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"any_root_operator_floor": "2305843191433738230", + "relative_gap_to_any_root_lower_bound": "576460752303423563/2305843191433738230", + "one_root_lower_bound": "4611686200647418020", + "two_root_lower_bound": "3458764696040564085", + "guaranteed_one_root_saving": "1729382256910256227/4611686200647418020", + "guaranteed_two_root_saving": "576460752303402292/3458764696040564085" + } + ], + "scope": "n+1 arbitrary dirty parent rows; paid full-row star transfers. Query tariffs only; no physical hosting, roundoff or kappa claim." +} diff --git a/research/bidirectional-connector/CALLER-SCREEN.json b/research/bidirectional-connector/CALLER-SCREEN.json new file mode 100644 index 0000000000..203c9a8739 --- /dev/null +++ b/research/bidirectional-connector/CALLER-SCREEN.json @@ -0,0 +1,61 @@ +{ + "schema": "retained-centre-contract-screen-v1", + "selected_kappa": "836330098538459/500000000000000000", + "artifact_scope": "Retained canonical centre interface included in selected source manifest; not a replay or census of the currently dispatched provider programs.", + "source_pins": { + "certificates/selected-result.json": "10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32", + "research/community-frontier1094-audit/SELECTED-SOURCE.json": "79b3de5db3dbcb9829789ba58e9e45758926031e2a7d80667a08429d369be53b", + "research/gauge44-slots-t16/evidence/local/CANONICAL-WORD.json.gz": "92941c2b718b533f1d3addb710d261a6e2b9ec5d19f0051d79775b08cb2571ed", + "research/gauge44-slots-t16/evidence/local/LOCAL-PROGRAMS.json.gz": "172dc3d23e437909ddc01d07b12ede735afbb5bb6145f1ddf5c2e03097dfebe2" + }, + "centre_carriers": [ + 92, + 57, + 81, + 224, + 11, + 240, + 9, + 256 + ], + "distinct_rank_eight_charts": 8, + "target_rows": 112, + "cut_scalar_adds": 224, + "signed_patterns": 24, + "source_pair_edges": 12, + "pair_components": [ + [ + 9, + 11, + 240, + 256 + ], + [ + 57, + 81, + 92, + 224 + ] + ], + "literal_private_preparation": { + "backward": { + "private_centre_copies": 0, + "private_centre_clears": 16, + "centre_path_events": 8 + }, + "forward": { + "private_centre_copies": 8, + "private_centre_clears": 16, + "centre_path_events": 8 + } + }, + "dirty_query_source_floor": 16, + "dirty_query_output_floor": 224, + "contract_mismatch": [ + "The selected batch has 112 signed two-source rows, not the universal 255-mask positive batch.", + "The literal program copies into and clears owned private centres; it does not start with two arbitrary dirty query roots.", + "Eight distinct rank-eight source charts and their nested centre paths require a new complete query/port/hosting invoice." + ], + "conclusion": "No selected-supplier replacement or new kappa follows from the palette/walk query savings.", + "scope": "Fresh source-bound shape/contract extraction only; no full native endpoint, owner, physical invoice or selected cold replay." +} diff --git a/research/bidirectional-connector/CERTIFICATE.json b/research/bidirectional-connector/CERTIFICATE.json new file mode 100644 index 0000000000..e16355e29b --- /dev/null +++ b/research/bidirectional-connector/CERTIFICATE.json @@ -0,0 +1,244 @@ +{ + "schema": "bidirectional-connector-v1", + "skeleton": [ + ["B", 0, 1], + ["C", 0], + ["B", 1, 1], + ["C", 1], + ["B", 2, 0], + ["C", 0], + ["B", 0, 0], + ["B", 3, 0], + ["C", 1], + ["B", 1, 0], + ["C", 0], + ["B", 4, 1], + ["C", 1], + ["B", 3, 1], + ["B", 2, 1], + ["B", 4, 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"guaranteed_saved_fraction_vs_every_one_root_word": "15967/138748" + }, + { + "theorem": "all-word query tariff bounds", + "sources": 18, + "source_price": 759, + "readout_price": 1, + "transfer_price": 1, + "one_root_lower_bound": 1074636, + "two_root_lower_bound": 811863, + "palette_cost": 920253, + "guaranteed_saved_fraction_vs_every_one_root_word": "51461/358212" + }, + { + "theorem": "all-word query tariff bounds", + "sources": 30, + "source_price": 46399, + "readout_price": 1, + "transfer_price": 1, + "one_root_lower_bound": 4297706104, + "two_root_lower_bound": 3224004099, + "palette_cost": 3360623613, + "guaranteed_saved_fraction_vs_every_one_root_word": "937082491/4297706104" + }, + { + "theorem": "all-word query tariff bounds", + "sources": 60, + "source_price": 1518500369, + "readout_price": 1, + "transfer_price": 1, + "one_root_lower_bound": 4611686200647417900, + "two_root_lower_bound": 3458764696040563785, + "palette_cost": 3463538004420722685, + "guaranteed_saved_fraction_vs_every_one_root_word": "25514404360593227/102481915569942620" + }, + { + "theorem": "characteristic-zero signed palette", + "sources": 9, + "source_price": 49, + "one_root_lower_bound": 2620, + "signed_palette_cost": 2569, + "guaranteed_saved_fraction_vs_every_one_root_word": "51/2620" + }, + { + "theorem": "characteristic-zero signed palette", + "sources": 12, + "source_price": 113, + "one_root_lower_bound": 18540, + "signed_palette_cost": 17041, + "guaranteed_saved_fraction_vs_every_one_root_word": "1499/18540" + }, + { + "theorem": "characteristic-zero signed palette", + "sources": 15, + "source_price": 285, + "one_root_lower_bound": 138748, + "signed_palette_cost": 122785, + "guaranteed_saved_fraction_vs_every_one_root_word": "15963/138748" + }, + { + "theorem": "characteristic-zero signed palette", + "sources": 18, + "source_price": 759, + "one_root_lower_bound": 1074636, + "signed_palette_cost": 920257, + "guaranteed_saved_fraction_vs_every_one_root_word": "154379/1074636" + }, + { + "theorem": "characteristic-zero signed palette", + "sources": 30, + "source_price": 46399, + "one_root_lower_bound": 4297706104, + "signed_palette_cost": 3360623617, + "guaranteed_saved_fraction_vs_every_one_root_word": "937082487/4297706104" + }, + { + "theorem": "characteristic-zero signed palette", + "sources": 60, + "source_price": 1518500369, + "one_root_lower_bound": 4611686200647417900, + "signed_palette_cost": 3463538004420722689, + "guaranteed_saved_fraction_vs_every_one_root_word": "1148148196226695211/4611686200647417900" + }, + { + "theorem": "all-word source-locality bound and signed triangle", + "sources": 9, + "source_price": 49, + "one_root_locality_lower_bound": 2638, + "two_root_locality_lower_bound": 2018, + "signed_triangle_cost": 2569, + "guaranteed_saved_fraction": "69/2638" + }, + { + "theorem": "all-word source-locality bound and signed triangle", + "sources": 12, + "source_price": 113, + "one_root_locality_lower_bound": 18564, + "two_root_locality_lower_bound": 14235, + "signed_triangle_cost": 17041, + "guaranteed_saved_fraction": "1523/18564" + }, + { + "theorem": "all-word source-locality bound and signed triangle", + "sources": 15, + "source_price": 285, + "one_root_locality_lower_bound": 138778, + "two_root_locality_lower_bound": 105621, + "signed_triangle_cost": 122785, + "guaranteed_saved_fraction": "15993/138778" + }, + { + "theorem": "all-word source-locality bound and signed triangle", + "sources": 18, + "source_price": 759, + "one_root_locality_lower_bound": 1074672, + "two_root_locality_lower_bound": 811953, + "signed_triangle_cost": 920257, + "guaranteed_saved_fraction": "154415/1074672" + }, + { + "theorem": "all-word source-locality bound and signed triangle", + "sources": 30, + "source_price": 46399, + "one_root_locality_lower_bound": 4297747752, + "two_root_locality_lower_bound": 3224004249, + "signed_triangle_cost": 3360623617, + "guaranteed_saved_fraction": "937124135/4297747752" + }, + { + "theorem": "all-word source-locality bound and signed triangle", + "sources": 60, + "source_price": 1518500369, + "one_root_locality_lower_bound": 4611686200647418020, + "two_root_locality_lower_bound": 3458764696040564085, + "signed_triangle_cost": 3463538004420722689, + "guaranteed_saved_fraction": "1148148196226695331/4611686200647418020" + } + ] +} diff --git a/research/bidirectional-connector/FRAME-RECEIPT.json b/research/bidirectional-connector/FRAME-RECEIPT.json new file mode 100644 index 0000000000..91ba8b4f90 --- /dev/null +++ b/research/bidirectional-connector/FRAME-RECEIPT.json @@ -0,0 +1,32 @@ +{ + "schema": "signed-triangle-frames-v1", + "generators": [ + [ + 0, + -1 + ], + [ + 0, + 1 + ], + [ + 1, + -1 + ], + [ + 1, + 1 + ] + ], + "complete_BFS_radius": 8, + "BFS_states": 2284, + "independent_half_word_radius": 4, + "independent_half_states": 115, + "endpoint_frames": 12, + "frame_pairs": 144, + "geometry_cases": 384, + "minimum_boundary_transfers": 7, + "total_transfer_formula": "sum(2^block_size)+4", + "coefficient_alphabet": "integer unit shears only; no coordinate/height cutoff", + "scope": "Fixed zero-sum triangle; all phase orders/signs/entry signatures, single cube visit and exactly one signature switch per nonzero vertex. Not unrestricted source-walk or frame optimality." +} diff --git a/research/bidirectional-connector/LICENSE b/research/bidirectional-connector/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/research/bidirectional-connector/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. Definitions. + + "License" shall mean the terms and conditions for use, reproduction, + and distribution as defined by Sections 1 through 9 of this document. + + "Licensor" shall mean the copyright owner or entity authorized by + the copyright owner that is granting the License. + + "Legal Entity" shall mean the union of the acting entity and all + other entities that control, are controlled by, or are under common + control with that entity. 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We also recommend that a + file or class name and description of purpose be included on the + same "printed page" as the copyright notice for easier + identification within third-party archives. + + Copyright [yyyy] [name of copyright owner] + + Licensed under the Apache License, Version 2.0 (the "License"); + you may not use this file except in compliance with the License. + You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + + Unless required by applicable law or agreed to in writing, software + distributed under the License is distributed on an "AS IS" BASIS, + WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + See the License for the specific language governing permissions and + limitations under the License. diff --git a/research/bidirectional-connector/PALETTE6.json b/research/bidirectional-connector/PALETTE6.json new file mode 100644 index 0000000000..c21be1449e --- /dev/null +++ b/research/bidirectional-connector/PALETTE6.json @@ -0,0 +1 @@ +{"sources":6,"word":[["A",1,0],["A",2,0],["A",3,0],["B",0,0],["A",1,0],["A",17,0],["A",21,0],["A",25,0],["A",29,0],["A",33,0],["A",37,0],["A",41,0],["A",45,0],["A",49,0],["A",53,0],["A",57,0],["A",61,0],["C",0],["A",5,0],["A",9,0],["A",13,0],["B",1,0],["A",7,0],["A",11,0],["A",15,0],["C",0],["A",3,0],["A",19,0],["A",23,0],["A",27,0],["A",31,0],["A",35,0],["A",39,0],["A",43,0],["A",47,0],["A",51,0],["A",55,0],["A",59,0],["A",63,0],["B",0,0],["A",2,0],["A",18,0],["A",22,0],["A",26,0],["A",30,0],["A",34,0],["A",38,0],["A",42,0],["A",46,0],["A",50,0],["A",54,0],["A",58,0],["A",62,0],["C",0],["A",6,0],["A",10,0],["A",14,0],["B",1,0],["C",1],["A",4,0],["A",8,0],["A",12,0],["B",2,0],["A",4,0],["A",5,0],["A",6,0],["A",7,0],["A",21,0],["A",22,0],["A",23,0],["A",37,0],["A",38,0],["A",39,0],["A",53,0],["A",54,0],["A",55,0],["C",0],["A",20,0],["A",36,0],["A",52,0],["B",3,0],["A",28,0],["A",44,0],["A",60,0],["C",0],["A",12,0],["A",13,0],["A",14,0],["A",15,0],["A",29,0],["A",30,0],["A",31,0],["A",45,0],["A",46,0],["A",47,0],["A",61,0],["A",62,0],["A",63,0],["B",2,0],["A",8,0],["A",9,0],["A",10,0],["A",11,0],["A",25,0],["A",26,0],["A",27,0],["A",41,0],["A",42,0],["A",43,0],["A",57,0],["A",58,0],["A",59,0],["C",0],["A",24,0],["A",40,0],["A",56,0],["B",3,0],["C",1],["A",16,0],["A",32,0],["A",48,0],["B",4,0],["A",16,0],["A",20,0],["A",21,0],["A",22,0],["A",23,0],["A",24,0],["A",25,0],["A",26,0],["A",27,0],["A",28,0],["A",29,0],["A",30,0],["A",31,0],["C",0],["A",17,0],["A",18,0],["A",19,0],["B",5,0],["A",49,0],["A",50,0],["A",51,0],["C",0],["A",48,0],["A",52,0],["A",53,0],["A",54,0],["A",55,0],["A",56,0],["A",57,0],["A",58,0],["A",59,0],["A",60,0],["A",61,0],["A",62,0],["A",63,0],["B",4,0],["A",32,0],["A",36,0],["A",37,0],["A",38,0],["A",39,0],["A",40,0],["A",41,0],["A",42,0],["A",43,0],["A",44,0],["A",45,0],["A",46,0],["A",47,0],["C",0],["A",33,0],["A",34,0],["A",35,0],["B",5,0],["C",1]]} diff --git a/research/bidirectional-connector/README.md b/research/bidirectional-connector/README.md new file mode 100644 index 0000000000..b2beaf30ea --- /dev/null +++ b/research/bidirectional-connector/README.md @@ -0,0 +1,545 @@ +# Dirty-connector lower bounds and a signed zero-sum triangle + +The primary results are **all-word one/two-root query lower bounds**, including +source-locality corrections and matching **4M/3M asymptotics**, and a **signed +triangle** with the F2 palette's source/read counts plus four transfers. +All children in the scalable constructions use physical root z0. +These are scoped exact query-model results, not a new multiplication exponent. + +Secondary results are a 73-call F2 extension of Math PR1's five-source tariff +comparison, a minimum-read F2 compiler, a minimum-source n9 lower bound, and +signed fixed-port parent caches. The six-transfer witness/census and all-n +F2 two-call obstruction already occur in [Math PR1](https://github.com/conorholds/math/pull/1) +and [Math PR2](https://github.com/conorholds/math/pull/2); retained versions here +are supporting fixtures and independent cross-checks, not additional novelty. +Their predecessor packages remain the canonical Math accounts. Upstream +[PR2065](https://github.com/CrocSwap/integer-mult-bounds/pull/2065) independently +establishes the six-transfer endpoint; it is credited as a baseline here. +[PR2182](https://github.com/CrocSwap/integer-mult-bounds/pull/2182) contains the +separate fixed-port/two-root-boundary submission from the same contributor. +Neither endpoint nor the n>=6 two-call obstruction is a new claim of this package. + +## Interface and paid scope + +Let M=2^n-1. Source rows x_j, target rows y_m and roots z_p are distinct, +aligned length-L arrays, arbitrary dirty on entry. For every nonzero mask m: + +```text +y_m += A_m sum_(j in m) B_j x_j; all x_j and roots restored. +``` + +Maps are arbitrary exact F2-linear or characteristic-zero linear maps, +possibly singular and noncommuting. The straight-line word is independent of +map entries/data. Calls are B(j,p): z_p+=B_j x_j and A(m,p): y_m+=A_m z_p; +the signed model also allows their additive inverses, not inverse matrices. +For two roots, U: z0+=z1 and V: z1+=z0, with signed inverses where applicable. +Sources are read-only and outputs unobserved until the whole batch completes. +All source, target and declared root rows are excluded from child scratch; +children preserve other rows and restore private work, frames and heads. +There are no free copies, resets, root rescaling/doubling, output borrowing, +combined queries or hidden persistent image caches. The cache section explicitly +changes the root stock and transfer alphabet. + +Prices b,a,tau mean **fixed complete-call tariffs**, including access, recursive +leaves/inverses, updates, restoration, frames, heads and dispatch. Comparisons +require actual fixed prices or certified lower bounds for every comparator +orientation/port. Orientation maxima are candidate upper bounds, never +comparator lower bounds. In the limit claims a=1 and b~sqrt(2M); equal port +prices are an assumption, not an inferred property of a physical caller. + +A transfer is a full-row pass with L updates plus actual routing/access costs. +Add H_word for costs outside the calls: extra root reservation, parking, +coefficient/input preparation, schedule generation/reads, counters, precision, +child-private work and tape/owner hosting. Different H_word values can erase a +query saving. No qualifying selected caller, contracting moment or kappa gain +is established. Exact arithmetic is not a floating-point error analysis. + +## All-word lower bounds and the optimal 25% limit + +Let k be the total B calls. Generic restoration forces k>=2n: a single +injection has a nonzero transported coefficient that invertible root transfers +cannot erase. Every target needs at least two A reads to cancel incoming dirt. +Necessity already follows from scalar identity maps and independent inputs; +these bounds concern words valid for every choice of maps. + +With one root, signed dirt cancellation forces an even number of reads for +each target, and source closure makes k even. The closed source-prefix walk +has at most k distinct states. At most choose(k,2) nonzero masks can be served +with two reads; other masks require at least four. Hence every word costs: + +```text +k*b + a*max(2M,4M-k(k-1)), k>=2n, k even. +``` + +With two roots write the state as G(d+Q), where G is the invertible scalar +root frame, d the incoming dirt and Q the two normalized source rows. Transfers +change G but not Q. Two reads cancelling dirt use one common functional l +(after accounting for signs), so their mask lies in the row space of Q_s-Q_t. +This has rank at most two. A rank-r subspace meets the binary mask cube in at +most 2^r points: project injectively onto r pivot coordinates. Including zero, +each prefix pair therefore supplies at most three nonzero masks. This works +in F2 and characteristic zero, even granting arbitrary scalar root frames free. +Closure repeats Q=0, so at most k distinct prefixes occur. Every two-root word +therefore costs at least: + +```text +k*b + a*max(2M,3M-3*k(k-1)/2), k>=2n. +``` + +These are optimistic union bounds; repeated masks only strengthen them. +No two-call incidence or transfer-depth restriction is used. Before capacity +saturates at M, the price expression is concave in k; afterwards it increases. +[families.py](families.py) minimizes over the admissible interval endpoints +with integer/Fraction arithmetic, no finite cutoff or floating roots. + +Let r_n be the first even k>=2n with k(k-1)>=2M and set +b_n=r_n-2+2n-1, a=1. Then b_n/sqrt(M)->sqrt(2). With x=k/sqrt(M), the +one-root lower expression tends to `sqrt(2)*x+max(2,4-x²)`, whose minimum is 4. +The two-root expression tends to `sqrt(2)*x+max(2,3-3*x²/2)`; its concave +branch endpoints are 3 and 2+2/sqrt(3)>3, followed by an increasing tail. +Thus the respective lower limits are 4M and 3M. + +Four balanced one-root Gray blocks give (4+o(1))M reads and O(M^(1/4)) B +calls; signed references visit positive/negative cubes with opposite reader +signs. At the declared b_n their source cost is o(M). The three-block palettes +below give (3+o(1))M reads and O(M^(1/3)) B/transfer calls, again costing o(M). +Therefore **OPT_one/M->4 and OPT_two/M->3**, a matching **25% limiting +query-tariff saving**, in both fields. Any fixed finite transfer tariff is +compatible with these limits; overhead H_word is not assumed to vanish. +Characteristics such as three do not inherit the even-readout argument. + +### Stronger source-locality correction + +Index the k source cuts cyclically, identifying the final cut with the first. +For 0<=h=2n. Legal radii h>=n yield capacity at least +M and cannot strengthen the saturated bound. Replace paired capacity in the +preceding prices by P_1 or P_3: +`k*b+a*max(2M,4M-2P_1)` or `k*b+a*max(2M,3M-P_3)`. +The h=1 term removes repeated singleton slots. Repeated prefix states are safe. + +Between intersections of deficit lines the unsaturated price remains concave; +after saturation it increases. `locality_lower_bound` checks both admissible +integer neighbors of every line intersection, the initial k and the saturation +boundary. Independent source-count enumeration checks this minimization on +small domains; actual closed walks check capacity. The 4M/3M limits persist. + +## F2 palette and signed zero-sum triangle + +Split sources into three nonempty blocks, q_i=2^(block size). Each block runs +one closed reflected Gray cycle. Every child uses z0, and z1 holds dirt only. +For F2 use normalized columns 10,01,11. At each nonzero vertex one U exposes +the second signature; a closing V changes/restores the companion dirt: + +| Block | Entry dirt (z0,z1) | z0 signatures | After closure and V | +|---|---|---|---| +| P | (d0,d1) | d0,d0+d1 | (d0+d1,d0) | +| Q | (d0+d1,d0) | d0+d1,d1 | (d1,d0+d1) | +| R | (d1,d0+d1) | d1,d0 | (d0,d1) | + +Pure targets read at zero and their block sum with matching dirt. Two-block +targets use the shared signature; three-block targets use 10,11,01, whose dirt +XOR is zero. Applying the same A_m gives exactly the requested source terms. +The invoice is B=sum(q_i), A=2M+product(q_i-1), T=B, two dirty roots. + +For characteristic zero use `vP=(1,0), vQ=(0,1), vR=(-1,-1)`. +There is still one positive subset cube per block in normalized coordinates; +physically R uses inverse B/A calls. No division, rescaling or clean row occurs. + +| Block | Entry dirt | z0 signatures | Read sign | Closing shears | +|---|---|---|---:|---| +| P | (d0,d1) | d0,d0-d1 | + | U+,U+,V-,U+ | +| Q | (d1,-d0) | d1,d1-d0 | + | U-,V+ | +| R | (d1,d1-d0) | d1,d0 | - | V+ | + +At nonzero vertices U signs alternate, starting -, +, - respectively. Each +q_i-1 is odd, so every phase exits on its second signature. The table's closing +shears reach the next entry and finally restore (d0,d1). P/Q reads cancel +(d0-d1)+(d1-d0); P/R cancel d0-d0; Q/R cancel d1-d1. Three-block targets use +P at d0, Q at d1-d0 and inverse R at d1. Pure targets use an opposite-sign +anchor read at zero. The negative physical R sum and inverse A reader make +all requested source contributions positive, with no commutation assumption. + +```text +B_signed=sum(q_i), A_signed=2M+product(q_i-1), T_signed=B_signed+4. +Two dirty roots; all A/B ports=0. +``` + +The replaced signed word used q0+2q1+2q2 B and q0+q1+2 transfers. The saving +is `(q1+q2)*b-(q2+2)*tau`; it weakly dominates that word when b>=tau. Equal +blocks give **40% fewer B calls**. At n=15, 160 B/66 transfers become +96 B/100 transfers, with the same 95,325 A calls. + +Read counts are sharp in the declared one-active-block geometry: two prefixes +touch at most two blocks, so three-block masks need three reads, other masks +two. At that floor both signatures must be exposed at each nonzero vertex, +requiring B-3 switches. [certify_frames.py](certify_frames.py) checks all 384 +phase-order/sign/entry cases with complete radius-eight SL2(Z) BFS and separate +literal radius-four halves, no height cutoff. All 144 endpoint distances agree; +minimum boundary cost is seven. Thus B+4 is optimal **within that fixed +triangle/one-switch-per-vertex geometry**, not over arbitrary programs. + +Every forward parent coefficient has absolute value at most one; root/output +dirt l1 norm is at most two, and source terms enter outputs positively once. +For |d_p|<=D, |B_j x_j|<=beta_j and induced infinity norm alpha_m of A_m, +roots are bounded by `2D+max_block sum(beta_j)` and output prefixes by +`|y_m(initial)|+alpha_m*(2D+sum_selected beta_j)`. These are parent bounds; +child-private work, rounding and physical precision still need separate charges. +[verify_signed.py](verify_signed.py) checks every prefix for n3..12. + +Exact signed examples with a=tau=1 and the locality lower bound: + +| n | b | Every one-root word >= | Triangle | Guaranteed saving | +|---:|---:|---:|---:|---:| +| 9 | 49 | 2,638 | 2,569 | at least 2.61% | +| 15 | 285 | 138,778 | 122,785 | at least 11.52% | +| 18 | 759 | 1,074,672 | 920,257 | at least 14.36% | +| 30 | 46,399 | 4,297,747,752 | 3,360,623,617 | at least 21.80% | + +n30 is formula arithmetic, not a materialized word. Explicit emission is capped +at n18; the inductive construction and bounds have no such mathematical cap. +[FRAME-RECEIPT.json](FRAME-RECEIPT.json), [SIGNED-RECEIPT.json](SIGNED-RECEIPT.json) +and [FAMILY-RECEIPT.json](FAMILY-RECEIPT.json) retain exact domains and invoices. + +## Secondary: the F2 73-call extension of Math PR1 + +[Math PR1](https://github.com/conorholds/math/pull/1), package +[bidirectional-universal-five](https://github.com/conorholds/math/blob/623039e5f0c7a7fe090789c79ff7e722f5404e9b/integer-mult-bounds/research/bidirectional-universal-five/README.md), +already gives a six-transfer witness, the 51,900,912-assignment four-transfer +exclusion at 72 A/B calls, and the 72c+6s versus 74c comparison. The different +[CERTIFICATE.json](CERTIFICATE.json) word here is another achieving fixture, +not a new six-transfer result. This section adds only the **73-call exclusion** +needed to extend that comparison to arbitrary call counts. + +At five sources/31 targets the generic operator floor is 72. Transfer counts +are even because U/V are odd permutations of the three binary root directions +and the final dirty frame is identity. At zero transfers every source/root +and target/root count is even, excluding 73 calls. The two-transfer possibilities +at 73 calls are one extra A read or one extra B call; [census.cpp](census.cpp) +exhausts both, without imposing even operator multiplicity: + +| 73-call domain | Canonical source words | B/C interleavings | Restored assignments | Universal words | +|---|---:|---:|---:|---:| +| 10 B, one three-read target | 945 | 124,740 | 1,740,960 | 0 | +| 11 B, paired targets | 17,325 | 2,702,700 | 18,214,560 | 0 | + +For the first domain at least 31 masks including zero must have paired reads; +the single missing nonzero mask is tested against all three dirty-signature +classes. The second domain uses one distinguished triple and four pairs; +11!/(3!*2^4*4!)=17,325. All restoring two-transfer words and physical port +assignments are covered. Literal replay follows normalized restoration filtering; +positive and failed three-read controls execute in every native run. + +Thus 73 A/B calls require at least four transfers. For c>0,s>=0, +73c+4s is dominated by 72c+6s when s<=c/3 and by 74c when s>=c/3. +Words with >=74 operator calls cost at least 74c. Together with PR1's 72-call +exclusion and attaining words, this gives **min(74c,72c+6s)** at equal A/B +price c and transfer price s, allowing arbitrary counts. H_word is additional; +unequal-price schedules are not ordered by this theorem. + +[PR1812](https://github.com/CrocSwap/integer-mult-bounds/pull/1812) explicitly +asked whether bidirectional transfers lower eight; the credited six-transfer +words answer that question. [Adam Gall PR1915](https://github.com/CrocSwap/integer-mult-bounds/pull/1915) +and [Arham Garg's connector-frame-73-exclusion](https://github.com/CrocSwap/integer-mult-bounds/tree/0fdd7d82/research/connector-frame-73-exclusion) +prove the framed **single-connector** 74-call bound. They are predecessors, +not exclusions in our changed two-root alphabet. The 74-call Richardson fixture +is replayed here as [ONE-ROOT74.json](references/ONE-ROOT74.json). +The 73-call native exclusion has one implementation; its independent written +case split does not constitute a second native enumeration. + +### Inherited F2 incidence result: independent census only + +[Math PR2](https://github.com/conorholds/math/pull/2), package +[scalable-dirty-connectors](https://github.com/conorholds/math/blob/623039e5f0c7a7fe090789c79ff7e722f5404e9b/integer-mult-bounds/research/scalable-dirty-connectors/README.md), already +proves F2 two roots cannot attain exactly two calls per source/output at n>=6, +using zero-map specialization for larger n. We adopt that simpler argument +rather than claim another all-n obstruction. The retained set/matching/Walsh +engines independently cross-check n5/n6: 945/10,395 source words, 14,175/322,245 +two-color cases, 175/0 universal covers and maxima 32/59 including zero. +Three occupied source colors cannot cover a mask meeting all three classes. +These are supporting checks; the obstruction itself is credited to PR2. + +## Secondary: minimum-read F2 walk compiler + +[walk.py](walk.py) accepts a closed source word with two occurrences per label, +each having a fixed normalized color in {10,01,11}. At cut t its query vectors +are `(l,l*Q(t))` in F2^(n+2). A clean target is `(00,m)`. Exact BFS minimizes +reads for every requested target, with no four-read cutoff; optional requested +subsets preserve unrequested outputs. Emission is capped at n12. + +For its **chosen** minimum-read decomposition, the deadline/frame DP considers +every placement at an available cut and every U/V path. States contain a frame +among the six GL2(F2) frames and delivered-generator bits; generators must be +served by their last available cut. Before a source call G*v_j=e0 is required, +so all A/B ports are z0; the final frame is identity. A 65,536-state overflow +raises an error, never a truncated-success claim. + +**Transfer cost depends on the decomposition; equal-read alternatives are not +jointly optimized.** For source word `[2,0,1,2,1,0]`, colors `[1,2,1]`, this +compiler uses 14 reads/10 transfers, while the reviewer's literal program uses +14 reads/6 transfers through z0 and restores every dirty row. Both programs +and a missing-transfer failure are checked in [test_walk.py](test_walk.py). +The retained 32/50 transfer bills are not certified minima across decompositions; +the toy counterexample alone does not prove better words for those larger walks. + +| n | B | A | Transfers | Query price (a=tau=1) | Every one-root >= | Guaranteed saving | +|---:|---:|---:|---:|---:|---:|---:| +| 9 | 18 | 1,404 | 32 | 2,318 at b=49 | 2,638 | at least 12.13% | +| 12 | 24 | 13,996 | 50 | 16,758 at b=113 | 18,564 | at least 9.72% | + +[WALKS.json](WALKS.json) binds literal program hashes and invoices. +[search_walk.cpp](search_walk.cpp) is heuristic discovery, not a proof dependency: +19 three-color partitions at n9/n12, 200,000 proposals each, six relabelings, +114 generic-checked programs in [WALK-SWEEP.json](WALK-SWEEP.json). The n9 read +histogram is 143/354/14 targets using 2/3/4 reads. At n12 fourteen targets need +five reads; the search's optimistic four-read bill was rejected. No global +source-word optimum or impossibility follows from this bounded sweep. + +### Within 2.98% at the minimum source-call count + +Exactly two B_j calls force a fixed normalized color. Let d(t) bound nonzero +prefix differences of a closed twice-occurring t-label walk. Separate complete +engines give d(5)=30,d(6)=48; otherwise use min(2^t-1,P_1(t,2t)), d(0)=0. +At most three nonempty color classes occur; every partition is considered. + +With one color, both two/three-read masks lie in one difference set, so +A>=4M-2d(n). With two sizes a,b, paired coverage P is at most +min(M,d(n)+d(a)+d(b)-n): singleton masks are counted twice. With three sizes +s_i it is at most min(M,sum_i d(n-s_i)-n); pairwise intersections contain +shared-class singletons and the three supports have no nonzero common mask. +For two/three classes, every <=3-read mask has each class component in its +class's difference set, since three-read dirt cancellation uses all three +functionals and each class appears twice. Thus at least +`2^n-product_i(d(s_i)+1)` targets require >=4 reads, giving +`A>=3M-P+2^n-product_i(d(s_i)+1)`. + +All twelve n9 partitions imply A>=1369; at b=49 every exactly-18-B word costs +at least 2251 with transfers granted free. The actual 2318-cost word is within +67/2251<2.98% of that class's optimum, irrespective of decomposition improvement. +This does **not** bound programs buying additional B calls, subset batches, +or physical overhead. [WALK-BOUND.json](WALK-BOUND.json) records the full cases. + +## Secondary: signed fixed-port parent cache + +Reserve n+1 arbitrary dirty parent rows R=z0,C_j=z_(j+1), all excluded from +child scratch. Every operator call uses physical z0; the added paid operation +is T(dest,src,sign), a full-row ADD with distinct endpoints, one being z0. +No clean row, reset, source mutation or inverse matrix is supplied. + +Let incoming R=d,C_j=c_j. A Hamiltonian cube path from zero visits every +nonempty mask once, maintains `R=d+sum_(j in m)c_j` by signed cache transfers, +and makes one negative A_m read per vertex. Opposite-parity endpoints admit +such a path: split on a differing bit, choose c neighboring the first endpoint +in its half, join recursively to c and from its cross-half neighbor to the +other endpoint. The halves are disjoint and the connecting edge differs in +one bit; the one-coordinate base is an edge. End at the full mask for odd n; +for even n end at full XOR bit0, then position at full with one extra transfer. +The full mask was already read in that even case. + +At the full-sum invariant R=d+sum_j C_j, populate each cache by: + +```text +C_j -= R; R += B_j x_j; C_j += R. +``` + +It changes C_j to c_j+B_j x_j and R by the same response, preserving the +invariant. A closed reflected Gray cycle starting at full now reads each +nonempty mask positively from `d+sum_(j in m)(c_j+B_j x_j)`. +The two A_m reads cancel the same arbitrary dirt and add the requested images. +At full, repeat the three-line update with inverse B_j to unpopulate caches, +then subtract all n restored C_j from R. Every source/root is restored. + +```text +B=2n; A=2M; T=2M+1+[n even]+5n; roots=n+1; persistent rows=2n+M+1. +``` + +The old path takes M+[n even] transfers, the new cycle M+1, population/cleanup +4n, and final restoration n. The written induction holds for all n>=1; +explicit emission is capped at n18. Generic single-injection/reader dirt +arguments give every allowed root count the operator lower bound 2n*b+2M*a. +This construction attains both operator floors, paying its remaining transfers. + +At a=1,b~sqrt(2M), its cost/M tends to 2+2*tau for fixed tau. At tau=1/4 the +limiting query savings are 37.5% versus one root and 16⅔% versus two. At +**tau=1/n²->0**, it matches the any-root 2M lower limit, giving 50%/33⅓% versus +the one/two-root optima. This last claim requires A to cost much more than a +full-row transfer; there is no proof that an actual caller has those prices. +The extra n-1 dirty rows versus two roots and all H_word charges still apply. +[CACHE-RECEIPT.json](CACHE-RECEIPT.json) retains the finite exact examples. + +This is **not a better F2 cache invoice** than Math PR2's star: at n>=4 that +family uses n-3 roots and 8(2^(n-4)-1) transfers when its distinct source ports +are admitted. The additional cache scope here is signed characteristic zero, +all n>=1 and every operator call at z0. No priority for the operator floors, +Gray paths or dirty-cache cancellation is claimed. + +Parent coefficients have absolute value <=1 but dirt l1 norm can reach n+1, +versus two for the triangle. With |d|,|c_j|<=D, roots are bounded by +`(n+1)D+sum_j beta_j`; output prefixes by +`|y_m(initial)|+alpha_m*((n+1)D+sum_selected beta_j)`. +[verify_cache.py](verify_cache.py) checks generic n1..12, every forward prefix, +683 paths, 1272 separate integer/F2 matrix cases, inverse/omission/sign/port +controls. No cache runtime benchmark or physical supplier admission was run. + +## RAM checks of the tariff regime + +[benchmark.py](benchmark.py) uses dense B and identity A, not a representative +integer-multiplication workload. Signed B traverses Theta(w²) coefficients; +identity A performs Theta(w) updates, so b/a grows with width by construction. +The signed crossover therefore tests this tariff regime, not independent +performance outside it. Width128 is the implementation cap and the only +positive signed point. F2 A is one big-integer XOR; its timings heavily reflect +Python instruction dispatch. Native tape/owner/precision costs are excluded. + +Both B coefficient traversals execute, arbitrary private work is restored, +and separate direct forward/inverse checks precede timing. At n15 the comparator +screens all count-Pareto one-root partitions (24 F2,23 signed), then takes the +fastest of three finalists with nine fresh alternating samples. Data/maps match; +the candidate admits an extra dirty root. Input copying is timed (deep copies +for signed arrays); shared coefficient/input/program preparation is excluded. +Copying tends to shrink differences. Results are host-load-sensitive, without +confidence intervals or unrestricted-comparator optimality. + +| Field | Width | Best reference blocks | Reference median | Palette median | Speedup | Time saved | +|---|---:|---|---:|---:|---:|---:| +| F2 | 64 | 7,8 | 12.342 ms | 11.445 ms | 1.08x | 7.27% | +| F2 | 128 | 3,3,4,5 | 14.772 ms | 12.253 ms | 1.21x | 17.05% | +| F2 | 256 | 3,4,4,4 | 17.484 ms | 15.659 ms | 1.12x | 10.44% | +| signed | 32 | 8,7 | 166.726 ms | 194.327 ms | 0.858x | -16.55% | +| signed | 64 | 8,7 | 380.732 ms | 405.463 ms | 0.939x | -6.50% | +| signed | 128 | 8,7 | 982.620 ms | 821.980 ms | 1.195x | 16.35% | + +[BENCHMARKS.json](BENCHMARKS.json) retains every positive/negative measurement, +including superseded variants. [test_families.py](test_families.py) checks all +23 relevant function hashes and rejects altered measured source. These pins +bind shipped methods, not an authentication of timing data. No multiplication +runtime, floating-complex timing or cache-family speedup is claimed. +Within the one-root Gray-block reference family, n18 at b=800,a=tau=1 +reduces tariff from 1,119,096 to 928,125 (17.06%); this is not an all-word +comparator lower bound. + +## Retained caller screen + +[screen_caller.py](screen_caller.py) extracts a source-bound interface included +in the selected manifest: eight distinct rank-eight centre charts, 112 signed +two-source targets, 224 additions, 24 patterns and a graph of two disjoint K4s. +Its retained forward word has eight private copies, sixteen clears and eight +centre descents. Those clean/owned buffers and sparse targets are a different +contract from our universal arbitrary-dirty-root batch. Complete chart, port, +recursive/head/stock and precision costs must be established before adoption. +This is **not a census of currently dispatched providers**, an endpoint/native +owner replay or a selected cold replay. [CALLER-SCREEN.json](CALLER-SCREEN.json) +records that scope; no supplier replacement or kappa follows. + +## Reproduce and verification limits + +All commands use Python's standard library; no package installation is needed. +From this Math repository root, set p to the package path below and run serially: + +```sh +p=integer-mult-bounds/research/bidirectional-connector +python3 -I -O -B "$p/verify.py" +python3 -I -O -B "$p/independent_check.py" +python3 -B "$p/verify_families.py" +python3 -B "$p/certify_cost.py" +python3 -B "$p/verify_signed.py" +python3 -B "$p/verify_walk.py" +python3 -B "$p/verify_cache.py" +python3 -B "$p/screen_caller.py" --repo /path/to/pinned-upstream-checkout +``` + +For the official hook, copy the package into an isolated CrocSwap checkout at +research/bidirectional-connector and run: +`python3.12 -B scripts/research_package.py --package research/bidirectional-connector`. +[VERIFY.json](VERIFY.json) declares the eight commands and deadlines; walk replay +has a 120-second deadline for CI headroom, not a mathematical search cutoff. + +Default `certify_cost.py` freshly runs the two Python n5/n6 engines and binds +the native receipt to census.cpp; it explicitly reports native **NOT_RUN**. +Fresh native enumeration requires `certify_cost.py --full`, Clang/GCC C++17. +On this host the installed compatible SDK was selected explicitly with +`--sdk /Library/Developer/CommandLineTools/SDKs/MacOSX15.2.sdk`, no global change. +The stored full replay covered 71,856,432 restored assignments, including +PR1's duplicated 72-call domain. The 73-call part has one native implementation. +No hosted-CI result is claimed. `make selected-record-check` checks source +integrity, not the complete multiplication theorem or selected cold replay. + +Receipt writers use explicit --write-receipt; fresh native COST regeneration +also requires --full. `verify_families.py` runs 11 family, six original and +384 frame controls; `verify_walk.py` runs ten regressions. No weaker tests or +regenerated timing evidence replace the original records. The PR9 agent review +reported independent rectangular/degenerate-map, bound and native replays; +its scratch artifacts remain local-only, not independent human/formal review. + +## Sources, status and attribution + +Scientific inputs and selection remain pinned to original main +`0b1cccf86e2f5132ed286a26ef0a681a495740ea`, task connector-alphabet-change, +revision3/nonce4097e9f6a5c8e30cb7274114770e40f8. The refreshed canonical snapshot +is `0fdd7d82`; all mathematical inputs and the selected record still match. +Only the originating catalogue changed (now priority4), so its original pin +remains historical provenance. Refreshed guidance was read; review corrections +continue this task, without a reroll or touching frozen sources. + +[SOURCES.json](SOURCES.json) records the byte-identical **merged PR1615** witness +(merged 2026-10-14 15:43:33Z), checked against refreshed main. It is replayed +as an eight-transfer comparator; its one-way native exclusion is not imported. +**PR1887 merged at 16:57:12Z**, and PR1915 at 17:06:51Z. PR1887's fixed-port +five-source two-projection/175-cover result is credited, not called pending or +concurrent. The distinct contributions here are the all-word priced bounds, +signed triangle and explicitly limited secondary extensions/cross-checks. + +[TASK.json](TASK.json) preserves historical overlap searches and their limits, +plus the PR9 review response. Inspected nearby work includes PR1811,1707,1708, +1717,1719,1954,1968,1972,2045,2050,2060 and Discussion2053; their targets or +allowed resources differ. Historical no-match reports are not novelty proofs. A fresh canonical-main and +live-overlap checkpoint is recorded in TASK.json for this submission. +The scientific package and review corrections are archived in Math PR9/PR11. +The user has explicitly approved submission of this package for upstream +mathematical review. The selected frontier is unchanged. + +## Open next questions + +1. Bind one actual caller with expensive B, cheap A, offline targets and aligned + paid root transfers. Charge extra stock, routing, precision/tape and all + H_word terms; adopt only if the complete overhead fits the query saving. +2. Optimize across minimum-read decompositions at a fixed source walk, rather + than only read placements, or bound cache transfers at positive prices. + Establish a complete small state model before expanding synthesis; neither + present routine claims an unrestricted transfer optimum. + +## Credit and license + +Prepared for conorholds with substantial OpenAI Codex assistance in +proofs, census, construction, both checkers, tests and writing; no subagents. +New material and the retained PR1615 certificate are Apache-2.0 under +[LICENSE](LICENSE). Retain Richardson PR943/934 for the universal prefix model, +read-only repair and Gray-block lineage; the six-source package by Douglas Colkitt and its +independent PR1215 audit for the preceding finite boundary; woklerx PR1438, +Gareth Davidson/bitplane PR1498, Cinna Davis Discussion1412 and Hanson Sun/bbMisk +PR1615 for the one-way root family; PR1767 for its complementary audit; +PR1812 for the bidirectional-transfer question; Adam Gall PR1915 and Arham +Garg's connector-frame-73-exclusion for the framed one-root 74-call bound; +and Cinna Davis PR1675, Charles Bethin PR1637 and Richardson PR944/1651 for +related signed bidirectional work. Retain martinxxx9 PR1088 and Hanson Sun +PR1526/1556 in the signed-query and paid-scaling lineage. Credit Cinna Davis's merged PR1887 for +fixed-port two-projection frames and the independently matching 175-cover +census. Adam Gall PR2065 is credited for the independent six-transfer endpoint. +Math PR1/PR2 are credited above for the six-transfer baseline and +all-n two-root incidence obstruction; neither is claimed as new here. No priority for Gray codes, elementary +compute/uncompute or dirty XOR cancellation is claimed. Retain shhxera/CubeJerry +PR889 and Chafik Boukhalfa PR628 in the dirty-commutator lineage. The selected +Rohan Arun/Jeremy Kothe construction and its cumulative credit remain unchanged. + +All-size compiler, common-label/mutable-source realization, native owner and +whole-call hosting, precision/tape, exact recovery and outer analytic +obligations remain uninstantiated. Exact local identities and priced research +constructions are not a complete multiplication theorem. diff --git a/research/bidirectional-connector/SIGNED-RECEIPT.json b/research/bidirectional-connector/SIGNED-RECEIPT.json new file mode 100644 index 0000000000..825849a126 --- /dev/null +++ b/research/bidirectional-connector/SIGNED-RECEIPT.json @@ -0,0 +1,220 @@ +{ + "schema": "signed-triangle-v1", + "records": [ + { + "sources": 3, + "counts": { + "sources": 3, + "blocks": [ + 1, + 1, + 1 + ], + "source_calls": 6, + "readout_calls": 15, + "transfers": 10, + "dirty_root_rows": 2 + }, + "prefix_bounds": { + "coefficient_absolute_max": 1, + "root_dirty_l1_max": 2, + "output_dirty_l1_max": 2 + }, + "word_sha256": "3ccbfe362d0c97b417c8d30e1380e3217ac99295d0267479e566d1687f2c8914" + }, + { + "sources": 4, + "counts": { + "sources": 4, + "blocks": [ + 2, + 1, + 1 + ], + "source_calls": 8, + "readout_calls": 33, + "transfers": 12, + "dirty_root_rows": 2 + }, + "prefix_bounds": { + 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"270186d9aaec00b410fddf7992815b3cf90a3a4de44a632f773f6403b92acbf4" + }, + { + "sources": 10, + "counts": { + "sources": 10, + "blocks": [ + 4, + 3, + 3 + ], + "source_calls": 32, + "readout_calls": 2781, + "transfers": 36, + "dirty_root_rows": 2 + }, + "prefix_bounds": { + "coefficient_absolute_max": 1, + "root_dirty_l1_max": 2, + "output_dirty_l1_max": 2 + }, + "word_sha256": "2c615cf58af8485fb20efc2dec311243c42353410b74969f155b59ba6836e537" + }, + { + "sources": 11, + "counts": { + "sources": 11, + "blocks": [ + 4, + 4, + 3 + ], + "source_calls": 40, + "readout_calls": 5669, + "transfers": 44, + "dirty_root_rows": 2 + }, + "prefix_bounds": { + "coefficient_absolute_max": 1, + "root_dirty_l1_max": 2, + "output_dirty_l1_max": 2 + }, + "word_sha256": "c21d9e4b61ca4f8bcbf52d383fd92eb4634cb7d46a2eae9e438cf8161a1f9f6f" + }, + { + "sources": 12, + "counts": { + "sources": 12, + "blocks": [ + 4, + 4, + 4 + ], + "source_calls": 48, + "readout_calls": 11565, + "transfers": 52, + "dirty_root_rows": 2 + }, + "prefix_bounds": { + "coefficient_absolute_max": 1, + "root_dirty_l1_max": 2, + "output_dirty_l1_max": 2 + }, + "word_sha256": "4e9c1206522e93aa3a4123c3a6c78ba15a3ea8b98feeaa7997103014645c6d15" + } + ], + "integer_dense_cases": 182, + "omission_controls": 31, + "sign_mutations": 3, + "inverse": "literal negated shears", + "height_scope": "Exact generic forward coefficients, no numerical roundoff or physical precision/tape invoice." +} diff --git a/research/bidirectional-connector/SOURCES.json b/research/bidirectional-connector/SOURCES.json new file mode 100644 index 0000000000..c7555a896e --- /dev/null +++ b/research/bidirectional-connector/SOURCES.json @@ -0,0 +1,108 @@ +{ + "schema_version": 1, + "base_commit": "0b1cccf86e2f5132ed286a26ef0a681a495740ea", + "files": [ + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "ae6a99f28aa468649eb66a361e764d769363bf11", + "sha256": 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"merged", + "merged_at": "2026-10-14T15:43:33Z", + "merge_commit": "299eb8effe080183313757ac36e76c1b98ed9fae", + "verified_on_main": "0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2" + }, + "upstream_checkpoint": { + "commit": "0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2", + "priority_revision": 4, + "original_pins": "Retained scientific baseline and selection provenance, not rewritten.", + "changed_original_pins": [ + "docs/research/agent-task-catalog.json" + ], + "mathematical_inputs_unchanged": true, + "merged_related_prs": { + "1887": { + "head": "025d4fcd87f1b6ea01aa1c52721f8f46389aacce", + "merged_at": "2026-10-14T16:57:12Z", + "merge_commit": "6aff82d6d346fb2238d061ef45066b82d48a9b67" + }, + "1915": { + "head": "d30d64fea909219c364b11c2452f2207326e2b1f", + "merged_at": "2026-10-14T17:06:51Z", + "merge_commit": "178a293edbd162fe3ce13e81a97af921366bd100" + } + }, + "connector_frame_73_exclusion": { + "commit": "0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2", + "path": "research/connector-frame-73-exclusion/README.md", + "sha256": "ec3cf13bb97839832e5416f437b6a8dfd622468a1864bbb5552f17f0c43a1bcf", + "credit": "Arham Garg; closes Adam Gall PR1915 single-connector 73-map question." + } + } +} diff --git a/research/bidirectional-connector/TASK.json b/research/bidirectional-connector/TASK.json new file mode 100644 index 0000000000..5465dfa7fc --- /dev/null +++ b/research/bidirectional-connector/TASK.json @@ -0,0 +1,596 @@ +{ + "schema_version": 1, + "task_id": "connector-alphabet-change", + "priority_revision": 3, + "base_commit": "0b1cccf86e2f5132ed286a26ef0a681a495740ea", + "original_card": { + "id": "connector-alphabet-change", + "question": "Does one explicit extension of the connector alphabet offer a favorable completed budget?", + "starting_points": [ + "research/universal-connector-boundary/README.md", + "certificates/selected-result.json" + ], + "methods": [ + "Construct and charge a legal extra operation on a minimal instance.", + "Prove a target-specific bound after adding one specified operation family." + ], + "acceptance_gate": "State which fixed-alphabet premise changes and charge its implementation; do not declare it free.", + "first_step": { + "command": [ + "python3", + "-B", + "research/universal-connector-boundary/verify.py" + ], + "expected": "PASS_UNIVERSAL_CONNECTOR_BOUNDARY", + "inspect": "Reproduce the 945-pairing control, then read Exact interface to list the allowed calls.", + "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay." + }, + "first_experiment": "Add exactly one legally priced operation and test a tiny dirty-input instance before enumerating larger cases.", + "bottleneck_link": "A new legal connector operation could change recursive interface cost; a larger census in the same alphabet is a separate side result.", + "allowed_variations": [ + "Choose one additional operation and a small source count for its first counterexample." + ], + "scope_change_triggers": [ + "Keeping the alphabet and only increasing the source count; record this as a changed assignment." + ], + "overlap_terms": [ + "universal connector", + "source-toggle", + "connector alphabet" + ] + }, + "scope_status": "changed", + "actual_scope": "Primary: all-word one/two-root query lower bounds, source-locality correction and matching 4M/3M limits in F2 and characteristic zero; signed zero-sum triangle at physical z0. Secondary: 73-call extension of Math PR1, limited minimum-read/decomposition-placement compiler and n9 minimum-source bound, signed n+1 fixed-port cache. Math PR1 six-transfer result and Math PR2 all-n two-call obstruction retained only as inherited fixtures/independent cross-checks. RAM checks of the specified tariff regime and retained-caller contract screen, no admitted supplier.", + "scope_change_reason": "The user explicitly requested considerable additional progress along this path. Further source-word brute force has less than three percent query headroom in the n9 minimum-B class; a paid parent-cache interface offers a larger algebraic resource trade. Extra rows and transfers are explicit, not free. No supplier replacement, physical memory-time theorem or exponent improvement follows.", + "bottleneck_link": "A caller must admit expensive generic B maps, cheaper A maps, paid aligned full-row transfers, offline targets and extra arbitrary dirty parent stock. The retained selected interface has sparse targets and different ownership; no qualifying dispatched occurrence is established.", + "budget_minutes": 240, + "stop_rule": "Submit the explicitly approved PR title and body to CrocSwap/integer-mult-bounds for review, then stop. No merge, unrelated PR changes or Discussion messages are authorized.", + "outcome": "completed", + "evidence": "Exact all-word proofs and source-bound receipts; signed triangle and prefix-height checks; native 73-call domains plus inherited PR1 census; independent n5/n6 incidence/difference engines cross-check PR2; n9 restricted gap below2.98%; benchmark source bindings now tested with a drift failure control; reviewer literal counterexample rejects unrestricted transfer-optimality interpretation. Prior native/benchmark results retained unchanged; current validation recorded below.", + "author": "conorholds, with OpenAI Codex assistance", + "ai_assistance": "Substantial OpenAI Codex assistance in algebra, implementation, checking and writing; no subagents.", + "open_questions": [ + { + "question": "Which actual admitted caller has these map tariffs, offline targets and enough arbitrary dirty parent rows?", + "why_it_matters": "Query savings affect a supplier moment only after routing, stock, heads, preparation, precision/tape and chronological hosting are charged.", + "first_step": "Bind one concrete caller and compare its complete physical overhead against the exact saved query invoice.", + "blocked_by": "No qualifying selected occurrence or completed physical invoice established." + }, + { + "question": "Can a paid cache reduce its O(M) transfer term at a fixed positive transfer price?", + "why_it_matters": "The cache attains all A/B floors but claims any-root optimality only as the relative transfer tariff tends to zero.", + "first_step": "Fix source count, declared root stock and positive transfer price; prove a complete state model before weighted synthesis.", + "blocked_by": "No unrestricted transfer lower bound or complete arbitrary-root optimizer in this package." + } + ], + "scope_key": "ff4f5113ed2256ab19ed", + "selector_nonce": "4097e9f6a5c8e30cb7274114770e40f8", + "local_claim_only": "User explicitly approved the upstream PR process using the reviewed draft; authorization is limited to publishing this contribution for review.", + "overlap": { + "coverage": "498 open PRs and 484 discussion/comment/reply records, complete pagination; 871 local records; no warnings", + "checked_at": "2026-10-14T11:52:12Z", + "closest_prs": { + "1438": "Integrated one-way four-transfer lower bound with free B ports", + "1498": "b7baacc8048ab11d31751aee065206f2725a1a16", + "1615": "96916897840829cc01b126f8f202a92d949d2bfc", + "1767": "ce50fccd8086bfeb8a61cc9eded572fb4741c387", + "1812": "e43abcde1c98c718f5b4d0b25cf4cd9c04200bd8" + }, + "distinction": "All threshold results fix a one-way root transfer; none of these matches analyzes both directions. No general novelty guarantee." + }, + "discovery": { + "seed": 4097, + "six_transfer_witness_trial_zero_based": 20900, + "four_transfer_probe_candidates": 100000, + "four_transfer_max_coverage": 31, + "four_transfer_status": "Heuristic search failure only, not an exclusion or minimality proof." + }, + "related_signed_bidirectional_pr": { + "number": 1675, + "head": "a8d459974abf7ba88316c87396565f7e5fc9656f", + "distinction": "Characteristic-zero signed 3x3 target, not the F2 universal five-source target." + }, + "validation": { + "environment": "macOS27.0.1 arm64, CPython3.14.3 and installed CPython3.12.11", + "commands": [ + { + "command": "python3.12 -B scripts/research_package.py --package research/bidirectional-connector", + "result": "PASS_REGISTERED_RESEARCH_PACKAGE research/bidirectional-connector outcome=completed; all8 registered commands and24 regression groups pass.", + "seconds": 33.513 + }, + { + "command": "make selected-record-check", + "result": "PASS selected record, exact kappa, original source inventory and proof supplement: 836330098538459/500000000000000000" + }, + { + "command": "git diff --check", + "result": "PASS" + } + ], + "not_run": [ + "Hosted CI.", + "Selected cold replay, dispatched-caller census, native physical supplier/owner/precision/tape integration and outer moment/analytic admission.", + "Independent second implementation of the native 73-call cost census; the shipped implementation has a fresh 71,856,432-assignment replay.", + "Parent-cache runtime measurement; cache performance claims are exact specified-tariff arithmetic." + ], + "benchmark_function_pins": "PASS all23 function hashes; timing kernels unchanged after measurement.", + "registered_python312": { + "argv": [ + "python3.12", + "-B", + "scripts/research_package.py", + "--package", + "research/bidirectional-connector" + ], + "upstream_head": "564148b82ae9df72163f22106f15e73efca8aff2", + "python": "3.12.11", + "exit_code": 0, + "seconds": 33.513, + "output": "CHECK Exact generic free-linear endpoint/inverse, per-port paid invoice, source-bound eight-transfer comparator and every single-instruction omission\nPASS_BIDIRECTIONAL_CONNECTOR masks=31 AB_calls=72 transfers=6 root_calls=78 predecessor_transfers=8 omission_controls=158 no_new_kappa\nCHECK Separate dense F2 implementation, all dirty basis columns/mixed states, singular and noncommuting maps, inverse and omission controls\nPASS_INDEPENDENT_BIDIRECTIONAL cases=2700 directions=2 widths=1,2,3,5 omission_controls=158 no_new_kappa\nPASS_INDEPENDENT_PALETTE sources=6 cases=2439 directions=2 omissions=177\nCHECK Generic F2 families n3..12, exact tariffs/locality, RAM controls, nine family and six original regression groups; complete signed-frame BFS and literal MITM, all384 cases, exact restricted transfer floor\nPASS_SIGNED_TRIANGLE_FRAMES cases=384 pairs=144 boundary_min=7 two_engines=checked\nPASS_PAID_PALETTE_FAMILY generic_n=3..12 exact_tariffs=4 global_bounds=6 tests=9+6 frame_cases=384 signed_triangle=checked locality_bounds=6 no_new_kappa\nCHECK Two full independent Python incidence engines on n5/n6 and source-bound native cost receipt; explicitly NOT a fresh native replay\nPASS_COST_CENSUSES native_replay=NOT_RUN_receipt_bound_only ideal_two_engines=5,6 elapsed=1.052s\nCHECK Signed one-visit triangle n3..12, exact invoice/prefix height and literal inverses, separate integer-matrix replay and omission/sign controls\nPASS_SIGNED_PALETTE generic_n=3..12 signed_one_root=1..12 integer_dense=182 inverse=checked omissions=31 no_new_kappa\nCHECK F2 n9/n12 source-floor constructions, exact min-read/all-placement DP, separate dense replay, omissions, 114-candidate sweep, complete n5/n6 dependency censuses and nine regressions; n9 restricted optimum gap below 3%\nPASS_CHARGED_SOURCE_WALKS n=9,12 generic=inverse_checked independent_dense=3216 omissions=1454 tests=9 sweep=114 source_count_gap_lt_3percent=checked no_new_kappa\nCHECK Paid n+1 dirty parent cache, fixed physical child port; generic integer identities/prefixes n1..12, separate integer/F2 dense basis and inverses, all small omissions, Hamiltonian paths and invalid transfer controls\nPASS_PAID_DIRTY_CACHE generic_n=1..12 paths=683 integer_F2_dense=1272 inverse=checked omissions=50 roots=n+1 no_new_kappa\nCHECK Source-bound extraction of a retained centre interface in selected manifest; not a census of dispatched providers or full native/owner/cold replay\nPASS_RETAINED_CENTRE_CONTRACT_SCREEN centres=8 targets=112 signed_patterns=24 graph=2K4 full_native=NOT_RUN no_new_kappa\nPASS_REGISTERED_RESEARCH_PACKAGE research/bidirectional-connector outcome=completed\n.........\n----------------------------------------------------------------------\nRan 9 tests in 0.123s\n\nOK\n......\n----------------------------------------------------------------------\nRan 6 tests in 0.362s\n\nOK\n.........\n----------------------------------------------------------------------\nRan 9 tests in 0.136s\n\nOK\n", + "interpreter_resolution": "Already installed uv-managed CPython3.12.11; executable resolved explicitly, no download/install." + }, + "registered_replay_read_only": "PASS all35 package files unchanged after registered replay." + }, + "expanded_request": { + "base_local_commit": "c7016028e931b8d9f336075d1342c36fadb77add", + "authorization": "Substantial additional local research and improvements; publishing still requires prior approval.", + "compute": "Serial native and benchmark runs; no repo-wide build, Docker, concurrency increase or subagents.", + "full_native_command": "python3 -B research/bidirectional-connector/certify_cost.py --full --write-receipt --sdk /Library/Developer/CommandLineTools/SDKs/MacOSX15.2.sdk", + "full_native_result": "Three native domains pass; 51,900,912 + 1,740,960 + 18,214,560 restored assignments; positive/failure controls. Exact Python engines agree, complete native/Python command elapsed 14.521s on this run." + }, + "continuation_request": { + "base_local_commit": "2201598", + "authorization": "User explicitly requests further substantial local progress, elegant solutions and useful targeted brute force; publication remains pending approval.", + "targets": [ + "Signed triangular source colors with opposite dirty functionals to avoid repeated negative source cubes; exact paid frame synthesis.", + "Inspect selected caller compatibility and favor completed query/caller budgets over additional search volume.", + "Exact minimum-read/frame compiler and minimum-source lower bound, stronger all-word locality.", + "Paid arbitrary-dirty parent cache reaching both operator-call floors; explicit row-stock and transfer tariff conditions." + ], + "stop_rule": "Bound algebra/synthesis and caller investigation; retain only verified improvements or exact obstructions. Reserve final work for validation and source/overlap review.", + "planning_budget_minutes": 120, + "budget_note": "Initial 120-minute planning estimate extended for user-requested substantial progress, exact compiler checks, fresh guidance/overlap and the final paid-cache pivot. This was not a user-imposed deadline.", + "compute": "Serial C++ proposal sweeps and alternating benchmarks; 19 partitions x 200000 proposals and six color relabelings, 114 generic-checked programs. No Docker, repository-wide compilation, concurrency changes or subagents." + }, + "current_upstream_checkpoint": { + "head": "564148b82ae9df72163f22106f15e73efca8aff2", + "input_files": 10, + "all_pins_match": false, + "changed_pins": [ + "docs/research/agent-task-catalog.json" + ], + "package_path_free": true, + "all_mathematical_inputs_match": true, + "selected_record_unchanged": true, + "original_priority_revision": 3, + "current_priority_revision": 4, + "checked_at": "2026-10-14T18:49:10Z", + "decision": "Continue and finish existing donor-expanded task, do not reroll. Read refreshed AGENTS/autoresearch, priority-4 log and review through2027. Connector-alphabet card is unchanged. Retain original catalogue and scientific source pins as historical provenance; all mathematical inputs and selected record still match. Central P104/QQ16/stock priorities are not addressed by this query-model contribution." + }, + "continuation_overlap": { + "status": "POSSIBLE_OVERLAP_NOT_A_NOVELTY_CERTIFICATE", + "searched_at": "2026-10-14T18:44:46.371852+00:00", + "terms": [ + "cache", + "dirty Gray", + "many roots" + ], + "coverage": { + "open_prs": { + "fetched_at": "2026-10-14T18:43:19.043811+00:00", + "complete_pagination": true, + "records": 348 + }, + "discussions": { + "fetched_at": "2026-10-14T18:44:46.320602+00:00", + "complete_pagination": true, + "records": 724 + } + }, + "local_records": 873, + "warnings": [], + "limits": "Remote PR scope is open PRs including drafts. Closed work is searched through local READMEs, TASK metadata and ledger only. No code diffs or arbitrary package files are searched. Recheck relevant heads before submission.", + "matches_total": 145, + "assessment": "145 broad matches; relevant clean-cache, dirty-gather, output-mixing and correlated-update bodies inspected. No duplicate arbitrary-dirty n+1 parent cache/all-mask operator-floor construction found in this bounded search. No novelty guarantee; no code-diff census.", + "related_heads": { + "1954": "027f06d32265b32085f60c20e14f127692c8acce", + "1968": "f039d4df1d2fa094771977fbe3584a9ba1149e86", + "1972": "fd82d172f46933fd253c2c6de4bd5eaff5429cfd", + "2045": "4b3fb343f3336d43db71beaf356c8cd0f2be8e46", + "2050": "a86b65e648f5b004f4aa68b3ed2c7975e8ca0163", + "2060": "3555161e4f292b49622ee05cfb3fbbb34ddfbf75" + }, + "latest_merges_inspected": [ + { + "head": "0f26ac2016777224e3c66c8ead77defbf3e526d2", + "merged_at": "2026-10-14T18:04:22Z", + "number": 1953, + "title": "Research: D10 inverse rotations retain four-call minimum" + }, + { + "head": "027f06d32265b32085f60c20e14f127692c8acce", + "merged_at": "2026-10-14T18:01:04Z", + "number": 1954, + "title": "Research: paid clean connector for distinct outputs (no new kappa)" + }, + { + "head": "f8003953e1719923f769df46c478aa0fa6d3ed9a", + "merged_at": "2026-10-14T18:01:04Z", + "number": 1956, + "title": "Audit: selected bootstrap cutoffs omit the carried constant (\u03ba unchanged)" + }, + { + "head": "6e66ea56138d21c65c0a71c7f5622b9a8b989767", + "merged_at": "2026-10-14T18:01:04Z", + "number": 1959, + "title": "Audit: mutant coverage of the selected T16 controller/owner audit (no gap found, no new kappa)" + }, + { + "head": "df468539cb55e3c90e0dc492394450b162beeb56", + "merged_at": "2026-10-14T18:01:04Z", + "number": 1960, + "title": "Bound mixed-rank diagonal blocks in selected provider" + }, + { + "head": "bcb7c7ddee555526b42638b70b01b2489bb69c24", + "merged_at": "2026-10-14T18:01:04Z", + "number": 1962, + "title": "Research: exact P112 shared-gauge decoder census" + }, + { + "head": "c9819a94f9c630f8b42ff5c3027965c4ba451653", + "merged_at": "2026-10-14T18:01:04Z", + "number": 1965, + "title": "Proof repair: bootstrap cutoffs need only a stock constant (repair (b) of #1956; \u03ba unchanged)" + }, + { + "head": "691e6eb9417384d1820de4fdc167fc3e9797b75e", + "merged_at": "2026-10-14T18:01:04Z", + "number": 1966, + "title": "Research: sharp odd-dihedral joint tariffs with dirty workspace" + }, + { + "head": "549bb87fa1106ae4cad35706bcd9b5c7cc6fd1e3", + "merged_at": "2026-10-14T18:01:04Z", + "number": 1967, + "title": "Research: Heisenberg central-pair call floor (no new kappa)" + }, + { + "head": "f039d4df1d2fa094771977fbe3584a9ba1149e86", + "merged_at": "2026-10-14T18:01:04Z", + "number": 1968, + "title": "Accumulate shared product sums before dirty-anchor fanout" + }, + { + "head": "a6e6ad3936f67b8f63b5b68c5e75d540610a65e7", + "merged_at": "2026-10-14T18:01:04Z", + "number": 1969, + "title": "Add native joint centre-query transfers on sixteen selected ports" + }, + { + "head": "9c2fdd89e553751e40ef8011716a249e8385d284", + "merged_at": "2026-10-14T18:01:04Z", + "number": 1970, + "title": "fix(research): support overlap pagination on older gh" + }, + { + "head": "165f08a694b26b0f4c521ce5e1132ede0b7362a2", + "merged_at": "2026-10-14T18:01:04Z", + "number": 1973, + "title": "Prove an all-length balance law for native source-code controllers" + }, + { + "head": "a4992da8e4e81a74cf1fd2b2d3af948662476d6e", + "merged_at": "2026-10-14T18:04:22Z", + "number": 1974, + "title": "Research: the 916 open mixed GL3 target pairs need exactly their direct cost (no new kappa)" + }, + { + "head": "ec0a05954acdbd8f3047c007b0249160d3c7274b", + "merged_at": "2026-10-14T18:01:03Z", + "number": 1975, + "title": "Research: joint late-entrance obstruction for PR589 (no new kappa)" + }, + { + "head": "ea021c002e61fea7f2f9cd1b613f65b88f7eb7e9", + "merged_at": "2026-10-14T18:01:03Z", + "number": 1977, + "title": "Research: Eisenstein E8 decoder copy floor 23 via submatrix-minrank certificates (past the clique-method limit; no \u03ba claim)" + }, + { + "head": "9ff4226c2e80b9ed45213c3ab2575ad5cf47bc94", + "merged_at": "2026-10-14T18:01:03Z", + "number": 1979, + "title": "Compose nineteen temporal gauges with exact fixed-menu optimality" + }, + { + "head": "264454acd8b94d926d42e94f3cb83ecd00a6daa9", + "merged_at": "2026-10-14T18:01:04Z", + "number": 1981, + "title": "Certify infinite-order growth of swapped source-code charts" + }, + { + "head": "b10c1a196cf5fbbdedc43c9fd26ff2e834849600", + "merged_at": "2026-10-14T18:01:03Z", + "number": 1982, + "title": "Independent verification: exact enclosure of the pivot-566+554 T74 complex root behind the top pending kappa claims (no new kappa)" + }, + { + "head": "9cb25cd2851fd4d4474abd515b63d721f5f370c7", + "merged_at": "2026-10-14T18:01:04Z", + "number": 1983, + "title": "Research: four signed-connector transfers force unit coefficients" + } + ] + }, + "original_witness_overlap": { + "searched_at": "2026-10-14T12:09:07.424591+00:00", + "coverage": { + "open_prs": { + "fetched_at": "2026-10-14T12:08:02.513795+00:00", + "complete_pagination": true, + "records": 521 + }, + "discussions": { + "fetched_at": "2026-10-14T12:09:07.332462+00:00", + "complete_pagination": true, + "records": 491 + } + }, + "local_records": 873, + "warnings": [], + "terms": [ + "bidirectional connector", + "six transfers", + "reverse-direction" + ], + "matches_total": 8, + "limits": "Remote PR scope is open PRs including drafts. Closed work is searched through local READMEs, TASK metadata and ledger only. No code diffs or arbitrary package files are searched. Recheck relevant heads before submission.", + "assessment": "Eight matches inspected: two are this local package; the remaining six are the known one-way binary family, signed 3x3 construction or unrelated cleanup fusion. No duplicate binary bidirectional six-transfer construction found; this is not a novelty guarantee.", + "main_head_rechecked": "0b1cccf86e2f5132ed286a26ef0a681a495740ea", + "pending_heads_rechecked": { + "1615": "96916897840829cc01b126f8f202a92d949d2bfc", + "1675": "a8d459974abf7ba88316c87396565f7e5fc9656f" + } + }, + "prior_expansion_overlap": { + "status": "POSSIBLE_OVERLAP_NOT_A_NOVELTY_CERTIFICATE", + "searched_at": "2026-10-14T14:12:28.737430+00:00", + "terms": [ + "palette", + "three-color", + "query tariff", + "25%", + "asymptotically optimal", + "one-root" + ], + "coverage": { + "open_prs": { + "fetched_at": "2026-10-14T14:11:09.021963+00:00", + "complete_pagination": true, + "records": 579 + }, + "discussions": { + "fetched_at": "2026-10-14T14:12:28.663755+00:00", + "complete_pagination": true, + "records": 547 + } + }, + "local_records": 873, + "warnings": [], + "limits": "Remote PR scope is open PRs including drafts. Closed work is searched through local READMEs, TASK metadata and ledger only. No code diffs or arbitrary package files are searched. Recheck relevant heads before submission.", + "matches_total": 22, + "assessment": "All 22 matches inspected: relevant signed-query work is credited; other matches concern different targets or runtime tooling. Prior three-color search also identified PR1887: related concurrent fixed-port five-source two-projection construction and 175-cover census, credited without claiming novelty for those ingredients. No matching all-size three-block/all-word 25% theorem found in this bounded search; no novelty guarantee.", + "main_head_rechecked": "0b1cccf86e2f5132ed286a26ef0a681a495740ea", + "related_1887": { + "head": "025d4fcd87f1b6ea01aa1c52721f8f46389aacce", + "scope": "Five-source fixed-port two-projection connector, ten transfers; concurrent 175-cover count credited." + } + }, + "math_review_publication": { + "authorization": "User requested a Math PR and explicitly authorized pushing its branch in the attached PR instructions. CrocSwap submission remains pending separate approval.", + "base_head": "c520b397ed4e91f3fdbbee1f8973b3889fbedaa1", + "related_existing_package": "integer-mult-bounds/research/scalable-dirty-connectors, merged Math PR2. F2 n-3-root/fewer-transfer family is preferable where its source ports are admitted; no priority or dominance over that archive is claimed. This cache additionally gives signed characteristic-zero and fixed-z0 operator queries." + }, + "review_response": { + "reviewed_math_commit": "623039e", + "review_basis": "User-supplied independent agent review of all PR9 commits, with local-only scratch at .context/review-pr9. No independent human or formal-kernel review claimed.", + "upstream_checkpoint": { + "commit": "0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2", + "priority_revision": 4, + "original_pins": "Retained scientific baseline and selection provenance, not rewritten.", + "changed_original_pins": [ + "docs/research/agent-task-catalog.json" + ], + "mathematical_inputs_unchanged": true, + "merged_related_prs": { + "1887": { + "head": "025d4fcd87f1b6ea01aa1c52721f8f46389aacce", + "merged_at": "2026-10-14T16:57:12Z", + "merge_commit": "6aff82d6d346fb2238d061ef45066b82d48a9b67" + }, + "1915": { + "head": "d30d64fea909219c364b11c2452f2207326e2b1f", + "merged_at": "2026-10-14T17:06:51Z", + "merge_commit": "178a293edbd162fe3ce13e81a97af921366bd100" + } + }, + "connector_frame_73_exclusion": { + "commit": "0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2", + "path": "research/connector-frame-73-exclusion/README.md", + "sha256": "ec3cf13bb97839832e5416f437b6a8dfd622468a1864bbb5552f17f0c43a1bcf", + "credit": "Arham Garg; closes Adam Gall PR1915 single-connector 73-map question." + } + }, + "changes": [ + "Center README on all-word lower bounds and signed triangle; shorten957lines to539, preserving proofs and reproducibility.", + "Credit Math PR1 for six-transfer witness/census/comparison; claim only73-call extension. Credit Math PR2 for all-n two-call obstruction; retain census as independent cross-check.", + "Credit PR1812 bidirectional question, Adam Gall PR1915 and Arham Garg connector-frame-73-exclusion.", + "Refresh merged PR1615/1887/1915 status and byte-check1615 against current main; retain scientific baseline pins.", + "Check all23 benchmark function segments in test_families and reject source drift in a temporary copied package.", + "Correct n18 comparator-family tariff percentage to17.06%.", + "Retain reviewer14-read/6-transfer counterexample beside compiler14-read/10-transfer output; check generic endpoints, physical ports and missing-transfer failure.", + "State32/50 bills are not certified minima across read decompositions. The toy counterexample does not prove better n9/n12 words.", + "Explain benchmark dense-B/identity-A width scaling, F2 dispatch cost, signed width cap and lack of performance evidence outside that regime.", + "Raise only walk replay deadline60to120seconds for hosted CI headroom; no search truncation/concurrency change." + ], + "algorithm_changes": "No construction, compiler, lower-bound algorithm, native census or measured benchmark kernel changed. Primary verifier only follows renamed merged-reference metadata.", + "verification_gaps": [ + "Hosted CI and physical caller/supplier/stock/precision/tape admission remain unrun.", + "73-call native exclusion has one implementation; prior complete native replay reused because its source/inputs are unchanged.", + "No new benchmark timing run; recorded outcomes and reviewer rerun kept distinct." + ], + "publication": "Review fixes local-only until separately authorized; CrocSwap submission remains pending approval.", + "validation": { + "command": "python3.12 -B scripts/research_package.py --package research/bidirectional-connector", + "python": "3.12.11", + "upstream_commit": "0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2", + "exit_code": 0, + "seconds": 33.312, + "package_unchanged": true, + "output": "CHECK Exact generic free-linear endpoint/inverse, per-port paid invoice, source-bound eight-transfer comparator and every single-instruction omission\nPASS_BIDIRECTIONAL_CONNECTOR masks=31 AB_calls=72 transfers=6 root_calls=78 predecessor_transfers=8 omission_controls=158 no_new_kappa\nCHECK Separate dense F2 implementation, all dirty basis columns/mixed states, singular and noncommuting maps, inverse and omission controls\nPASS_INDEPENDENT_BIDIRECTIONAL cases=2700 directions=2 widths=1,2,3,5 omission_controls=158 no_new_kappa\nPASS_INDEPENDENT_PALETTE sources=6 cases=2439 directions=2 omissions=177\nCHECK Generic F2 families n3..12, exact tariffs/locality, RAM controls, eleven family and six original regression groups; complete signed-frame BFS and literal MITM, all384 cases, exact restricted transfer floor; all23 recorded benchmark function hashes and altered-source rejection\nPASS_SIGNED_TRIANGLE_FRAMES cases=384 pairs=144 boundary_min=7 two_engines=checked\nPASS_PAID_PALETTE_FAMILY generic_n=3..12 exact_tariffs=4 global_bounds=6 tests=11+6 benchmark_pins=23 drift_control=checked frame_cases=384 signed_triangle=checked locality_bounds=6 no_new_kappa\nCHECK Two full independent Python incidence engines on n5/n6 and source-bound native cost receipt; explicitly NOT a fresh native replay\nPASS_COST_CENSUSES native_replay=NOT_RUN_receipt_bound_only ideal_two_engines=5,6 elapsed=1.070s\nCHECK Signed one-visit triangle n3..12, exact invoice/prefix height and literal inverses, separate integer-matrix replay and omission/sign controls\nPASS_SIGNED_PALETTE generic_n=3..12 signed_one_root=1..12 integer_dense=182 inverse=checked omissions=31 no_new_kappa\nCHECK F2 n9/n12 source-floor constructions, exact min-read/all-placement DP, separate dense replay, omissions, 114-candidate sweep, complete n5/n6 dependency censuses and ten regressions; n9 restricted optimum gap below 3%; literal counterexample to transfer optimality across minimum-read decompositions\nPASS_CHARGED_SOURCE_WALKS n=9,12 generic=inverse_checked independent_dense=3216 omissions=1454 tests=10 sweep=114 decomposition_counterexample=checked source_count_gap_lt_3percent=checked no_new_kappa\nCHECK Paid n+1 dirty parent cache, fixed physical child port; generic integer identities/prefixes n1..12, separate integer/F2 dense basis and inverses, all small omissions, Hamiltonian paths and invalid transfer controls\nPASS_PAID_DIRTY_CACHE generic_n=1..12 paths=683 integer_F2_dense=1272 inverse=checked omissions=50 roots=n+1 no_new_kappa\nCHECK Source-bound extraction of a retained centre interface in selected manifest; not a census of dispatched providers or full native/owner/cold replay\nPASS_RETAINED_CENTRE_CONTRACT_SCREEN centres=8 targets=112 signed_patterns=24 graph=2K4 full_native=NOT_RUN no_new_kappa\nPASS_REGISTERED_RESEARCH_PACKAGE research/bidirectional-connector outcome=completed\n...........\n----------------------------------------------------------------------\nRan 11 tests in 0.375s\n\nOK\n......\n----------------------------------------------------------------------\nRan 6 tests in 0.365s\n\nOK\n..........\n----------------------------------------------------------------------\nRan 10 tests in 0.136s\n\nOK\n", + "regression_groups": 27, + "benchmark_kernel_function_pins": 23, + "selected_record_check": "PASS exact kappa 836330098538459/500000000000000000, original source inventory and proof supplement unchanged.", + "diff_check": "PASS", + "readme_lines": 539 + } + }, + "draft_submission": { + "status": "user_approved_upstream_submission", + "target_repository": "CrocSwap/integer-mult-bounds", + "target_branch": "main", + "base_commit": "0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2", + "checked_at": "2026-10-14T23:50:02.543862+00:00", + "scientific_archive": "https://github.com/conorholds/math/pull/9", + "review_corrections_archive": "https://github.com/conorholds/math/pull/11", + "distinction": "All-word query bounds and the signed triangle are primary. PR2065 six-transfer result and PR2182 fixed-port/two-call boundaries are credited supporting baselines, not new claims.", + "validation": { + "registered_python": "3.12.11", + "registered_commands": 8, + "regression_groups": 27, + "exit_code": 0, + "elapsed_seconds": 32.944, + "reuse_basis": "All 35 scientific source, receipt and verifier files, including retained reference fixtures, are byte-identical to the tested Math archive; canonical upstream remains 0fdd7d82. Only README and TASK publication metadata differ.", + "fresh_native_assignments": 71856432, + "fresh_native_elapsed_seconds": 11.585 + }, + "not_run": [ + "Hosted CI", + "Independent second native implementation of the 73-call exclusion", + "Physical caller, tape, stock/precision and supplier admission" + ], + "live_overlap": { + "searched_at": "2026-10-14T23:53:01.037642+00:00", + "coverage": { + "open_prs": { + "fetched_at": "2026-10-14T23:47:04.342393+00:00", + "complete_pagination": true, + "records": 445 + }, + "discussions": { + "fetched_at": "2026-10-14T23:53:00.255598+00:00", + "complete_pagination": true, + "records": 896 + } + }, + "local_records": 1538, + "warnings": [], + "reviewed_heads": { + "2201": "21fee7f7fb9ed42298ee998dbc120e684ca7fb71", + "2182": "dc252de1cc594829c3031abdb4de104713bc474a", + "2128": "697369a971eed02c0fbcd75ebefec9f59945f08e", + "2156": "05b4672fa4450ef50b06315e3a0893d4ba43d42d", + "2146": "302b0e87d9328fabc2a670248afb357bbb44041b", + "2134": "388a63c83cf24c3355be9798bde5a381188dadb3", + "2065": "2721b1e31d718a6e70266a99521f629ce2e1d259", + "2063": "4caa7660fa4a31c4cfeaf177fabc3b56549dd065" + }, + "distinction": "No exact overlap found for the all-word priced bounds or signed zero-sum triangle in the inspected records; not a novelty certificate. PR2065 and PR2182 supply credited endpoint/two-call baselines; DUO/TRIO papers change the source alphabet; common-A broadcast changes output-map sharing." + } + }, + "upstream_submission": { + "approval": "User explicitly instructed: go ahead and do the PR process upstream now; follow their guidelines and use the approved draft.", + "repository": "CrocSwap/integer-mult-bounds", + "pull_request": 2208, + "reuse_existing_pr": "Reopen the existing closed PR to avoid a duplicate contribution.", + "approved_title": "Research: all-word dirty-connector bounds and signed triangle (no new \u03ba)", + "approved_body_sha256": "e727a3747cc71dca5198c05c826fb9cb5db8678dd5769044654639c35faaebc4", + "base_commit": "0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2", + "latest_overlap_refresh": { + "checked_at": "2026-10-15T01:03:16.293608+00:00", + "previous_discussion_snapshot": "2026-10-14T23:58:06.140108+00:00", + "updated_discussions": [ + 1163, + 1166, + 1167, + 1587, + 2179, + 2205, + 2209, + 2211, + 2218, + 2221, + 2223 + ], + "coverage": { + "open_prs": { + "records": 465, + "fetched_at": "2026-10-15T01:03:08.511203+00:00", + "complete_pagination": true + }, + "discussions": { + "records": 924, + "fetched_at": "2026-10-15T01:03:16.257821+00:00", + "complete_pagination": true + } + }, + "limits": "Complete prior snapshot plus full reload of every discussion updated since prior fetch; deleted untouched threads are not independently re-enumerated.", + "primary_term_matches": [ + { + "kind": "discussion-comment", + "number": 1317, + "title": "Binary affine addresses: exact paid-call floor with arbitrary dirty registers", + "hits": [ + "all-word" + ], + "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1317#discussioncomment-18912673" + }, + { + "kind": "discussion-comment", + "number": 1929, + "title": "Round 2: ten independently seeded parallel research instances", + "hits": [ + "all-word" + ], + "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1929#discussioncomment-18925900" + } + ], + "reviewed_heads": { + "2227": "514f75b9f311438aaef07cd577a39cd330cf4330", + "2201": "21fee7f7fb9ed42298ee998dbc120e684ca7fb71", + "2182": "dc252de1cc594829c3031abdb4de104713bc474a", + "2128": "697369a971eed02c0fbcd75ebefec9f59945f08e", + "2156": "05b4672fa4450ef50b06315e3a0893d4ba43d42d", + "2146": "302b0e87d9328fabc2a670248afb357bbb44041b", + "2134": "388a63c83cf24c3355be9798bde5a381188dadb3", + "2065": "2721b1e31d718a6e70266a99521f629ce2e1d259", + "2063": "4caa7660fa4a31c4cfeaf177fabc3b56549dd065" + }, + "additional_reviewed_heads": { + "2229": "b4eab83755969d406edba9f25b7890e4db4c4931", + "2230": "daae61425c07268ecfe220f7996415105c466ef1" + }, + "additional_distinctions": { + "2229": "Seven-source sparse-mask census at exactly fourteen toggles, rather than all nonzero masks and all-word priced bounds.", + "2230": "Packets heterogeneous output events while retaining both paid child calls; no reduction of the counted A/B child evaluations." + } + }, + "verification_reuse": "Scientific files and reference fixtures are byte-identical to the previously passing Math archive; only README and TASK publication metadata changed.", + "not_authorized": [ + "Merge", + "Unrelated PR changes", + "Discussion posts or other messages" + ] + } +} diff --git a/research/bidirectional-connector/VERIFY.json b/research/bidirectional-connector/VERIFY.json new file mode 100644 index 0000000000..7bc05e17a0 --- /dev/null +++ b/research/bidirectional-connector/VERIFY.json @@ -0,0 +1,93 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [ + "research/two-connector-transfer-boundary/README.md", + "research/universal-connector-boundary/CERTIFICATE.json", + "research/universal-connector-six-source/README.md", + "research/universal-connector-six-source/EXPECTED.json", + "research/community-frontier1094-audit/SELECTED-SOURCE.json", + "research/gauge44-slots-t16/evidence/local/CANONICAL-WORD.json.gz", + "research/gauge44-slots-t16/evidence/local/LOCAL-PROGRAMS.json.gz" + ], + "commands": [ + { + "argv": [ + "{python}", + "-I", + "-O", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 30, + "checks": "Exact generic free-linear endpoint/inverse, per-port paid invoice, source-bound eight-transfer comparator and every single-instruction omission" + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-B", + "{package}/independent_check.py" + ], + "timeout_seconds": 30, + "checks": "Separate dense F2 implementation, all dirty basis columns/mixed states, singular and noncommuting maps, inverse and omission controls" + }, + { + "argv": [ + "{python}", + "-B", + "{package}/verify_families.py" + ], + "timeout_seconds": 60, + "checks": "Generic F2 families n3..12, exact tariffs/locality, RAM controls, eleven family and six original regression groups; complete signed-frame BFS and literal MITM, all384 cases, exact restricted transfer floor; all23 recorded benchmark function hashes and altered-source rejection" + }, + { + "argv": [ + "{python}", + "-B", + "{package}/certify_cost.py" + ], + "timeout_seconds": 60, + "checks": "Two full independent Python incidence engines on n5/n6 and source-bound native cost receipt; explicitly NOT a fresh native replay" + }, + { + "argv": [ + "{python}", + "-B", + "{package}/verify_signed.py" + ], + "timeout_seconds": 60, + "checks": "Signed one-visit triangle n3..12, exact invoice/prefix height and literal inverses, separate integer-matrix replay and omission/sign controls" + }, + { + "argv": [ + "{python}", + "-B", + "{package}/verify_walk.py" + ], + "timeout_seconds": 120, + "checks": "F2 n9/n12 source-floor constructions, exact min-read/all-placement DP, separate dense replay, omissions, 114-candidate sweep, complete n5/n6 dependency censuses and ten regressions; n9 restricted optimum gap below 3%; literal counterexample to transfer optimality across minimum-read decompositions" + }, + { + "argv": [ + "{python}", + "-B", + "{package}/verify_cache.py" + ], + "timeout_seconds": 60, + "checks": "Paid n+1 dirty parent cache, fixed physical child port; generic integer identities/prefixes n1..12, separate integer/F2 dense basis and inverses, all small omissions, Hamiltonian paths and invalid transfer controls" + }, + { + "argv": [ + "{python}", + "-B", + "{package}/screen_caller.py" + ], + "timeout_seconds": 30, + "checks": "Source-bound extraction of a retained centre interface in selected manifest; not a census of dispatched providers or full native/owner/cold replay" + } + ] +} diff --git a/research/bidirectional-connector/WALK-BOUND.json b/research/bidirectional-connector/WALK-BOUND.json new file mode 100644 index 0000000000..3f81b467c4 --- /dev/null +++ b/research/bidirectional-connector/WALK-BOUND.json @@ -0,0 +1,329 @@ +{ + "schema": "minimum-source-bound-v1", + "difference_censuses": [ + { + "sources": 5, + "complete_words": 945, + "max_nonzero_differences": 30 + }, + { + "sources": 6, + "complete_words": 10395, + "max_nonzero_differences": 48 + } + ], + "records": [ + { + "sources": 9, + "readout_lower": 1369, + "query_lower_bound": 2251, + "cases": [ + { + "color_sizes": [ + 1, + 1, + 7 + ], + "paired_capacity_upper": 218, + "missing_two_or_three_reads_lower": 172, + "readout_lower": 1487 + }, + { + "color_sizes": [ + 1, + 2, + 6 + ], + "paired_capacity_upper": 194, + "missing_two_or_three_reads_lower": 120, + "readout_lower": 1459 + }, + { + "color_sizes": [ + 1, + 3, + 5 + ], + "paired_capacity_upper": 166, + "missing_two_or_three_reads_lower": 16, + "readout_lower": 1383 + }, + { + "color_sizes": [ + 1, + 4, + 4 + ], + "paired_capacity_upper": 163, + "missing_two_or_three_reads_lower": 0, + "readout_lower": 1370 + }, + { + "color_sizes": [ + 1, + 8 + ], + "paired_capacity_upper": 248, + "missing_two_or_three_reads_lower": 286, + "readout_lower": 1571 + }, + { + "color_sizes": [ + 2, + 2, + 5 + ], + "paired_capacity_upper": 174, + "missing_two_or_three_reads_lower": 16, + "readout_lower": 1375 + }, + { + "color_sizes": [ + 2, + 3, + 4 + ], + "paired_capacity_upper": 153, + "missing_two_or_three_reads_lower": 0, + "readout_lower": 1380 + }, + { + "color_sizes": [ + 2, + 7 + ], + "paired_capacity_upper": 222, + "missing_two_or_three_reads_lower": 172, + "readout_lower": 1483 + }, + { + "color_sizes": [ + 3, + 3, + 3 + ], + "paired_capacity_upper": 135, + "missing_two_or_three_reads_lower": 0, + "readout_lower": 1398 + }, + { + "color_sizes": [ + 3, + 6 + ], + "paired_capacity_upper": 190, + "missing_two_or_three_reads_lower": 120, + "readout_lower": 1463 + }, + { + "color_sizes": [ + 4, + 5 + ], + "paired_capacity_upper": 180, + "missing_two_or_three_reads_lower": 16, + "readout_lower": 1369 + }, + { + "color_sizes": [ + 9 + ], + "paired_capacity_upper": 144, + "missing_two_or_three_reads_lower": 367, + "readout_lower": 1756 + } + ], + "scope": "F2, all nonzero masks, exactly two B calls per active source; 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Not extra-B or subset programs." + } + ] +} diff --git a/research/bidirectional-connector/WALK-SWEEP.json b/research/bidirectional-connector/WALK-SWEEP.json new file mode 100644 index 0000000000..a757a215c5 --- /dev/null +++ b/research/bidirectional-connector/WALK-SWEEP.json @@ -0,0 +1,4280 @@ +{ + "schema": "walk-partition-proposal-sweep-v1", + "not_global_optimality": true, + "records": [ + { + "sources": 9, + "class_sizes": [ + 1, + 1, + 7 + ], + "source_word": [ + 2, + 0, + 3, + 4, + 5, + 3, + 1, + 8, + 7, + 5, + 8, + 0, + 6, + 4, + 1, + 2, + 7, + 6 + ], + "proposals": 200000, + "seed": 4106, + "orientations": [ + { + "colors": [ + 1, + 2, + 3, + 3, + 3, + 3, + 3, + 3, + 3 + ], + "counts": { + "sources": 9, + "target_outputs": 511, + "source_calls": 18, + "readout_calls": 1588, + "readout_multiplicity_histogram": { + "2": 173, + "3": 110, + "4": 228 + }, + "transfers": 28, + "dirty_root_rows": 2, + "frame_dp_peak_states": 16 + }, + "query_cost": 2498, + "word_sha256": 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Apache-2.0; conorholds with Codex assistance. +""" +import argparse +import json +from pathlib import Path +import random +from statistics import median +from time import perf_counter + +import families + + +def run_inplace(word, data, maps, n, roots): + root_base = n + (1 << n) - 1 + private = root_base + roots + scratch = data[private] + incoming_scratch = scratch + for op in word: + if op[0] == "A": + data[n + op[1] - 1] ^= data[root_base + op[2]] + elif op[0] == "C": + data[root_base + op[1]] ^= data[root_base + 1 - op[1]] + elif op[0] == "B": + j, port = op[1:] + source = data[j] + value = data[root_base + port] + for coordinate, coefficients in enumerate(maps[j]): + # A dirty scalar echo. Both coefficient/source traversals are executed. + value ^= scratch << coordinate + scratch ^= (coefficients & source).bit_count() & 1 + value ^= scratch << coordinate + scratch ^= (coefficients & source).bit_count() & 1 + data[root_base + port] = value + else: + raise ValueError("unknown RAM instruction") + if scratch != incoming_scratch: + raise ValueError("private scalar was not restored") + data[private] = scratch + + +def incoming_data(n, width, roots, rng): + return [rng.getrandbits(width) for _ in range(n + (1 << n) - 1 + roots)] + [rng.randrange(2)] + + +def expected(data, maps, n, roots): + out = list(data) + images = [sum(((row & data[j]).bit_count() & 1) << i for i, row in enumerate(matrix)) + for j, matrix in enumerate(maps)] + # This direct evaluator is outside timing; neither benchmark caches these images. + sums = [0] * (1 << n) + for mask in range(1, 1 << n): + bit = mask & -mask + sums[mask] = sums[mask ^ bit] ^ images[bit.bit_length() - 1] + out[n + mask - 1] ^= sums[mask] + return out + + +def measure_frontier(n, width, rounds=9): + """Screen every count-Pareto reference, then compare the best three afresh.""" + if not (3 <= n <= 18 and 1 <= width <= 4096 and rounds >= 3): + raise ValueError("n=3..18, width=1..4096 and rounds>=3 required") + rng = random.Random(20261014 + n * 1009 + width) + maps = [[rng.getrandbits(width) for _ in range(width)] for _ in range(n)] + data2 = incoming_data(n, width, 2, rng) + data1 = data2[:-2] + [data2[-1]] + sizes = families.balanced_three(n) + candidate = families.construct_palette(sizes) + candidate_want = expected(data2, maps, n, 2) + check = list(data2); run_inplace(candidate, check, maps, n, 2) + if check != candidate_want: + raise ValueError("palette benchmark endpoint") + screen = [] + for partition in families.single_frontier(n): + word = families.construct(partition) + check = list(data1); run_inplace(word, check, maps, n, 1) + if check != expected(data1, maps, n, 1): + raise ValueError("reference benchmark endpoint") + timings = [] + for _ in range(3): + start = perf_counter(); values = list(data1); run_inplace(word, values, maps, n, 1) + timings.append(perf_counter() - start) + screen.append({"blocks": list(partition), "counts": families.screen(partition), + "seconds": timings, "median_seconds": median(timings)}) + finalists = sorted(screen, key=lambda row: row["median_seconds"])[:3] + results = [] + for finalist in finalists: + reference = families.construct(finalist["blocks"]) + trials = [[], []] + for r in range(rounds): + for index in ((0, 1) if r % 2 == 0 else (1, 0)): + word, data, roots = (reference, data1, 1) if index == 0 else (candidate, data2, 2) + start = perf_counter(); values = list(data); run_inplace(word, values, maps, n, roots) + trials[index].append(perf_counter() - start) + results.append({"reference_blocks": finalist["blocks"], "reference_seconds": trials[0], + "palette_seconds": trials[1], "reference_median": median(trials[0]), + "palette_median": median(trials[1]), "speedup": median(trials[0]) / median(trials[1])}) + best = min(results, key=lambda row: row["reference_median"]) + return {"sources": n, "width": width, "rounds": rounds, "candidate_counts": families.palette_screen(sizes), + "reference_family": "Every count-Pareto one-root Gray-block partition, three screening trials; three fastest references receive fresh alternating comparisons. Not unrestricted synthesis.", + "reference_screen": screen, "finalists": results, "best_reference": best, + "speedup": best["speedup"], "fraction_time_saved": 1 - 1 / best["speedup"], + "timing_scope": "RAM batch with dense B, identity A, no persistent map-image cache, exact dirty scalar restoration. Input copying included; shared coefficient and program preparation excluded. Extra root and Python arithmetic temporaries are explicit; no native tape, supplier or multiplication-runtime claim."} + + +def run_signed_inplace(word, data, maps, n, roots): + """Integer RAM child with two coefficient traversals and arbitrary dirty work.""" + base = n + (1 << n) - 1 + scratch = data[-1] + old_scratch = scratch + for op in word: + sign = op[-1] + if op[0] == "B": + source = data[op[1]] + target = data[base + op[2]] + for coordinate, row in enumerate(maps[op[1]]): + target[coordinate] -= sign * scratch + for coefficient, value in zip(row, source): + scratch += coefficient * value + target[coordinate] += sign * scratch + for coefficient, value in zip(row, source): + scratch -= coefficient * value + else: + if op[0] == "A": + source = data[base + op[2]] + target = data[n + op[1] - 1] + elif op[0] == "C": + source = data[base + 1 - op[1]] + target = data[base + op[1]] + else: + raise ValueError("unknown signed RAM instruction") + for coordinate, value in enumerate(source): + target[coordinate] += sign * value + if scratch != old_scratch: + raise ValueError("signed private work was not restored") + data[-1] = scratch + + +def expected_signed(data, maps, n): + out = [list(row) for row in data[:-1]] + [data[-1]] + images = [[sum(coefficient * value for coefficient, value in zip(row, data[j])) + for row in matrix] for j, matrix in enumerate(maps)] + sums = [[0] * len(data[0]) for _ in range(1 << n)] + for mask in range(1, 1 << n): + bit = mask & -mask + sums[mask] = [a+b for a,b in zip(sums[mask ^ bit], images[bit.bit_length()-1])] + out[n+mask-1] = [a+b for a,b in zip(out[n+mask-1], sums[mask])] + return out + + +def measure_signed_frontier(n, width, rounds=9): + if not (3 <= n <= 15 and 1 <= width <= 128 and rounds >= 3): + raise ValueError("signed benchmark requires n=3..15, width=1..128, rounds>=3") + rng = random.Random(20261014 + n*1009 + width) + maps = [[[rng.randrange(-2,3) for _ in range(width)] for _ in range(width)] for _ in range(n)] + data2 = [[rng.randrange(-3,4) for _ in range(width)] for _ in range(n+(1<0, 'positive source count required') + m=(1<=0 for j in coordinates) + and len(set(coordinates))==len(coordinates), 'invalid cube coordinates') + f.require(type(a) is int and type(b) is int and a>=0 and b>=0, 'invalid path vertices') + mask=sum(1<0 and a>0 and t>=0, 'invalid fixed call tariff') + floor=2*n*b+2*((1< +#include +#include +#include +#include +#include +#include +#include +using Word = std::vector; +struct Result { uint64_t words=0,placements=0,assignments=0,universal=0,three_readout=0; std::array hist{}; }; +int parity(int x) {return __builtin_popcount(unsigned(x))&1;} +int mv(const std::array& g,int v){return parity(g[0]&v)|(parity(g[1]&v)<<1);} +int bitfirst(uint32_t x){return __builtin_ctz(x);} +uint32_t differences(uint32_t points){uint32_t out=0;for(uint32_t a=points;a;a&=a-1)for(uint32_t b=points;b;b&=b-1)out|=uint32_t(1)<<(bitfirst(a)^bitfirst(b));return out;} +bool three(const std::array& present,int missing) { + for(uint32_t a=present[1];a;a&=a-1)for(uint32_t b=present[2];b;b&=b-1) + if(present[3]&(uint32_t(1)<<(missing^bitfirst(a)^bitfirst(b))))return true; + return false; +} +void controls() { + const int ops[16][3]={{0,0,1},{1,0,0},{0,1,1},{1,1,0},{0,2,0},{1,0,0},{0,0,0},{0,3,0},{1,1,0},{0,1,0},{1,0,0},{0,4,1},{1,1,0},{0,3,1},{0,2,1},{0,4,1}}; + int roots[2]={32,64};std::array present{};present[1]=present[2]=1; + for(const auto& op:ops){if(op[0])roots[op[1]]^=roots[1-op[1]];else roots[op[2]]^=1<>5]|=uint32_t(1)<<(roots[p]&31);} + if(roots[0]!=32||roots[1]!=64||__builtin_popcount(differences(present[1])|differences(present[2])|differences(present[3]))!=32)std::abort(); + present={0,1,1,uint32_t(1)<<7};if(!three(present,7))std::abort();present[3]=0;if(three(present,7))std::abort(); +} +Result census(int t,bool triple) { + Result r; int length=10+int(triple); Word source,counts(5),directions; + std::vector ds; + for(int bits=0;bits<(1< g{1,2};Word d;for(int i=0;i>i)&1;d.push_back(p);g[p]^=g[1-p];}if(g==std::array{1,2})ds.push_back(d);} + std::function source_rec; + source_rec=[&](int opened){ + if(int(source.size())==length){ + if(triple ? counts[0]!=3 : opened!=5)return; + ++r.words; + for(const auto& dirs:ds){ + Word skeleton; std::array g{1,2}; std::vector> frames; + std::function merge; + merge=[&](int bi,int ci){ + if(bi==length && ci==t){ + ++r.placements; + std::array,5> options; + for(int j=0;j<5;++j){ + Word at;for(int i=0;i>i)&1;int normalized=0;for(int v=1;v<=3;++v)if(mv(frames[at[i]],v)==(1< assign; + assign=[&](int j,uint16_t port_bits){ + if(j<5){for(auto option:options[j])assign(j+1,port_bits|option);return;} + ++r.assignments;std::array present{};int roots[2]={32,64};present[1]=present[2]=1;int index=0; + for(int op:skeleton){if(op<0){int p=-op-1;roots[p]^=roots[1-p];}else{int p=(port_bits>>index)&1;roots[p]^=1<>5]|=uint32_t(1)<<(roots[p]&31);} + if(roots[0]!=32||roots[1]!=64)std::abort(); + uint32_t cover=differences(present[1])|differences(present[2])|differences(present[3]);int size=__builtin_popcount(cover);++r.hist[size];if(size==32)++r.universal; + if(!triple && t==2 && size==31){int missing=bitfirst(~cover); + if(three(present,missing))++r.three_readout; + } + }; + assign(0,0);return; + } + if(bi4){std::cerr<<"domain 0<=t<=4\n";return 2;}controls();auto begin=std::chrono::steady_clock::now();auto r=census(t,triple); + std::cout<<"{\"transfers\":"<(std::chrono::steady_clock::now()-begin).count()<<"}\n"; +} diff --git a/research/bidirectional-connector/certify_cost.py b/research/bidirectional-connector/certify_cost.py new file mode 100644 index 0000000000..d3369a74b2 --- /dev/null +++ b/research/bidirectional-connector/certify_cost.py @@ -0,0 +1,165 @@ +#!/usr/bin/env python3 +"""Full native cost exclusions and independent Python all-transfer incidence bound. + +Native receipt binding alone is explicitly not a fresh native exclusion replay. +conorholds with substantial Codex assistance. Apache-2.0. +""" +import argparse +from collections import Counter +from hashlib import sha256 +import json +from math import comb, factorial +from pathlib import Path +import subprocess +import tempfile +from time import monotonic + +HERE = Path(__file__).resolve().parent + + +def require(ok, message): + if not ok: + raise ValueError(message) + + +def pair_words(n): + count = [0] * n; word = [] + def visit(opened): + if len(word) == 2 * n: + yield tuple(word); return + for label in range(min(opened + 1, n)): + if count[label] < 2: + count[label] += 1; word.append(label) + yield from visit(max(opened, label + 1)) + word.pop(); count[label] -= 1 + yield from visit(0) + + +def difference_set(word): + prefix = 0; points = {0} + for label in word: + prefix ^= 1 << label; points.add(prefix) + return {a ^ b for a in points for b in points} + + +def matching_words(n): + """Separate least-unmatched perfect-matching enumeration.""" + word = [-1] * (2 * n) + def visit(label): + if label == n: + yield tuple(word); return + first = word.index(-1) + for second in range(first + 1, 2 * n): + if word[second] == -1: + word[first] = word[second] = label + yield from visit(label + 1) + word[first] = word[second] = -1 + yield from visit(0) + + +def walsh_cover(word, n): + size = 1 << n; a = [0] * size; prefix = 0; a[0] = 1 + for label in word: + prefix ^= 1 << label; a[prefix] = 1 + def transform(a): + step = 1 + while step < len(a): + for start in range(0, len(a), 2 * step): + for j in range(start, start + step): + x, y = a[j], a[j + step]; a[j], a[j + step] = x + y, x - y + step *= 2 + transform(a); a = [x * x for x in a]; transform(a) + require(all(x >= 0 and x % size == 0 for x in a), "invalid exact autocorrelation") + return {i for i, x in enumerate(a) if x > 0} + + +def ideal_census(n): + # All three normalized directions cannot cover a mask meeting every color. + # Two colors see D(w), its projection on one color, and the complementary projection. + primary = {word: difference_set(word) for word in pair_words(n)} + independent = {word: walsh_cover(word, n) for word in matching_words(n)} + require(primary == independent, "set/matching/Walsh census disagreement") + require(len(primary) == factorial(2*n) // (2**n * factorial(n)), "incomplete source pairings") + full = (1 << n) - 1; histogram = Counter(); universal = 0 + for word, differences in primary.items(): + for group in range(1, full): + if not group & 1: + continue # unordered complementary color classes + other = full ^ group + cover = differences | {mask & group for mask in differences} | {mask & other for mask in differences} + histogram[len(cover)] += 1 + universal += int(len(cover) == (1 << n)) + return {"sources": n, "words": len(primary), "partitions": sum(histogram.values()), + "max_coverage": max(histogram), "universal": universal, + "histogram": {str(k): histogram[k] for k in sorted(histogram)}} + + +def native_core(row): + return {k: row[k] for k in ("transfers", "triple", "words", "placements", "assignments", "universal", "three_readout", "histogram", "controls")} + + +def check_native_domains(rows): + require([(r["transfers"], r["triple"]) for r in rows] == [(4, False), (2, False), (2, True)], "native domain missing") + for row in rows: + expected_words = 17325 if row["triple"] else 945 + length = 11 if row["triple"] else 10 + direction_words = 6 if row["transfers"] == 4 else 2 + require(row["words"] == expected_words, "canonical source domain mismatch") + require(row["placements"] == expected_words * direction_words * comb(length + row["transfers"], row["transfers"]), "incomplete interleavings") + require(sum(row["histogram"]) == row["assignments"] and row["histogram"][32] == 0, + "native histogram or exhaustive exclusion mismatch") + require(row["universal"] == row["three_readout"] == 0 and row["controls"] == 3, "exclusion or positive/failure controls failed") + + +def native_replay(compiler, sdk): + with tempfile.TemporaryDirectory(prefix="connector-census-") as temp: + binary = str(Path(temp) / "census") + argv = [compiler, "-std=c++17", "-O3", "-Wall", "-Wextra", "-pedantic"] + if sdk: + require(sdk.is_dir(), "missing explicitly supplied SDK") + argv += ["-isysroot", str(sdk)] + argv += [str(HERE / "census.cpp"), "-o", binary] + subprocess.run(argv, check=True, timeout=120) + rows = [] + for transfers, triple in ((4, 0), (2, 0), (2, 1)): + result = subprocess.run([binary, str(transfers), str(triple)], capture_output=True, + text=True, check=True, timeout=300) + row = json.loads(result.stdout); rows.append(row) + print(f"NATIVE t={transfers} triple={triple} assignments={row['assignments']} " + f"elapsed={row['elapsed_seconds']:.3f}s", flush=True) + check_native_domains(rows) + return rows + + +def main(): + p = argparse.ArgumentParser() + p.add_argument("--full", action="store_true") + p.add_argument("--write-receipt", action="store_true") + p.add_argument("--compiler", default="c++") + p.add_argument("--sdk", type=Path) + args = p.parse_args() + require(not args.write_receipt or args.full, "receipt regeneration requires full native replay") + path = HERE / "COST-RECEIPT.json" + old = json.loads(path.read_text()) if path.exists() else None + start = monotonic() + ideals = [ideal_census(n) for n in (5, 6)] + require(ideals[0]["max_coverage"] == 32 and ideals[0]["universal"] == 175, "five-source positive control") + require(ideals[1]["max_coverage"] == 59 and ideals[1]["universal"] == 0, "six-source optimistic exclusion") + digest = sha256((HERE / "census.cpp").read_bytes()).hexdigest() + if args.full: + rows = native_replay(args.compiler, args.sdk) + else: + require(old is not None and old["native_source_sha256"] == digest, "unbound native source/receipt") + rows = old["native"]; check_native_domains(rows) + result = {"schema": "connector-cost-v1", "native_source_sha256": digest, + "native": [native_core(row) for row in rows], "ideal": ideals} + if args.write_receipt: + path.write_text(json.dumps(result, indent=2) + "\n") + else: + require(old == result, "proof receipt differs; regenerate only with a full replay") + print(f"PASS_COST_CENSUSES native_replay={'fresh' if args.full else 'NOT_RUN_receipt_bound_only'} " + f"ideal_two_engines=5,6 elapsed={monotonic()-start:.3f}s") + + +if __name__ == "__main__": + main() diff --git a/research/bidirectional-connector/certify_frames.py b/research/bidirectional-connector/certify_frames.py new file mode 100644 index 0000000000..5d5aae5acb --- /dev/null +++ b/research/bidirectional-connector/certify_frames.py @@ -0,0 +1,147 @@ +#!/usr/bin/env python3 +"""Exact shortest unit-shear paths in SL(2,Z), with a separate meet-in-middle. + +The optimality claim fixes the signed triangle and exactly one dirt-signature +switch at every nonzero single-visit cube vertex. It is not unrestricted synthesis. +Apache-2.0. conorholds with substantial OpenAI Codex assistance. +""" +from collections import deque +from itertools import permutations, product +import json +from pathlib import Path + +IDENTITY = (1, 0, 0, 1) +GENERATORS = tuple(product((0, 1), (-1, 1))) +PAIRS = (((1, 0, 0, 1), (1, -1, 0, 1)), + ((0, 1, -1, 0), (-1, 1, -1, 0)), + ((-1, 0, 1, -1), (0, -1, 1, -1))) +HERE = Path(__file__).resolve().parent + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def step(frame, port, sign): + a, b, c, d = frame + return (a + sign*c, b + sign*d, c, d) if port == 0 else (a, b, c + sign*a, d + sign*b) + + +def ball(radius): + seen = {IDENTITY: ()} + pending = deque([IDENTITY]) + while pending: + frame = pending.popleft() + word = seen[frame] + if len(word) == radius: + continue + for port, sign in GENERATORS: + following = step(frame, port, sign) + if following not in seen: + seen[following] = word + ((port, sign),) + pending.append(following) + return seen + + +def multiply(a, b): + return tuple(sum(a[2*i+k]*b[2*k+j] for k in range(2)) + for i in range(2) for j in range(2)) + + +def inverse(a): + x, y, z, w = a + need(x*w-y*z == 1, 'unit determinant required') + return (w, -y, -z, x) + + +def independent_half_ball(radius): + # Enumerate all literal words rather than using BFS deduplication to grow. + matrices = ((1, -1, 0, 1), (1, 1, 0, 1), (1, 0, -1, 1), (1, 0, 1, 1)) + distances = {IDENTITY: 0} + for length in range(1, radius + 1): + for word in product(matrices, repeat=length): + frame = IDENTITY + for matrix in word: + frame = multiply(matrix, frame) + distances.setdefault(frame, length) + return distances + + +def verify(): + radius = 8 + primary = ball(radius) + halves = independent_half_ball(radius//2) + frames = {IDENTITY} + for pair in PAIRS: + frames.update(pair) + frames.update(tuple(-x for x in frame) for frame in pair) + distances = {} + for start, end in product(sorted(frames), repeat=2): + relative = multiply(end, inverse(start)) + need(relative in primary, 'declared radius does not cover a frame pair') + distance = len(primary[relative]) + # relative = right * left, with both factors in the radius-four ball. + independent = min(halves[left] + halves[right] for left in halves + if (right := multiply(relative, inverse(left))) in halves) + need(distance == independent, 'BFS / literal-half-word disagreement') + actual = start + for port, sign in primary[relative]: + actual = step(actual, port, sign) + need(actual == end, 'wrong chronological shear path') + distances[start, end] = distance + scores = [] + for order in permutations(range(3)): + for choices in product(range(4), repeat=3): + endpoints = [] + for phase, choice in zip(order, choices): + sign = 1 if choice < 2 else -1 + entry = choice % 2 + pair = PAIRS[phase] + endpoints.append((tuple(sign*x for x in pair[entry]), + tuple(sign*x for x in pair[1-entry]))) + boundaries = [(IDENTITY, endpoints[0][0]), + (endpoints[0][1], endpoints[1][0]), + (endpoints[1][1], endpoints[2][0]), + (endpoints[2][1], IDENTITY)] + scores.append(sum(distances[edge] for edge in boundaries)) + need(len(scores) == 384 and min(scores) == 7, 'geometry optimum changed') + # Literal constructor's four, two and one closing shears attain seven. + need(distances[PAIRS[0][1], PAIRS[1][0]] == 4, 'first closure floor') + need(distances[PAIRS[1][1], tuple(-x for x in PAIRS[2][1])] == 2, 'second closure floor') + need(distances[tuple(-x for x in PAIRS[2][0]), IDENTITY] == 1, 'final closure floor') + bad = (1, 0, 0, -1) + need(bad not in primary, 'determinant-minus-one frame accepted') + try: + inverse(bad) + except ValueError: + pass + else: + raise ValueError('non-SL2 inverse accepted') + return {'schema': 'signed-triangle-frames-v1', 'generators': [list(g) for g in GENERATORS], + 'complete_BFS_radius': radius, 'BFS_states': len(primary), + 'independent_half_word_radius': radius//2, 'independent_half_states': len(halves), + 'endpoint_frames': len(frames), 'frame_pairs': len(distances), + 'geometry_cases': len(scores), 'minimum_boundary_transfers': min(scores), + 'total_transfer_formula': 'sum(2^block_size)+4', + 'coefficient_alphabet': 'integer unit shears only; no coordinate/height cutoff', + 'scope': 'Fixed zero-sum triangle; all phase orders/signs/entry signatures, single cube visit and exactly one signature switch per nonzero vertex. Not unrestricted source-walk or frame optimality.'} + + +def main(): + import argparse + parser = argparse.ArgumentParser() + parser.add_argument('--write-receipt', action='store_true') + args = parser.parse_args() + result = verify() + path = HERE/'FRAME-RECEIPT.json' + if args.write_receipt: + path.write_text(json.dumps(result, indent=2)+'\n') + else: + need(json.loads(path.read_text()) == result, 'frame receipt differs') + print(f"PASS_SIGNED_TRIANGLE_FRAMES cases={result['geometry_cases']} " + f"pairs={result['frame_pairs']} boundary_min=7 two_engines=checked") + + +if __name__ == '__main__': + main() diff --git a/research/bidirectional-connector/families.py b/research/bidirectional-connector/families.py new file mode 100644 index 0000000000..96c06c22ba --- /dev/null +++ b/research/bidirectional-connector/families.py @@ -0,0 +1,401 @@ +#!/usr/bin/env python3 +"""Paid dirty-connector cube schedules and exact cost screens. Apache-2.0. + +conorholds with substantial OpenAI Codex assistance. +""" +from fractions import Fraction +from itertools import accumulate +from math import comb, prod + + +def require(ok, message): + if not ok: + raise ValueError(message) + + +def validate(sizes): + require(isinstance(sizes, (list, tuple)) and sizes and + all(type(s) is int and s > 0 for s in sizes), "positive nonempty block sizes required") + return sum(sizes) + + +def blocks(sizes): + validate(sizes) + starts = [0, *accumulate(sizes)] + return [list(range(starts[i], starts[i + 1])) for i in range(len(sizes))] + + +def cycle(coordinates): + """Closed reflected Gray cycle; every nonzero block sum is visited.""" + for step in range(1, 1 << len(coordinates)): + yield coordinates[(step & -step).bit_length() - 1] + yield coordinates[-1] + + +def readout_count(sizes): + n = validate(sizes) + odd = ((1 << n) - prod(2 - (1 << s) for s in sizes)) // 2 + incidence = sum(((1 << s) - 1) * (1 << (n - s)) for s in sizes) + return incidence + odd + + +def screen(sizes): + n = validate(sizes) + return {"sources": n, "blocks": list(sizes), "source_calls": sum(1 << s for s in sizes), + "readout_calls": readout_count(sizes), "transfers": 0, + "dirty_root_rows": 1} + + +def cost(sizes, b, a): + b, a = map(Fraction, (b, a)) + require(b > 0 and a > 0, "invalid complete-call tariff") + counts = screen(sizes) + return counts["source_calls"] * b + counts["readout_calls"] * a + + +def partitions(n, minimum=1): + """All unordered positive partitions, without exponential output enumeration.""" + require(type(n) is int and n > 0, "positive source count required") + for first in range(minimum, n + 1): + if first == n: + yield (first,) + else: + for tail in partitions(n - first, first): + yield (first, *tail) + + +def best_single(n, b, a): + return min(partitions(n), key=lambda sizes: (cost(sizes, b, a), sizes)) + + +def balanced_three(n): + require(type(n) is int and n >= 3, "three nonempty blocks require n>=3") + q, r = divmod(n, 3) + return tuple(q + int(i < r) for i in range(3)) + + +def construct(sizes): + """One-root reference with exactly the necessary odd-dirt compensation.""" + n = validate(sizes) + require(n <= 18, "explicit program emission is bounded to n<=18; screen has no such limit") + groups = blocks(sizes) + masks = [sum(1 << j for j in group) for group in groups] + reads = [dict() for _ in sizes]; word = [] + for target in range(1, 1 << n): + parts = [target & group for group in masks] + if sum(part != 0 for part in parts) & 1: + word.append(["A", target, 0]) + for phase, part in enumerate(parts): + if part: + reads[phase].setdefault(part, []).append(target) + for phase, group in enumerate(groups): + value = 0 + for source in cycle(group): + word.append(["B", source, 0]); value ^= 1 << source + if value: + word.extend(["A", target, 0] for target in reads[phase].get(value, [])) + require(value == 0, "Gray cycle did not restore") + counts = screen(sizes) + require(len(word) == counts["source_calls"] + counts["readout_calls"], + "constructor invoice differs from exact formula") + return word + + +def palette_screen(sizes): + n = validate(sizes) + require(len(sizes) == 3, "palette construction requires three blocks") + vertices = [1 << s for s in sizes] + return {"sources": n, "blocks": list(sizes), "source_calls": sum(vertices), + "readout_calls": 2 * ((1 << n) - 1) + prod(q - 1 for q in vertices), + "transfers": sum(vertices), + "dirty_root_rows": 2} + + +def construct_palette(sizes): + """Both palettes through physical z0; the companion carries incoming dirt only.""" + n = validate(sizes) + require(len(sizes) == 3 and n <= 18, "three blocks and bounded explicit n<=18 required") + groups = blocks(sizes) + masks = [sum(1 << j for j in group) for group in groups] + available = ((1, 3), (2, 3), (1, 2)) + starts = (1, 3, 2) + reads = [{1: {}, 2: {}, 3: {}} for _ in range(3)] + for target in range(1, 1 << n): + parts = [target & mask for mask in masks] + active = [i for i, part in enumerate(parts) if part] + if len(active) == 1: + phase = active[0]; signature = starts[phase] + reads[phase][signature].setdefault(0, []).append(target) + reads[phase][signature].setdefault(parts[phase], []).append(target) + elif len(active) == 2: + first, second = active + signature = next(iter(set(available[first]) & set(available[second]))) + for phase in active: + reads[phase][signature].setdefault(parts[phase], []).append(target) + else: + for phase, signature in enumerate((1, 3, 2)): + reads[phase][signature].setdefault(parts[phase], []).append(target) + word = []; frame = [1, 2] + def transfer(port): + word.append(["C", port]); frame[port] ^= frame[1-port] + def read(phase, value): + signature = frame[0] + word.extend(["A", target, 0] for target in reads[phase][signature].get(value, [])) + for phase, group in enumerate(groups): + require(frame[0] == starts[phase], "phase entry dirt signature") + value = 0; read(phase, value) + for source in cycle(group): + word.append(["B", source, 0]); value ^= 1 << source + if value: + read(phase, value) + transfer(0) + read(phase, value) + require(value == 0, "palette source closure") + # At this cut z0 contains only incoming dirt. One V changes the + # companion's signature for the next color, or closes the whole frame. + transfer(1) + require(frame == [1, 2], "palette root-frame closure") + counts = palette_screen(sizes) + require(len(word) == sum(counts[name] for name in ("source_calls", "readout_calls", "transfers")), + "palette formula differs from emitted program") + return word + + +def single_frontier(n): + """Count-Pareto one-root Gray-block references over every integer partition.""" + candidates = [(screen(sizes)["source_calls"], screen(sizes)["readout_calls"], sizes) + for sizes in partitions(n)] + frontier = []; best_a = None + for b, a, sizes in sorted(candidates): + if best_a is None or a < best_a: + frontier.append(sizes); best_a = a + return frontier + + +def signed_single_frontier(n): + """All count-Pareto signed references; put the largest cube first.""" + candidates = [] + for partition in partitions(n): + sizes = tuple(reversed(partition)) + counts = signed_single_screen(sizes) + candidates.append((counts["source_calls"], counts["readout_calls"], sizes)) + frontier = [] + best_a = None + for b, a, sizes in sorted(candidates): + if best_a is None or a < best_a: + frontier.append(sizes) + best_a = a + return frontier + + +def palette_cost(sizes, b, a, transfer): + b,a,transfer=map(Fraction,(b,a,transfer)) + require(b>0 and a>0 and transfer>=0,"invalid complete-call tariff") + counts=palette_screen(sizes) + return counts['source_calls']*b+counts['readout_calls']*a+counts['transfers']*transfer + + +def best_palette(n,b,a,transfer): + require(type(n) is int and n>=3,"three nonempty blocks require n>=3") + candidates=[tuple(reversed(sizes)) for sizes in partitions(n) if len(sizes)==3] + # Count formulas are symmetric in block sizes; this ordering is deterministic. + return min(candidates,key=lambda sizes:(palette_cost(sizes,b,a,transfer),sizes)) + + +def capacity_threshold(n, roots): + """First admissible source count whose optimistic paired cover reaches every mask.""" + require(type(n) is int and n>0 and roots in (1,2),"positive n and one/two roots required") + masks=(1<=2*masks:hi=mid + else:lo=mid+1 + if roots==1 and lo&1:lo+=1 + return lo + + +def global_lower_bound(n,b,a,roots=1): + """All-word query-tariff lower bound, not merely a Gray-family cost screen. + + One root: absent paired masks need >=4 reads (dirty parity). + Two roots: absent paired masks need >=3 reads; all root frames are granted free. + The concave branch is minimized at its endpoints, then the linear tail increases. + """ + b,a=map(Fraction,(b,a)) + require(b>0 and a>0,"positive complete-call prices required") + threshold=capacity_threshold(n,roots);minimum=2*n + step=2 if roots==1 else 1 + candidates={minimum,threshold} + if threshold-step>=minimum:candidates.add(threshold-step) + masks=(1< 0 and type(k) is int and k >= 2*n + and roots in (1, 2), "invalid source-prefix capacity domain") + multiplier = 1 if roots == 1 else 3 + supported = 0 + deficit = 0 + for radius in range(1, n): + supported += comb(n, radius) + deficit = max(deficit, multiplier*k*radius - supported) + return multiplier*k*(k-1)//2 - deficit + + +def locality_lower_bound(n, b, a, roots=1): + """Exact endpoint minimization of the stronger all-word locality bound.""" + b, a = map(Fraction, (b, a)) + require(b > 0 and a > 0 and roots in (1, 2), "invalid complete query prices/roots") + require(type(n) is int and n > 0, "positive source count required") + masks = (1 << n) - 1 + minimum = 2*n + multiplier = 1 if roots == 1 else 3 + step = 2 if roots == 1 else 1 + lo, hi = minimum, minimum + while locality_capacity(n, hi, roots) < masks: + hi *= 2 + while lo < hi: + mid = (lo+hi)//2 + if locality_capacity(n, mid, roots) >= masks: + hi = mid + else: + lo = mid+1 + threshold = lo + (lo % 2 if roots == 1 else 0) + candidates = {minimum, threshold} + if threshold-step >= minimum: + candidates.add(threshold-step) + supported = [0] + for radius in range(1, n): + supported.append(supported[-1] + comb(n, radius)) + # Between intersections of the deficit lines, the unsaturated expression + # is concave. Include the adjacent admissible integers at every intersection. + for h in range(1, n): + for g in range(h): + crossing = Fraction(supported[h]-supported[g], multiplier*(h-g)) + if minimum <= crossing <= threshold: + lower = crossing.numerator//crossing.denominator + lower -= (lower-minimum) % step + candidates.update(k for k in (lower, lower+step) if minimum <= k <= threshold) + base = 4 if roots == 1 else 3 + return min(k*b + a*max(2*masks, base*masks - (base-2)*locality_capacity(n, k, roots)) + for k in candidates) + + +def critical_tariff(n): + """Integer source price asymptotic to sqrt(2M), in unit-readout prices.""" + return capacity_threshold(n,1)-2+2*n-1 + + +def signed_palette_screen(sizes): + n = validate(sizes) + require(len(sizes) == 3, "signed palette needs three blocks") + q = [1 << s for s in sizes] + return {"sources": n, "blocks": list(sizes), "source_calls": sum(q), + "readout_calls": 2 * ((1 << n) - 1) + prod(x - 1 for x in q), + "transfers": sum(q) + 4, "dirty_root_rows": 2} + + +def construct_signed_palette(sizes): + """Signed triangular colors: one cube per block, fixed physical child port. + + Normalized columns e0, e1, -e0-e1 form a zero-sum triangle. Each vertex + exposes two dirty functionals, so mixed targets need no negative-cube revisit. + """ + n = validate(sizes) + require(len(sizes) == 3 and n <= 18, "three blocks and bounded explicit n<=18 required") + groups = blocks(sizes) + masks = [sum(1 << j for j in group) for group in groups] + reads = [{} for _ in groups] + anchors = [[] for _ in groups] + polarity = (1, 1, -1) + signatures = (((1, 0), (1, -1)), ((0, 1), (-1, 1)), ((0, 1), (1, 0))) + for target in range(1, 1 << n): + parts = [target & mask for mask in masks] + active = tuple(i for i, part in enumerate(parts) if part) + if len(active) == 1: + phase = active[0] + anchors[phase].append(target) + choices = ((phase, 0),) + elif active == (0, 1): + choices = ((0, 1), (1, 1)) + elif active == (0, 2): + choices = ((0, 0), (2, 1)) + elif active == (1, 2): + choices = ((1, 0), (2, 0)) + else: + choices = ((0, 0), (1, 1), (2, 0)) + for phase, direction in choices: + reads[phase].setdefault((direction, parts[phase]), []).append(target) + word = [] + frame = [[1, 0], [0, 1]] + closures = (((0, 1), (0, 1), (1, -1), (0, 1)), + ((0, -1), (1, 1)), ((1, 1),)) + def transfer(port, sign): + word.append(["C", port, sign]) + frame[port] = [a + sign * b for a, b in zip(frame[port], frame[1 - port])] + for phase, group in enumerate(groups): + require(tuple(frame[0]) == signatures[phase][0], "signed triangle entry frame") + word.extend(["A", target, 0, -polarity[phase]] for target in anchors[phase]) + value = 0 + for source in cycle(group): + before = bool(value & (1 << source)) + value ^= 1 << source + word.append(["B", source, 0, polarity[phase] * (-1 if before else 1)]) + if value: + direction = signatures[phase].index(tuple(frame[0])) + word.extend(["A", target, 0, polarity[phase]] + for target in reads[phase].get((direction, value), [])) + sign = (-1, 1, -1)[phase] * (-1 if direction else 1) + transfer(0, sign) + direction = 1 - direction + require(tuple(frame[0]) == signatures[phase][direction], "signed vertex frame") + word.extend(["A", target, 0, polarity[phase]] + for target in reads[phase].get((direction, value), [])) + require(value == 0, "signed triangle source closure") + for port, sign in closures[phase]: + transfer(port, sign) + require(frame == [[1, 0], [0, 1]], "signed triangle root restoration") + counts = signed_palette_screen(sizes) + require(len(word) == sum(counts[k] for k in ("source_calls", "readout_calls", "transfers")), + "unpaid signed instruction") + return word + + +def signed_single_screen(sizes): + n=validate(sizes);q=[1<= 2: + # Explicit E12 / E21 on the first two coordinates: noncommuting and singular. + random_maps["B0"] = [2, 0] + [0] * (width - 2) + random_maps["A1"] = [0, 1] + [0] * (width - 2) + ensure(apply(random_maps["A1"], apply(random_maps["B0"], 2)) != + apply(random_maps["B0"], apply(random_maps["A1"], 2)), "commutation control") + return [all_identity, singular, random_maps] + + +def run(): + cert = json.loads((HERE / "CERTIFICATE.json").read_text()) + reference = json.loads((HERE / "references/PR1615-CERTIFICATE.json").read_text()) + programs = [cert["word"], comparator_word(reference)] + cases = 0 + for width in (1, 2, 3, 5): + zero = dict.fromkeys(NAMES, 0) + inputs = [] + for role in NAMES: + for column in range(width): + state = dict(zero) + state[role] = 1 << column + inputs.append(state) + rng = random.Random(881 + width) + inputs += [{role: rng.randrange(1 << width) for role in NAMES} for _ in range(8)] + for matrices in banks(width): + for incoming in inputs: + want = direct(incoming, matrices) + for word in programs: + actual = replay(word, incoming, matrices) + ensure(actual == want, "dense arbitrary-dirty endpoint mismatch") + ensure(replay(list(reversed(word)), actual, matrices) == incoming, "dense inverse mismatch") + cases += 1 + # Independently reject every single omission using full incoming basis vectors. + mutations = 0 + for word in programs: + matrices = banks(2)[2] + basis = [] + for role in NAMES: + for bit in (1, 2): + state = dict.fromkeys(NAMES, 0) + state[role] = bit + basis.append(state) + for index in range(len(word)): + changed = word[:index] + word[index + 1:] + # One concrete bank can mask omissions through singular maps, so + # also use the identity bank; acceptance requires both to agree. + ensure(any(replay(changed, state, bank) != direct(state, bank) + for bank in (matrices, banks(2)[0]) for state in basis), + "dense omission control accepted") + mutations += 1 + print(f"PASS_INDEPENDENT_BIDIRECTIONAL cases={cases} directions=2 " + f"widths=1,2,3,5 omission_controls={mutations} no_new_kappa") + return cases, mutations + + +def check_palette(): + literal = json.loads((HERE / "PALETTE6.json").read_text()) + n = literal["sources"]; word = literal["word"] + ensure(n == 6, "palette domain") + names = [f"x{j}" for j in range(n)] + [f"y{m}" for m in range(1, 1 << n)] + ["z0", "z1"] + cases = 0 + for width in (1, 2, 3, 5): + inputs = [] + for name in names: + for bit in range(width): + state = dict.fromkeys(names, 0); state[name] = 1 << bit; inputs.append(state) + rng = random.Random(711 + width) + inputs.extend({name: rng.randrange(1 << width) for name in names} for _ in range(8)) + for bank in banks(width, n): + for state in inputs: + actual = replay(word, state, bank) + ensure(actual == direct(state, bank, n), "palette dense endpoint") + ensure(replay(list(reversed(word)), actual, bank) == state, "palette dense inverse") + cases += 1 + basis = [] + for name in names: + for bit in (1, 2): + state = dict.fromkeys(names, 0); 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13, + 1 + ] + ], + "29": [ + [ + 1, + 1 + ], + [ + 13, + 1 + ] + ], + "30": [ + [ + 8, + 1 + ], + [ + 14, + 1 + ] + ], + "31": [ + [ + 3, + 1 + ], + [ + 13, + 1 + ] + ] + } +} diff --git a/research/bidirectional-connector/screen_caller.py b/research/bidirectional-connector/screen_caller.py new file mode 100644 index 0000000000..ee52478199 --- /dev/null +++ b/research/bidirectional-connector/screen_caller.py @@ -0,0 +1,98 @@ +#!/usr/bin/env python3 +"""Source-bound screen of a retained centre interface in the selected manifest. + +Eight clean/private centre copies and different rank-eight charts are outside +this package's two arbitrary dirty roots and fixed complete-query tariffs. +Apache-2.0. conorholds with substantial OpenAI Codex assistance. +""" +import argparse +from collections import Counter, defaultdict +import gzip +from hashlib import sha256 +from itertools import combinations +import json +from pathlib import Path + +HERE=Path(__file__).resolve().parent +MANIFEST='research/community-frontier1094-audit/SELECTED-SOURCE.json' +PREFIX='research/gauge44-slots-t16/' +WORD=PREFIX+'evidence/local/CANONICAL-WORD.json.gz' +PROGRAMS=PREFIX+'evidence/local/LOCAL-PROGRAMS.json.gz' + + +def need(ok,message): + if not ok:raise ValueError(message) + + +def run(repo): + pins=json.loads((HERE/'SOURCES.json').read_text()) + expected={r['path']:r['sha256'] for r in pins['files']} + payloads={} + for name in ('certificates/selected-result.json',MANIFEST,WORD,PROGRAMS): + raw=(repo/name).read_bytes() + need(name in expected and sha256(raw).hexdigest()==expected[name], 'caller source pin mismatch: '+name) + payloads[name]=json.loads(gzip.decompress(raw) if name.endswith('.gz') else raw) + selected=payloads['certificates/selected-result.json'];manifest=payloads[MANIFEST] + need(selected['source_manifest']==MANIFEST,'not the selected source manifest') + need(all(manifest['files'][name]==expected[name] for name in (WORD,PROGRAMS)), + 'caller artifacts are not bound by selected manifest') + word=payloads[WORD];programs=payloads[PROGRAMS] + centres=word['centers'];frames=[word['frames'][i] for i in word['center_frames']] + need(len(centres)==len(set(centres))==len(frames)==8,'centre interface changed') + need(all(len(frame)==8 for frame in frames),'centre rank changed') + need(len({tuple(frame) for frame in frames})==8,'centre charts are no longer distinct') + targets=defaultdict(list) + for op in word['cut']: + need(op[0]=='add' and op[2] in centres and op[3] in (-1,1) and op[4]==4, + 'cut is outside signed quarter-read class') + targets[op[1]].append((op[2],op[3],op[4])) + need(len(targets)==112 and all(len(terms)==2 for terms in targets.values()),'two-read centre target shape changed') + edges={tuple(sorted(term[0] for term in terms)) for terms in targets.values()} + graph={source:set() for source in centres} + for a,b in edges:graph[a].add(b);graph[b].add(a) + components=[];unseen=set(centres) + while unseen: + pending=[min(unseen)];component=set() + while pending: + node=pending.pop() + if node in component:continue + component.add(node);pending.extend(graph[node]-component) + unseen-=component;components.append(sorted(component)) + need(len(components)==2 and all(len(c)==4 for c in components),'centre graph changed') + need(all(tuple(pair) in edges for c in components for pair in combinations(c,2)), 'centre components are not K4') + preparations={} + for orientation,events in programs.items(): + copies=[op for op in events if op[0]=='scalar' and op[1][0]=='copy' and op[1][1][0]=='C'] + clears=[op for op in events if op[0]=='scalar' and op[1][0]=='clear' and op[1][1][0]=='C'] + descents=[op for op in events if op[0]=='center'] + preparations[orientation]={'private_centre_copies':len(copies),'private_centre_clears':len(clears), + 'centre_path_events':len(descents)} + need(preparations['forward']=={'private_centre_copies':8,'private_centre_clears':16,'centre_path_events':8}, + 'forward clean-centre preparation changed') + patterns=Counter(tuple(terms) for terms in targets.values()) + return {'schema':'retained-centre-contract-screen-v1','selected_kappa':selected['kappa'], + 'artifact_scope':'Retained canonical centre interface included in selected source manifest; not a replay or census of the currently dispatched provider programs.', + 'source_pins':{name:expected[name] for name in payloads},'centre_carriers':centres, + 'distinct_rank_eight_charts':8,'target_rows':len(targets),'cut_scalar_adds':len(word['cut']), + 'signed_patterns':len(patterns),'source_pair_edges':len(edges),'pair_components':components, + 'literal_private_preparation':preparations, + 'dirty_query_source_floor':2*len(centres),'dirty_query_output_floor':2*len(targets), + 'contract_mismatch':['The selected batch has 112 signed two-source rows, not the universal 255-mask positive batch.', + 'The literal program copies into and clears owned private centres; it does not start with two arbitrary dirty query roots.', + 'Eight distinct rank-eight source charts and their nested centre paths require a new complete query/port/hosting invoice.'], + 'conclusion':'No selected-supplier replacement or new kappa follows from the palette/walk query savings.', + 'scope':'Fresh source-bound shape/contract extraction only; no full native endpoint, owner, physical invoice or selected cold replay.'} + + +def main(): + parser=argparse.ArgumentParser() + parser.add_argument('--repo',type=Path,default=HERE.parent.parent) + parser.add_argument('--write-receipt',action='store_true') + args=parser.parse_args();result=run(args.repo) + path=HERE/'CALLER-SCREEN.json' + if args.write_receipt:path.write_text(json.dumps(result,indent=2)+'\n') + else:need(json.loads(path.read_text())==result,'caller screen receipt changed') + print('PASS_RETAINED_CENTRE_CONTRACT_SCREEN centres=8 targets=112 signed_patterns=24 graph=2K4 full_native=NOT_RUN no_new_kappa') + + +if __name__=='__main__':main() diff --git a/research/bidirectional-connector/search_walk.cpp b/research/bidirectional-connector/search_walk.cpp new file mode 100644 index 0000000000..6c15ebfb6f --- /dev/null +++ b/research/bidirectional-connector/search_walk.cpp @@ -0,0 +1,38 @@ +// Heuristic proposal search only, never an exclusion or optimality certificate. +// Fixed three-color classes; exact acceptance is in verify_walk.py. +// Cross-platform shuffle/library differences may change the proposed word. +// Apache-2.0. conorholds with substantial OpenAI Codex assistance. +#include +#include +#include +#include +#include +#include +#include +struct Eval {int score,paired,three;}; +Eval evaluate(const std::vector& word,int n,int first,int second) { + std::array,3> values; std::array,3> seen{}; + int p=0,q=0; + auto cut=[&](){std::array v{p,q,p^q};for(int d=0;d<3;d++)if(!seen[d][v[d]]){seen[d][v[d]]=true;values[d].push_back(v[d]);}}; + cut();for(int j:word){int color=j cover{}; + for(auto& v:values)for(int a:v)for(int b:v)cover[a^b]=2; + for(int a:values[0])for(int b:values[1])for(int c:values[2])if(!cover[a^b^c])cover[a^b^c]=1; + int paired=0,three=0;for(int i=1;i<(1<1?std::stoi(argv[1]):12;int trials=argc>2?std::stoi(argv[2]):200000; + int first=argc>3?std::stoi(argv[3]):n/3;int second=argc>4?std::stoi(argv[4]):n/3; + if((n!=9&&n!=12)||trials<=0||trials>2000000||first<=0||second<=0||first+second>=n)return 2;std::mt19937 rng(4097+n); + std::vector w,best;for(int j=0;j(rng)>std::exp((now.score-old.score)/temperature))std::swap(w[a],w[b]);else old=now; + if(old.score>bestscore){bestscore=old.score;best=w;be=old;} + } + std::cout<<"{\"n\":"<1: + maps['B0']=[[int(i==0 and j==1) for j in range(width)] for i in range(width)] + maps['A1']=[[int(i==1 and j==0) for j in range(width)] for i in range(width)] + inputs=[] + for name in names: + for column in range(width): + incoming={role:[0]*width for role in names};incoming[name][column]=1;inputs.append(incoming) + for _ in range(8): + inputs.append({role:[rng.randrange(2) if modulus else rng.randrange(-3,4) + for _ in range(width)] for role in names}) + for incoming in inputs: + expected={key:list(value) for key,value in incoming.items()} + for mask in range(1,1<=baseline:raise ValueError('declared positive tariff does not improve') + examples.append({'sources':n,'B_price':b,'A_price':1,'transfer_price':1,'best_one_root_blocks':list(reference),'reference_cost':int(baseline),'palette_cost':candidate,'saved_units':int(baseline-candidate),'fraction_saved':str(Fraction(baseline-candidate,baseline))}) + for n in (9,12,15,18,30,60): + price=f.critical_tariff(n) + lower=f.global_lower_bound(n,price,1,1) + two_lower=f.global_lower_bound(n,price,1,2) + achieved=f.palette_cost(f.balanced_three(n),price,1,1) + if achieved>=lower or achieved=lower:raise ValueError('signed global separation failed') + examples.append({'theorem':'characteristic-zero signed palette','sources':n,'source_price':b, + 'one_root_lower_bound':int(lower),'signed_palette_cost':achieved, + 'guaranteed_saved_fraction_vs_every_one_root_word':str(Fraction(lower-achieved,lower))}) + for n in (9,12,15,18,30,60): + b=f.critical_tariff(n) + lower=f.locality_lower_bound(n,b,1,1) + two_lower=f.locality_lower_bound(n,b,1,2) + signed=f.signed_palette_screen(f.balanced_three(n)) + achieved=signed['source_calls']*b+signed['readout_calls']+signed['transfers'] + if achieved>=lower or achieved1 for term in poly), 'companion acquired source data') + else: + dirty = sum(abs(poly.get((f'A{target[1:]}',f'z{p}'),0)) for p in (0,1)) + maximum["output_dirty_l1_max"] = max(maximum["output_dirty_l1_max"], dirty) + need(all(value==1 for term,value in poly.items() if len(term)==3), + 'output source contribution lost positivity') + need(dirty<=2, 'palette dirty-height growth') + polynomial(word,n,2,observe) + return maximum + + +def dense(word,incoming,maps): + state={role:list(value) for role,value in incoming.items()} + def image(matrix,value):return [sum(a*b for a,b in zip(row,value)) for row in matrix] + for op in word: + if op[0]=='B':source=f'x{op[1]}';target='z0';add=image(maps[f'B{op[1]}'],state[source]) + elif op[0]=='A':source='z0';target=f'y{op[1]}';add=image(maps[f'A{op[1]}'],state[source]) + else:source=f'z{1-op[1]}';target=f'z{op[1]}';add=state[source] + state[target]=[a+op[-1]*b for a,b in zip(state[target],add)] + return state + + +def main(): + import argparse + parser=argparse.ArgumentParser() + parser.add_argument('--write-receipt',action='store_true') + args=parser.parse_args() + records=[] + for n in range(3,13): + sizes=f.balanced_three(n);word=f.construct_signed_palette(sizes) + check(word,n) + counts=f.signed_palette_screen(sizes) + for kind,key in (('A','readout_calls'),('B','source_calls'),('C','transfers')): + need(sum(op[0]==kind for op in word)==counts[key],'unpaid signed invoice') + records.append({'sources':n,'counts':counts,'prefix_bounds':prefix_bounds(word,n), + 'word_sha256':sha256(json.dumps(word,separators=(',',':')).encode()).hexdigest()}) + check(f.construct_signed_palette((1,3,1)),5) + for n in range(1,13): + count=min(n,4);q,r=divmod(n,count) + sizes=tuple(q+int(i0 and a>0,'positive complete query prices required') + masks=(1<