diff --git a/research/signed-rank9-rank8-split/CUT-PROOF.md b/research/signed-rank9-rank8-split/CUT-PROOF.md new file mode 100644 index 0000000000..8b64f7624f --- /dev/null +++ b/research/signed-rank9-rank8-split/CUT-PROOF.md @@ -0,0 +1,52 @@ +# Rank-eight helper split on the exact #7108 word + +The input is the #7108 normalized native word with canonical SHA-256 `34085a6c502ac07530001bdcbc85ad0ec9637f5dda28c9593a0b0d6dd6613d24`. It has 71,238 events, 1,481 public fields and 51 owned labels. The independent `cut.py` replay authenticates that payload and derives the exact transferred split at source cut 37412. This is the rank-eight helper split from the #7107 authors, applying Ali Romman's helper-split construction with the retained owned-label convention. [Pinned #7107 witness](https://github.com/dillona/integer-mult-bounds/blob/5b59588fbf54c392dfb90aa4a7e7e60f0c41c351/research/p104-rank8-retimed-split/WITNESS.json), [retiming emitter](https://github.com/dillona/integer-mult-bounds/blob/5b59588fbf54c392dfb90aa4a7e7e60f0c41c351/research/p104-rank8-retimed-split/construct.py), [split emitter](https://github.com/dillona/integer-mult-bounds/blob/5b59588fbf54c392dfb90aa4a7e7e60f0c41c351/research/p104-rank8-retimed-split/split.py) + +## Literal changes + +All indices refer to the #7108 source word. Its only contact with role 533 in [37403,39691) is the public MOVE 3→747 at 38784. Move that paid contact to cut 37412 and divide it into 3→745 and 745→747. Both chart paths strictly nest. The cut basis sits between the two new moves. At the raw cut, roles 843, 1454 and 1468 are already in chart 745, and the first new move puts role 533 there. Role 1251 is in chart 747 at that cut and does not occur in the cut basis. + +The retained pivot is 1468. Append the fresh helper role 1481, increase all old owned role labels by one, set the retained pivot's final chart to 745 and give the new role initial/final charts 745/245. Prepend the inverse input basis at chart 3, then apply the cut basis J and its inverse rebound onto the successor at chart 745. Rename role 1468 to 1481 at exactly seven source suffix contacts, 38770, 38771, 38772, 40911, 40914, 42636 and 42638. Finish with the rebound output basis at chart 245. The receipt lists every inserted and rebound event. + +The canonical result has SHA-256 `db9b86eba69ca556be5abc1eb85292566fc065ddebad9a26b2da0475f22aec6b`, 71,253 events and 1,482 public fields. The audit checks each chart argument, all 155 owned-motion events under the label shift, and seven affected endpoint rows. Per LOCAL the paid delta is +2 at rank three and −1 at rank six. The productive delta is +1 each at ranks three and five and −1 at rank eight. The complete signed gain is positive for 0<κ<1 by strict concavity of x^(1−κ). + +## Full-domain normalized map + +Let P and S be the normalized scalar prefix and suffix at the intermediate cut after retiming role 533. A MOVE is the identity in normalized coordinates. The moved contacts are isolated throughout the stated interval, so the retiming leaves the old full normalized map T=SP unchanged. Every scalar operation in each basis takes place at one chart. The exact backward row and forward column checks give + +``` +a = e533* − 2 e1454* +b = e533 + e1468 − e843 +c = e533* + 4 e1251* + e1468* − 2 e1454* +d = e1468 + +a P = c +S b = d +a b = c d = 1 +``` + +These are full vectors, including all public coordinates and the owned-label state. The suffix direction at the earlier split's cut 43039 has zero entries at roles 843, 1123 and 1480 and entry one at 1468. The two split operations therefore introduce no conflicting cargo at that cut. + +Write p=1468, and let G be the boundary basis with pivot row c and Gd=e_p. Let J have pivot row a and Jb=e_p. The explicit ADD lists satisfy these identities. For the old full endpoint, the audit also checks e_p*T=e_p*, T e_p=e_p and αT=α with α=c−e_p*. Since G=I+e_pα, these identities give GT=TG on the full normalized state. + +For arbitrary old public input x and fresh scalar z, with the owned state initially zero, the state just after J is JP G^-1 x. Its pivot coordinate is cG^-1x=x_p. Freeze that coordinate as the retained output. Replacing it by z for the rebound suffix adds (z−x_p)b after J^-1. The output basis and suffix therefore produce + +``` +G S (P G^-1 x + (z−x_p)b) + = T x + (z−x_p)e_p . +``` + +Thus the retained pivot returns x_p at chart 745, the successor returns the independent input z at chart 245, and every old nonpivot output is unchanged. The suffix correction has no owned component. The calculation is coordinatewise in the normalized chart columns, so it applies to all columns under the retained exact child and native all-column contracts. Physical Clifford, complete invoice, compiler and outer gate verification are separate from this cut audit. + +## Replay + +Run the registered package from the repository root. + +```sh +python3.12 -B scripts/research_package.py --package research/signed-rank9-rank8-split +``` + +The verifier reruns the independent cut emitter against the +reconstructed #7108 source and compares its exact CUT.json. + +Prior CrocSwap native, caller and rank-eight helper work supplies the inputs. Codex assisted the independent transfer audit and proof. diff --git a/research/signed-rank9-rank8-split/CUT.json b/research/signed-rank9-rank8-split/CUT.json new file mode 100644 index 0000000000..6a98ee6ead --- /dev/null +++ b/research/signed-rank9-rank8-split/CUT.json @@ -0,0 +1,315 @@ +{ + "status": "PASS_FULL_DOMAIN_RANK8_SPLIT_CUT_IDENTITIES", + "independent_emitter_canonical_sha256": "db9b86eba69ca556be5abc1eb85292566fc065ddebad9a26b2da0475f22aec6b", + "all_charts_checked": 71253, + "explicit_endpoint_rows_checked": [ + 533, + 843, + 1251, + 1454, + 1468, + 1480, + 1481 + ], + "owned_motion_events_preserved": 155, + "canonical_word_sha256": "34085a6c502ac07530001bdcbc85ad0ec9637f5dda28c9593a0b0d6dd6613d24", + "source_events": 71238, + "source_public": 1481, + "contact_free_interval": [ + 37403, + 39691 + ], + "old_move_index": 38784, + "insert_before": 37412, + "old_frames_at_cut": { + "533": 3, + "843": 745, + "1251": 747, + "1454": 745, + "1468": 745 + }, + "split_pivot": 1468, + "new_public_role": 1481, + "old_pivot_final": 745, + "new_initial_final": [ + 745, + 245 + ], + "exact_prefix_row": { + "533": "1", + "1251": "4", + "1454": "-2", + "1468": "1" + }, + "exact_suffix_column": { + "1468": "1" + }, + "existing_split_cut_direction": { + "843": "0", + "1123": "0", + "1468": "1", + "1480": "0" + }, + "full_old_pivot_row": { + "1468": "1" + }, + "full_old_pivot_column": { + "1468": "1" + }, + "full_old_boundary_adjoint": { + "533": "1", + "1251": "4", + "1454": "-2" + }, + "inserted": { + "input": [ + [ + "ADD", + 1468, + 1454, + "2", + 3 + ], + [ + "ADD", + 1468, + 1251, + "-4", + 3 + ], + [ + "ADD", + 1468, + 533, + "-1", + 3 + ] + ], + "at_cut": [ + [ + "MOVE", + 533, + 3, + 745, + false + ], + [ + "ADD", + 533, + 1468, + "-1", + 745 + ], + [ + "ADD", + 843, + 1468, + "1", + 745 + ], + [ + "ADD", + 1468, + 533, + "1", + 745 + ], + [ + "ADD", + 1468, + 1454, + "-2", + 745 + ], + [ + "ADD", + 1481, + 1454, + "2", + 745 + ], + [ + "ADD", + 1481, + 533, + "-1", + 745 + ], + [ + "ADD", + 843, + 1481, + "-1", + 745 + ], + [ + "ADD", + 533, + 1481, + "1", + 745 + ], + [ + "MOVE", + 533, + 745, + 747, + false + ] + ], + "output": [ + [ + "ADD", + 1481, + 533, + "1", + 245 + ], + [ + "ADD", + 1481, + 1251, + "4", + 245 + ], + [ + "ADD", + 1481, + 1454, + "-2", + 245 + ] + ] + }, + "rebound": [ + { + "source_index": 38770, + "before": [ + "ADD", + 1468, + 73, + "-1", + 745 + ], + "after": [ + "ADD", + 1481, + 73, + "-1", + 745 + ] + }, + { + "source_index": 38771, + "before": [ + "MOVE", + 1468, + 745, + 917, + false + ], + "after": [ + "MOVE", + 1481, + 745, + 917, + false + ] + }, + { + "source_index": 38772, + "before": [ + "ADD", + 1468, + 1251, + "-1", + 917 + ], + "after": [ + "ADD", + 1481, + 1251, + "-1", + 917 + ] + }, + { + "source_index": 40911, + "before": [ + "ADD", + 533, + 1468, + "-1", + 917 + ], + "after": [ + "ADD", + 533, + 1481, + "-1", + 917 + ] + }, + { + "source_index": 40914, + "before": [ + "MOVE", + 1468, + 917, + 245, + false + ], + "after": [ + "MOVE", + 1481, + 917, + 245, + false + ] + }, + { + "source_index": 42636, + "before": [ + "ADD", + 1468, + 73, + "1", + 245 + ], + "after": [ + "ADD", + 1481, + 73, + "1", + 245 + ] + }, + { + "source_index": 42638, + "before": [ + "ADD", + 843, + 1468, + "1", + 245 + ], + "after": [ + "ADD", + 843, + 1481, + "1", + 245 + ] + } + ], + "predicted_events": 71253, + "paid_delta": { + "3": 2, + "6": -1 + }, + "target_delta": { + "3": 1, + "5": 1, + "8": -1 + } +} diff --git a/research/signed-rank9-rank8-split/README.md b/research/signed-rank9-rank8-split/README.md new file mode 100644 index 0000000000..c48f9c7900 --- /dev/null +++ b/research/signed-rank9-rank8-split/README.md @@ -0,0 +1,53 @@ +# Rank-eight helper split on the signed rank-nine caller + +The complete conditional certificate gives κ = **0.003635479112372** +in T(n) = O(n (log n)^(1−κ)). The exact gain over the hosted #7108 +certificate κ = 0.003635302061475 is +177050897/1000000000000000 = 0.000000177050897. The independent raw +crossing lies in +(.00363547911237276261060913791895826, + .00363547911237276261060913791895827). + +Transfer #7107's causal split to the exact #7108 native word. +At cut 37412, retime role 533 from one 3→747 move to 3→745→747. +A checked input basis and cut basis isolate the old helper-1468 +coordinate. The retained helper ends at 745 with rank three. +A fresh arbitrary helper starts at 745 and takes the old suffix, +ending at 245 with rank five. The signed rank-nine caller stays +byte-identical. [Exact cut proof](CUT-PROOF.md) + +The paid delta per native call is {3:+2, 6:−1} and the productive +delta is {3:+1, 5:+1, 8:−1}. The 18-call invoice has 117,148 paid +and 23,428 productive requests, rank surplus 1,520 and zero +empty-root credits. The modeled ordinary bill is 847,308,544 +of 10^9. The paired BIT cap is .00376669. The exact grid remains +S=1125 and context c=1342. + +Run the registered check under CPython 3.12. + + python3.12 -B scripts/research_package.py --package research/signed-rank9-rank8-split + +The pinned archive rebuilds both the #7108 source and the new +word. It checks all 1,482 public outputs, all 512 columns and +absolute phase of each changed chart pair, all signed caller +routes, exact ownership and grid, the full precision envelope, +two directed price engines and the compiler and outer gates. +The old invoice rejects the new claim. Scalar and chart-phase +mutations fail. The regenerated grid, route and result receipts +must match byte for byte. + +## Open next questions + +The complete bound retains the all-column native, owned erasure, +uniform compiler, fixed-tape precision, analytic recovery, A6, +exact-child, LAMBDA, one-field idle, per-port caller, paired +E-free BIT and modeled ordinary tariff premises. Physical +fixed-tape realization, a rounded provider and the #6998 +physical tariff bridge remain open. The next provider audit +should bind the retimed helper normalizers and signed routes +to the same exact tape tariff. + +This package credits the #7107 contributors, the helper-split +method of Ali Romman and CubeJerry, and CrocSwap's coupled-native, +signed Clifford and interval predecessors. Codex assisted the +transfer, independent construction and replay. diff --git a/research/signed-rank9-rank8-split/REPLAY.tar.gz b/research/signed-rank9-rank8-split/REPLAY.tar.gz new file mode 100644 index 0000000000..39df7d287c Binary files /dev/null and b/research/signed-rank9-rank8-split/REPLAY.tar.gz differ diff --git a/research/signed-rank9-rank8-split/RESULT.json b/research/signed-rank9-rank8-split/RESULT.json new file mode 100644 index 0000000000..85219001ee --- /dev/null +++ b/research/signed-rank9-rank8-split/RESULT.json @@ -0,0 +1 @@ +{"caller": {"bad_outputs": [], "caller_denominator_height_bound": 431, "caller_mass_bound": "2031778024781380738667307850969872261300825114412066667930609010754885615256246771273722516797028373875488084463456734932931819440254377992064287155336455679722182496470290893143689397339193405421398373633/137438953472", "caller_mass_ceiling_bits": 642, "max_terms": 3998}, "caller_sha256": "9557f713ab4ffb91ede05e8a6d5668c694b9940fc16f2f2d657e2f2b2cac2d3f", "gate": {"BIT_margin": "13121088762793/100000000000000000", "BIT_pin": "376669/100000000", "H": "16465200000000000000000", "alpha": [0.9999999999999991, 0.9999999999999991], "claim": "908869778093/250000000000000", "compiler_gap": "1/100000000000000000", "delta": [0.8765995821347601, 0.8765995821347601], "derivative_upper": -407984.94505855616, "gamma": [0.9499601327710583, 0.9499601327710583], "input_lift": {"derivative_upper_on_required_interval": "-2299831290525933154178526076272396899996972093654613095735772838275432653960006518819/2500000000000000000000000000000000000000000000000000000000000000000000000000000000000000", "interval_kappa_cap": "376669/100000000", "margins": {"363547911237207/100000000000000000": ["62024371905905908222877843773236793548479272214353070325013552723176941571109/50000000000000000000000000000000000000000000000000000000000000000000000000000000", "24809748762362363289151137509294717419391708885741228130005421089270776628831/20000000000000000000000000000000000000000000000000000000000000000000000000000000"], "908869778093/250000000000000": ["15506092976476191194921007353255300474186237569924778354725925707858509929437/12500000000000000000000000000000000000000000000000000000000000000000000000000000", "24809748762361905911873611765208480758697980111879645367561481132573615887493/20000000000000000000000000000000000000000000000000000000000000000000000000000000"]}, "source_BIT_wide_crude_bound_would_be": "-2299831290525933154178526076272396899996972093654613095735772838275432653960006518819/2500000000000000000000000000000000000000000000000000000000000000000000000000000000000000"}, "minimum_log_power": 2230, "moment_margin_float": {"18177395561863813053045689594791/5000000000000000000000000000000000": [2.5068609125670018e-29, 2.5068609125670018e-29], "363547911237207/100000000000000000": [2.8740337839784485e-10, 2.8740337839784485e-10], "36354791123727626106091379189583/10000000000000000000000000000000000": [-1.6427055914109074e-29, -1.6427055914109074e-29]}, "moment_margins": {"18177395561863813053045689594791/5000000000000000000000000000000000": ["156678807035437618683823795147766346039924158341943/6250000000000000000000000000000000000000000000000000000000000000000000000000000", "626715228141750474735295180591065384159696643862493/25000000000000000000000000000000000000000000000000000000000000000000000000000000"], "363547911237207/100000000000000000": ["14370168919892243757782138790047448501323271378996568871701152513413537/50000000000000000000000000000000000000000000000000000000000000000000000000000000", "14370168919892243757782138790047448501323271378996568871701152534417919/50000000000000000000000000000000000000000000000000000000000000000000000000000000"], "36354791123727626106091379189583/10000000000000000000000000000000000": ["-821352795705453736876192448706592973576534934367167/50000000000000000000000000000000000000000000000000000000000000000000000000000000", "-821352795705453736876192448706592973576534913427523/50000000000000000000000000000000000000000000000000000000000000000000000000000000"]}, "outer": {"BIT_just_below_effective_rejected": true, "functional_count": 4, "minimum_margin": "1/1000000000000000000", "strict_count": 54}, "raw_bracket": ["18177395561863813053045689594791/5000000000000000000000000000000000", "36354791123727626106091379189583/10000000000000000000000000000000000"], "tested": "363547911237207/100000000000000000", "written_log_power": 2231}, "invoice": {"P": {"1": 72888, "2": 15174, "3": 14706, "4": 4266, "5": 5886, "6": 288, "7": 216, "8": 780, "9": 32, "16": 416, "24": 416, "32": 416, "40": 416, "48": 416, "56": 416, "64": 416}, "S": 1520, "T": {"1": 252, "2": 324, "3": 810, "4": 3870, "5": 1242, "6": 738, "7": 324, "8": 1008, "9": 11324, "17": 416, "25": 416, "33": 416, "41": 416, "49": 416, "57": 416, "65": 416, "73": 416, "145": 208}, "empty_root_credits": 0, "no_E_credit_crossing": "0.0036354791123727626106091379189582604125975608257758558983878762244", "raw_crossing": "0.0036354791123727626106091379189582604125975608257758558983878762244"}, "mutation_bad_inputs": [1454], "native": {"bad_inputs": [], "events": 71253, "helpers": {"1": 14, "2": 18, "3": 45, "4": 215, "5": 69, "6": 41, "7": 18, "8": 56, "9": 606}, "lifetimes": 54, "owned_peak": 43, "paid": {"1": 4028, "2": 843, "3": 817, "4": 237, "5": 327, "6": 16, "7": 12, "8": 6}, "public": 1482, "rises": {"1": 10, "2": 4, "3": 1, "4": 6, "5": 1, "6": 1}}, "ordinary": {"caller_items": {"A": {"envelope": 124674048, "field_boundary": 94848, "fused_routes": 0, "idle_routes": 185472000, "output_routes": 229056000, "query_routes": 1152000, "thin": 6144}, "B": {"envelope": 39515136, "field_boundary": 7904, "fused_routes": 1168000, "idle_routes": 19552000, "output_routes": 19088000, "query_routes": 0, "thin": 0}}, "caller_total": 619786080, "conservative_total": 847308544, "extra_B_scalar_surcharge": 784256, "init_clear_allowance": 216, "lambda_paid_rank1_would_reduce_S_by": 14384, "lambda_second_charge": 14384000, "margin_to_billion": 152691456, "odd_divisions": {"ADD": 4079, "SCALE": 64}, "per_input_conversion": 2774304, "raw_upper": 829365984, "route_items": {"first_main_adapter": 416, "first_main_boundary": 208, "helper_boundary": 2164, "moves": 6286, "owned_lifetime": 216, "second_main_adapter": 384, "second_main_boundary": 192}, "routing": 9866000, "scalar_upper": 1777328}, "precision": {"Kstar_bits": 14093, "caller": {"denominator_height": 431, "maximum_mass": "2031778024781380738667307850969872261300825114412066667930609010754885615256246771273722516797028373875488084463456734932931819440254377992064287155336455679722182496470290893143689397339193405421398373633/137438953472", "pre_joint_height": 426, "pre_joint_mass": 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"106523307213816187766193716729111647841679597111109230623129120800225893093065165782942865402653350851353684525808180977928803112873409709724655541986939962919740519508853143434507363426831108801342558091853328252329828518299557581873678708866829642495548175595057908700527639002372668790500342725191/24065554363707792544038974914560000000000000000", "strict_power_of_two": 840, "witness": {"cut": 5112, "factor": "1", "kind": "public-return", "register": 75}}, "M_caller": {"exact": "71139049377586862629418871698937610393019572652137611543732392122728862032234875850426792200611955874649536689056011773263916935707559511365401032013880904413645069177668118198332454710167691/32768", "strict_power_of_two": 619, "witness": {"cut": 5076, "event": 5075, "factor": "1", "kind": "stored", "register": 75}}, "M_context": {"exact": "63921579596774808543096825261851903075574668004799743143943421883100375820078753700765848212865310828952259326052944609127829993628113963157908056368224749817953941957101535562337322647052925111089262578797724105170195826506481630463773238411850160787189106940005821258427710028463684011176238052166541/28522138505135161533675822120960000000000000000", "strict_power_of_two": 849, "witness": {"cut": 4983, "event": 4982, "factor": "1", "kind": "stored", "register": null}}, "M_joint_entrance": {"exact": "66231921216838714175335242310174311625441766070329537281095337280001689425837300045521194678022507207573740758259597518292006513594483309822197449388620837179777160688120985448681075810705/4096", "strict_power_of_two": 612, "witness": {"cut": 4982, "event": 4982, "factor": "1", "kind": "stored", "register": 39}}, "Sigma_caller": {"exact": "106523307213816187766193716729111647841679597111109230623129120800225893093065165782942865402653350851353684525808180977928803112873409709724655541986939962919740519508853143434507363426831108801342558091853328252329828518299557581873678708866829642495548175595057908700527639002372668790500342725191/24065554363707792544038974914560000000000000000", "strict_power_of_two": 840, "witness": {"cut": 5098, "event": 5097, "factor": "1", "kind": "stored", "register": 75}}, "Sigma_context": {"exact": 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393216, "max_numerator": 14729531, "numerator_bits": 24, "opcodes": {"ADD": 61196, "CLEAR": 54, "COPY": 1, "INIT": 54, "MOVE": 6286, "SCALE": 3662}, "owned_labels": 51, "peak_owned": 43, "public": 1482, "scalars": {"dyadic": 60716, "integer": 38918, "noninteger": 25941, "odd": 4143}}, "independent_adjoint": {"Gamma": {"active_residual_sites": 24517, "entrance_mass": "14476760998861861302944912510523645403533730458331551801951984348669962992247520957465861449097781106116821932685203/104451190814703960694613606400000000000000000", "residual_mass": "148410063514995949252033673132766658208646581676660814013068921571937684977713978341894633696507250255802399438531/3672112177079436118170009600000000000000000"}, "M": {"active_residual_sites": 24517, "entrance_mass": "14476760998861861302944912510523645403533730458331551801951984348669962992247520957465861449097781106116821932685203/104451190814703960694613606400000000000000000", "residual_mass": "148410063514995949252033673132766658208646581676660814013068921571937684977713978341894633696507250255802399438531/3672112177079436118170009600000000000000000"}, "Sigma": {"active_residual_sites": 24517, "entrance_mass": "14476760998861861302944912510523645403533730458331551801951984348669962992247520957465861449097781106116821932685203/104451190814703960694613606400000000000000000", "residual_mass": "148410063514995949252033673132766658208646581676660814013068921571937684977713978341894633696507250255802399438531/3672112177079436118170009600000000000000000"}}}, "scope": "Exact-child grid and attributed all-fibre error envelope, with one signed unitary per fused event", "word": {"coefficient_visits": 14087858, "dyadic_height": 24, "mass_witness": [63454, "stored add"], "maximum_scaled_mass": "1636346757402225/16384", "numerator_bits": 24, "odd_scale_lcm": 1125}}, "price": {"baseline_rejects_new_claim": true, "candidate_margin_at_old_upper": ["1836711857173393381033692603752712636612751772965812569045643333297856405082237/25000000000000000000000000000000000000000000000000000000000000000000000000000000", "1836711857173393381033692603752712636612751772965812569045643333297856414409729/25000000000000000000000000000000000000000000000000000000000000000000000000000000"], "claim_decimal": "0.003635479112372", "gain": "1.77050897E-7", "gain_exact": "177050897/1000000000000000", "independent_raw_bracket": ["0.00363547911237276261060913791895826", "0.00363547911237276261060913791895827"], "previous_claim": "145412082459/40000000000000", "raw_bracket": ["0.0036354791123727626106091379189582", "0.0036354791123727626106091379189583"]}, "status": "PASS_SIGNED_RANK9_RANK8_SPLIT_GATES", "word_sha256": "db9b86eba69ca556be5abc1eb85292566fc065ddebad9a26b2da0475f22aec6b"} diff --git a/research/signed-rank9-rank8-split/SOURCES.json b/research/signed-rank9-rank8-split/SOURCES.json new file mode 100644 index 0000000000..b06c2f774e --- /dev/null +++ b/research/signed-rank9-rank8-split/SOURCES.json @@ -0,0 +1,18 @@ +{ + "schema_version": 1, + "base_commit": "17469fff78c22941280f04d39dc5a1faee09c840", + "files": [ + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "3404fbdd5e7529a0674eef26114b5071e4586cec", + "sha256": "ead6cdc9d0af6d58e8a49744d8ec8c7c15e13d2ba93c276c434bcf9b51b93a81" + }, + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "d59b5035e7b4cbaa9d688a1d32dd0d6eb79c466a", + "sha256": "9b8d0eea95b3bf0dfcb7938a732a6439b87a2685dec2a5ab9e525b3b34debbfa" + } + ] +} diff --git a/research/signed-rank9-rank8-split/TASK.json b/research/signed-rank9-rank8-split/TASK.json new file mode 100644 index 0000000000..377fec5273 --- /dev/null +++ b/research/signed-rank9-rank8-split/TASK.json @@ -0,0 +1,115 @@ +{ + "schema_version": 1, + "task_id": "p104-side-correction", + "base_commit": "17469fff78c22941280f04d39dc5a1faee09c840", + "original_card": { + "id": "p104-side-correction", + "question": "Can joint helper bases and a legal causal split improve the complete P104 productive/paid invoice?", + "starting_points": [ + "docs/research/current-priorities.md", + "docs/research/research-family-status.md", + "certificates/selected-result.json", + "docs/research/pr-intake-evidence/pr5599-completion/PROOF-REVIEW.md", + "research/p104-helper-subspace-splits/README.md", + "research/dyadic-helper-channel-capacity/README.md" + ], + "methods": [ + "Construct and independently check one source-bound instance of the stated first experiment.", + "Seek an exact counterexample or target-specific complete-budget obstruction to that same proposed change." + ], + "acceptance_gate": "An exact arbitrary-input identity, source/target frame availability and restoration at the chosen cut, plus the complete channel+correction+idle/hosting bill or an explicit favorable bound. The native channel alone is not a supplier. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_selected_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read revision 8, the selected review and live exact-source handoffs. Then follow this card's bounded first_experiment.", + "scope": "Source-bound orientation only, not a supplier replay or theorem proof." + }, + "first_experiment": "Start with the selected #5599 emitted word and review pending #5718 distinct input/output bases plus #5717/#5719 coverage before claiming work. Pick one uncovered source word, helper group and cut region. Prove the arbitrary-input relation and legal entry/exit corrections, then compare full target and paid profiles. Reject if completion, owned lifetimes or consumer costs repay the gain. A static pairing rank alone is not a physical split.", + "bottleneck_link": "Judge the actual current supplier contract and complete signed target/paid bill; frozen-profile ceilings require an applicability proof.", + "allowed_variations": [ + "One exact source head, helper/cut region or quantified proposition and changed hypothesis; check live handoffs first. Different seeds are not different scopes." + ], + "scope_change_triggers": [ + "Changing source head, helper/cut domain, operation alphabet or caller boundary without recording the new scope.", + "Treating an archived proposal or local numerical pass as complete supplier admission." + ], + "overlap_terms": [ + "P104", + "helper basis", + "helper split", + "5718", + "dyadic capacity" + ], + "existing_checks": [ + { + "scope": "PR #4133: literal-slot defect", + "evidence": "research/p104-literal-slot-defect/README.md", + "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.", + "status": "author-checked", + "source_commit": "88666f1dee93fbd85b31fd5d6f91a219e111b5f4", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4136: uniform commutation gap", + "evidence": "research/p104-uniform-commutation-gap/README.md", + "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.", + "status": "author-checked", + "source_commit": "281ce601a8be9db470de630759179c23e1dfaa88", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4140: uniform encoding gap", + "evidence": "research/p104-uniform-encoding-gap/README.md", + "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.", + "status": "author-checked", + "source_commit": "de25c6525aa866962309df5d107b32d55e6e5628", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4153: source-chart shortcut exhausts its optimistic allowance", + "evidence": "research/p104-source-chart-shortcut/README.md", + "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.", + "status": "author-checked", + "source_commit": "9123241fea53df77e51ffe30d9aca1625d4bf3a8", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4154: fiber-tag seam mismatch", + "evidence": "research/p104-fiber-tag-seam/README.md", + "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.", + "status": "author-checked", + "source_commit": "4ffcdaee5d6255a9cea1fe53a5424435068089d0", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "Selected PR5599: complete helper-subspace construction and independent caller replay; five framework assumptions remain.", + "evidence": "docs/research/pr-intake-evidence/pr5599-completion/PROOF-REVIEW.md", + "remaining": "The next experiment must identify uncovered source-specific work. Successor archive intake does not transfer this admission.", + "status": "reviewed", + "source_commit": "09dd0965711ca7eeb169057a420abab1c9052137", + "selected_record_sha256": "2a0220e866417774606e0f991e41b9c1d26b1f43b97857238cf478dbc7d330b5" + } + ] + }, + "scope_status": "changed", + "actual_scope": "Transfer the #7107 retimed rank-eight helper split to the exact #7108 signed rank-nine certificate.", + "scope_change_reason": "The new independent helper split and the signed caller may compose; a literal joint replay and full price determine the gain.", + "bottleneck_link": "Compare the complete signed productive and paid profile on the unchanged complex supplier contract.", + "stop_rule": "Require zero exact endpoint failures, all changed chart columns and signed routes, two strict rational price engines, and clean replay.", + "outcome": "completed", + "evidence": "README.md, CUT-PROOF.md, RESULT.json and the hash-bound REPLAY.tar.gz.", + "author": "ToikY", + "ai_assistance": "Substantial OpenAI Codex assistance with exact construction and independent verification.", + "open_questions": [ + { + "question": "Can a total physical provider and common-volume tariff bridge admit the retained odd-scalar word?", + "why_it_matters": "The exponent retains the source tariff and all-width contracts.", + "first_step": "Start from #6998 and audit the source/provider conversion and A6 trace under one tape width model.", + "blocked_by": "The fixed-tape conversion and total rounded provider are unresolved." + } + ] +} diff --git a/research/signed-rank9-rank8-split/VERIFY.json b/research/signed-rank9-rank8-split/VERIFY.json new file mode 100644 index 0000000000..f13d57a73c --- /dev/null +++ b/research/signed-rank9-rank8-split/VERIFY.json @@ -0,0 +1,19 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [], + "commands": [ + { + "argv": [ + "{python}", + "-I", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 600, + "checks": "Clean exact normalized native and caller replay, changed chart maps and phase, precision, both directed prices and negative controls." + } + ] +} diff --git a/research/signed-rank9-rank8-split/cut.py b/research/signed-rank9-rank8-split/cut.py new file mode 100644 index 0000000000..7268778426 --- /dev/null +++ b/research/signed-rank9-rank8-split/cut.py @@ -0,0 +1,191 @@ +"""Independent exact cut, operand rebinding and full-domain split identities.""" +from fractions import Fraction as Q +import gzip +from hashlib import sha256 +import json +from pathlib import Path +import sys + +WORD='34085a6c502ac07530001bdcbc85ad0ec9637f5dda28c9593a0b0d6dd6613d24' +CUT=37412 +LO,HI=37403,39691 +MOVE=38784 +ROLE,PIVOT,FRAME=533,1468,745 +A={533:Q(1),1454:Q(-2)} +B={533:Q(1),1468:Q(1),843:Q(-1)} +C={533:Q(1),1251:Q(4),1468:Q(1),1454:Q(-2)} +D={1468:Q(1)} +G=[['ADD',1468,533,'1',3],['ADD',1468,1251,'4',3],['ADD',1468,1454,'-2',3]] +J=[['ADD',533,1468,'-1',745],['ADD',843,1468,'1',745], + ['ADD',1468,533,'1',745],['ADD',1468,1454,'-2',745]] + + +def update(v,k,a): + x=v.get(k,Q(0))+a + if x:v[k]=x + else:v.pop(k,None) + + +def row(vector,events): + v=vector.copy() + for e in reversed(events): + op,r=e[:2] + a=v.get(r,Q(0)) + if not a or op=='MOVE':continue + if op in ('INIT','CLEAR'): + del v[r] + elif op=='SCALE': + update(v,r,a*(Q(e[-2])-1)) + elif op=='COPY': + del v[r] + update(v,e[2],a*Q(e[-2])) + elif op=='ADD': + update(v,e[2],a*Q(e[-2])) + else:raise AssertionError(op) + return v + + +def column(vector,events): + v=vector.copy() + for e in events: + op,r=e[:2] + if op=='MOVE':continue + if op in ('INIT','CLEAR'): + v.pop(r,None) + elif op=='SCALE': + update(v,r,v.get(r,Q(0))*(Q(e[-2])-1)) + elif op=='COPY': + value=Q(e[-2])*v.get(e[2],Q(0)) + v.pop(r,None) + update(v,r,value) + elif op=='ADD': + update(v,r,Q(e[-2])*v.get(e[2],Q(0))) + else:raise AssertionError(op) + return v + + +def operands(e): + return (1,2) if e[0] in ('ADD','COPY') else (1,) + + +def inverse(events): + return [[*e[:-2],str(-Q(e[-2])),e[-1]] for e in reversed(events)] + + +def span(basis): + s={0} + for x in basis: + assert x not in s + s|={v^x for v in s} + return s + + +def fmt(v): + return {str(k):str(x) for k,x in sorted(v.items())} + + +def main(path): + raw=gzip.decompress(path.read_bytes()) + assert sha256(raw).hexdigest()==WORD + w=json.loads(raw); seq=w['program']; n=w['public'] + assert n==1481 and w['owned_fields']==51 and len(seq)==71238 + assert seq[MOVE]==['MOVE',533,3,747,False] + contacts=[i for i in range(LO,HI) if any(seq[i][k]==ROLE for k in operands(seq[i]))] + assert contacts==[MOVE] and LO<=CUT=n:z[i]+=1 + elif successor and z[i]==PIVOT:z[i]=n + return z + rebound=[{'source_index':i,'before':e,'after':shift(e,True)} + for i,e in enumerate(seq) if i>=CUT and any(e[k]==PIVOT for k in operands(e))] + inserted={'input':inverse(G),'at_cut':[['MOVE',533,3,745,False]]+J+ + [shift(e,True) for e in inverse(J)]+[['MOVE',533,745,747,False]], + 'output':[shift([*e[:-1],245],True) for e in G]} + program=inserted['input']+[shift(e) for e in seq[:CUT]]+inserted['at_cut'] + program += [shift(e,True) for i,e in enumerate(seq[CUT:],CUT) if i!=MOVE] + program += inserted['output'] + final=w['final']+[245] + final[PIVOT]=745 + new=dict(w,public=n+1,initial=w['initial']+[745],final=final,program=program) + current=new['initial']+[None]*w['owned_fields'] + old_owned=[]; new_owned=[] + for i,e in enumerate(program): + op,r=e[:2] + if op=='MOVE': + assert current[r]==e[2] and e[4]==(r>=n+1) + current[r]=e[3] + elif op=='INIT': + assert r>=n+1 and current[r] is None + current[r]=e[2] + elif op=='CLEAR': + assert r>=n+1 and current[r]==e[2] + current[r]=None + else: + assert current[r]==e[-1] + if op in ('ADD','COPY'):assert current[e[2]]==e[-1] + if op in ('INIT','CLEAR') or op=='MOVE' and e[4]: + new_owned.append([op,r-1,*e[2:]]) + for e in seq: + if e[0] in ('INIT','CLEAR') or e[0]=='MOVE' and e[4]:old_owned.append(e) + assert current==final+[None]*w['owned_fields'] and old_owned==new_owned + checked=(533,843,1251,1454,1468,1480,n) + for r in checked: + expected=row({r:Q(1)},seq) if r=n and r