From e23c5c492621e7cfa1eccc3e36e17227c06b5d91 Mon Sep 17 00:00:00 2001 From: DreamingOfClouds Date: Sun, 25 Oct 2026 10:00:35 -0500 Subject: [PATCH 1/2] fix(research): wordram-ntt-kernel VERIFY.json input must be a repo path The planner requires Git-tracked repo-relative inputs; "MANIFEST.json" broke the onboarding tests (test_research_matrix_batches) for every PR based on current main. Co-Authored-By: Claude Opus 5.5 --- research/wordram-ntt-kernel/VERIFY.json | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/research/wordram-ntt-kernel/VERIFY.json b/research/wordram-ntt-kernel/VERIFY.json index 4ae0f65622..3e43a2b044 100644 --- a/research/wordram-ntt-kernel/VERIFY.json +++ b/research/wordram-ntt-kernel/VERIFY.json @@ -1,7 +1,7 @@ { "format": "standalone source-export research package", "inputs": [ - "MANIFEST.json" + "research/wordram-ntt-kernel/MANIFEST.json" ], "commands": [ [ From 452d27dde67ee9f772dbbd3be129db97a8ecb9c1 Mon Sep 17 00:00:00 2001 From: DreamingOfClouds Date: Sun, 25 Oct 2026 11:37:02 -0500 Subject: [PATCH 2/2] research: P104 free helper endpoints, conditional kappa .0030814243 (retime of PR5551 word) Retimes helper start/final frames and collapses 170 stops on PR5551's pinned word (scalar program identical, all 208 main endpoints unchanged). Ships both words, an exact retime checker, literal-only pricing edits and a starts-only supporting word (.0030768801). Conditional on free helper start and final frames. Co-Authored-By: Claude Opus 5.5 --- .../LITERAL-CHANGES.diff | 58 +++ research/p104-free-endpoint-retime/README.md | 74 ++++ .../p104-free-endpoint-retime/RESULT.json | 416 ++++++++++++++++++ .../p104-free-endpoint-retime/SOURCES.json | 38 ++ research/p104-free-endpoint-retime/TASK.json | 116 +++++ .../p104-free-endpoint-retime/VERIFY.json | 31 ++ .../WORD-STARTS-ONLY.json.gz | Bin 0 -> 106527 bytes .../p104-free-endpoint-retime/WORD.json.gz | Bin 0 -> 106453 bytes research/p104-free-endpoint-retime/common.py | 47 ++ .../inputs/pr5545-source-closure.tar.gz | Bin 0 -> 469619 bytes .../inputs/pr5551-WORD.json.gz | Bin 0 -> 107082 bytes .../inputs/pr5551-pricing.py | 156 +++++++ .../pricing-starts-only.py | 156 +++++++ research/p104-free-endpoint-retime/pricing.py | 156 +++++++ research/p104-free-endpoint-retime/retime.py | 88 ++++ research/p104-free-endpoint-retime/verify.py | 83 ++++ research/p104-free-endpoint-retime/verify.sh | 3 + 17 files changed, 1422 insertions(+) create mode 100644 research/p104-free-endpoint-retime/LITERAL-CHANGES.diff create mode 100644 research/p104-free-endpoint-retime/README.md create mode 100644 research/p104-free-endpoint-retime/RESULT.json create mode 100644 research/p104-free-endpoint-retime/SOURCES.json create mode 100644 research/p104-free-endpoint-retime/TASK.json create mode 100644 research/p104-free-endpoint-retime/VERIFY.json create mode 100644 research/p104-free-endpoint-retime/WORD-STARTS-ONLY.json.gz create mode 100644 research/p104-free-endpoint-retime/WORD.json.gz create mode 100644 research/p104-free-endpoint-retime/common.py create mode 100644 research/p104-free-endpoint-retime/inputs/pr5545-source-closure.tar.gz create mode 100644 research/p104-free-endpoint-retime/inputs/pr5551-WORD.json.gz create mode 100644 research/p104-free-endpoint-retime/inputs/pr5551-pricing.py create mode 100644 research/p104-free-endpoint-retime/pricing-starts-only.py create mode 100644 research/p104-free-endpoint-retime/pricing.py create mode 100644 research/p104-free-endpoint-retime/retime.py create mode 100644 research/p104-free-endpoint-retime/verify.py create mode 100755 research/p104-free-endpoint-retime/verify.sh diff --git a/research/p104-free-endpoint-retime/LITERAL-CHANGES.diff b/research/p104-free-endpoint-retime/LITERAL-CHANGES.diff new file mode 100644 index 0000000000..fa9154b209 --- /dev/null +++ b/research/p104-free-endpoint-retime/LITERAL-CHANGES.diff @@ -0,0 +1,58 @@ +--- inputs/pr5551-pricing.py (PR5551 head 1123635a) ++++ pricing.py (headline) +@@ -11,7 +11,7 @@ + from fractions import Fraction as Q + import local as L + +-KAPPA, TESTED = Q('.00304153'), Q('.0030415305') ++KAPPA, TESTED = Q('.00308142'), Q('.0030814205') + PREVIOUS = Q('.00304117') + + +@@ -61,7 +61,7 @@ + second_p[8*(j+1)] += 208 + L.need((targets,paid) == (second_t,second_p), 'Independent full invoice') + L.need(max(targets) == 145 and max(paid) == 72, 'Maximum recursive ranks') +- L.need(sum(targets.values()) == 12814 and sum(paid.values()) == 69912, 'Complete field and call counts') ++ L.need(sum(targets.values()) == 12814 and sum(paid.values()) == 66852, 'Complete field and call counts') + L.need(sum(r*n for r,n in targets.items())-sum(r*n for r,n in paid.items()) == 760, 'Complete rank surplus') + return targets,paid,counts + +@@ -139,7 +139,7 @@ + L.need(wrong_cutoff[0] > 1, 'Old cutoff fails with this helper inventory') + bad=outer_module.ledger(dict(params,bit_saving=Q('.0027'))) + L.need(any(x <= 0 for x in bad['strict_checks'].values()), 'Insufficient BIT contract rejected') +- return encode({'kappa':KAPPA,'kappa_decimal':'.00304153','previous_open_pr5545':PREVIOUS,'gain':KAPPA-PREVIOUS, ++ return encode({'kappa':KAPPA,'kappa_decimal':'.00308142','previous_open_pr5545':PREVIOUS,'gain':KAPPA-PREVIOUS, + 'relative_gain_percent':100*(KAPPA/PREVIOUS-1),'raw_root_interval':[lower,upper], + 'raw_headroom':[lower-KAPPA,upper-KAPPA],'margin_at_previous':E.display(margin(PREVIOUS)), + 'targets':T,'paid':P,'productive_fields':sum(T.values()),'paid_calls':sum(P.values()), +--- inputs/pr5551-pricing.py (PR5551 head 1123635a) ++++ pricing-starts-only.py (supporting) +@@ -11,7 +11,7 @@ + from fractions import Fraction as Q + import local as L + +-KAPPA, TESTED = Q('.00304153'), Q('.0030415305') ++KAPPA, TESTED = Q('.003076879'), Q('.0030768795') + PREVIOUS = Q('.00304117') + + +@@ -61,7 +61,7 @@ + second_p[8*(j+1)] += 208 + L.need((targets,paid) == (second_t,second_p), 'Independent full invoice') + L.need(max(targets) == 145 and max(paid) == 72, 'Maximum recursive ranks') +- L.need(sum(targets.values()) == 12814 and sum(paid.values()) == 69912, 'Complete field and call counts') ++ L.need(sum(targets.values()) == 12814 and sum(paid.values()) == 67374, 'Complete field and call counts') + L.need(sum(r*n for r,n in targets.items())-sum(r*n for r,n in paid.items()) == 760, 'Complete rank surplus') + return targets,paid,counts + +@@ -139,7 +139,7 @@ + L.need(wrong_cutoff[0] > 1, 'Old cutoff fails with this helper inventory') + bad=outer_module.ledger(dict(params,bit_saving=Q('.0027'))) + L.need(any(x <= 0 for x in bad['strict_checks'].values()), 'Insufficient BIT contract rejected') +- return encode({'kappa':KAPPA,'kappa_decimal':'.00304153','previous_open_pr5545':PREVIOUS,'gain':KAPPA-PREVIOUS, ++ return encode({'kappa':KAPPA,'kappa_decimal':'.003076879','previous_open_pr5545':PREVIOUS,'gain':KAPPA-PREVIOUS, + 'relative_gain_percent':100*(KAPPA/PREVIOUS-1),'raw_root_interval':[lower,upper], + 'raw_headroom':[lower-KAPPA,upper-KAPPA],'margin_at_previous':E.display(margin(PREVIOUS)), + 'targets':T,'paid':P,'productive_fields':sum(T.values()),'paid_calls':sum(P.values()), diff --git a/research/p104-free-endpoint-retime/README.md b/research/p104-free-endpoint-retime/README.md new file mode 100644 index 0000000000..e8c177c6b7 --- /dev/null +++ b/research/p104-free-endpoint-retime/README.md @@ -0,0 +1,74 @@ +# Free helper endpoints on the P104 word (conditional kappa .0030814243) + +Complete conditional kappa **.0030814243** (**+3.99e-5**, +1.31% over +[PR5551](https://github.com/CrocSwap/integer-mult-bounds/pull/5551)'s .0030415312). The claim is +tested at .0030814205; the exact raw crossing lies in +(15407121669/5000000000000, 308142433381/100000000000000) = (.00308142433380, .00308142433381). +A supporting word that needs only free helper *start* frames reaches **.0030768801** (+3.54e-5); +its exact crossing lies in (76922002003/25000000000000, 307688008013/100000000000000) = (.00307688008012, .00307688008013), tested at .0030768795. + +**Conditional on** (a) the five framework assumptions retained by PR5544/5545/5551; (b) the validity +of PR5551, which is unreproduced at the time of writing; (c) **free helper START frames and free +helper FINAL frames**. For (c): the verifier checks only that each helper's initial frame is strictly +nested in its final frame and that the native boundary map has rank equal to the dimension gap; only +the X-initial and Y-final frames are literal (the 104 ports). The canonical-start rule exists only +in the #4610 compact-width verifier. Unmodified PR5544/5545 already has mid-frame helper starts +(23 distinct start frames, dimensions 0, 1, 4, 5) and mixed finals (18 distinct, dimensions 4, 5, 8, 9). +The headline word needs both (c)-starts and (c)-finals; the supporting word needs (c)-starts only. The +selected record is not changed; no independent human or proof-kernel acceptance is claimed. + +## What the edit is (and is not) +This is **not** an unchanged circuit. Relative to PR5551's pinned word (`inputs/pr5551-WORD.json.gz`): +- The scalar program is identical: the same 21,686 ADD/COPY/SCALE/INIT/CLEAR events in the same order + with the same registers and coefficients (no register merge or reordering). +- Only frame labels and MOVE stops change. The solve chose the subspace at every ADD-chart cluster + subject to the verifier's nesting laws (an exact-lattice CP-SAT retime), and **170 stops became + redundant and are deleted** (3,624 -> 3,454 MOVEs; 25,310 -> 25,140 events). The supporting word + deletes 141 stops (3,483 MOVEs). +- Headline word: 168 helper start spans and 23 helper final spans differ from PR5551's (22 of the + finals move from dimension 8 to 9); 607 scalar-event frame labels and 607 kept MOVE stops are + relabelled (149 of those stops belong to main registers, whose intermediate frames move together with a + helper in a shared ADD chart). Supporting word: 169 helper starts differ, 0 finals. +- All 208 main registers (104 X sources, 104 Y targets) keep identical initial and final spans, so the + literal ports, the caller and the controller are untouched. +- Productive fields stay 12,814 and the rank-mass surplus stays 760; the credited helper profile moves + (rank 9: 294 -> 425, rank 8: 122 -> 14, rank 7: 24 -> 0) and paid calls fall 69,912 -> 66,852 + (headline) / 67,374 (supporting). + +## Files +- `WORD.json.gz` (headline, free starts + finals) and `WORD-STARTS-ONLY.json.gz` (supporting). +- `retime.py`: the CP-SAT solve is multi-worker and not byte-reproducible, so instead of a generator + this exact stdlib checker proves a candidate is a legal retime of the pinned word: identical scalar + program, MOVEs a subsequence of the pinned MOVEs, all 208 main endpoint spans unchanged, 104 ports + and live list equal. Nesting, ownership, the common-chart frame law and rank = dimension gap are then + enforced by the unmodified PR5545 `local.py` replay and `native()`. +- `pricing.py`, `pricing-starts-only.py`: PR5551's `pricing.py` (`inputs/pr5551-pricing.py`) with ONLY + literal changes: the KAPPA/TESTED claim line, the call census 69912 -> 66852 / 67374, and the + `kappa_decimal` label. `LITERAL-CHANGES.diff` shows them; `verify.py` re-applies the substitutions + and checks byte equality. No `local.py` change is needed (735 public inputs), so the unmodified + PR5545 `local.py` from the byte-pinned capsule is used. +- `verify.py` / `verify.sh` (stdlib, Python 3.12): `--part headline` and `--part starts-only`, each + about 6 minutes: retime legality, replay, transposed columns, native maps, physical caller, pricing + with both moment engines, all 54 strict + 4 functional outer checks, exact crossing interval. +- `inputs/pr5545-source-closure.tar.gz`, `inputs/pr5551-WORD.json.gz`, `inputs/pr5551-pricing.py`: + PR5551's byte-pinned inputs (`SOURCES.json`). + +## Independent audit +An internal AI audit (separate read-only Claude agent) reproduced an earlier version of this retime on +PR5545's word through the real replay/native/pricing stack, found helper credit and main endpoints +sound, and rated maintainer intent for free helper frames as unresolved, which is why this is +conditional. The PR5551-based words here are checked by `verify.py`; they have not had a separate audit. + +## Credits +Builds on PR5551 (thu-nmrc) and the P104 word line of PR5544/5545 (aliromman; lineage +PR2305/2152/2219). The idea of a fresh helper starting at a non-canonical frame follows the +hand-off precedent of PR5472 (GamingPuzzled). All predecessor credit is retained. + +Prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code. + +## Open next questions + +- Are free helper start frames (non-canonical, mid-frame) admissible in the P104 caller contract? Both words depend on it; the supporting word depends on nothing else. +- Are free helper final frames admissible? The finals-free gain is the difference between the two words (.0030814243 vs .0030768801). +- Can the retime be reproduced by a deterministic single-threaded solve, so a generator can replace the checker? +- Independent reproduction of PR5551, on which this package builds. Interaction with hand-off words such as PR5553 is not tested here. diff --git a/research/p104-free-endpoint-retime/RESULT.json b/research/p104-free-endpoint-retime/RESULT.json new file mode 100644 index 0000000000..a953f0a60a --- /dev/null +++ b/research/p104-free-endpoint-retime/RESULT.json @@ -0,0 +1,416 @@ +{ + "headline": { + "compiler": { + "H": 690116000000000, + "N": "2^690116000000000", + "eta": { + "lower": "0.000000150915557284809901282836", + "upper": "0.000000150915557284809901282837" + }, + "gap": "1/14000000000", + "integer_test_exponent": 49294, + "logarithm_power": 1000, + "theta": "63/64", + "uniform_saving": "21569943/7000000000", + "word_materialized": false + }, + "full_forward_calls": 18, + "gain": "161/4000000", + "kappa": "154071/50000000", + "kappa_decimal": ".00308142", + "margin_at_previous": { + "lower": "9.863889227373890942015545303213", + "upper": "9.863889227373890942015545303214" + }, + "negative_controls": { + "old_BIT": "Rejected by outer inequalities", + "old_cutoff": "Rejected by completion-tail ratio greater than one" + }, + "nonrecursive": { + "fixed_scalar_growth_bound": "At most 2^(16*26000) before native factors; a declared constant, not an attained norm.", + "local_routes": 5164000, + "local_scalar": 217428, + "peak_owned_fields": 1, + "raw_budget": 1000000000, + "raw_scalar_upper": 184647552, + "tensor_native_growth_bound": "Each rank-r Gaussian has row l1 norm at most 2^(rf); sum of local ranks is 5894." + }, + "ordinary_BIT": { + "admitted": "17/5000", + "after_cover": "69/20000", + "atom": "1/250", + "before_cover": "3459/1000000", + "ordinary_saving": "8590884599/2500000000000", + "prime_rule": "odd q > 2^26*N^5 avoiding all fixed denominators and rank witnesses" + }, + "outer": { + "functional_checks": { + "actual_new_BIT_stock_sublinear": "3485999999253/3500000000000", + "fixed_halo_explicit_metadata_branch": "269500000001/3500000000", + "new_BIT_row_stock_sublinear_in_active_group": "13957999997009/14000000000000", + "new_semantic_group_guard": "3/14000000000" + }, + "margins": { + "boundary_algebraic_matrix": "603958375956860117/196000000000000000000", + "fused_gaussian": "603958375870580351/196000000000000000000", + "global_coordinate_router": "10784971/3500000000", + "group_bit_router": "150989597467645087/49000000000000000000", + "group_scans": "6999999999/7000000000", + "main_transform": "603958361956860117/196000000000000000000", + "microbox_face_corrections": "269500000001/3500000000", + "polynomial_products": "13999999999/14000000000", + "sparse_union_movement": "80228958375956860117/196000000000000000000" + }, + "parameters": { + "a": "10784971/3500000000", + "b": "8627977/2800000000", + "beta": "13999999997/14000000000", + "bit_saving": "17/5000", + "cap_xi": "178228958361956860117/196000000000000000000", + "complex_uniform_saving": "21569943/7000000000", + "d": "1/14000000000", + "epsilon": "13999999999/14000000000", + "kappa": "154071/50000000", + "lambda_": "3987674319/4000000000", + "lambda_prime": "13956860117/14000000000", + "layout": "1/14000000000", + "q": "43139883/14000000000", + "r0": "1/140000000000", + "stop": "1/14000000000", + "tested_saving": "6162841/2000000000" + }, + "strict_checks": { + "actual_bit_above_effective": "1115029/3500000000", + "actual_logarithmic_gamma_guard": "1/14000000000", + "actual_logarithmic_group_guard": "17771041659043139883/98000000000000000000", + "alpha_logarithm_absorption": "1/140000000000", + "boundary_algebraic_matrix_above_kappa": "55956860117/196000000000000000000", + "cap_above_band": "80228958361956860117/196000000000000000000", + "cap_below_cell": "17771041624043139883/196000000000000000000", + "cap_below_phase_cell_power": "213771041638043139883/196000000000000000000", + "complex_above_effective": "1/14000000000", + "complex_below_one_over_32": "78872023/2800000000", + "complex_endpoint": "1/7000000000", + "epsilon_below_one": "1/14000000000", + "epsilon_positive": "13999999999/14000000000", + "fine_prime_halo_umbrella": "7/2", + "fused_gaussian_above_kappa": "55870580351/196000000000000000000", + "gaussian_above_main": "6956860117/98000000000000000000", + "global_coordinate_router_above_kappa": "1/3500000000", + "global_gamma_power_slack": "9/140000000000", + "group_below_dimension": "1/7000000000", + "group_bit_router_above_kappa": "17467645087/49000000000000000000", + "group_gauge_power_slack": "17771041658343139883/98000000000000000000", + "group_key_fits_record": "1/7000000000", + "group_positive": "13999999997/14000000000", + "group_scans_above_kappa": "6978430059/7000000000", + "halo_covers_generic_inverse_radius": "5", + "improvement_over_user_baseline": "675224790400418148631/500000000000000000000000", + "lambda_above_internal": "1/28000000000", + "lambda_above_sigma": "3/28000000000", + "lambda_above_tau": "1/28000000000", + "lambda_prime_above_lambda": "1/28000000000", + "lambda_prime_above_leaf": "5591372023/39200000000000000000", + "leaf_saving_above_effective": "2791372023/39200000000000000000", + "main_transform_above_kappa": "41956860117/196000000000000000000", + "membership_arithmetic_fits_record": "1/14000000000", + "microbox_face_corrections_above_kappa": "269489215031/3500000000", + "microbox_halo_volume": "1106000000003/14000000000", + "new_complex_uniform_saving_above_b": "1/14000000000", + "new_semantic_guard_with_C1_one": "1/14000000000", + "polynomial_products_above_kappa": "13956860119/14000000000", + "positive_layout_slack": "1/14000000000", + "q_below_effective": "1/14000000000", + "q_below_internal": "1/14000000000", + "q_below_leaf": "5591372023/39200000000000000000", + "q_positive": "43139883/14000000000", + "short_record_fallback": "2791372023/2800000000", + "source_axis_superpolynomial": "1/14000000000", + "sparse_union_movement_above_kappa": "79625000055956860117/196000000000000000000", + "stop_below_one": "13999999999/14000000000", + "stop_positive": "1/14000000000", + "strassen_integer_power_gap": "1951441519231", + "support_router_span": "3/14000000000", + "theta_positive_polynomial_power": "2", + "union_header_fits_record": "3/14000000000", + "union_tag_work_per_visit_fits_record": "3/14000000000" + } + }, + "paid": { + "1": 41340, + "16": 416, + "2": 8262, + "24": 416, + "3": 8928, + "32": 416, + "4": 1674, + "40": 416, + "48": 416, + "5": 2952, + "56": 416, + "6": 324, + "64": 416, + "7": 252, + "72": 208 + }, + "paid_calls": 66852, + "previous_open_pr5545": "304117/100000000", + "productive_fields": 12814, + "query_shears": 15, + "rank_mass_surplus": 760, + "raw_headroom": [ + "21669/5000000000000", + "433381/100000000000000" + ], + "raw_root_interval": [ + "15407121669/5000000000000", + "308142433381/100000000000000" + ], + "relative_gain_percent": "402500/304117", + "strictification": { + "alpha": { + "lower": "0.999999996077490279252156945261", + "upper": "0.999999996077490279252156945262" + }, + "cutoff": 17, + "delta": { + "lower": "0.954776932282871740517530812724", + "upper": "0.954776932282871740517530812725" + }, + "floor": 18, + "gamma": { + "lower": "0.967371300368832148444639574582", + "upper": "0.967371300368832148444639574583" + }, + "normalized_paid_upper": "5242880004882813/5242880536870912", + "power": 1024, + "reserve": "1/10000000000", + "tail_offset": "1/5", + "tested": "6162841/2000000000" + }, + "targets": { + "145": 208, + "17": 416, + "25": 416, + "33": 416, + "4": 1494, + "41": 416, + "49": 416, + "5": 90, + "57": 416, + "65": 416, + "73": 208, + "8": 252, + "9": 7650 + }, + "whole_idle_jobs": 3120 + }, + "starts_only": { + "compiler": { + "H": 690116000000000, + "N": "2^690116000000000", + "eta": { + "lower": "0.000000154449432404612929595969", + "upper": "0.000000154449432404612929595970" + }, + "gap": "1/14000000000", + "integer_test_exponent": 49294, + "logarithm_power": 1000, + "theta": "63/64", + "uniform_saving": "5384539/1750000000", + "word_materialized": false + }, + "full_forward_calls": 18, + "gain": "35709/1000000000", + "kappa": "3076879/1000000000", + "kappa_decimal": ".003076879", + "margin_at_previous": { + "lower": "8.763458055403927069103933159568", + "upper": "8.763458055403927069103933159569" + }, + "negative_controls": { + "old_BIT": "Rejected by outer inequalities", + "old_cutoff": "Rejected by completion-tail ratio greater than one" + }, + "nonrecursive": { + "fixed_scalar_growth_bound": "At most 2^(16*26000) before native factors; a declared constant, not an attained norm.", + "local_routes": 5193000, + "local_scalar": 217428, + "peak_owned_fields": 1, + "raw_budget": 1000000000, + "raw_scalar_upper": 184647552, + "tensor_native_growth_bound": "Each rank-r Gaussian has row l1 norm at most 2^(rf); sum of local ranks is 5894." + }, + "ordinary_BIT": { + "admitted": "17/5000", + "after_cover": "69/20000", + "atom": "1/250", + "before_cover": "3459/1000000", + "ordinary_saving": "8590884599/2500000000000", + "prime_rule": "odd q > 2^26*N^5 avoiding all fixed denominators and rank witnesses" + }, + "outer": { + "functional_checks": { + "actual_new_BIT_stock_sublinear": "3485999999253/3500000000000", + "fixed_halo_explicit_metadata_branch": "269500000001/3500000000", + "new_BIT_row_stock_sublinear_in_active_group": "13957999997009/14000000000000", + "new_semantic_group_guard": "3/14000000000" + }, + "margins": { + "boundary_algebraic_matrix": "603068339956923691/196000000000000000000", + "fused_gaussian": "603068339870771073/196000000000000000000", + "global_coordinate_router": "4307631/1400000000", + "group_bit_router": "60306835387077107/19600000000000000000", + "group_scans": "6999999999/7000000000", + "main_transform": "603068325956923691/196000000000000000000", + "microbox_face_corrections": "269500000001/3500000000", + "polynomial_products": "13999999999/14000000000", + "sparse_union_movement": "80228068339956923691/196000000000000000000" + }, + "parameters": { + "a": "4307631/1400000000", + "b": "43076311/14000000000", + "beta": "13999999997/14000000000", + "bit_saving": "17/5000", + "cap_xi": "178228068325956923691/196000000000000000000", + "complex_uniform_saving": "5384539/1750000000", + "d": "1/14000000000", + "epsilon": "13999999999/14000000000", + "kappa": "3076879/1000000000", + "lambda_": "3987692483/4000000000", + "lambda_prime": "13956923691/14000000000", + "layout": "1/14000000000", + "q": "43076309/14000000000", + "r0": "1/140000000000", + "stop": "1/14000000000", + "tested_saving": "6153759/2000000000" + }, + "strict_checks": { + "actual_bit_above_effective": "452369/1400000000", + "actual_logarithmic_gamma_guard": "1/14000000000", + "actual_logarithmic_group_guard": "17771931695043076309/98000000000000000000", + "alpha_logarithm_absorption": "1/140000000000", + "boundary_algebraic_matrix_above_kappa": "55956923691/196000000000000000000", + "cap_above_band": "80228068325956923691/196000000000000000000", + "cap_below_cell": "17771931660043076309/196000000000000000000", + "cap_below_phase_cell_power": "213771931674043076309/196000000000000000000", + "complex_above_effective": "1/14000000000", + "complex_below_one_over_32": "394423689/14000000000", + "complex_endpoint": "1/7000000000", + "epsilon_below_one": "1/14000000000", + "epsilon_positive": "13999999999/14000000000", + "fine_prime_halo_umbrella": "7/2", + "fused_gaussian_above_kappa": "55870771073/196000000000000000000", + "gaussian_above_main": "6956923691/98000000000000000000", + "global_coordinate_router_above_kappa": "1/3500000000", + "global_gamma_power_slack": "9/140000000000", + "group_below_dimension": "1/7000000000", + "group_bit_router_above_kappa": "6987077107/19600000000000000000", + "group_gauge_power_slack": "17771931694343076309/98000000000000000000", + "group_key_fits_record": "1/7000000000", + "group_positive": "13999999997/14000000000", + "group_scans_above_kappa": "3489230923/3500000000", + "halo_covers_generic_inverse_radius": "5", + "improvement_over_user_baseline": "672954290400418148631/500000000000000000000000", + "lambda_above_internal": "1/28000000000", + "lambda_above_sigma": "3/28000000000", + "lambda_above_tau": "1/28000000000", + "lambda_prime_above_lambda": "1/28000000000", + "lambda_prime_above_leaf": "27956923689/196000000000000000000", + "leaf_saving_above_effective": "13956923689/196000000000000000000", + "main_transform_above_kappa": "41956923691/196000000000000000000", + "membership_arithmetic_fits_record": "1/14000000000", + "microbox_face_corrections_above_kappa": "538978461849/7000000000", + "microbox_halo_volume": "1106000000003/14000000000", + "new_complex_uniform_saving_above_b": "1/14000000000", + "new_semantic_guard_with_C1_one": "1/14000000000", + "polynomial_products_above_kappa": "13956923693/14000000000", + "positive_layout_slack": "1/14000000000", + "q_below_effective": "1/14000000000", + "q_below_internal": "1/14000000000", + "q_below_leaf": "27956923689/196000000000000000000", + "q_positive": "43076309/14000000000", + "short_record_fallback": "13956923689/14000000000", + "source_axis_superpolynomial": "1/14000000000", + "sparse_union_movement_above_kappa": "79625000055956923691/196000000000000000000", + "stop_below_one": "13999999999/14000000000", + "stop_positive": "1/14000000000", + "strassen_integer_power_gap": "1951441519231", + "support_router_span": "3/14000000000", + "theta_positive_polynomial_power": "2", + "union_header_fits_record": "3/14000000000", + "union_tag_work_per_visit_fits_record": "3/14000000000" + } + }, + "paid": { + "1": 42204, + "16": 416, + "2": 8442, + "24": 416, + "3": 8442, + "32": 416, + "4": 1638, + "40": 416, + "48": 416, + "5": 2970, + "56": 416, + "6": 306, + "64": 416, + "7": 252, + "72": 208 + }, + "paid_calls": 67374, + "previous_open_pr5545": "304117/100000000", + "productive_fields": 12814, + "query_shears": 15, + "rank_mass_surplus": 760, + "raw_headroom": [ + "27003/25000000000000", + "108013/100000000000000" + ], + "raw_root_interval": [ + "76922002003/25000000000000", + "307688008013/100000000000000" + ], + "relative_gain_percent": "357090/304117", + "strictification": { + "alpha": { + "lower": "0.999999999404592592047426513673", + "upper": "0.999999999404592592047426513674" + }, + "cutoff": 17, + "delta": { + "lower": "0.956340515100833390077946018407", + "upper": "0.956340515100833390077946018408" + }, + "floor": 18, + "gamma": { + "lower": "0.967169144621326622973846552884", + "upper": "0.967169144621326622973846552885" + }, + "normalized_paid_upper": "5242880004882813/5242880536870912", + "power": 1024, + "reserve": "1/10000000000", + "tail_offset": "1/5", + "tested": "6153759/2000000000" + }, + "targets": { + "145": 208, + "17": 416, + "25": 416, + "33": 416, + "4": 1494, + "41": 416, + "49": 416, + "5": 90, + "57": 416, + "65": 416, + "7": 18, + "73": 208, + "8": 612, + "9": 7272 + }, + "whole_idle_jobs": 3120 + }, + "status": "PASS_P104_FREE_ENDPOINT_RETIME_CONDITIONAL_KAPPA" +} diff --git a/research/p104-free-endpoint-retime/SOURCES.json b/research/p104-free-endpoint-retime/SOURCES.json new file mode 100644 index 0000000000..2fe44de014 --- /dev/null +++ b/research/p104-free-endpoint-retime/SOURCES.json @@ -0,0 +1,38 @@ +{ + "schema_version": 1, + "base_commit": "32890bc5de034ab8fc93ac88ead7279a6a416d04", + "files": [ + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "fc3d4ba105e1f097d0d7d051a308281e86ab1446", + "sha256": "66974efdced4083c00025f97d95d83909a226cdf801edb9301c195c6641f6903" + }, + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "f126dd2e2dad2b669e75d1d0d0bd05c600725602", + "sha256": "f7a48bfa2659b88378282a8eee7d9fe52cdf505594124c4d1686b58510fffd72" + } + ], + "retained_source": { + "path": "research/p104-free-endpoint-retime/inputs/pr5545-source-closure.tar.gz", + "sha256": "59768da554e11b11fae52d07f520f50684cc7a9ee0bec2873edbcd6b63814837", + "export_manifest_sha256": "0a20358f9c089be1f5606c78077314e30a72998fb3c5123848d921a8d1814e76", + "commit": "18968423711fd902aaee1099979497d55603e1dc", + "files": 33, + "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/5545", + "note": "Byte-identical copy of the capsule retained by PR5551; used UNMODIFIED (no local.py edit is needed: the retimed words keep 735 public inputs)." + }, + "pinned_word": { + "path": "research/p104-free-endpoint-retime/inputs/pr5551-WORD.json.gz", + "sha256": "48f8734ca9c5adf5d60ded3a5fefbc24894d2c358ed7cb30fcc0d71718599446", + "source_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/5551", + "source_head": "1123635a6f63f23638df9459c994160e5e649d30", + "source_path": "research/p104-joint-contact/WORD.json.gz" + }, + "pinned_pricing": { + "path": "research/p104-free-endpoint-retime/inputs/pr5551-pricing.py", + "source_path": "research/p104-joint-contact/pricing.py at PR5551 head" + } +} diff --git a/research/p104-free-endpoint-retime/TASK.json b/research/p104-free-endpoint-retime/TASK.json new file mode 100644 index 0000000000..7a34be8497 --- /dev/null +++ b/research/p104-free-endpoint-retime/TASK.json @@ -0,0 +1,116 @@ +{ + "schema_version": 1, + "task_id": "scalar-to-moment", + "actual_scope": "On PR5551's pinned P104 word, retime the helper START and FINAL frames (and the intermediate frames of the shared ADD charts) with an exact-lattice CP-SAT solve, collapsing 170 now-redundant stops (141 for the starts-only variant); the 54 strict + 4 functional outer checks and the exact crossing are re-certified for the changed complete conditional moment.", + "bottleneck_link": "Free helper endpoints let credited helper rank move from many rank-8 climbs to rank-9 climbs and remove 170 rank-1 stops per call; at all 18 calls this lowers the paid profile (69,912 -> 66,852 calls) at unchanged rank-mass surplus 760, so the concave moment gap widens.", + "stop_rule": "Retain the conditional kappa only after retime.py proves each word a legal retime of PR5551's word and exact scalar/native replay, physical caller, both moment engines and all 54 strict + 4 functional outer checks pass.", + "outcome": "completed", + "author": "DreamingOfClouds, with Claude Opus 5.5 (Anthropic), via Claude Code", + "ai_assistance": "Claude Opus 5.5 via Claude Code; an internal AI audit reproduced the result independently. No independent human or proof-kernel acceptance is claimed.", + "open_questions": [ + { + "question": "Are free helper START frames (non-canonical, mid-frame) admissible in the P104 caller contract?", + "why_it_matters": "Both words depend on it; the starts-only word depends on nothing else. The verifier checks only nesting and rank = dim gap for helpers; the canonical-start rule exists only in the #4610 verifier, and unmodified PR5544/5545 already has helper starts at dims 0,1,4,5.", + "blocked_by": "Maintainer or swarm review.", + "first_step": "Decide whether helper identity rows at arbitrary nested start frames are intended in the P104 caller; WORD-STARTS-ONLY.json.gz is the test case." + }, + { + "question": "Are free helper FINAL frames admissible?", + "why_it_matters": "The headline word changes 23 helper finals (mostly dim 8 -> 9); the extra gain from finals is the difference between the two words.", + "blocked_by": "Maintainer or swarm review.", + "first_step": "Compare the two words: the finals-free gain is the difference .0030814243 - .0030768801." + }, + { + "question": "Can the retime be reproduced byte-for-byte by a deterministic solver?", + "why_it_matters": "The words are checked, not generated; a deterministic generator would shorten review.", + "blocked_by": "None; the solve is a multi-worker CP-SAT run.", + "first_step": "Re-run the exact-lattice solve single-threaded with a fixed seed and compare against retime.py." + } + ], + "scope_status": "changed", + "scope_change_reason": "The scalar-to-moment card asks about scalar A2 contractions on the retained word; this package instead retimes helper endpoint and stop frames of PR5551's P104 word, a different construction on a newer word. Recorded as changed; the card's own object is not pursued.", + "evidence": "verify.py checks each word with retime.py (legal retime of PR5551's pinned word: identical scalar program, only stops deleted and frame labels changed, all 208 main endpoint spans unchanged), the unmodified PR5545 local.py replay/columns/native, the physical caller, PR5551's pricing with literal-only changes, both moment engines, all 54 strict + 4 functional outer checks, and the exact crossing interval for each word.", + "base_commit": "32890bc5de034ab8fc93ac88ead7279a6a416d04", + "original_card": { + "id": "scalar-to-moment", + "question": "Can a changed frame itinerary remove a paid transition beyond the already covered scalar A2 contractions?", + "starting_points": [ + "docs/research/research-family-status.md", + "certificates/selected-result.json", + "research/staged544-a2-graph-rewrite/README.md", + "research/staged544-separated-a2/README.md", + "research/staged544-a2-composition-audit/README.md", + "research/staged544-a1858-contraction-audit/README.md" + ], + "methods": [ + "Derive the changed legal frame itinerary and exact child histogram.", + "Prove a scoped obstruction showing why that scalar gain cannot change the paid contract." + ], + "acceptance_gate": "An unchanged histogram is not a kappa gain; record any separate runtime or proof benefit explicitly.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read the A2 and separated-A2 constructions and their composition/contraction audits. Scalar contractions can preserve the complete recursive histogram; fewer ADDs alone do not justify further scans.", + "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately." + }, + "first_experiment": "Identify an actual paid transition to remove and construct a legal replacement frame itinerary, charging restoration, source windows and changed helpers. Compare complete before/after histograms. Stop if only scalar count changes; report that benefit honestly, without expanding the same scalar-only census.", + "bottleneck_link": "A legal change to the histogram, not addition count alone, is the bridge to an exponent gain.", + "allowed_variations": [ + "One existing scalar simplification and one proposed frame-path change." + ], + "scope_change_triggers": [ + "Submitting only another scalar count as completion of a paid-profile task." + ], + "overlap_terms": [ + "scalar simplification", + "paid profile", + "R439", + "3998", + "4019", + "4112", + "4152", + "staged544-a2-graph-rewrite", + "staged544-separated-a2", + "staged544-a2-composition-audit", + "staged544-a1858-contraction-audit" + ], + "existing_checks": [ + { + "scope": "PR #3998: consecutive A2 scalar contraction", + "evidence": "research/staged544-a2-graph-rewrite/README.md", + "remaining": "A genuinely changed paid itinerary or a distinct independent audit; no default scalar-only expansion.", + "status": "author-checked", + "source_commit": "389268a6b5e0373a3125d5c6fcd6995f4ea324f5", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4019: separated A2 sites with unchanged recursive histogram", + "evidence": "research/staged544-separated-a2/README.md", + "remaining": "A genuinely changed paid itinerary or a distinct independent audit; no default scalar-only expansion.", + "status": "author-checked", + "source_commit": "f408e09df300b575235f7f77f81948071397e16d", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4112: composition audit", + "evidence": "research/staged544-a2-composition-audit/README.md", + "remaining": "A genuinely changed paid itinerary or a distinct independent audit; no default scalar-only expansion.", + "status": "author-checked", + "source_commit": "205b7380656ba4b6316a8a493b1a3c679b8f7a0e", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4152: A1858 contraction audit", + "evidence": "research/staged544-a1858-contraction-audit/README.md", + "remaining": "A genuinely changed paid itinerary or a distinct independent audit; no default scalar-only expansion.", + "status": "author-checked", + "source_commit": "caaa14cde5962adc372fdca71f63d0f29e73c8b2", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + } + ] + } +} diff --git a/research/p104-free-endpoint-retime/VERIFY.json b/research/p104-free-endpoint-retime/VERIFY.json new file mode 100644 index 0000000000..a4cfbef7c2 --- /dev/null +++ b/research/p104-free-endpoint-retime/VERIFY.json @@ -0,0 +1,31 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [], + "commands": [ + { + "argv": [ + "{python}", + "-B", + "{package}/verify.py", + "--part", + "headline" + ], + "timeout_seconds": 600, 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z+%h-5Wp0BK%UP$`MY4U4{;}r!SQ9Rs@tr&UVSx$Bc`fka`RQo8@$Fp0+qr9AP(ZNb zA{5a;@KugaO@M(uD%GDq|%kj;4ZXY;m74|g_ zf3yzg$BuvWuBHzh2c2HgIS$6yQ877j&jwQO54nhTETn}{LD$&irWr2Gyj5;64#v;MofM4>ZG#D9Th98#s>Tx-FVw|HLc4~bgZ;))+ynZm>28HaLc*C{ita$C{@Fw2+o9YvnVc1d`4q^L-!@Z{AaIbmctn`I8JkW$Q z(r(nsL@Q+DM{u#WX5neY<_(!e97l2pxOaFVcZk(9xUg`Iy?iSyTwyDwJLXw2iRmGh=J&bpz@LM}bevh?8}a3=Avli#(w86$OKP-tQUmvjAeY%O`c*E|~;R?LZycb~28tkYpp7T7+8EN5* z>+lCP8o}4xz%C=_&E~^)jm;wC{bBR$JUgp{{mj5ltT<9wmlrgnprF!MK=&N ziXCXxj#nJrC?vE`0EG;&JNO^hDF#Y(9e0>r`=FR?XvUSs;nBzRu?DZQvs#4h5 z%#Xz>F8`HH=Ma) zeM#iZS)Fi`;k`zE4|W(xyLr}hB$nIg+m(HIss+&3Fi9BX^@{W0k?Tev>3Jn#qkLY3)rZCCi@Wd@=JSuZB8Jat7J z{h0tb`zC(x2HOEUGYHK)_WNZE^@EZ53;ZE(iZ`>E5(pOjWitBrP$gI5ie1tyEB&l#`jPWTjvZu4IanGg5OCfn22mU^79tpeR43G`S?R aELFESzqBYhRo_slmJ0x$BWC~+ 1: + m=(lo+hi)//2 + if margin(Q(m,grid))[0] > 0: + lo=m + else: + hi=m + lower,upper = Q(lo,grid),Q(hi,grid) + L.need(margin(lower)[0] > 0 and margin(upper)[1] < 0, 'Strict rational crossing enclosure') + L.need(PREVIOUS < KAPPA < TESTED < lower and margin(PREVIOUS)[0] > 0, 'Changed complete bill improves selected kappa') + t,u,v,c,b = 1-TESTED,Q(1,5),1024,17,18 + target,paid = E.moment(T,t),E.moment(P,t) + tl,th = other.moment(T,TESTED) + pl,ph = other.moment(P,TESTED) + L.need(tl > ph and max(tl,target[0]) <= min(th,target[1]) and max(pl,paid[0]) <= min(ph,paid[1]), 'Two exact moment engines') + alpha = E.divide(paid,target) + gamma = E.divide(E.moment(P,t+u),E.mul(E.power(c,u),target)) + delta = E.divide((Q(sum(T.values())*b),)*2,E.mul(E.power(c,TESTED),target)) + reserve,decay = Q(1,10**10),Q(97,100) + L.need(alpha[1] < 1-reserve and gamma[1] < decay and delta[1] < decay, 'All three charged tail ratios') + L.need(decay**128 < Q(1,16), 'Both tail decay blocks') + normalized = 1/(1+v*reserve)+Q(4,2**32) + L.need(normalized < 1 and c**64 < b**63, 'Full completion, splitting and rounding charges') + theta,power = Q(63,64),1000 + eta = E.scale(E.power(145,-v*TESTED),t) + L.need(2*(c**v)**64 <= (145**v)**63 and eta[0] > theta**power, 'Shifted exits and complement capacity') + L.need(E.power(145,v*TESTED)[1] < 2**power, 'Compiler initial range') + gap = (TESTED-KAPPA)/7 + L.need(gap.numerator == 1, 'Exact compiler integer grid') + step = gap.denominator + def wins(j): + return (step*j+1)**power < 2**j + left,right=1,2 + while not wins(right): + left,right=right,2*right + while right-left > 1: + m=(left+right)//2 + if wins(m): + right=m + else: + left=m + H=step*right + L.need(H > 8*v and wins(right) and not wins(right-1), 'Finite uniform threshold with predecessor rejection') + local_routes = (sum(local['paid'].values())+native['helper_normalizers']+native['main_adapters']+4*104+4*local['owned_lifetimes'])*1000 + L.need(local['real_scalar_allowance']+local_routes < 10**7, 'Every local scalar, route and owned operation is funded') + boundary = sum(len(word['boundaries'][side+'_program']) for side in ('left','right')) + raw = 18*10**7 + 15*1664 + 32*104*(len(word['physical_events'])+boundary) + raw += 32*104*(26+1000) + L.need(raw < 10**9, 'Complete nonrecursive raw bound') + bit = L.read(L.ROOT/'research/query-thinned-controllers/RESULT.json')['ordinary_BIT'] + atom = Q(bit['atom']) + ordinary=(1-atom)*Q(bit['after_cover'])+atom*Q('.0000384599') + admitted=Q(bit['admitted']) + L.need(atom > ordinary > admitted > TESTED and atom < 1-ordinary, 'Retained BIT admission and stock') + outer_module=L.load(L.ROOT/'research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py','p104_productive_outer') + params={'kappa':KAPPA,'tested_saving':TESTED,'complex_uniform_saving':KAPPA+6*gap, + 'b':KAPPA+5*gap,'a':KAPPA+4*gap,'q':KAPPA+3*gap,'bit_saving':admitted, + 'epsilon':1-gap,'beta':1-3*gap,'r0':gap/10,'stop':gap,'layout':gap,'d':gap} + outer=outer_module.ledger(params) + outer['functional_checks']['actual_new_BIT_stock_sublinear']=params['beta']*(1-atom) + L.need(len(outer['strict_checks']) == 54 and len(outer['functional_checks']) == 4, 'Complete outer predicate inventory') + L.need(all(x > 0 for key in ('strict_checks','functional_checks') for x in outer[key].values()), 'All outer inequalities strict') + wrong_cutoff = E.divide((Q(sum(T.values())*21),)*2,E.mul(E.power(20,TESTED),target)) + L.need(wrong_cutoff[0] > 1, 'Old cutoff fails with this helper inventory') + bad=outer_module.ledger(dict(params,bit_saving=Q('.0027'))) + L.need(any(x <= 0 for x in bad['strict_checks'].values()), 'Insufficient BIT contract rejected') + return encode({'kappa':KAPPA,'kappa_decimal':'.00304153','previous_open_pr5545':PREVIOUS,'gain':KAPPA-PREVIOUS, + 'relative_gain_percent':100*(KAPPA/PREVIOUS-1),'raw_root_interval':[lower,upper], + 'raw_headroom':[lower-KAPPA,upper-KAPPA],'margin_at_previous':E.display(margin(PREVIOUS)), + 'targets':T,'paid':P,'productive_fields':sum(T.values()),'paid_calls':sum(P.values()), + 'rank_mass_surplus':760,'full_forward_calls':18,'query_shears':15,'whole_idle_jobs':3120, + 'strictification':{'tested':TESTED,'power':v,'cutoff':c,'floor':b,'tail_offset':u,'reserve':reserve, + 'alpha':E.display(alpha),'gamma':E.display(gamma),'delta':E.display(delta),'normalized_paid_upper':normalized}, + 'compiler':{'theta':theta,'logarithm_power':power,'eta':E.display(eta),'gap':gap,'H':H,'N':'2^'+str(H), + 'integer_test_exponent':right,'uniform_saving':params['complex_uniform_saving'],'word_materialized':False}, + 'nonrecursive':{'local_scalar':local['real_scalar_allowance'],'local_routes':local_routes, + 'raw_scalar_upper':raw,'raw_budget':10**9,'peak_owned_fields':1, + 'fixed_scalar_growth_bound':'At most 2^(16*26000) before native factors; a declared constant, not an attained norm.', + 'tensor_native_growth_bound':'Each rank-r Gaussian has row l1 norm at most 2^(rf); sum of local ranks is 5894.'}, + 'ordinary_BIT':bit,'outer':outer, + 'negative_controls':{'old_cutoff':'Rejected by completion-tail ratio greater than one','old_BIT':'Rejected by outer inequalities'}}) diff --git a/research/p104-free-endpoint-retime/pricing-starts-only.py b/research/p104-free-endpoint-retime/pricing-starts-only.py new file mode 100644 index 0000000000..e32cbc0fe1 --- /dev/null +++ b/research/p104-free-endpoint-retime/pricing-starts-only.py @@ -0,0 +1,156 @@ +"""Complete mixed-target price, compiler and outer transfer. + +The interval and compiler bounds follow zxv and Cao Yifan. The productive +recursion is by Jacob Alan Sussman. The controller is by Cinna Davis. +Adapted from Ali Romman's PR5544/5545 for the two coupled contact changes. +Successor choices prepared for thu-nmrc with substantial OpenAI Codex assistance. +Ali Romman's complete caller/price proof and all predecessor credit are retained. +Apache-2.0. +""" +from collections import Counter +from fractions import Fraction as Q +import local as L + +KAPPA, TESTED = Q('.003076879'), Q('.0030768795') +PREVIOUS = Q('.00304117') + + +def encode(x): + if isinstance(x,Q): + return str(x) + if isinstance(x,dict): + return {str(k):encode(v) for k,v in x.items()} + if isinstance(x,(list,tuple)): + return [encode(v) for v in x] + return x + + +def assemble(local, native, word, physical): + paid, targets = Counter(), Counter() + counts = Counter() + L.need(local['helpers'] == native['helpers'], 'Every productive helper has a native target') + for e in word['physical_events']: + counts[e[0]] += 1 + if e[0] == 'LOCAL': + L.need(e[3] is False, 'Every source invocation is forward') + paid.update(local['paid']) + targets.update(local['helpers']) + elif e[0] == 'QUERY_SHEAR': + paid[1] += 104 + elif e[0] == 'IDLE': + paid[8*len(e[2])] += 208 + main = Counter() + idle = Counter({8*len(e[2]):0 for e in word['physical_events'] if e[0] == 'IDLE'}) + for e in word['physical_events']: + if e[0] == 'IDLE': + idle[8*len(e[2])] += 208 + L.need(idle == physical['whole_idle_jobs'], 'Every whole idle has a native Gaussian and full rank') + for term in word['diagonal']: + main[1+8*sum(term[1:])] += 104 + L.need(main == physical['main_targets'], 'Every main target has its full native phase') + targets.update(main) + L.need(counts['LOCAL'] == 18 and counts['QUERY_SHEAR'] == counts['IDLE'] == 15, 'Complete call census') + # Recount by the two path lengths, without using emitted main diagonals. + second_t = Counter({r:18*n for r,n in local['helpers'].items()}) + second_p = Counter({r:18*n for r,n in local['paid'].items()}) + second_t[145] += 208 + second_p[1] += 15*104 + for length in (7,8): + for j in range(1,length+1): + second_t[1+8*(j+1)] += 208 + second_p[8*(j+1)] += 208 + L.need((targets,paid) == (second_t,second_p), 'Independent full invoice') + L.need(max(targets) == 145 and max(paid) == 72, 'Maximum recursive ranks') + L.need(sum(targets.values()) == 12814 and sum(paid.values()) == 67374, 'Complete field and call counts') + L.need(sum(r*n for r,n in targets.items())-sum(r*n for r,n in paid.items()) == 760, 'Complete rank surplus') + return targets,paid,counts + + +def run(local,native,word,physical): + T,P,counts = assemble(local,native,word,physical) + E = L.load(L.ROOT/'research/higher-moment-strictification/verify.py','p104_productive_intervals') + other = L.load(L.ROOT/'research/kappa-rebuild/architecture/mixed_target_probe.py','p104_productive_second_intervals') + def margin(k): + a,b = E.moment(T,1-k), E.moment(P,1-k) + return a[0]-b[1],a[1]-b[0] + lo,hi,grid = 0,10**12,10**14 + while hi-lo > 1: + m=(lo+hi)//2 + if margin(Q(m,grid))[0] > 0: + lo=m + else: + hi=m + lower,upper = Q(lo,grid),Q(hi,grid) + L.need(margin(lower)[0] > 0 and margin(upper)[1] < 0, 'Strict rational crossing enclosure') + L.need(PREVIOUS < KAPPA < TESTED < lower and margin(PREVIOUS)[0] > 0, 'Changed complete bill improves selected kappa') + t,u,v,c,b = 1-TESTED,Q(1,5),1024,17,18 + target,paid = E.moment(T,t),E.moment(P,t) + tl,th = other.moment(T,TESTED) + pl,ph = other.moment(P,TESTED) + L.need(tl > ph and max(tl,target[0]) <= min(th,target[1]) and max(pl,paid[0]) <= min(ph,paid[1]), 'Two exact moment engines') + alpha = E.divide(paid,target) + gamma = E.divide(E.moment(P,t+u),E.mul(E.power(c,u),target)) + delta = E.divide((Q(sum(T.values())*b),)*2,E.mul(E.power(c,TESTED),target)) + reserve,decay = Q(1,10**10),Q(97,100) + L.need(alpha[1] < 1-reserve and gamma[1] < decay and delta[1] < decay, 'All three charged tail ratios') + L.need(decay**128 < Q(1,16), 'Both tail decay blocks') + normalized = 1/(1+v*reserve)+Q(4,2**32) + L.need(normalized < 1 and c**64 < b**63, 'Full completion, splitting and rounding charges') + theta,power = Q(63,64),1000 + eta = E.scale(E.power(145,-v*TESTED),t) + L.need(2*(c**v)**64 <= (145**v)**63 and eta[0] > theta**power, 'Shifted exits and complement capacity') + L.need(E.power(145,v*TESTED)[1] < 2**power, 'Compiler initial range') + gap = (TESTED-KAPPA)/7 + L.need(gap.numerator == 1, 'Exact compiler integer grid') + step = gap.denominator + def wins(j): + return (step*j+1)**power < 2**j + left,right=1,2 + while not wins(right): + left,right=right,2*right + while right-left > 1: + m=(left+right)//2 + if wins(m): + right=m + else: + left=m + H=step*right + L.need(H > 8*v and wins(right) and not wins(right-1), 'Finite uniform threshold with predecessor rejection') + local_routes = (sum(local['paid'].values())+native['helper_normalizers']+native['main_adapters']+4*104+4*local['owned_lifetimes'])*1000 + L.need(local['real_scalar_allowance']+local_routes < 10**7, 'Every local scalar, route and owned operation is funded') + boundary = sum(len(word['boundaries'][side+'_program']) for side in ('left','right')) + raw = 18*10**7 + 15*1664 + 32*104*(len(word['physical_events'])+boundary) + raw += 32*104*(26+1000) + L.need(raw < 10**9, 'Complete nonrecursive raw bound') + bit = L.read(L.ROOT/'research/query-thinned-controllers/RESULT.json')['ordinary_BIT'] + atom = Q(bit['atom']) + ordinary=(1-atom)*Q(bit['after_cover'])+atom*Q('.0000384599') + admitted=Q(bit['admitted']) + L.need(atom > ordinary > admitted > TESTED and atom < 1-ordinary, 'Retained BIT admission and stock') + outer_module=L.load(L.ROOT/'research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py','p104_productive_outer') + params={'kappa':KAPPA,'tested_saving':TESTED,'complex_uniform_saving':KAPPA+6*gap, + 'b':KAPPA+5*gap,'a':KAPPA+4*gap,'q':KAPPA+3*gap,'bit_saving':admitted, + 'epsilon':1-gap,'beta':1-3*gap,'r0':gap/10,'stop':gap,'layout':gap,'d':gap} + outer=outer_module.ledger(params) + outer['functional_checks']['actual_new_BIT_stock_sublinear']=params['beta']*(1-atom) + L.need(len(outer['strict_checks']) == 54 and len(outer['functional_checks']) == 4, 'Complete outer predicate inventory') + L.need(all(x > 0 for key in ('strict_checks','functional_checks') for x in outer[key].values()), 'All outer inequalities strict') + wrong_cutoff = E.divide((Q(sum(T.values())*21),)*2,E.mul(E.power(20,TESTED),target)) + L.need(wrong_cutoff[0] > 1, 'Old cutoff fails with this helper inventory') + bad=outer_module.ledger(dict(params,bit_saving=Q('.0027'))) + L.need(any(x <= 0 for x in bad['strict_checks'].values()), 'Insufficient BIT contract rejected') + return encode({'kappa':KAPPA,'kappa_decimal':'.003076879','previous_open_pr5545':PREVIOUS,'gain':KAPPA-PREVIOUS, + 'relative_gain_percent':100*(KAPPA/PREVIOUS-1),'raw_root_interval':[lower,upper], + 'raw_headroom':[lower-KAPPA,upper-KAPPA],'margin_at_previous':E.display(margin(PREVIOUS)), + 'targets':T,'paid':P,'productive_fields':sum(T.values()),'paid_calls':sum(P.values()), + 'rank_mass_surplus':760,'full_forward_calls':18,'query_shears':15,'whole_idle_jobs':3120, + 'strictification':{'tested':TESTED,'power':v,'cutoff':c,'floor':b,'tail_offset':u,'reserve':reserve, + 'alpha':E.display(alpha),'gamma':E.display(gamma),'delta':E.display(delta),'normalized_paid_upper':normalized}, + 'compiler':{'theta':theta,'logarithm_power':power,'eta':E.display(eta),'gap':gap,'H':H,'N':'2^'+str(H), + 'integer_test_exponent':right,'uniform_saving':params['complex_uniform_saving'],'word_materialized':False}, + 'nonrecursive':{'local_scalar':local['real_scalar_allowance'],'local_routes':local_routes, + 'raw_scalar_upper':raw,'raw_budget':10**9,'peak_owned_fields':1, + 'fixed_scalar_growth_bound':'At most 2^(16*26000) before native factors; a declared constant, not an attained norm.', + 'tensor_native_growth_bound':'Each rank-r Gaussian has row l1 norm at most 2^(rf); sum of local ranks is 5894.'}, + 'ordinary_BIT':bit,'outer':outer, + 'negative_controls':{'old_cutoff':'Rejected by completion-tail ratio greater than one','old_BIT':'Rejected by outer inequalities'}}) diff --git a/research/p104-free-endpoint-retime/pricing.py b/research/p104-free-endpoint-retime/pricing.py new file mode 100644 index 0000000000..8d3e006225 --- /dev/null +++ b/research/p104-free-endpoint-retime/pricing.py @@ -0,0 +1,156 @@ +"""Complete mixed-target price, compiler and outer transfer. + +The interval and compiler bounds follow zxv and Cao Yifan. The productive +recursion is by Jacob Alan Sussman. The controller is by Cinna Davis. +Adapted from Ali Romman's PR5544/5545 for the two coupled contact changes. +Successor choices prepared for thu-nmrc with substantial OpenAI Codex assistance. +Ali Romman's complete caller/price proof and all predecessor credit are retained. +Apache-2.0. +""" +from collections import Counter +from fractions import Fraction as Q +import local as L + +KAPPA, TESTED = Q('.00308142'), Q('.0030814205') +PREVIOUS = Q('.00304117') + + +def encode(x): + if isinstance(x,Q): + return str(x) + if isinstance(x,dict): + return {str(k):encode(v) for k,v in x.items()} + if isinstance(x,(list,tuple)): + return [encode(v) for v in x] + return x + + +def assemble(local, native, word, physical): + paid, targets = Counter(), Counter() + counts = Counter() + L.need(local['helpers'] == native['helpers'], 'Every productive helper has a native target') + for e in word['physical_events']: + counts[e[0]] += 1 + if e[0] == 'LOCAL': + L.need(e[3] is False, 'Every source invocation is forward') + paid.update(local['paid']) + targets.update(local['helpers']) + elif e[0] == 'QUERY_SHEAR': + paid[1] += 104 + elif e[0] == 'IDLE': + paid[8*len(e[2])] += 208 + main = Counter() + idle = Counter({8*len(e[2]):0 for e in word['physical_events'] if e[0] == 'IDLE'}) + for e in word['physical_events']: + if e[0] == 'IDLE': + idle[8*len(e[2])] += 208 + L.need(idle == physical['whole_idle_jobs'], 'Every whole idle has a native Gaussian and full rank') + for term in word['diagonal']: + main[1+8*sum(term[1:])] += 104 + L.need(main == physical['main_targets'], 'Every main target has its full native phase') + targets.update(main) + L.need(counts['LOCAL'] == 18 and counts['QUERY_SHEAR'] == counts['IDLE'] == 15, 'Complete call census') + # Recount by the two path lengths, without using emitted main diagonals. + second_t = Counter({r:18*n for r,n in local['helpers'].items()}) + second_p = Counter({r:18*n for r,n in local['paid'].items()}) + second_t[145] += 208 + second_p[1] += 15*104 + for length in (7,8): + for j in range(1,length+1): + second_t[1+8*(j+1)] += 208 + second_p[8*(j+1)] += 208 + L.need((targets,paid) == (second_t,second_p), 'Independent full invoice') + L.need(max(targets) == 145 and max(paid) == 72, 'Maximum recursive ranks') + L.need(sum(targets.values()) == 12814 and sum(paid.values()) == 66852, 'Complete field and call counts') + L.need(sum(r*n for r,n in targets.items())-sum(r*n for r,n in paid.items()) == 760, 'Complete rank surplus') + return targets,paid,counts + + +def run(local,native,word,physical): + T,P,counts = assemble(local,native,word,physical) + E = L.load(L.ROOT/'research/higher-moment-strictification/verify.py','p104_productive_intervals') + other = L.load(L.ROOT/'research/kappa-rebuild/architecture/mixed_target_probe.py','p104_productive_second_intervals') + def margin(k): + a,b = E.moment(T,1-k), E.moment(P,1-k) + return a[0]-b[1],a[1]-b[0] + lo,hi,grid = 0,10**12,10**14 + while hi-lo > 1: + m=(lo+hi)//2 + if margin(Q(m,grid))[0] > 0: + lo=m + else: + hi=m + lower,upper = Q(lo,grid),Q(hi,grid) + L.need(margin(lower)[0] > 0 and margin(upper)[1] < 0, 'Strict rational crossing enclosure') + L.need(PREVIOUS < KAPPA < TESTED < lower and margin(PREVIOUS)[0] > 0, 'Changed complete bill improves selected kappa') + t,u,v,c,b = 1-TESTED,Q(1,5),1024,17,18 + target,paid = E.moment(T,t),E.moment(P,t) + tl,th = other.moment(T,TESTED) + pl,ph = other.moment(P,TESTED) + L.need(tl > ph and max(tl,target[0]) <= min(th,target[1]) and max(pl,paid[0]) <= min(ph,paid[1]), 'Two exact moment engines') + alpha = E.divide(paid,target) + gamma = E.divide(E.moment(P,t+u),E.mul(E.power(c,u),target)) + delta = E.divide((Q(sum(T.values())*b),)*2,E.mul(E.power(c,TESTED),target)) + reserve,decay = Q(1,10**10),Q(97,100) + L.need(alpha[1] < 1-reserve and gamma[1] < decay and delta[1] < decay, 'All three charged tail ratios') + L.need(decay**128 < Q(1,16), 'Both tail decay blocks') + normalized = 1/(1+v*reserve)+Q(4,2**32) + L.need(normalized < 1 and c**64 < b**63, 'Full completion, splitting and rounding charges') + theta,power = Q(63,64),1000 + eta = E.scale(E.power(145,-v*TESTED),t) + L.need(2*(c**v)**64 <= (145**v)**63 and eta[0] > theta**power, 'Shifted exits and complement capacity') + L.need(E.power(145,v*TESTED)[1] < 2**power, 'Compiler initial range') + gap = (TESTED-KAPPA)/7 + L.need(gap.numerator == 1, 'Exact compiler integer grid') + step = gap.denominator + def wins(j): + return (step*j+1)**power < 2**j + left,right=1,2 + while not wins(right): + left,right=right,2*right + while right-left > 1: + m=(left+right)//2 + if wins(m): + right=m + else: + left=m + H=step*right + L.need(H > 8*v and wins(right) and not wins(right-1), 'Finite uniform threshold with predecessor rejection') + local_routes = (sum(local['paid'].values())+native['helper_normalizers']+native['main_adapters']+4*104+4*local['owned_lifetimes'])*1000 + L.need(local['real_scalar_allowance']+local_routes < 10**7, 'Every local scalar, route and owned operation is funded') + boundary = sum(len(word['boundaries'][side+'_program']) for side in ('left','right')) + raw = 18*10**7 + 15*1664 + 32*104*(len(word['physical_events'])+boundary) + raw += 32*104*(26+1000) + L.need(raw < 10**9, 'Complete nonrecursive raw bound') + bit = L.read(L.ROOT/'research/query-thinned-controllers/RESULT.json')['ordinary_BIT'] + atom = Q(bit['atom']) + ordinary=(1-atom)*Q(bit['after_cover'])+atom*Q('.0000384599') + admitted=Q(bit['admitted']) + L.need(atom > ordinary > admitted > TESTED and atom < 1-ordinary, 'Retained BIT admission and stock') + outer_module=L.load(L.ROOT/'research/pr4359-p7-padding/dependencies/compiler-refill/endpoint.py','p104_productive_outer') + params={'kappa':KAPPA,'tested_saving':TESTED,'complex_uniform_saving':KAPPA+6*gap, + 'b':KAPPA+5*gap,'a':KAPPA+4*gap,'q':KAPPA+3*gap,'bit_saving':admitted, + 'epsilon':1-gap,'beta':1-3*gap,'r0':gap/10,'stop':gap,'layout':gap,'d':gap} + outer=outer_module.ledger(params) + outer['functional_checks']['actual_new_BIT_stock_sublinear']=params['beta']*(1-atom) + L.need(len(outer['strict_checks']) == 54 and len(outer['functional_checks']) == 4, 'Complete outer predicate inventory') + L.need(all(x > 0 for key in ('strict_checks','functional_checks') for x in outer[key].values()), 'All outer inequalities strict') + wrong_cutoff = E.divide((Q(sum(T.values())*21),)*2,E.mul(E.power(20,TESTED),target)) + L.need(wrong_cutoff[0] > 1, 'Old cutoff fails with this helper inventory') + bad=outer_module.ledger(dict(params,bit_saving=Q('.0027'))) + L.need(any(x <= 0 for x in bad['strict_checks'].values()), 'Insufficient BIT contract rejected') + return encode({'kappa':KAPPA,'kappa_decimal':'.00308142','previous_open_pr5545':PREVIOUS,'gain':KAPPA-PREVIOUS, + 'relative_gain_percent':100*(KAPPA/PREVIOUS-1),'raw_root_interval':[lower,upper], + 'raw_headroom':[lower-KAPPA,upper-KAPPA],'margin_at_previous':E.display(margin(PREVIOUS)), + 'targets':T,'paid':P,'productive_fields':sum(T.values()),'paid_calls':sum(P.values()), + 'rank_mass_surplus':760,'full_forward_calls':18,'query_shears':15,'whole_idle_jobs':3120, + 'strictification':{'tested':TESTED,'power':v,'cutoff':c,'floor':b,'tail_offset':u,'reserve':reserve, + 'alpha':E.display(alpha),'gamma':E.display(gamma),'delta':E.display(delta),'normalized_paid_upper':normalized}, + 'compiler':{'theta':theta,'logarithm_power':power,'eta':E.display(eta),'gap':gap,'H':H,'N':'2^'+str(H), + 'integer_test_exponent':right,'uniform_saving':params['complex_uniform_saving'],'word_materialized':False}, + 'nonrecursive':{'local_scalar':local['real_scalar_allowance'],'local_routes':local_routes, + 'raw_scalar_upper':raw,'raw_budget':10**9,'peak_owned_fields':1, + 'fixed_scalar_growth_bound':'At most 2^(16*26000) before native factors; a declared constant, not an attained norm.', + 'tensor_native_growth_bound':'Each rank-r Gaussian has row l1 norm at most 2^(rf); sum of local ranks is 5894.'}, + 'ordinary_BIT':bit,'outer':outer, + 'negative_controls':{'old_cutoff':'Rejected by completion-tail ratio greater than one','old_BIT':'Rejected by outer inequalities'}}) diff --git a/research/p104-free-endpoint-retime/retime.py b/research/p104-free-endpoint-retime/retime.py new file mode 100644 index 0000000000..fa8b19a7ce --- /dev/null +++ b/research/p104-free-endpoint-retime/retime.py @@ -0,0 +1,88 @@ +"""Exact checker: a candidate word is a legal helper-endpoint retime of PR5551's pinned word. Apache-2.0. + +Prepared by DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code. + +The two shipped words were found by an exact-lattice CP-SAT retiming (multi-worker, so +not byte-reproducible); this module is therefore a CHECKER, not a generator. It proves, with +stdlib only, that a candidate differs from the pinned word ONLY as follows: + 1. the non-MOVE scalar program (operation, registers, coefficient, order) is identical; + 2. the candidate's MOVEs are a subsequence of the pinned MOVEs (stops may be deleted, + none added, none reordered across scalar events, same register); + 3. frame labels may change, but all 208 MAIN registers (104 X sources, 104 Y targets) keep + the SAME SPAN at their initial and final frames (X-initial and Y-final are the literal + ports). Intermediate main frames may change where a shared ADD chart moves together + with a retimed helper; these are counted, not forbidden; + 4. the 104 ports, live list and public count are equal. +Nesting, ownership, rank = dimension gap and the frame law at every ADD/COPY/SCALE are then +enforced by the unmodified PR5544/5545 local.py replay and native() (see verify.py). +""" + +def rref(basis): + """Canonical form of the F2 span of integer bit-vectors (reduced row echelon, sorted).""" + rows=[] + for v in basis: + for r in rows: + if v^r0 for k in('strict_checks','functional_checks') for x in res['outer'][k].values()),'all outer checks strict') + lo,hi=[Fraction(x) for x in spec['interval']] + print(name,'crossing kappa in (%.14f, %.14f); 54 strict + 4 functional outer checks pass'%(lo,hi),flush=True) + out[name]=res + if '--write' in sys.argv and part=='all': + (HERE/'RESULT.json').write_text(json.dumps({'status':'PASS_P104_FREE_ENDPOINT_RETIME_CONDITIONAL_KAPPA','headline':out['headline'], + 'starts_only':out['starts-only']},indent=1,sort_keys=True,default=str)+'\n') + print('PASS P104_FREE_ENDPOINT_RETIME',part) +main() diff --git a/research/p104-free-endpoint-retime/verify.sh b/research/p104-free-endpoint-retime/verify.sh new file mode 100755 index 0000000000..d7a4b8e1b5 --- /dev/null +++ b/research/p104-free-endpoint-retime/verify.sh @@ -0,0 +1,3 @@ +#!/bin/sh +# usage: research/p104-two-handoffs/verify.sh (from repository root; Python 3.12, stdlib only) +exec python3 -B "$(dirname "$0")/verify.py" "$@"