odd noncharacteristic line') + if not q & 1: + transvections = [1 ^ q] + else: + j = next(j for j in range(1, 9) if not q >> j & 1) + transvections = [1 ^ (1 << j), (1 << j) ^ q] + cols = [] + for j in range(9): + x = 1 << j + for v in transvections: + x ^= v if ce.parity(x & v) else 0 + cols.append(x) + G = ce.transpose(cols, 9) + z = sum((((row.bit_count() - 1) // 2) & 1) << j for j, row in enumerate(G)) + K = ce.perm(9, G).then(ce.diag(9, (0,) * 9, tuple(2 * ((z >> j) & 1) for j in range(9)))) + need(equal(K.then(R), R.then(K)), 'mode K/R absolute phase') + need(all((ce.mv(ce.transpose(G, 9), x).bit_count() - x.bit_count() + - 2 * ce.parity(z & x)) % 4 == 0 for x in range(512)), 'K weight congruence') + F8 = frame(r['frame'], True) + need(rank(F8) == 8, 'actual cache rank') + Km[k] = compile_monomial(K) + N[k] = compile_monomial(K.then(F8).adjoint().then(D)) + records[k] = {'mode': k, 'owner': MODE[k], 'cache_slot': 633 + i, + 'witness_row': i, 'frame': r['frame'], 'missing_line': q, + 'cache_scalar': str(1 / (2 * F(r['zero_factor']) * sign[i])), + 'input_K': receipt(Km[k]), 'output_N': receipt(N[k])} + Kp = [literal(r['K_word']) for r in normal['ports']] + checks = Counter() + for j, port in enumerate(normal['ports']): + need(port['port'] == j and rank(Kp[j]) == 0 and equal(Kp[j].then(R), R.then(Kp[j])), + 'port K binding and R commutation') + wrappers = port['compiled_wrappers'] + BX, BY, OX, OY = [literal(wrappers[key]['word']) for key in + ('backward_input_X', 'backward_input_Y', 'backward_output_X', 'backward_output_Y')] + birth, final, finalY = frame(c['start'][j], True), frame(c['final'][j], True), frame(c['final'][112 + j], True) + need(equal(BX.then(birth.adjoint()).then(final).then(OX), D), 'X diagonal physical block') + need(equal(BY.then(finalY).then(OY), D), 'Y diagonal physical block') + need(equal(BY.then(final).then(OX), R), 'main shear physical block') + checks['main_diagonal_and_shear'] += 3 + for k in range(8): + if not M[k][j]: + continue + need(equal(Km[k].then(final).then(OX), Km[k].then(Kp[j].adjoint()).then(R)), + 'helper-to-main physical coupling') + F8 = frame(records[k]['frame'], True) + need(equal(BY.then(F8).then(N[k]), Kp[j].then(Km[k].adjoint()).then(D)), + 'main-to-helper physical coupling') + checks['two_coupling_directions'] += 2 + for k in range(8): + need(equal(Km[k].then(frame(records[k]['frame'], True)).then(N[k]), D), + 'helper diagonal physical block') + checks['helper_diagonal'] += 1 + need(dict(checks) == {'main_diagonal_and_shear': 336, 'two_coupling_directions': 896, + 'helper_diagonal': 8}, '1,240 physical bindings') + autonomous = Counter(len(c['frames'][c['final'][j]]) - len(c['frames'][c['start'][j]]) + for j in range(224, 632) if j not in MODE) + need(autonomous == Counter({4: 28, 7: 7, 8: 47, 9: 318}), '400 retained native helper jobs') + # Physical normalization precedes a complete-field SWAP, including chart tags. + for r in records: + owner, cache = r['owner'], r['cache_slot'] + need(not endpoint[owner], 'SWAP destination must be identically zero') + endpoint[owner], endpoint[cache] = endpoint[cache], endpoint[owner] + need(all(not endpoint[j] for j in range(632, 641)), 'all owned outputs clean') + + # Failure controls invoke the same predicates as the construction. + controls = [] + bad_c = dict(c) + bad_c['start'] = c['start'][:] + bad_c['start'][0] = 0 + try: + replay([['zero_retag', 0, 0, 1]], bad_c, 641) + except ValueError as e: + need(str(e) == 'zero retag has nonzero input', 'wrong rejection') + controls.append('nonzero zero-retag rejected') + need(len(controls) == 1, 'zero-retag control accepted') + corrupted = [e[:] for e in entrance] + mutated = next(e for e in corrupted if e[0] == 'add') + mutated[3] = str(F(mutated[3]) + 1) + try: + check_basis(apply_ordinary(corrupted, identity)) + except ValueError as e: + need(str(e) == 'literal L program', 'wrong basis rejection') + controls.append('one altered basis ADD coefficient rejected') + need(len(controls) == 2, 'basis coefficient mutation accepted') + badN = ce.Op(9, N[0].tab, N[0].circuit + [('phase', 1)]) + need(badN.tab == N[0].tab and not equal(Km[0].then(frame(records[0]['frame'], True)).then(badN), D), + 'phase-only error escaped') + controls.append('same-tableau phase-only cache error rejected') + wrong = dict(first_cache) + add(wrong, {MODE[perm[0]]: F(1)}) + try: + check_cache(0, wrong) + except ValueError as e: + need(str(e) == 'composed retained cache', 'wrong cache rejection') + controls.append('one altered saved-cache coefficient rejected') + need(len(controls) == 4, 'saved-cache coefficient mutation accepted') + + # An explicit, conservative local error-amplification bound for this finite + # schedule. Gaussian and monomial field maps have Euclidean norm one. + def log2_bound(a): + a, exponent = max(F(1), a), 0 + while a > 1: + a /= 2 + exponent += 1 + return exponent + amplification = 0 + for e in changed['word']: + if e[0] == 'scalar': + op = e[1] + if op[0] == 'add': + amplification += log2_bound(1 + abs(F(op[3], op[4]))) + elif op[0] == 'scale': + amplification += log2_bound(abs(F(op[2], op[3]))) + for e in entrance + exitword: + amplification += log2_bound(1 + abs(F(e[3]))) if e[0] == 'add' else log2_bound(abs(F(e[2]))) + amplification += 8 * log2_bound(F(2)) + amplification += sum(log2_bound(abs(F(r['cache_scalar']))) for r in records) + + artifact = { + 'schema_version': 1, 'source_payload_sha256': SOURCE_HASH, + 'candidate_witness_sha256': WITNESS_HASH, + 'word_payload_sha256': sha256(gzip.decompress((HERE / 'WORD.json.gz').read_bytes())).hexdigest(), + 'basis_roles': roles, 'mode_owners': MODE, + 'candidate_mode_permutation': perm, 'candidate_mode_signs': list(map(str, sign)), + 'canonical_retraction_E': [enc(row) for row in E], + 'input_basis_program': entrance, 'output_basis_program': exitword, + 'mode_boundaries': records, + 'ordered_schedule': [ + 'Main input wrappers: NORMALIZERS.ports[j].compiled_wrappers.backward_input_X/Y.', + 'On each mode owner apply input_K and scalar 2; run input_basis_program.', + 'Run every instruction of WORD.json.gz; C0..C8 initially arbitrary.', + 'Run output_basis_program on the 122 persistent common-chart helpers.', + 'For each mode apply cache_scalar and output_N to its owned cache; SWAP the whole field and chart with its zero original owner; CLEAR the owned zero.', + 'Main output wrappers: NORMALIZERS.ports[j].compiled_wrappers.backward_output_X/Y.' + ], + 'paid': dict(sorted(paid.items())), 'autonomous_native_helpers': dict(sorted(autonomous.items())), + 'owned_fields': {'count': 9, 'initial_values': 'arbitrary', 'final_values': 'zero', 'productive_credit': 0}, + 'added_ordinary_work_vs_original_raw_source': { + 'ADD': 1644, 'SCALE': 40, 'COPY': 16, 'CLEAR': 24, 'whole_field_SWAP': 8, + 'monomial_field_maps': 464, + 'monomial_breakdown': {'fused_inherited_main_standardizers': 448, 'mode_inputs': 8, 'cache_outputs': 8}}, + 'local_error_amplification_power2_bound': amplification, + 'source_original_scalar_counts': dict(sorted(oldscalar.items())), + 'source_changed_scalar_counts': dict(sorted(scalars.items())), + 'physical_phase_bindings': dict(checks), 'exact_zero_retags': zeros, + 'formula': {'X': 'D x - R y + R W h', 'Y': 'D y', 'H': 'D (h - Z y)', + 'W': 'diag(K_port^-1) M diag(K_mode)/2', + 'Z': 'diag(K_mode^-1) M^T diag(K_port)/2'}, + 'failure_controls': controls, + 'scope': 'Changed coupled backward provider. No autonomous credit for eight coupled outputs; no completed caller, inverse/transpose implementation, new kappa or selected-result change.' + } + artifact = json.loads(json.dumps(artifact)) + path = HERE / 'PROVIDER.json' + if emit: + path.write_text(json.dumps(artifact, indent=2) + '\n') + else: + need(json.loads(path.read_text()) == artifact, 'committed boundary recipe differs from replay') + print('PASS_NATIVE_RANK8_HELPER_PROVIDER ' + json.dumps({ + 'original_inputs': 632, 'arbitrary_owned_inputs': 9, 'owned_outputs_zero': 9, + 'autonomous_helpers': 400, 'coupled_helpers': 8, 'paid': dict(sorted(paid.items())), + 'phase_bindings': sum(checks.values()), 'seconds': round(time.monotonic() - started, 3)})) + + +if __name__ == '__main__': + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--emit', action='store_true', help='regenerate the package-local boundary recipe') + main(parser.parse_args().emit)