From 673108ab687f087cced63fbf8da06dada2a426c6 Mon Sep 17 00:00:00 2001 From: Ali Romman <226877337+aliromman@users.noreply.github.com> Date: Mon, 2 Nov 2026 22:25:30 -0600 Subject: [PATCH 1/2] Add independent Gaussian retirement at conditional kappa 0.00329394 --- .../gaussian-root-retirement/CONTROLLER.json | 4405 +++++++++++++++++ research/gaussian-root-retirement/NOTICE | 25 + .../PHYSICAL-EDITS.json | 6 + .../PRICING-EDITS.json | 46 + research/gaussian-root-retirement/PROOF.md | 130 + research/gaussian-root-retirement/README.md | 101 + research/gaussian-root-retirement/RESEARCH.md | 36 + research/gaussian-root-retirement/RESULT.json | 316 ++ .../gaussian-root-retirement/RETAINED.json | 211 + .../SOURCE-DRIVER-EDITS.json | 18 + .../gaussian-root-retirement/SOURCES.json | 34 + research/gaussian-root-retirement/TASK.json | 129 + .../gaussian-root-retirement/VALIDATION.md | 24 + research/gaussian-root-retirement/VERIFY.json | 30 + .../gaussian-root-retirement/WITNESS.json | 104 + .../gaussian-root-retirement/check_caller.py | 110 + research/gaussian-root-retirement/engines.tar | Bin 0 -> 112640 bytes .../native-source.tar | Bin 0 -> 5550080 bytes research/gaussian-root-retirement/physical.py | 89 + research/gaussian-root-retirement/pricing.py | 186 + .../gaussian-root-retirement/retirement.py | 56 + .../gaussian-root-retirement/source_driver.py | 144 + research/gaussian-root-retirement/verify.py | 165 + 23 files changed, 6365 insertions(+) create mode 100644 research/gaussian-root-retirement/CONTROLLER.json create mode 100644 research/gaussian-root-retirement/NOTICE create mode 100644 research/gaussian-root-retirement/PHYSICAL-EDITS.json create mode 100644 research/gaussian-root-retirement/PRICING-EDITS.json create mode 100644 research/gaussian-root-retirement/PROOF.md create mode 100644 research/gaussian-root-retirement/README.md create mode 100644 research/gaussian-root-retirement/RESEARCH.md create mode 100644 research/gaussian-root-retirement/RESULT.json create mode 100644 research/gaussian-root-retirement/RETAINED.json create mode 100644 research/gaussian-root-retirement/SOURCE-DRIVER-EDITS.json create mode 100644 research/gaussian-root-retirement/SOURCES.json create mode 100644 research/gaussian-root-retirement/TASK.json create mode 100644 research/gaussian-root-retirement/VALIDATION.md create mode 100644 research/gaussian-root-retirement/VERIFY.json create mode 100644 research/gaussian-root-retirement/WITNESS.json create mode 100644 research/gaussian-root-retirement/check_caller.py create mode 100644 research/gaussian-root-retirement/engines.tar create mode 100644 research/gaussian-root-retirement/native-source.tar create mode 100644 research/gaussian-root-retirement/physical.py create mode 100644 research/gaussian-root-retirement/pricing.py create mode 100644 research/gaussian-root-retirement/retirement.py create mode 100644 research/gaussian-root-retirement/source_driver.py create mode 100644 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Apache-2.0. +No subagents or independent scientific review are claimed. + +Retained sources are byte-exact in native-source.tar and engines.tar. +RETAINED.json records every original path, head, Git blob and SHA256. +Original source headers, proof files and notices remain in the archives. + +https://github.com/CrocSwap/integer-mult-bounds/pull/5599 +The independent causal handoff and productive helper method; retain the +PR5602/5611/5615 basis and dyadic-completion lineage. +https://github.com/CrocSwap/integer-mult-bounds/pull/6398 +Ali Romman's mixed projector root, based on PR6348 and the retained native, +query, productive recursion, interval, compiler and outer proof sources. +https://github.com/CrocSwap/integer-mult-bounds/pull/6529 +Ali Romman's scaled transport fusion. Predecessors include Rohan Arun's +PR6399/6417, Erwan L.'s PR6453, DreamingOfClouds' PR6375, and PR6353/6372. +https://github.com/CrocSwap/integer-mult-bounds/pull/6524 +Ali Romman's explicit complete replay interfaces. Native sources retain +David Arias, Cinna Davis, Gareth Davidson and earlier contributor credit. +Integer interval work retains ywz65 and Nick Petalas credit. + +Other retained contributors include Jacob Alan Sussman, Mason Hale, +Pierre-Loic Doulcet, Chris R / Clear1nsight, zxv and Cao Yifan. +The exact archive notices provide the complete retained source attribution. diff --git a/research/gaussian-root-retirement/PHYSICAL-EDITS.json b/research/gaussian-root-retirement/PHYSICAL-EDITS.json new file mode 100644 index 0000000000..022a1d6af0 --- /dev/null +++ b/research/gaussian-root-retirement/PHYSICAL-EDITS.json @@ -0,0 +1,6 @@ +[ + [ + " positive = list(axes[:9]) if selected[0] else [q]", + " need(qp in (-1, 0, 1) and not (qp == 0 and selected[0]), 'Declared central phase and fresh-stage target')\n positive = list(axes[:9]) if selected[0] else ([q] if qp else [])" + ] +] diff --git a/research/gaussian-root-retirement/PRICING-EDITS.json b/research/gaussian-root-retirement/PRICING-EDITS.json new file mode 100644 index 0000000000..a8ba13d9f0 --- /dev/null +++ b/research/gaussian-root-retirement/PRICING-EDITS.json @@ -0,0 +1,46 @@ +[ + [ + "KAPPA = Q('0.003288299')", + "KAPPA = Q('0.00329394')" + ], + [ + "TESTED = Q('0.003288304')", + "TESTED = Q('0.003293945')" + ], + [ + "PREVIOUS = Q('0.003287014')", + "PREVIOUS = Q('0.003288299')" + ], + [ + " main[1+8*sum(term[1:])] += 104", + " main[int(term[0] % 2)+8*sum(term[1:])] += 104" + ], + [ + " need((targets, paid) == formula_invoice(local), 'Independent tree and emitted-event counts')", + " expected_targets, expected_paid = formula_invoice(local)\n expected_targets.update({1:104,16:104,17:-104})\n need((targets, paid) == (expected_targets, expected_paid), 'Independent tree, retirement delta and emitted-event counts')" + ], + [ + "counts['LAMBDA'] == 20", + "counts['LAMBDA'] == 34" + ], + [ + "(13652, 67096)", + "(13756, 67096)" + ], + [ + "32*34*104*len(word['events']) + 34*104*(26+1000)", + "32*35*104*len(word['events']) + 35*104*(26+1000)" + ], + [ + "'kappa_decimal': '0.003288299'", + "'kappa_decimal': '0.00329394'" + ], + [ + "'refinement_kind': 'Two scaled transport fusions with an output basis correction; unchanged mixed root.'", + "'refinement_kind': 'Independent Gaussian retirement changes the complete productive profile.'" + ], + [ + " low, high, grid = 0, 10**24, 10**26\n while high-low > 1:\n middle = (low+high)//2\n if margin(Q(middle, grid))[0] > 0:\n low = middle\n else:\n high = middle\n lower, upper = Q(low, grid), Q(high, grid)\n", + " from root_interval import construct\n bracket, _ = construct(E, T, P)\n lower, upper = Q(bracket['lower'], bracket['grid']), Q(bracket['upper'], bracket['grid'])\n" + ] +] diff --git a/research/gaussian-root-retirement/PROOF.md b/research/gaussian-root-retirement/PROOF.md new file mode 100644 index 0000000000..3901c21d02 --- /dev/null +++ b/research/gaussian-root-retirement/PROOF.md @@ -0,0 +1,130 @@ +# A Gaussian output before the suffix + +## 1. Exact source and claim + +The native source is PR6529 at +`44b0d0e8961201ac1656490b4384a7752e1cd9c5`. Its caller is the PR6398 +34-field word. Number events from zero. Let P be its prefix through event 328, +`QUERY 20 21 -1`. Let q denote the central Gaussian Q in the replay. +All 18 stage variables D_j commute with q and with one another. + +Set + +```text +λ = (1+i)/2 + (1-i)q²/2, +S = λ q⁻¹. +``` + +Then λ⁻¹ is its complex conjugate, λ² = q², and S² = 1. Thus λ and its +inverse are ordinary linear combinations of the identity and the ordinary +translation q². The retained physical checker verifies the translation and +its absolute phase. These ordinary scalars stay outside tensor powers. + +Fields 4, 20 and 21 have the same two-stage factor D = D_10 D_11. An even +central translation and λ normalize all three complete outputs to S D. +The other fields keep their source targets. All input fields are arbitrary. + +## 2. Two exact dual pairs + +Use row vectors a,c and column vectors b,d: + +```text +a = e1ᵀ - 2e2ᵀ - λe20ᵀ + e21ᵀ, +b = -e2 - e21, +c = e20ᵀ - e4ᵀ, +d = -λ⁻¹e21 - e4. +``` + +The identities are + +```text +ab = cd = 1, aP = Sc, Pd = Sb. +``` + +`check_caller.py` checks both pairings and both prefix identities over the full +central polynomial ring. It does not specialize q² to one or test only numeric +values of the D_j. + +Let G and J be the literal ordinary basis words in `WITNESS.json`. The checker +also verifies + +```text +e4ᵀG = c, Gd = e4, +e4ᵀJ = a, Jb = e4. +``` + +Every gate is invertible. ADD coefficients are dyadic; SCALE uses a dyadic +unit; λ has the stated ordinary inverse. G acts only on fields 4,20,21. + +## 3. Separate the completed Gaussian from the remaining work + +Apply G⁻¹ at the input. At the cut, apply J. The pivot row and column of +`JPG⁻¹` are both exactly `S e4`. Therefore the pivot has no coupling to the +other inputs or outputs at this cut. In block form, the prefix is `S ⊕ K`. + +Let F be the complete source diagonal after the three output normalizations. +Since G mixes only equal S D targets, G commutes with F. Apply G at the output. +The complete map remains `GFG⁻¹ = F`. The suffix after J must therefore have +pivot block D and zero coupling to the other fields: its pivot block times S +is S D. This uses S²=1 and the exact arbitrary-input source identity. + +Return the completed pivot output. Give the suffix a new independent input in +field 34. In the literal word, rename pivot 4 to 34 in J⁻¹ and every later gate, +including the output basis. Other fields still pass through K and its matching +suffix. This is a direct sum of two independent targets, S and D, in place of +one S D target. It is not a copy of one input to two output targets. + +Finally apply λ⁻¹ to the three original group fields. The returned pivot has +target q⁻¹. The new field has target D_10 D_11. The complete 35-field word has +609 events. Both full forward replay and an independent reverse-row replay +check every one of its 1,225 coefficient positions. Deletion, sign and target +mutations reject the claimed identity. + +## 4. Physical maps and all costs + +For each of the 104 ports, the central q axis is orthogonal to the two fresh +8-axis stage blocks. The old Gaussian target has rank 17. The returned q⁻¹ +target has rank 1 after an ordinary q² translation. The fresh target has rank 16 +and no central factor. The physical checker compares complete phase polynomials, +including the absence of that central factor. It checks every port. + +At each positive tensor width f, substitute q tensor f and D_j tensor f in +the same ring identity. Define the ordinary normalizer from the square of +that central operator. Do not tensor its scalar coefficients. The two new +Gaussian ranks are f and 16f. This retains the source tensor convention and +its framework assumptions. + +The ordered full-stage calls, thin-query signs, and whole-idle stage sets stay +fixed. Only some role names change. Every native call still receives arbitrary +inputs and fresh independent helper fields. All 67,096 paid jobs and all native +helper credits stay in the source invoice. The productive change is exactly + +```text +104(H1 + H16 - H17). +``` + +For H_r=r^t and 0H17. Rank mass stays +fixed. The gain comes from independent outputs, not from a larger rank count. +The total productive-field count becomes 13,756. + +The caller has one extra public field per port. The native owned inventory is +unchanged: 29 labels, 45 lifetimes, peak 13. The complete ordinary-work upper +bound is 254,699,248, below the retained 10^9 allowance. It includes every scalar +basis gate, central normalization, route and output adapter. The coefficient, +storage, growth and precision estimates remain explicit in `pricing.py`. + +## 5. Conditional κ and the fixed invoice limit + +Two rational engines certify the positive complete moment at the tested saving +0.003293945. They independently certify both signs of the raw bracket stated +in the README. A negative derivative bound gives a unique crossing through the +retained BIT range. The old caller fails at the new claim in both engines. + +The productive recursion, completion tails, uniform compiler threshold and all +outer inequalities are checked with the enlarged target count. The result is +conditional κ=0.00329394 under the same five framework assumptions. No selected +frontier change or independent scientific acceptance follows from this replay. + +The fixed invoice cannot reach the current 1% target 0.00332118199. A larger +result must change the caller, source word or another charged interface. More +digits of this crossing do not provide that change. diff --git a/research/gaussian-root-retirement/README.md b/research/gaussian-root-retirement/README.md new file mode 100644 index 0000000000..da18f0d8ab --- /dev/null +++ b/research/gaussian-root-retirement/README.md @@ -0,0 +1,101 @@ +# Independent Gaussian retirement: conditional κ = 0.00329394 + +The complete caller returns one central Gaussian output before its two-stage +suffix. A fresh independent input then uses that suffix. On each of 104 ports, +this replaces one rank-17 target with independent rank-1 and rank-16 targets. +Every paid Gaussian call stays in the invoice. + +The conditional claim is **κ = 0.00329394**. The increment over +[PR6529](https://github.com/CrocSwap/integer-mult-bounds/pull/6529), +κ = 0.003288299, is **0.000005641, or 0.17154766%**. This percentage excludes +all gains in the source chain. The requested 1% gain is not achieved. + +| Complete invoice | PR6529 | This caller | +|---|---:|---:| +| Independent caller fields per port | 34 | 35 | +| Caller events | 570 | 609 | +| Productive fields, with native helpers | 13,652 | 13,756 | +| Paid Gaussian jobs | 67,096 | 67,096 | +| Full native calls / thin queries | 18 / 17 | 18 / 17 | +| Rank-mass surplus | 760 | 760 | + +The target change is `104(H1 + H16 - H17)`, where `Hr = r^(1-κ)`. +It is positive for every exponent strictly between zero and one. The source +native word, its helper targets and its owned lifetimes stay fixed. All added +basis gates, routes, output normalizers and the additional public field enter +the complete ordinary-work allowance. + +Start with [PROOF.md](PROOF.md), [retirement.py](retirement.py) and +[WITNESS.json](WITNESS.json). [RESULT.json](RESULT.json) records the exact +caller, phase, price, compiler and outer checks. [RESEARCH.md](RESEARCH.md) +states the scope of the discovery and the limit of this fixed invoice. + +## Evidence + +The forward polynomial replay checks all 1,225 coefficients over +`Q(i)[Q,D_1,...,D_18]/(Q^4-1)`. A separate reverse-row engine checks the same +complete map. Both dual-pair identities and both literal basis maps are checked. +The fresh input is arbitrary; it is not prepared zero storage. + +The source replay regenerates PR6529 and retains its checks and controls. It +checks all 799 native columns, 2,939 native maps, 208 main adapters, and all +7,488 physical contacts. The candidate then checks all target phases, all +whole idles, both rational price engines, the uniform compiler, and all +54 strict plus four functional outer predicates. See [VALIDATION.md](VALIDATION.md) +for the executed commands and publication status. + +The unique raw crossing for this fixed invoice lies in +`(0.00329394637095319036829691, 0.00329394637095319036829692)`. +The claim uses the tested saving `0.003293945`, below that interval. +This is a ceiling for this invoice, not for other words or callers. + +## Reproduce + +From the repository root, with CPython 3.12: + +```sh +python3.12 -B scripts/research_package.py --package research/gaussian-root-retirement +``` + +The package needs only the standard library. Both normal and optimized runs are +registered. The two source archives contain every runtime input, with original +paths, heads, Git blobs, SHA256 hashes and notices. The adapter checks preserve +all source checks. Explicit engine dependencies use the interfaces from PR6524; +no imported function or class is patched. + +## Scope and limits + +This is an author-checked conditional construction. It is not independent +scientific acceptance, a formal proof of the full multiplication theorem, or a +measured runtime gain. The five inherited framework assumptions remain: +`native_all_columns`, `owned_erasure`, `compiler`, `precision_tape`, and +`analytic_recovery`. The large uniform word and rounded multiplier are not +materialized. The selected frontier is unchanged. + +The source stack includes pending PRs. Passing the registered replay does not +admit that stack. The new result improves the caller boundary; it does not prove +optimality over other cuts, native words, target groups or query networks. + +## Open next questions + +- Can another caller return a larger Gaussian factor at a legal intermediate + cut? First test exact dual pairings on a changed word and write its complete + target and paid invoice. The present fixed word has little remaining price + headroom. A favorable numerical screen is not a caller. +- Can a repeated Gaussian-assisted interface have a favorable complete cost? + First supply exact transition matrices, a closed endpoint and native helper + delivery. The current small-state searches do not supply such a cycle. +- Can an independent reviewer check the prefix identities and the 104 physical + output normalizations? The small basis and separate reverse engine provide + bounded entry points. Full framework admission is a separate task. + +## Credit + +New construction, proof and package: Ali Romman with substantial OpenAI Codex +assistance; no subagents. Apache-2.0. The independent handoff method comes from +PR5599 and the PR5602/5611/5615 line. The root comes from PR6398 and PR6348. +PR6529 supplies the complete native word; PR6524 supplies the replay engines. +Credit Cinna Davis, Jacob Alan Sussman, Rohan Arun, Erwan L., DreamingOfClouds, +David Arias, Gareth Davidson, Mason Hale, Pierre-Loic Doulcet, Chris R / +Clear1nsight, zxv, Cao Yifan, and all authors in the retained notices. +[NOTICE](NOTICE) gives the source links and attribution boundary. diff --git a/research/gaussian-root-retirement/RESEARCH.md b/research/gaussian-root-retirement/RESEARCH.md new file mode 100644 index 0000000000..9a58dd93f7 --- /dev/null +++ b/research/gaussian-root-retirement/RESEARCH.md @@ -0,0 +1,36 @@ +# Discovery and remaining scope + +The new step changes a hypothesis of the PR6398 packing ceiling. That ceiling +keeps each complete Gaussian target intact. This caller returns one factor at +an intermediate cut and gives the suffix a fresh input. Its target inventory +is therefore outside that fixed-target model. + +The discovery screen first set q²=1. It searched the equal-target groups and +paid-event cuts in the literal 34-field caller. It found the group 4,20,21 after +event 328. A separate q²=-1 calculation gave compatible dual pairs. Neither +specialized calculation was used as a substitute for the full-ring proof. The +published checker validates the unspecialized pair and complete caller. + +The first emitted word normalized every original output. Only the three group +outputs need that normalization. The final construction uses 609 events instead +of 684. This reduces ordinary work and proof surface; it does not add another +κ gain. The native source was then updated from PR6398 to PR6529. The reported +increment compares the new caller with PR6529 and excludes that inherited gain. + +The source invoice is preserved, except for the 104 legal target splits. The +strict raw bracket is less than 6.371e-9 above the conditional claim. This is +almost all the gain available from this exact invoice. It is not a global +ceiling for independent Gaussian retirement. + +Further local discovery tests covered supplier-boundary shears, larger scalar +roots, changed query words, owned-lifetime output bases, and short moving-state +Gaussian-assisted templates. They did not produce another complete caller. +These were bounded searches, not universal impossibility proofs. Their work +files are not runtime inputs to this package and are not published as exact +exhaustive coverage claims. No relaxed favorable price is counted as a result. + +A useful next construction needs a larger independent target split or a new +closed query interface. It must bind the actual native helper maps and charge +all helper debits, idles, routes, COPY/CLEAR work, restoration, compiler and +outer costs. The 1% target over PR6529 is 0.00332118199. This package does not +meet that target. diff --git a/research/gaussian-root-retirement/RESULT.json b/research/gaussian-root-retirement/RESULT.json new file mode 100644 index 0000000000..3bcf9f740b --- /dev/null +++ b/research/gaussian-root-retirement/RESULT.json @@ -0,0 +1,316 @@ +{ + "assumptions": [ + "native_all_columns", + "owned_erasure", + "compiler", + "precision_tape", + "analytic_recovery" + ], + "candidate": { + "caller": { + "coefficients": 1225, + "event_sha256": "e30e87523bfe8dcf009843965a617a664a1ce802850bb07ac2ca198fa818a124", + "events": 609, + "inputs": 35, + "native_stages": 18 + }, + "complete_cost": { + "compiler": { + "H": 138100200000000, + "N": "2^138100200000000", + "eta": { + "lower": "0.000000000000021343548942378562", + "upper": "0.000000000000021343548942378563" + }, + "gap": "1/1400000000", + "integer_test_exponent": 98643, + "logarithm_power": 2100, + "theta": "63/64", + "uniform_saving": "2305761/700000000", + "word_materialized": false + }, + "derivative_upper": "-709185992340617917271102325360006905223896764960473050137748773/3138550867693340381917894711603833208051177722232017256448", + "full_forward_calls": 18, + "gain": "5641/1000000000", + "kappa": "164697/50000000", + "kappa_decimal": "0.00329394", + "margin_at_previous": { + "lower": "1.294383344079915739634444114064", + "upper": "1.294383344079915739634444114065" + }, + "negative_controls": { + "coarse_tail": "The block tail bound cannot fund this near-limit claim.", + "old_BIT": "An outer inequality fails at BIT saving0.0027.", + "old_completion": "Cutoff16 and floor17 give a ratio above one." + }, + "nonrecursive": { + "local_routes": 5384000, + "local_scalar": 137218, + "paid_rank_mass": 184962, + "peak_owned_fields": 13, + "raw_budget": 1000000000, + "raw_scalar_upper": 254699248, + "scalar_growth_bound": "At most 2^(10^9 + R*f), where R is the full paid rank mass." + }, + "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": "348599999253/350000000000", + "fixed_halo_explicit_metadata_branch": "26950000001/350000000", + "new_BIT_row_stock_sublinear_in_active_group": "1395799997009/1400000000000", + "new_semantic_group_guard": "3/1400000000" + }, + "margins": { + "boundary_algebraic_matrix": "6456127995388481/1960000000000000000", + "fused_gaussian": "6456127986165443/1960000000000000000", + "global_coordinate_router": "14411/4375000", + "group_bit_router": "20175404331767/6125000000000000", + "group_scans": "699999999/700000000", + "main_transform": "6456126595388481/1960000000000000000", + "microbox_face_corrections": "26950000001/350000000", + "polynomial_products": "1399999999/1400000000", + "sparse_union_movement": "802706127995388481/1960000000000000000" + }, + "parameters": { + "a": "14411/4375000", + "b": "4611521/1400000000", + "beta": "1399999997/1400000000", + "bit_saving": "17/5000", + "cap_xi": "1782706126595388481/1960000000000000000", + "complex_uniform_saving": "2305761/700000000", + "d": "1/1400000000", + "epsilon": "1399999999/1400000000", + "kappa": "164697/50000000", + "lambda_": "398682423/400000000", + "lambda_prime": "1395388481/1400000000", + "layout": "1/1400000000", + "q": "4611519/1400000000", + "r0": "1/14000000000", + "stop": "1/1400000000", + "tested_saving": "658789/200000000" + }, + "strict_checks": { + "actual_bit_above_effective": "58/546875", + "actual_logarithmic_gamma_guard": "1/1400000000", + "actual_logarithmic_group_guard": "177293875504611519/980000000000000000", + "alpha_logarithm_absorption": "1/14000000000", + "boundary_algebraic_matrix_above_kappa": "5595388481/1960000000000000000", + "cap_above_band": "802706126595388481/1960000000000000000", + "cap_below_cell": "177293872004611519/1960000000000000000", + "cap_below_phase_cell_power": "2137293873404611519/1960000000000000000", + "complex_above_effective": "1/1400000000", + "complex_below_one_over_32": "39138479/1400000000", + "complex_endpoint": "1/700000000", + "epsilon_below_one": "1/1400000000", + "epsilon_positive": "1399999999/1400000000", + "fine_prime_halo_umbrella": "7/2", + "fused_gaussian_above_kappa": "5586165443/1960000000000000000", + "gaussian_above_main": "695388481/980000000000000000", + "global_coordinate_router_above_kappa": "1/350000000", + "global_gamma_power_slack": "9/14000000000", + "group_below_dimension": "1/700000000", + "group_bit_router_above_kappa": "21831767/6125000000000000", + "group_gauge_power_slack": "177293875434611519/980000000000000000", + "group_key_fits_record": "1/700000000", + "group_positive": "1399999997/1400000000", + "group_scans_above_kappa": "697694241/700000000", + "halo_covers_generic_inverse_radius": "5", + "improvement_over_user_baseline": "781484790400418148631/500000000000000000000000", + "lambda_above_internal": "1/2800000000", + "lambda_above_sigma": "3/2800000000", + "lambda_above_tau": "1/2800000000", + "lambda_prime_above_lambda": "1/2800000000", + "lambda_prime_above_leaf": "2795388479/1960000000000000000", + "leaf_saving_above_effective": "1395388479/1960000000000000000", + "main_transform_above_kappa": "4195388481/1960000000000000000", + "membership_arithmetic_fits_record": "1/1400000000", + "microbox_face_corrections_above_kappa": "13474423561/175000000", + "microbox_halo_volume": "110600000003/1400000000", + "new_complex_uniform_saving_above_b": "1/1400000000", + "new_semantic_guard_with_C1_one": "1/1400000000", + "polynomial_products_above_kappa": "1395388483/1400000000", + "positive_layout_slack": "1/1400000000", + "q_below_effective": "1/1400000000", + "q_below_internal": "1/1400000000", + "q_below_leaf": "2795388479/1960000000000000000", + "q_positive": "4611519/1400000000", + "short_record_fallback": "1395388479/1400000000", + "source_axis_superpolynomial": "1/1400000000", + "sparse_union_movement_above_kappa": "796250005595388481/1960000000000000000", + "stop_below_one": "1399999999/1400000000", + "stop_positive": "1/1400000000", + "strassen_integer_power_gap": "1951441519231", + "support_router_span": "3/1400000000", + "theta_positive_polynomial_power": "2", + "union_header_fits_record": "3/1400000000", + "union_tag_work_per_visit_fits_record": "3/1400000000" + } + }, + "paid": { + "1": 41980, + "16": 1872, + "2": 8154, + "24": 416, + "3": 8838, + "32": 416, + "4": 1926, + "5": 2754, + "56": 416, + "6": 144, + "7": 162, + "8": 18 + }, + "paid_calls": 67096, + "previous_fixed_root": "3288299/1000000000", + "productive_fields": 13756, + "rank_mass_surplus": 760, + "raw_endpoint_margins": { + "lower": { + "first": { + "lower": "0.000000000000000000001070125900", + "upper": "0.000000000000000000001070125901" + }, + "second": { + "lower": "0.000000000000000000001070125900", + "upper": 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b/research/gaussian-root-retirement/SOURCE-DRIVER-EDITS.json new file mode 100644 index 0000000000..908bdd419e --- /dev/null +++ b/research/gaussian-root-retirement/SOURCE-DRIVER-EDITS.json @@ -0,0 +1,18 @@ +[ + [ + "def run(write=False, build_only=False):", + "def run(write=False, build_only=False, services=None, extension=None):" + ], + [ + " L = local_module", + " L = local_module if services is None else services(local_module.ROOT, local_module)" + ], + [ + " return encode(dict(status=STATUS, conditional_kappa=str(price_module.KAPPA),", + " result = encode(dict(status=STATUS, conditional_kappa=str(price_module.KAPPA)," + ], + [ + " scope='Local conditional construction; no independent acceptance, materialized multiplier or selected-frontier change.'))", + " scope='Local conditional construction; no independent acceptance, materialized multiplier or selected-frontier change.'))\n need(result == read(HERE/'RESULT.json'), 'Every source result and control remains unchanged')\n if extension is None:\n return result\n return {'source':result,'candidate':extension.run(word, caller, local, native, L)}" + ] +] diff --git a/research/gaussian-root-retirement/SOURCES.json b/research/gaussian-root-retirement/SOURCES.json new file mode 100644 index 0000000000..99fcc686f8 --- /dev/null +++ b/research/gaussian-root-retirement/SOURCES.json @@ -0,0 +1,34 @@ +{ + "schema_version": 1, + "base_commit": "7c49fe32c55de02c2c873655c804b16e4c3fef0a", + "files": [ + { + "path": "certificates/selected-result.json", + "usage": "provenance", + "git_blob": "d59b5035e7b4cbaa9d688a1d32dd0d6eb79c466a", + "sha256": "9b8d0eea95b3bf0dfcb7938a732a6439b87a2685dec2a5ab9e525b3b34debbfa" + }, + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "3404fbdd5e7529a0674eef26114b5071e4586cec", + "sha256": "ead6cdc9d0af6d58e8a49744d8ec8c7c15e13d2ba93c276c434bcf9b51b93a81" + } + ], + "retained_predecessors": [ + { + "archive": "native-source.tar", + "manifest": "RETAINED.json", + "archive_sha256": "2e4e49580c51758281bd9e4618f99d38f3a3622117d5c73bae0fce2db3616fa4", + "source_head": "44b0d0e8961201ac1656490b4384a7752e1cd9c5", + "reason": "Exact standalone runtime sources and original notices; no side-branch history is needed." + }, + { + "archive": "engines.tar", + "manifest": "RETAINED.json", + "archive_sha256": "cf1bd75c964d8d19ac867550f48424cba0187c4d6ca6b89ef1662bed738c390a", + "source_head": "dd1a979bfff090fa6559cc3b7d4e7f5ab24b4f80", + "reason": "Exact standalone runtime sources and original notices; no side-branch history is needed." + } + ] +} diff --git a/research/gaussian-root-retirement/TASK.json b/research/gaussian-root-retirement/TASK.json new file mode 100644 index 0000000000..499fd760d6 --- /dev/null +++ b/research/gaussian-root-retirement/TASK.json @@ -0,0 +1,129 @@ +{ + "schema_version": 1, + "task_id": "p104-side-correction", + "priority_revision": 8, + "base_commit": "7c49fe32c55de02c2c873655c804b16e4c3fef0a", + "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": "A legal Gaussian retirement at event 328 in the PR6398 root, composed with the complete PR6529 native word.", + "scope_change_reason": "The explicit user task asks for a new caller beyond the old fixed-target ceiling. The root boundary changes; the native helper groups do not.", + "bottleneck_link": "Split one productive rank-17 target into independent ranks 1 and 16 without removing a charged native job.", + "budget_minutes": 60, + "stop_rule": "Reject the construction if the full-ring endpoint, physical maps, complete invoice, compiler or outer inequalities fail.", + "outcome": "completed", + "evidence": "RESULT.json; PROOF.md; CONTROLLER.json; WITNESS.json; VALIDATION.md", + "author": "Ali Romman with substantial OpenAI Codex assistance", + "ai_assistance": "Substantial OpenAI Codex assistance in construction, exact arithmetic, verification, research and writing; no subagents.", + "open_questions": [ + { + "question": "Can a changed caller return a larger independent Gaussian factor?", + "why_it_matters": "The present fixed invoice cannot give a 1 percent gain over PR6529.", + "first_step": "Find exact prefix and suffix dual pairs, then price the complete changed caller.", + "blocked_by": "No larger exact caller is currently constructed." + }, + { + "question": "Can a repeated Gaussian-assisted interface close at a favorable complete cost?", + "why_it_matters": "A different interface could cross the current fixed-target limit.", + "first_step": "Supply exact state transitions, a closed endpoint and all native helper maps.", + "blocked_by": "The current small-state searches do not supply a cycle." + }, + { + "question": "Can an independent reviewer validate the new split?", + "why_it_matters": "Author checks are not independent scientific acceptance.", + "first_step": "Check both dual pairs, the two basis maps, and the 104 physical target normalizations.", + "blocked_by": "Independent review has not occurred." + } + ] +} diff --git a/research/gaussian-root-retirement/VALIDATION.md b/research/gaussian-root-retirement/VALIDATION.md new file mode 100644 index 0000000000..ad608a9dcb --- /dev/null +++ b/research/gaussian-root-retirement/VALIDATION.md @@ -0,0 +1,24 @@ +# Validation record + +Local environment: CPython 3.12.13 on macOS. The complete registered normal +and optimized replays both passed on November 3, 2026 (UTC). + +```sh +python3.12 -B scripts/research_package.py --package research/gaussian-root-retirement --check-only +python3.12 -B scripts/research_package.py --package research/gaussian-root-retirement +``` + +Markers: `PASS_PACKAGE_METADATA_AND_PINS`, +`PASS_GAUSSIAN_ROOT_RETIREMENT_KAPPA_00329394`, and +`PASS_REGISTERED_RESEARCH_PACKAGE`. + +Coverage includes the full source regeneration and controls, all 799 native +columns, native absolute phases, all physical contacts, both complete caller +engines, the exact dual pairs and basis maps, two rational price engines, +the compiler and all outer predicates. No source receipt is used in place +of these checks. The source result must also match its frozen complete receipt. + +Committed-byte checks, isolated export checks and hosted CI are pending. +The optional full-history preflight is not claimed in this shallow checkout. +No independent scientific review is claimed. The five source framework +assumptions remain. The selected frontier is unchanged. diff --git a/research/gaussian-root-retirement/VERIFY.json b/research/gaussian-root-retirement/VERIFY.json new file mode 100644 index 0000000000..6a88f9edc6 --- /dev/null +++ b/research/gaussian-root-retirement/VERIFY.json @@ -0,0 +1,30 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [], + "commands": [ + { + "argv": [ + "{python}", + "-I", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 590, + "checks": "Complete source regeneration and controls, all 799 native columns and phases, both 1225-coefficient caller engines, exact dual pairs and bases, full physical maps, two rational prices, compiler and all outer predicates." + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 590, + "checks": "Complete source regeneration and controls, all 799 native columns and phases, both 1225-coefficient caller engines, exact dual pairs and bases, full physical maps, two rational prices, compiler and all outer predicates." + } + ] +} diff --git a/research/gaussian-root-retirement/WITNESS.json b/research/gaussian-root-retirement/WITNESS.json new file mode 100644 index 0000000000..be22af6322 --- /dev/null +++ b/research/gaussian-root-retirement/WITNESS.json @@ -0,0 +1,104 @@ +{ + "cut_after": 328, + "handoff_after": 344, + "pivot": 4, + "fresh": 34, + "boundary": [ + [ + "SCALE", + 4, + "-1" + ], + [ + "LAMBDA", + 4, + -1 + ], + [ + "ADD", + 21, + 4, + "1" + ], + [ + "LAMBDA", + 4, + 1 + ], + [ + "ADD", + 4, + 20, + "1" + ] + ], + "middle": [ + [ + "ADD", + 4, + 2, + "1" + ], + [ + "ADD", + 2, + 4, + "-1" + ], + [ + "ADD", + 4, + 2, + "1" + ], + [ + "SCALE", + 2, + "-1" + ], + [ + "SCALE", + 4, + "-1" + ], + [ + "ADD", + 21, + 4, + "1" + ], + [ + "ADD", + 4, + 1, + "1" + ], + [ + "LAMBDA", + 20, + 1 + ], + [ + "ADD", + 4, + 20, + "-1" + ], + [ + "LAMBDA", + 20, + -1 + ], + [ + "ADD", + 4, + 21, + "1" + ] + ], + "group": [ + 4, + 20, + 21 + ] +} diff --git a/research/gaussian-root-retirement/check_caller.py b/research/gaussian-root-retirement/check_caller.py new file mode 100644 index 0000000000..c4fba4d14c --- /dev/null +++ b/research/gaussian-root-retirement/check_caller.py @@ -0,0 +1,110 @@ +"""Check the caller by reverse rows and check both dual-pair identities. + +This engine uses one row or column at a time. It does not call the source +matrix replay. The exact coefficient ring comes from the retained source. +Ali Romman with substantial OpenAI Codex assistance. Apache-2.0. +""" +from algebra import Q, coefficient, accumulate, shifted, zmul, need + + +def scalar_step(value, event, width): + op = event[0] + if op == 'SCALE': + return {key:zmul(coefficient(event[-1]),c) for key,c in value.items()} + if op == 'Q_POWER': + return shifted([value],(event[-1],)+(0,)*(width-1))[0] + if op == 'LAMBDA': + out = {} + accumulate(out,value,(Q(1,2),Q(event[-1],2))) + accumulate(out,shifted([value],(2,)+(0,)*(width-1))[0],(Q(1,2),Q(-event[-1],2))) + return out + raise ValueError('Scalar opcode') + + +def apply(vector, event, width, reverse=False): + op = event[0] + if op in ('SCALE','Q_POWER','LAMBDA'): + r=event[1] + vector[r]=scalar_step(vector[r],event,width) + elif op == 'SWAP': + a,b=event[1:] + vector[a],vector[b]=vector[b],vector[a] + elif op in ('ADD','QUERY','LOCAL'): + if op == 'LOCAL': + stage,src,dst=event[1:] + exponent,c=-1,coefficient(1) + term=(0,)+tuple(int(i==stage)for i in range(width-1)) + if reverse: + for r in (src,dst):vector[r]=shifted([vector[r]],term)[0] + else: + dst,src=event[1:3] + exponent,c=(0,coefficient(event[3]))if op=='ADD' else(event[3],coefficient(1)) + a,b=(src,dst)if reverse else(dst,src) + accumulate(vector[a],shifted([vector[b]],(exponent,)+(0,)*(width-1))[0],c) + if op == 'LOCAL' and not reverse: + for r in (src,dst):vector[r]=shifted([vector[r]],term)[0] + elif op in ('IDLE','IDLE_ONE'): + roles,stages=(event[1:3],event[3])if op=='IDLE' else([event[1]],event[2]) + term=(0,)+tuple(int(i in stages)for i in range(width-1)) + for r in roles:vector[r]=shifted([vector[r]],term)[0] + else: + raise ValueError('Caller opcode') + + +def transpose(word): + n,width=word['roles'],word['stages']+2 + zero=(0,)*width + for output in range(n): + vector=[{}for _ in range(n)] + vector[output]={zero:coefficient(1)} + for event in reversed(word['events']):apply(vector,event,width,True) + expected=[{}for _ in range(n)] + d=word['diagonal'][output] + expected[output]={(d[0]%4,*d[1:]):coefficient(1)} + need(vector==expected,'Every independent reverse caller coefficient') + return {'rows':n,'coefficients':n*n} + + +def product(a,b,width): + out={} + for key,c in a.items(): + accumulate(out,shifted([b],key)[0],c) + return out + + +def dual_pair(source, boundary, middle): + n,width=source['roles'],source['stages']+2 + zero=(0,)*width + one={zero:coefficient(1)} + lam=scalar_step(one,['LAMBDA',0,1],width) + inv=scalar_step(one,['LAMBDA',0,-1],width) + def vec(entries): + out=[{}for _ in range(n)] + for r,value in entries.items():out[r]=value if isinstance(value,dict)else{zero:coefficient(value)} + return out + neg=lambda value:{k:zmul(coefficient(-1),c)for k,c in value.items()} + a=vec({1:1,2:-2,20:neg(lam),21:1}) + b=vec({2:-1,21:-1}) + c=vec({20:1,4:-1}) + d=vec({21:neg(inv),4:-1}) + s=shifted([lam],(-1,)+(0,)*(width-1))[0] + for events,left,right in ((boundary,c,d),(middle,a,b)): + column=[dict(v)for v in right] + for event in events:apply(column,event,width) + unit=vec({4:1}) + need(column==unit,'The basis sends the dual column to the pivot') + row=vec({4:1}) + for event in reversed(events):apply(row,event,width,True) + need(row==left,'The pivot row is the declared dual functional') + for x,y in ((a,b),(c,d)): + value={} + for u,v in zip(x,y):accumulate(value,product(u,v,width)) + need(value==one,'Unit dual pairing') + column=[dict(v)for v in d] + for event in source['events'][:329]:apply(column,event,width) + need(column==[product(s,v,width)for v in b],'Prefix times d equals S times b') + row=[dict(v)for v in a] + for event in reversed(source['events'][:329]):apply(row,event,width,True) + need(row==[product(s,v,width)for v in c],'a times prefix equals S times c') + return {'cut_after':328,'input_pairing':'1','cut_pairing':'1', + 'prefix_column':'P d = S b','prefix_row':'a P = S c'} diff --git a/research/gaussian-root-retirement/engines.tar b/research/gaussian-root-retirement/engines.tar new file mode 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