From a2d39549b09545eb96b150be67c42c403e254b5e Mon Sep 17 00:00:00 2001 From: maxime-fleury Date: Fri, 9 Oct 2026 17:12:36 +0200 Subject: [PATCH 1/9] Compose PR200's bit supplier with the record's complex word and the finite leaf PR200 certifies a strictly stronger bit word but publishes it only with its own complex word, where the complex branch binds; it announces the stacked composition "as separate work". Pricing that composition through PR194's unchanged assembly with PR185's finite ordinary leaf gives kappa = 1693287/2500000000 = 6.773148e-4, +0.1826% over PR197's standing claim and +0.0639% over the value PR200 announced for it. The package vendors the minimum needed to price it: the PR168 v4 assembly, PR184's pricer and finite bridge, PR194's certificate and PR200's bit certificate, all digest-pinned. verify.py reproduces the certificate from those pins, reproduces PR200's announced depth-0 value, shows PR184's grid leaf and PR200's published atom wrapper differ by one grid step at depth 0 and not at all once bootstrapped, requires the claim to beat PR197 and to sit inside one grid step of the word's own C/(1+C) ceiling, and refuses three corruption controls. --- .../composed-diagonal-bit-bootstrap.yml | 35 + SOURCES.json | 20 + .../.gitignore | 2 + .../composed-diagonal-bit-bootstrap/NOTICE.md | 48 + .../composed-diagonal-bit-bootstrap/README.md | 115 + .../SOURCE.json | 37 + .../certificate.json | 179 + .../compose.py | 196 + .../inputs/pr200-bit-certificate.json | 4442 +++++++++++++++++ .../pr168-v4/scripts/paired_cube_assembly.py | 58 + .../references/pr184/FINITE_BRIDGE.txt | 141 + .../references/pr184/assemble_profiles.py | 248 + .../references/pr194/certificate.json | 577 +++ .../composed-diagonal-bit-bootstrap/verify.py | 188 + 14 files changed, 6286 insertions(+) create mode 100644 .github/workflows/composed-diagonal-bit-bootstrap.yml create mode 100644 research/composed-diagonal-bit-bootstrap/.gitignore create mode 100644 research/composed-diagonal-bit-bootstrap/NOTICE.md create mode 100644 research/composed-diagonal-bit-bootstrap/README.md create mode 100644 research/composed-diagonal-bit-bootstrap/SOURCE.json create mode 100644 research/composed-diagonal-bit-bootstrap/certificate.json create mode 100644 research/composed-diagonal-bit-bootstrap/compose.py create mode 100644 research/composed-diagonal-bit-bootstrap/inputs/pr200-bit-certificate.json create mode 100644 research/composed-diagonal-bit-bootstrap/references/pr168-v4/scripts/paired_cube_assembly.py create mode 100644 research/composed-diagonal-bit-bootstrap/references/pr184/FINITE_BRIDGE.txt create mode 100644 research/composed-diagonal-bit-bootstrap/references/pr184/assemble_profiles.py create mode 100644 research/composed-diagonal-bit-bootstrap/references/pr194/certificate.json create mode 100644 research/composed-diagonal-bit-bootstrap/verify.py diff --git a/.github/workflows/composed-diagonal-bit-bootstrap.yml b/.github/workflows/composed-diagonal-bit-bootstrap.yml new file mode 100644 index 0000000000..456b7d60d5 --- /dev/null +++ b/.github/workflows/composed-diagonal-bit-bootstrap.yml @@ -0,0 +1,35 @@ +name: Verify the composed diagonal-bit bootstrap record + +on: + push: + paths: + - 'research/composed-diagonal-bit-bootstrap/**' + - '.github/workflows/composed-diagonal-bit-bootstrap.yml' + pull_request: + paths: + - 'research/composed-diagonal-bit-bootstrap/**' + - '.github/workflows/composed-diagonal-bit-bootstrap.yml' + workflow_dispatch: + +permissions: + contents: read + +jobs: + verify: + runs-on: ubuntu-24.04 + timeout-minutes: 20 + strategy: + fail-fast: false + matrix: + python-version: ['3.11', '3.13'] + steps: + - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1 # v7 + with: + persist-credentials: false + - uses: actions/setup-python@5fda3b95a4ea91299a34e894583c3862153e4b97 # v7 + with: + python-version: ${{ matrix.python-version }} + - name: Reproduce the composed record and check every pinned byte + run: python3 -B research/composed-diagonal-bit-bootstrap/verify.py + - name: Require an unchanged tree + run: git diff --exit-code diff --git a/SOURCES.json b/SOURCES.json index d391fc1066..c59c77b76c 100644 --- a/SOURCES.json +++ b/SOURCES.json @@ -533,5 +533,25 @@ "175": "f1081fabbfadaaaaf7292a40d428dbbb865ce920" }, "notices": "research/coordinated-frames-and-entrance-banks/UPSTREAM-NOTICE.md" + }, + "composed_diagonal_bit_bootstrap": { + "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/200", + "contributor": "Maxime Fleury", + "research_assistance": "Codebuff", + "kappa": "1693287/2500000000", + "gain_vs_pr197": "0.001826", + "gain_vs_pr200_announced": "0.000639", + "package": "research/composed-diagonal-bit-bootstrap", + "certificate": "research/composed-diagonal-bit-bootstrap/certificate.json", + "verify": "research/composed-diagonal-bit-bootstrap/verify.py", + "inputs": { + "bit": "PR200 certified fixed-coordinate and face-diagonal bit local circuit (chafreaky): m=72, W=20634, deficit 1936, 34 sinks, coarse saving 677773948354561/10^18", + "complex": "PR193 complex word as carried by PR194 (ikeboy): saving 219037/312500000", + "assembly": "PR194 unchanged 47-constraint balanced assembly, PR168 v4 paired_cube_assembly.py (eumemic)", + "leaf": "PR185 finite acyclic ordinary-leaf wrapper recurrence (rohanarun)", + "pricing": "PR184 assemble_profiles.py and FINITE_BRIDGE.txt (icekylinx, GPT-6 Astra), carried by PR194", + "pinned_source": "PR168 v4 modules, eumemic, commit fd25adb7fbaa12ee761d02c733c54d1d2a7687ee" + }, + "scope": "Conditional composition of two supplied words through the record's unchanged assembly: PR200's bit supplier with PR193/PR194's complex, priced by PR185's finite leaf. The bit branch binds and the claim sits under one 10^-10 grid step below the word's own C/(1+C) ceiling. Physical words are inherited pinned inputs, vendored and priced, not rebuilt or replayed; the wrapper's realization is PR185's construction, not one built here. No new word, no new all-size hypothesis." } } diff --git a/research/composed-diagonal-bit-bootstrap/.gitignore b/research/composed-diagonal-bit-bootstrap/.gitignore new file mode 100644 index 0000000000..979e0f37c6 --- /dev/null +++ b/research/composed-diagonal-bit-bootstrap/.gitignore @@ -0,0 +1,2 @@ +.work/ +__pycache__/ diff --git a/research/composed-diagonal-bit-bootstrap/NOTICE.md b/research/composed-diagonal-bit-bootstrap/NOTICE.md new file mode 100644 index 0000000000..d07d5e8333 --- /dev/null +++ b/research/composed-diagonal-bit-bootstrap/NOTICE.md @@ -0,0 +1,48 @@ +# Notice and attribution + +This package is a composition. It adds no word, no construction and no all-size +hypothesis; it prices suppliers that other contributors certified, and it retains +their notices and authorship. + +## Vendored inputs, byte-identical + +* `references/pr168-v4/scripts/paired_cube_assembly.py` — the exact balanced + assembly with the RaD (hipotures) balanced prefix and the gates adapted from + Zhihao Chen's PR23; prepared by **eumemic** with Anthropic Claude assistance, + PR168 v4 at `fd25adb7fbaa12ee761d02c733c54d1d2a7687ee`. Apache-2.0. +* `references/pr184/assemble_profiles.py` and `references/pr184/FINITE_BRIDGE.txt` + — the exact rational pricing, the accepted profiles and the finite bridge; + **icekylinx** and **GPT-6 Astra**, carried by ikeboy's PR194. The rational + enclosures are retained from icekylinx's `three_stage_cover_network.py`. + Apache-2.0. +* `references/pr194/certificate.json` — PR194's published complex profile, + complex saving, assembly record and kappa (`1668581/2500000000`); **ikeboy** + (evmckinney9), building on icekylinx's source-assisted line and PR168 v4. + Apache-2.0. +* `inputs/pr200-bit-certificate.json` — the certified fixed-coordinate and + face-diagonal bit local circuit, its physical layer, 34 terminal sinks and paid + moment; **chafreaky** (Chafik Boukhalfa), PR200, with substantial Anthropic + Claude and OpenAI Codex assistance, and with James Chang's PR166 terminal-output + substitution, DaysSky's PR162 carrier rule, icekylinx's PR144 configurable + circuit and the PR189/#196 lineage. Apache-2.0. + +## Methods credited + +* the finite acyclic ordinary-leaf wrapper and its recurrence + `a_{n+1} = (1-C)C + C a_n` — **rohanarun**, PR185; +* the packing mechanism on a bit word — **evmckinney9**, PR197 (referenced here + only as a published figure for what lowering `W` was worth on a different word); +* the endpoint-frame descent — **sennemmi**, PR198 (same, referenced as a + published figure); +* the pricing recurrence applied to a composed supplier — **Maxime Fleury**, PR199, + from which this package takes the same operation and generalises it to an + arbitrary certified bit profile. + +## This package + +`compose.py`, `verify.py`, `certificate.json`, the workflow and this notice were +prepared by Maxime Fleury with Codebuff assistance, 2026-10-09. Apache-2.0. + +The result is conditional. A finite certificate checked here is not a formal +verification of the full multiplication theorem, and no claim is made about the +practical cost of the construction. diff --git a/research/composed-diagonal-bit-bootstrap/README.md b/research/composed-diagonal-bit-bootstrap/README.md new file mode 100644 index 0000000000..63183dc505 --- /dev/null +++ b/research/composed-diagonal-bit-bootstrap/README.md @@ -0,0 +1,115 @@ +# Composing the stronger bit supplier with the record's assembly + +Under the retained interfaces of the pinned suppliers, this package prices PR200's +bit supplier with PR184's finite leaf bootstrap and PR193's complex word through +PR194's unchanged assembly: + +$$\kappa = \frac{1693287}{2500000000} = 6.773148\cdot10^{-4},$$ + +**+0.1826%** over the standing claim (#197, `135216063303877/2e17 = +6.76080316519385e-4`) and **+0.0639%** over the value PR200 announces for this +same composition (`6768823/10e9 = 6.768823e-4`), which it says it is preparing as +separate work. + +| PR | author | kappa | what it changed | +| --- | --- | --- | --- | +| #200 | chafreaky | 6.65046903615388e-4 | new bit **and** complex word; with its *own* complex word the complex branch binds and the headline equals #196. Its README: the bit supplier "would give about 6.769e-4" composed with #193/#194's complex — "which I am preparing as a separate stacked composition". | +| **#197** | evmckinney9 | **6.76080316519385e-4** | packed #187 rank-4/rank-24 residuals + #193 complex + the finite leaf. The standing claim. | +| #198 | sennemmi | 6.679123e-4 | 102 lowered #189 endpoint frames + the finite leaf; a draft that does not claim the record. | +| this | Maxime Fleury | **6.773148e-4** | #200's bit word + #193's complex + #185's finite leaf, on PR194's assembly. | + +## Result + +Exactly three things are inherited: the bit supplier's certificate (#200), the +complex supplier and the 47-constraint assembly (#193/#194), and the finite +ordinary-leaf wrapper's recurrence (#185). Nothing is re-derived; the one operation +is pricing. + +| depth | bit leaf | kappa | vs #197 | vs the unbootstrapped composition | +| --- | --- | --- | --- | --- | +| 0 (PR184's legacy atom wrapper, = #200's announced value) | 6.77340866500955e-4 | 6768823/10000000000 = 6.768823e-4 | +0.1186% | — | +| 1 | 6.77773606501196e-4 | 1354629/2000000000 = 6.773145e-4 | +0.1825% | +0.0639% | +| 2, 3, 8 | 6.77773899999987e-4 | **1693287/2500000000 = 6.773148e-4** | **+0.1826%** | +0.0639% | + +The bit profile priced here has `m = 72`, `W = 20634`, rank deficit 1936 and 34 +terminal sinks; the complex saving is `219037/312500000 = 7.009184e-4`, so the bit +branch binds at every depth and the complex side is not a constraint. + +## Why this is the last pricing room on this word + +For a fixed bit word the assembly's `kappa` is capped by the word's own coarse +saving: `kappa <= C/(1+C)`. For #200's certificate `C = 6777739/10^10` and + +$$C/(1+C) = 6.7731483368\cdot10^{-4},$$ + +so the claimed value sits **3.4e-11** below that ceiling — under a third of one +`10^-10` selection step. The finite-leaf recurrence + +$$a_{n+1} = (1-C)\,C + C\,a_n = C - C^{\,n}(C-a_0)$$ + +recovers the whole `4.33e-7` of slack the legacy atom wrapper leaves below `C`, and +depths 2, 3 and 8 return the same grid value, so **no further leaf work can move +this number**. Both remaining levers reduce `W` on this word, and both are new +constructions on #200's graph rather than a recomposition: + +* **endpoint-frame descent** — what #198 did on #189's word, worth +0.0090% of + coarse saving there (`6.68298937775631e-4 -> 6.6835882709e-4`); +* **residual packing** — #197's mechanism, bound to #187's word, worth +0.8403% of + coarse saving there (`6.70899981048852e-4 -> 6.76537710350481e-4`), the largest + single bit-side gain in the queue. + +Because the bit branch binds, complex-side work is worthless here until a bit +coarse saving passes the complex word's `7.009184e-4`. + +## Cross-checks against published numbers + +The harness is independent of the numbers it is asked to confirm, and this package +checks it twice against public statements: + +* **depth 0 reproduces #200's own value** for this composition: `6.768823e-4` + against its announced "about 6.769e-4". Since depth 0 is PR184's legacy wrapper + applied to #200's certificate, agreement pins the whole pricing path (profile + reading, `select()`, assembly, grid). +* **PR184's grid legacy leaf agrees with #200's published atom wrapper**: + `6.77340866500955e-4` versus `6.77340914792209e-4` from its documented + `theta = 677340914792209011107/10^24` and `a_0 = 677773948354561/10^18`, a + difference of `4.83e-11` that floors to the same grid value. The residual is the + suppliers' own choice of wrapper precision, and it is recorded rather than + smoothed over. + +## Scope and limits + +* The physical complex and bit words, their frames, sinks and paid moments are the + suppliers' certified artifacts, vendored byte-identically and **priced, not + rebuilt or replayed**. In particular #200's bit certificate is taken as its + author's finite witness; this package does not re-run its checks. +* The wrapper is PR185's construction, not one built here. +* Conditional on PR184's finite bridge and closed-form acceptance arithmetic, and + on the retained contracts of the pinned suppliers. The full multiplication + theorem remains conditional; a finite certificate is not a proof of it. +* The improvement is small and lives on the `10^-10` selection grid, and it + depends on an unmerged bit supplier (#200) and an unmerged complex/assembly line + (#193/#194). +* This is not claimed as a new word, a new all-size hypothesis, or the public + record: it is a composition, and it is superseded the moment a lower-`W` bit word + appears. + +## Reproduce + +```bash +python3 -B research/composed-diagonal-bit-bootstrap/verify.py +``` + +`compose.py` performs the pricing; `verify.py` pins every byte against +`SOURCE.json`, reproduces `certificate.json` from the pins, re-checks the two +published cross-checks above, requires the claim to beat #197, requires it to sit +inside one grid step of the word's ceiling, re-derives the leaf tolls in closed +form, and refuses three corruption controls. + +## Credits + +Bit supplier: chafreaky (#200, with the #189/#196 lineage). Complex word and +assembly: icekylinx, GPT-6 Astra and ikeboy (#182/#184/#193/#194). Finite leaf +wrapper and its recurrence: rohanarun (#185). Paired-cube frame and balanced-prefix +construction: eumemic (#168 v4). Predecessor notices are retained in +[NOTICE.md](NOTICE.md). Apache-2.0. diff --git a/research/composed-diagonal-bit-bootstrap/SOURCE.json b/research/composed-diagonal-bit-bootstrap/SOURCE.json new file mode 100644 index 0000000000..ac91144c31 --- /dev/null +++ b/research/composed-diagonal-bit-bootstrap/SOURCE.json @@ -0,0 +1,37 @@ +{ + "package": "composed-diagonal-bit-bootstrap", + "date_utc": "2026-10-09", + "claim": { + "kappa": "1693287/2500000000", + "kappa_decimal": 0.0006773148, + "best_depth": 2, + "binding": "bit", + "standing_claim_pr197": "135216063303877/200000000000000000", + "gain_vs_pr197": 0.001826, + "pr200_announced_for_this_composition": "6768823/10000000000", + "gain_vs_pr200_announced": 0.000639, + "bit_branch_ceiling": "6773148336836464/10000000000000000000", + "distance_below_ceiling": "3.37e-11", + "scope": "Conditional composition. The complex and bit words are the suppliers' certified artifacts, vendored byte-identically and priced here, not rebuilt or replayed. The ordinary leaf is PR185's finite acyclic wrapper, not one built here." + }, + "composition": { + "bit": "PR200 certified fixed-coordinate and face-diagonal bit local circuit (chafreaky); m=72, W=20634, rank deficit 1936, 34 terminal sinks, coarse saving 677773948354561/10^18", + "complex": "PR193 complex word as carried by PR194 (ikeboy); saving 219037/312500000 = 7.009184e-4", + "assembly": "PR194's unchanged 47-constraint balanced assembly (PR168 v4 paired_cube_assembly.py, eumemic)", + "leaf": "PR185 finite acyclic ordinary-leaf wrapper (rohanarun), a_{n+1} = (1-C)C + C a_n", + "pricing": "PR184 assemble_profiles.py (icekylinx, GPT-6 Astra), carried by PR194", + "pinned_source": "PR168 v4 at fd25adb7fbaa12ee761d02c733c54d1d2a7687ee" + }, + "files": { + "research/composed-diagonal-bit-bootstrap/compose.py": "5122db672a30e3119e5004a873354d608dfe34f0c8b15731c683e624c0f71c76", + "research/composed-diagonal-bit-bootstrap/verify.py": "e54e071f9b9b8b3941932009ddea291d5c1403e2b4cdf632a1ac7dccba11a880", + "research/composed-diagonal-bit-bootstrap/certificate.json": "0a844fb88811af915ae5198aab07b79f61c29cc9c68b1752733d30a4c189cfc4", + "research/composed-diagonal-bit-bootstrap/README.md": "a9bb09620cc78ce58a6be787f1f44cd610e246dadbf956f34d71650c72f0d3b2", + "research/composed-diagonal-bit-bootstrap/NOTICE.md": "d3127dcacf595f645e64e8b4cdb3f63e17c3785f9dbc65c08653aabdd25c38d1", + "research/composed-diagonal-bit-bootstrap/references/pr168-v4/scripts/paired_cube_assembly.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c", + "research/composed-diagonal-bit-bootstrap/references/pr184/assemble_profiles.py": "c56d0638d4bc1ac3f70c78778ea824f3a2ba23c31f7eeff3c93cf17df3f2e0de", + "research/composed-diagonal-bit-bootstrap/references/pr184/FINITE_BRIDGE.txt": "66d8f4ea8752abd89952d6674a636575a0db16e18b1c16e293f48f64242f0c46", + "research/composed-diagonal-bit-bootstrap/references/pr194/certificate.json": "1600b77cb1f41c0f87967f20133eccda5e6c5f215b70361dfd0c49c861248e59", + "research/composed-diagonal-bit-bootstrap/inputs/pr200-bit-certificate.json": "853afa75980e11ce16b333c28311c4f635e84065867c049fda9916c2419091ed" + } +} diff --git a/research/composed-diagonal-bit-bootstrap/certificate.json b/research/composed-diagonal-bit-bootstrap/certificate.json new file mode 100644 index 0000000000..e72fb933d9 --- /dev/null +++ b/research/composed-diagonal-bit-bootstrap/certificate.json @@ -0,0 +1,179 @@ +{ + "assembly": { + "margin_count": 7, + "pr168_v4_assembly_sha256": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c", + "pr184": "assemble_profiles.py", + "pr184_sha256": "c56d0638d4bc1ac3f70c78778ea824f3a2ba23c31f7eeff3c93cf17df3f2e0de", + "strict_constraint_count": 47 + }, + "bit_coarse_saving": "6777739/10000000000", + "bit_supplier": { + "W_per_vertex": 20634, + "deficit_per_vertex": 1936, + "m": 72, + "profile": { + "R": 17114, + "W_per_vertex": 20634, + "active_virtual_R": 18874, + "changed_operation_frames": 7282, + "child_histogram": { + "1": 125772, + "10": 2022, + "11": 1212, + "12": 4062, + "13": 1626, + "14": 3672, + "15": 864, + "16": 2988, + "17": 1356, + "18": 1614, + "19": 648, + "2": 58654, + "20": 5280, + "21": 15018, + "22": 6672, + "3": 30930, + "4": 9588, + "5": 8070, + "6": 4152, + "60": 2200, + "7": 4080, + "8": 2514, + "9": 1752 + }, + "deficit_per_vertex": 1936, + "foreign_producer_replays": 0, + "frames_not_contained_in_original": 84, + "h": 24, + "loss": 528, + "m": 72, + "maxchild": 60, + "physical_internal_histogram": { + "1": 35764, + "10": 674, + "11": 404, + "12": 1354, + "13": 542, + "14": 1207, + "15": 288, + "16": 993, + "17": 452, + "18": 533, + "19": 208, + "2": 17469, + "21": 4160, + "22": 1344, + "3": 10301, + "4": 3196, + "5": 2673, + "6": 1384, + "7": 1359, + "8": 838, + "9": 583 + }, + "physical_target_histogram": { + "1": 4400, + "14": 17, + "16": 3, + "18": 5, + "19": 8, + "2": 29, + "20": 880, + "21": 846, + "3": 9, + "5": 17, + "7": 1, + "9": 1 + }, + "rank_per_vertex": 1483712, + "reused_registers": 1760, + "scalar_role_reserve": 18908, + "selected_rank_histogram": { + "20": 2200 + }, + "selected_roles": 2200, + "terminal_sinks": 34, + "v": 1760, + "virtual_R": 18908 + }, + "sha256": "853afa75980e11ce16b333c28311c4f635e84065867c049fda9916c2419091ed", + "source": "pr200-bit-certificate.json", + "terminal_sinks": 34 + }, + "ceiling": "6777739/10006777739", + "ceiling_decimal": 0.0006773148336836464, + "claim": { + "best_depth": 2, + "binding": "bit", + "gain_vs_pr197": 0.001825942052225986, + "gain_vs_pr200_announced_legacy": 0.0006389589445609672, + "kappa": "1693287/2500000000", + "kappa_decimal": 0.0006773148 + }, + "comparisons": { + "pr194_published": "1668581/2500000000", + "pr197_published": "135216063303877/200000000000000000", + "pr200_announced_legacy": "6768823/10000000000" + }, + "complex_supplier": { + "published_kappa": "1668581/2500000000", + "saving": "219037/312500000", + "sha256": "1600b77cb1f41c0f87967f20133eccda5e6c5f215b70361dfd0c49c861248e59", + "source": "certificate.json" + }, + "depths": { + "0": { + "assembly_source_sha256": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c", + "binding": "bit", + "kappa": "6768823/10000000000", + "kappa_decimal": 0.0006768823, + "leaf": "338670433250477381/500000000000000000000", + "leaf_decimal": 0.0006773408665009548, + "minimum_margin": "564450705150607418699608700159127/833897784044128447859984087300000000", + "minimum_margin_decimal": 0.0006768823661015241 + }, + "1": { + "assembly_source_sha256": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c", + "binding": "bit", + "kappa": "1354629/2000000000", + "kappa_decimal": 0.0006773145, + "leaf": "3388868032505982607313821559/5000000000000000000000000000000", + "leaf_decimal": 0.0006777736065011965, + "minimum_margin": "5648113218066570516513249734636457821273853/8338981446607881036595323615687872614700000000", + "minimum_margin_decimal": 0.0006773145202720294 + }, + "2": { + "assembly_source_sha256": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c", + "binding": "bit", + "kappa": "1693287/2500000000", + "kappa_decimal": 0.0006773148, + "leaf": "33888694990053708566050912573619475101/50000000000000000000000000000000000000000", + "leaf_decimal": 0.0006777738998010741, + "minimum_margin": "56481156622321442736964422671389685170997102823158367/83389814490520466347941627902087668706047684163300000000", + "minimum_margin_decimal": 0.0006773148131747202 + }, + "3": { + "assembly_source_sha256": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c", + "binding": "bit", + "kappa": "1693287/2500000000", + "kappa_decimal": 0.0006773148, + "leaf": "338886949999932586632642757346135811087551576639/500000000000000000000000000000000000000000000000000", + "leaf_decimal": 0.0006777738999998652, + "minimum_margin": "564811566388873590686758597255617362053381188732691530567192213/833898144905370322644389985041155467773608058924813280778700000000", + "minimum_margin_decimal": 0.000677314813373242 + }, + "8": { + "assembly_source_sha256": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c", + "binding": "bit", + "kappa": "1693287/2500000000", + "kappa_decimal": 0.0006773148, + "leaf": "33888694999999999999999999999035793121769166659567411393981444370015282231565601126323952500698661/50000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000", + "leaf_decimal": 0.0006777739, + "minimum_margin": "773714474505460200404999999977986144993045041407557898648229097352836299712237629735442123837906649402526715519/1142326225897767719178082191780799903952992084571328403611932265216675488466467122294406665067904557328448100000000", + "minimum_margin_decimal": 0.0006773148133733766 + } + }, + "legacy_leaf": "338670433250477381/500000000000000000000", + "old_leaf": "384599/10000000000", + "scope": "Conditional composition: the physical complex and bit words are the suppliers' certified artifacts, vendored and priced, not rebuilt or replayed. The finite leaf wrapper is PR185's construction, not one built here." +} diff --git a/research/composed-diagonal-bit-bootstrap/compose.py b/research/composed-diagonal-bit-bootstrap/compose.py new file mode 100644 index 0000000000..5241ceb119 --- /dev/null +++ b/research/composed-diagonal-bit-bootstrap/compose.py @@ -0,0 +1,196 @@ +#!/usr/bin/env python3 +"""Compose a certified bit supplier with PR184's finite leaf and PR194's complex. + +The record's assembly sets + + a = min(bit_effective, (1-stop)*complex_saving - 1/SELECT_GRID), + kappa = floor( (1-eta)*q/(1+q) * SELECT_GRID ) / SELECT_GRID, q = a*(1-2*eta), + +with the case-dependent `eta`, `stop` of PR184's `assemble_profiles.py`. Every bit +supplier published so far has been handed to it through PR184's *legacy* ordinary +leaf, `effective = (1-beta)*C + beta*OLD` with `OLD = 384599/10^10`, which holds +the effective value strictly below the supplier's coarse saving `C`. PR185 +replaced that leaf by a finite acyclic wrapper whose value obeys + + a_0 = legacy effective, a_{n+1} = (1-C)*C + C*a_n = C - C^n (C - a_0). + +This script applies that recurrence to an arbitrary certified bit profile, +composes it with a certified complex profile through PR194's unchanged assembly, +and reports the exact kappa at each depth together with the bit branch's own +ceiling `C/(1+C)`. + + python3 -B compose.py [--out certificate.json] + +Inputs, digests and provenance are in SOURCE.json; the paths below are the +vendored pins, so this runs from the package directory alone. +""" +import argparse +import hashlib +import importlib.util +import json +import sys +from fractions import Fraction as Q +from pathlib import Path + +HERE = Path(__file__).resolve().parent +SELECT_GRID = 10 ** 10 +OLD = Q(384599, SELECT_GRID) +DEFAULTS = dict( + bit=HERE / "inputs/pr200-bit-certificate.json", + complex=HERE / "references/pr194/certificate.json", + pr184=HERE / "references/pr184/assemble_profiles.py", + pr168_v4=HERE / "references/pr168-v4", + finite_bridge=HERE / "references/pr184/FINITE_BRIDGE.txt", +) + + +def load(path, name): + spec = importlib.util.spec_from_file_location(name, path) + module = importlib.util.module_from_spec(spec) + sys.modules[name] = module + spec.loader.exec_module(module) + return module + + +def digest(path): + return hashlib.sha256(Path(path).read_bytes()).hexdigest() + + +def bit_profile(certificate): + """The bit profile block of a supplier certificate.""" + node = certificate["bit"]["profile"] if "bit" in certificate else certificate + for key in ("m", "W_per_vertex", "deficit_per_vertex", "child_histogram"): + assert key in node, "bit profile lacks " + key + return node + + +def complex_profile(certificate): + if "complex_profile" in certificate: + return certificate["complex_profile"] + if "combined_fixed_boundary_profile" in certificate: + return certificate["combined_fixed_boundary_profile"] + if "complex" in certificate and "profile" in certificate["complex"]: + return certificate["complex"]["profile"] + raise SystemExit("complex profile not found in the complex certificate") + + +def bootstrap_chain(coarse, initial, depth): + values = [initial] + for _ in range(depth): + values.append((1 - coarse) * coarse + coarse * values[-1]) + assert values[-1] == coarse - coarse ** depth * (coarse - initial) + return values + + +def price(pr184, complex_row, bit_row, coarse, chain, work): + """Assemble one bootstrapped leaf, returning the exact record row.""" + leaf = chain[-1] + assert chain[0] == bit_row["effective_saving"] + if len(chain) > 1: + assert chain[0] < leaf < coarse < 1 - leaf + boot = dict(bit_row) + boot.update(effective_saving=leaf, effective_saving_decimal=float(leaf), + ordinary_leaf_saving=leaf, atom_exponent=coarse) + out = pr184.assemble(complex_row, boot, work["pr168_v4"], work["finite_bridge"]) + assembly = out["assembly"] + assert len(assembly["strict_constraints"]) == 47, "strict constraints" + assert len(assembly["margins"]) == 7, "margins" + assert all(Q(v) > 0 for v in assembly["strict_constraints"].values()) + kappa = Q(out["kappa"]) + assert all(Q(v) > kappa for v in assembly["margins"].values()) + margin = Q(assembly["minimum_margin"]) + assert 0 < margin <= coarse / (1 + coarse), "the bit branch ceiling" + assert kappa <= margin < kappa + Q(1, SELECT_GRID), "kappa is the last grid point" + return dict(leaf=str(leaf), leaf_decimal=float(leaf), kappa=str(kappa), + kappa_decimal=float(kappa), + minimum_margin=str(assembly["minimum_margin"]), + minimum_margin_decimal=float(assembly["minimum_margin"]), + binding="bit" if coarse <= complex_row["saving"] else "complex", + assembly_source_sha256=out["assembly_source_sha256"]) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--bit-certificate", type=Path, default=DEFAULTS["bit"]) + parser.add_argument("--complex-certificate", type=Path, default=DEFAULTS["complex"]) + parser.add_argument("--pr184", type=Path, default=DEFAULTS["pr184"]) + parser.add_argument("--pr168-v4", type=Path, default=DEFAULTS["pr168_v4"]) + parser.add_argument("--finite-bridge", type=Path, default=DEFAULTS["finite_bridge"]) + parser.add_argument("--depths", type=int, nargs="+", default=[0, 1, 2, 3, 8]) + parser.add_argument("--out", type=Path, default=HERE / "certificate.json") + args = parser.parse_args() + if hasattr(sys, "set_int_max_str_digits"): + sys.set_int_max_str_digits(0) + assert not sys.flags.optimize, "assertions must stay enabled" + pr184 = load(args.pr184.resolve(), "composed_pr184") + work = dict(pr168_v4=args.pr168_v4.resolve(), finite_bridge=args.finite_bridge.resolve()) + assert (work["pr168_v4"] / "scripts/paired_cube_assembly.py").is_file(), "assembly pin" + assert work["finite_bridge"].is_file(), "finite bridge pin" + + bit_cert = json.loads(args.bit_certificate.read_text()) + complex_cert = json.loads(args.complex_certificate.read_text()) + row = bit_profile(bit_cert) + complex_row = pr184.select(pr184.normalize(complex_profile(complex_cert))) + bit_row = pr184.select(pr184.normalize(row), True) + coarse, initial = Q(bit_row["saving"]), Q(bit_row["effective_saving"]) + assert initial < coarse, "the legacy leaf must sit below the coarse saving" + print(f"[bit supplier] m={row['m']} W={row['W_per_vertex']} " + f"deficit={row['deficit_per_vertex']} sinks={row.get('terminal_sinks')} " + f"coarse={coarse} ({float(coarse):.15g}) " + f"legacy leaf={initial} ({float(initial):.15g})") + print(f"[complex] saving={complex_row['saving']} " + f"({float(complex_row['saving']):.15g})") + + rows = {} + for depth in args.depths: + chain = bootstrap_chain(coarse, initial, depth) + rows[str(depth)] = price(pr184, complex_row, bit_row, coarse, chain, work) + print(f"[depth {depth}] leaf={rows[str(depth)]['leaf_decimal']:.15g} " + f"kappa={rows[str(depth)]['kappa']} " + f"({rows[str(depth)]['kappa_decimal']:.15g}) " + f"[47 strict constraints, 7 margins, binding {rows[str(depth)]['binding']}]") + + ceiling = coarse / (1 + coarse) + best_depth = max(rows, key=lambda d: rows[d]["kappa_decimal"]) + best = Q(rows[best_depth]["kappa"]) + assert best <= ceiling, "kappa cannot exceed the bit branch ceiling" + print(f"[bit ceiling] C/(1+C) = {float(ceiling):.15g}; best depth {best_depth} sits " + f"{float(ceiling - best):.3g} below it (grid {1 / SELECT_GRID:.1g})") + for name, value in (("#197 packed bit", Q(135216063303877, 200000000000000000)), + ("#200 legacy, announced", Q(6768823, SELECT_GRID))): + print(f"[comparison] vs {name}: {float(best / value - 1) * 100:+.4f}%") + comparisons = { + "pr197_published": str(Q(135216063303877, 200000000000000000)), + "pr200_announced_legacy": str(Q(6768823, SELECT_GRID)), + "pr194_published": str(Q(complex_cert["kappa"])) if "kappa" in complex_cert else None, + } + out = dict( + claim=dict(kappa=str(best), kappa_decimal=float(best), best_depth=int(best_depth), + binding=rows[best_depth]["binding"], + gain_vs_pr197=float(best / Q(comparisons["pr197_published"]) - 1), + gain_vs_pr200_announced_legacy=float( + best / Q(comparisons["pr200_announced_legacy"]) - 1)), + bit_supplier=dict(source=args.bit_certificate.name, sha256=digest(args.bit_certificate), + m=row["m"], W_per_vertex=row["W_per_vertex"], + deficit_per_vertex=row["deficit_per_vertex"], + terminal_sinks=row.get("terminal_sinks"), + profile=row), + complex_supplier=dict(source=args.complex_certificate.name, + sha256=digest(args.complex_certificate), + saving=str(complex_row["saving"]), + published_kappa=complex_cert.get("kappa")), + assembly=dict(pr184=args.pr184.name, pr184_sha256=digest(args.pr184), + pr168_v4_assembly_sha256=rows[best_depth]["assembly_source_sha256"], + strict_constraint_count=47, margin_count=7), + bit_coarse_saving=str(coarse), legacy_leaf=str(initial), old_leaf=str(OLD), + ceiling=str(ceiling), ceiling_decimal=float(ceiling), + depths=rows, comparisons={k: v for k, v in comparisons.items() if v}, + scope=("Conditional composition: the physical complex and bit words are the suppliers' " + "certified artifacts, vendored and priced, not rebuilt or replayed. The finite " + "leaf wrapper is PR185's construction, not one built here.")) + args.out.write_text(json.dumps(out, indent=1, sort_keys=True) + "\n") + print(f"[write] {args.out}") + + +if __name__ == "__main__": + main() diff --git a/research/composed-diagonal-bit-bootstrap/inputs/pr200-bit-certificate.json b/research/composed-diagonal-bit-bootstrap/inputs/pr200-bit-certificate.json new file mode 100644 index 0000000000..7b80d2cd04 --- /dev/null +++ b/research/composed-diagonal-bit-bootstrap/inputs/pr200-bit-certificate.json @@ -0,0 +1,4442 @@ +{ + "arithmetic": { + "actual_uniform_bit_saving": "677340914792209011106157466449676890973/1000000000000000000000000000000000000000000", + "adverse_control_count": 21, + "adverse_controls": [ + "full group stock replaced by local W", + "old ordinary reserve omitted", + "conservative old coarse reserve omitted", + "uniform supplier replaced by fictional finite profile", + "actual ordinary saving overstated", + "unpaid previous atom grid", + "scalar role reserve collapsed to physical stock", + "terminal removals omitted", + "terminal removals counted as aliases", + "odd divisor silently changed to 21", + "C0 detached from scalar charge", + "scalar group charge omitted", + "stale total row coefficient", + "inadequate polynomial row degree", + "float in otherwise unused metadata", + "noncontracting maximum child", + "transfer saving exceeds actual uniform supplier", + "old prefix charged at balanced parameters", + "old nonlinear scalar guard", + "old separate movement exposures", + "next final 1e-18 kappa grid point" + ], + "assembly": { + "absorption_gap": "14997626888680345751524011177060836353630220354194253091514663/500332244410424089575910423090842681151818848181152485337000000000000000000000000", + "constraints": { + "K_dominates_log": "332744409924090075910047758473270852729147270729394494318848181151818847514663/500332244410424089575910423090842681151818848181152485337000000000000000000000000", + "K_geometry": "375332369410299089700910423090842681151818848181152485337/500332244410424089575910423090842681151818848181152485337000000000000000000000000", + "a_below_b": "666489485337/1000000000000000000000000000000000000000", + "a_positive": "665489485336999999999999333510514663/1000000000000000000000000000000000000000", + "alpha_below_one": "999999000000999999000000500332244410424089575910423090842681151818848181152485337/1000664488820848179151820846181685362303637696362304970674000000000000000000000000", + "alpha_below_one_fourth": "249500633385363864636134865695980388696361303638694362837181151818848181152485337/1000664488820848179151820846181685362303637696362304970674000000000000000000000000", + "alpha_positive": "665488819848180151820345849440951879548120451881879831318848181151818847514663/1000664488820848179151820846181685362303637696362304970674000000000000000000000000", + "artificial_boundary": "28021267642263141736858268578810664824988675011325028334096043455456544543457456011/4002657955283392716607283384726741449214550785449219882696000000000000000000000000", + "b_below_one_over32": "30584510514663/1000000000000000", + "beta_below_one": "999999999999999999999999/1000000000000000000000000", + "beta_positive": "1/1000000000000000000000000", + "c_below_one": "499667255257331499999999875998734228005499999999999333510514663/500000000000000000000000000000000000000000000000000000000000000", + "c_positive": "332744742668500000000124001265771994500000000000666489485337/500000000000000000000000000000000000000000000000000000000000000", + "cell_above_band": "999999000000999998999999499667755589575910424089576909157318848181151818847514663/2001328977641696358303641692363370724607275392724609941348000000000000000000000000", + "compact_leaf": "665989485336999999999999333510514663/500000000000000000000000000000000000000000000000000000000000000", + "compact_reservations": "1/4000000000000000000000000", + "delta_below_one_eighth": "999999999999999999999999/8000000000000000000000000", + "delta_positive": "1/8000000000000000000000000", + "epsilon_below_one": "332744409924090075910423090842681151818848181152485337/500332244410424089575910423090842681151818848181152485337", + "epsilon_positive": "499999500000499999500000000000000000000000000000000000000/500332244410424089575910423090842681151818848181152485337", + "g1_above_kappa": "3749531805231189043903396771870981799077843043260608561/125083061102606022393977605772710670287954712045288121334250000000000000000", + "g2_above_kappa": "442581721611999999999333510514663/1000000000000000000000000000000000000000", + "g3_above_kappa": "14997626888680345751524011177060836353630220354194253091514663/500332244410424089575910423090842681151818848181152485337000000000000000000000000", + "g4_above_kappa": "442581721611999999999333510514663/1000000000000000000000000000000000000000", + "g5_above_kappa": 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a/research/composed-diagonal-bit-bootstrap/references/pr168-v4/scripts/paired_cube_assembly.py b/research/composed-diagonal-bit-bootstrap/references/pr168-v4/scripts/paired_cube_assembly.py new file mode 100644 index 0000000000..43007488ad --- /dev/null +++ b/research/composed-diagonal-bit-bootstrap/references/pr168-v4/scripts/paired_cube_assembly.py @@ -0,0 +1,58 @@ +#!/usr/bin/env python3 +"""Exact semantic assembly with the balanced prefix, for the paired-cube network. + +Prepared by eumemic with Anthropic Claude assistance. Apache-2.0. The 47 strict constraints, the seven margins and +the finite bridge are unchanged from icekylinx's scripts/structured_bulk_assembly.py (PR144, adapted from Zhihao +Chen's PR23). The prefix is the RaD project's (hipotures) balanced positional transform, reviewed in +references/semantic-bulk/rad20/reports/review-balanced-transform.md: the prefix margin becomes 1-eps instead of +1-eps(1+c), and eps(1+c)<1 remains a strict geometric condition (K_geometry) whose gap need not exceed kappa. +The parameters c=q+eta/4 and eps=(1-eta)/(1+q) are those of the reviewed balanced assembly in +research/copied-fixed/balanced_assembly.py, with its backoff h equal to eta. Nothing else differs from +structured_bulk_assembly.assembly. +""" +from fractions import Fraction as Q + + +def assembly(bit_saving,complex_saving,bridge,kappa,eta=Q(1,10**8),beta=Q(1,4)): + a,b=bit_saving,complex_saving + tau,sigma=1-a,1-b + q=a*(1-2*eta); lp=1-q; lam=(tau+lp)/2 + c=q+eta/4; eps=(1-eta)/(1+q) + minimum=eps*q; r=(minimum+1-eps)/2; delta=eta/8 + internal=tau+(1-beta)*max(sigma-tau,Q(0));leaf=sigma+beta*(1-sigma) + margins=dict(balanced_prefix=1-eps,coordinate_movement=a, + compact_phase_layer=minimum,bulk_exposure=a, + Gaussian_arithmetic=min(1-eps-delta,r-delta), + scalar_work=1-eps-delta,dimension=eps) + slacks=dict(bit_positive=a,complex_above_bit=b-a, + complex_below_one_over32=Q(1,32)-b,beta_positive=beta, + beta_below_one=1-beta,leaf_saving_above_bit=(1-beta)*b-a, + q_positive=q,q_below_internal=1-internal-q,q_below_leaf=1-leaf-q, + c_positive=c,c_below_one=1-c,q_below_reservations=c-q, + lambda_above_tau=lam-tau,lambda_above_sigma=lam-sigma, + lambda_above_internal=lam-internal,lambda_prime_above_lambda=lp-lam, + compact_leaf=lp-leaf,compact_reservations=lp-(1-c), + lambda_prime_below_one=q,epsilon_positive=eps,epsilon_below_one=1-eps, + guard_width=1-eps,K_geometry=1-eps*(1+c),K_dominates_log=eps*c, + record_suffix=1-eps,phase_local=1-eps-delta,phase_boundary=r-delta, + gamma_sublinear=1-eps-r,cell_above_band=eps-(1-r)/2, + prime_interval_packing=1-eps,alpha_positive=r,alpha_below_one=1-r, + alpha_below_one_fourth=Q(1,4)-r,delta_positive=delta, + delta_below_one_eighth=Q(1,8)-delta,short_record_fallback=eps-a, + small_field_exposure=1-eps-minimum, + artificial_boundary=8-eps+r-delta-minimum, + literal_scalar_guard=Q(bridge['semantic']['strict_literal_gap']), + row_product_gap=bridge['rows']['degree_gap']) + slacks.update({name+'_above_kappa':val-kappa for name,val in margins.items()}) + assert len(slacks)==47 and len(margins)==7 + assert all(v>0 for v in slacks.values()),{k:str(v) for k,v in slacks.items() if v<=0} + assert min(margins.values())==minimum + assert margins['balanced_prefix']-minimum==eta and 1-eps-r==eta/2 + assert 1-eps*(1+c)==eta-eps*eta/4 + return dict(parameters=dict(a_bit=a,a_complex=b,tau=tau,sigma=sigma, + eta=eta,beta=beta,q=q,c=c,epsilon=eps,lambda_=lam, + lambda_prime=lp,alpha_squared_power=r,delta=delta, + C0=bridge['semantic']['C0'],C1=1,kappa=kappa), + strict_constraints=slacks,margins=margins,minimum_margin=minimum, + absorption_gap=minimum-kappa, + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c)) diff --git a/research/composed-diagonal-bit-bootstrap/references/pr184/FINITE_BRIDGE.txt b/research/composed-diagonal-bit-bootstrap/references/pr184/FINITE_BRIDGE.txt new file mode 100644 index 0000000000..c1a8843611 --- /dev/null +++ b/research/composed-diagonal-bit-bootstrap/references/pr184/FINITE_BRIDGE.txt @@ -0,0 +1,141 @@ +FINITE ROUTER, ROW-STOCK, AND SEMANTIC BRIDGE FOR ROUND 13 + +Prepared for icekylinx by GPT-6 Astra, 9 October 2026. Apache-2.0. + +This bridge applies to a completed, physically proved round-13 profile. +It cannot make a numerically attractive but unconstructed profile valid. +The local source/target flags, controlled injections, old-response +subtraction, inverse cleanup, and retained alias boundaries are separate +construction obligations. assemble_profiles.py records their role as +proof dependencies and independently checks the exact arithmetic. + +1. The inherited uniform interfaces + +Retain the three completed-core cover of PR144/PR168 and all of its +analytic and fixed-tape assumptions. The complex cover is O(m,2), m<=72, +with order V<2^(m*m)<=2^5184. No new independent cover coordinates are +introduced by common-frame scalar lifts or source-controlled local +rewrites. Every stage still uses one completed invocation at each vertex. + +For a supplied profile with W0<10^7 roles per cover vertex, the full +physical stock W=V W0 is less than2^5208. Its total rank s is less +than mW<2^5215. The profile's actual proper-child maximum is retained; +the selected complex maximum must be less than m/2. The script checks +these inequalities rather than assuming that fewer auxiliary rows imply +a better contraction or a shorter recursion. + +The bit word uses the same weighted q-adic frame interface and the same +internally borrowed selectors as its pinned parent. New source controls +must use existing nondegenerate source-meeting planes or separately +certified new frames. All zero-rank adapters remain charged scalar work. +The group-size factor is not omitted and is not inserted into an external +polynomial row reserve. The inherited ordinary leaf saving is exactly +384599/10^10. The bad-row allowance is1/10^16; the charged fallback per +edge is32m^2. Its inequality2m^3/2^80<1/10^16 is checked explicitly. + +2. A deliberately loose finite scalar bound + +The pinned words and round-13 modifications are finite straight-line +programs with fewer than2^40 stored nodes, roles, coefficients, and +boundary entries. Scalar sum/difference lifts use actual invertible +matrices and are executed pointwise at common frame representatives. +For the selected dyadic rewrite, new elementary coefficients are +dyadic; the inherited center scatters retain their fixed odd divisor3. +No unrecorded new odd denominator may be included under this bridge. + +Fixed integer multipliers can be expanded into scalar doublings and +additions; dyadic divisions can be expanded into halvings. The explicit +low words and full-frame inverses are much smaller than2^4096 primitive +scalar/movement groups per invocation. Even constructing their fixed +old-response matrices by exact elimination is dominated by this bound: +matrix order is below2^40, original finite-word coefficient bit lengths +are below2^80, and the elementary elimination and coefficient expansion +bounds are below2^1024. No input-size-dependent dense elimination is +being performed. These are constants of the chosen finite construction. + +Consequently all3V invocation words, endpoint adapters, and finite role +bookkeeping fit within K<2^9300 logical groups. The retained universal +router is overcharged by a full W-role permutation for every group: + + 64 (m+1)^3 (K+1) (W+1)^2 < 2^20000. + +Choose the exact dominating scalar/router budget G=2^30000. This also +dominates the primitive arithmetic required to realize the fixed scalar +coefficients and source-controlled inverse cleanup. The router still +uses a fixed number of tapes, with sequential reuse of row stock. + +3. Explicit semantic constants + +Choose the exact integer E=2^100000 and put B=s+E. Then + + 2 G W^2 + 8s + 4W + 4 + 32m < 2^40500 < E, + E <= B < 2^100001. + +For the actual maximum child r= s+E >= 1. + +Choose C0=2^210000 and C1=1. These dominate both the retained semantic +requirement32m B^2 and2B+18. The reported strict_literal_gap=1 and +induction_gap_lower=1 are proved lower bounds on the positive actual +integer gaps; they are not claims that those gaps equal one. + +Use the inherited common dyadic grid with fixed3^(-K') exposure and +retain its precision/rounding contract. No child receives an independent +rounding allowance and no source-controlled injection is treated as an +unpaid numerical operation. + +4. External rows and stopping + +The complex child maximum below m/2 gives halving degree1, while +log2 W<5208<10000. Keep the deliberately conservative inherited bit +coarse reserve9909 and ordinary-leaf reserve252. Thus the external +row coefficient is bounded by + + A=10000+9909+252=20161. + +Choose degree D=1000000 and suffix slope4D. The exact row gap is + + D - (51/25)A > 0. + +The q-adic selector fields and source-control labels remain internally +borrowed and restored. Increasing these finite overcharges changes +constants and the all-size bridge, not the selected exponent saving. + +5. Exact supplier moments and balanced assembly + +For each actual histogram, assemble_profiles.py proves + + sum_r n_r r exp(a log(m/r))/(mW0) + bad_allowance < 1 + +using rational upper bounds, with upward rounding on the2^120 grid. +The bit atom stop is the first10^(-12) grid point above +a/(1+a-old), which implies both required strict toll inequalities. +Its effective saving is(1-beta)a+beta*old. This stopping rule is the +already reviewed PR158 edge rule, not a new local-word contribution. + +The final assembly uses the substantial PR168 balanced-prefix adapter, +with eta=10^(-8) and phase stop10^(-9), retaining all47 strict +constraints and all7 margins. The selected final kappa is rounded +down on the10^(-10) grid below the minimum complete margin. The +script checks every constraint exactly and reports whether the fixed +target0.0009218338 is reached. + +This is a conditional bound of the retained theorem form + + T(n)=O(n (log n)^(1-kappa)). + +The improvement ratio refers to kappa, the logarithmic exponent saving. +It is not a measurement of practical multiplication throughput. + +Credits + +The base supplier, scalar/frame verification, and actual profiles are +pinned to PR168 fd25adb7fbaa12ee761d02c733c54d1d2a7687ee, eumemic +(Anthropic Claude assistance), building on icekylinx's PR144. The +balanced prefix is RaD/hipotures; the semantic constraints are retained +from the reviewed PR23 line; completed-core sharing is credited to +an664 PR128; the atom-edge stop is credited to geckods PR158. Existing +source notices retain their more detailed upstream attributions. +The new source-controlled boundary construction, this conservative +bridge, and its integration are GPT-6 Astra's round-13 work. diff --git a/research/composed-diagonal-bit-bootstrap/references/pr184/assemble_profiles.py b/research/composed-diagonal-bit-bootstrap/references/pr184/assemble_profiles.py new file mode 100644 index 0000000000..1f5672db45 --- /dev/null +++ b/research/composed-diagonal-bit-bootstrap/references/pr184/assemble_profiles.py @@ -0,0 +1,248 @@ +#!/usr/bin/env python3 +"""Price complete supplied profiles and perform the exact balanced assembly. + +New integration for icekylinx: GPT-6 Astra, 2026-10-09. Apache-2.0. +The rational enclosures are retained from icekylinx's three_stage_cover_network.py; +the balanced assembly is PR168's paired_cube_assembly.py (eumemic, Anthropic +Claude assistance), retaining the RaD/hipotures balanced prefix and PR23 gates. + +This tool certifies arithmetic and binds the supplied construction receipts. +It is not a substitute for regenerating their exact flow and boundary checks. +""" +import argparse +from fractions import Fraction as Q +from hashlib import sha256 +import importlib.util +import json +import math +from pathlib import Path + +HERE = Path(__file__).resolve().parent +PIN = HERE.parent / "public/pr168_fd25adb7" +GRID = 1 << 120 +SELECT_GRID = 10**10 +OLD = Q(384599, SELECT_GRID) +BAD = Q(1, 10**16) +BASE = Q(4609169, SELECT_GRID) + + +def serial(x): + if isinstance(x, Q): + return str(x) + if isinstance(x, dict): + return {str(k): serial(v) for k, v in x.items()} + if isinstance(x, (list, tuple)): + return [serial(v) for v in x] + return x + + +def up(x): + return Q((x.numerator*GRID+x.denominator-1)//x.denominator, GRID) + + +def log_upper(x): + assert x >= 1 + p = 0 + while x >= 2: + x /= 2 + p += 1 + def small(y): + z = (y-1)/(y+1) + return (2*sum((z**(2*j+1)/(2*j+1) for j in range(32)), Q(0)) + + 2*z**65/(65*(1-z*z))) + return up(p*small(Q(2))+small(x)) + + +def exp_upper(u): + assert 0 <= u < 3 + return up(1+u+u*u/(2*(1-u/3))) + + +def normalize(data): + p = data.get("combined_fixed_boundary_profile") or data + m = int(p.get("m", 3*int(p.get("h",0)))) + W = Q(p.get("W_per_vertex", p.get("W", p.get("new_W")))) + hist = {int(r): Q(n) for r, n in p["child_histogram"].items() if int(r) and n} + delta = Q(p.get("deficit_per_vertex", p.get("delta", p.get("deficit")))) + assert all(0 < r < m and n > 0 for r, n in hist.items()) + mass = sum((r*n for r, n in hist.items()), Q(0)) + assert m*W-mass == delta > 0 + return dict(m=m, W=W, delta=delta, histogram=hist, + mass=mass, edge_count=sum(hist.values()), maxchild=max(hist)) + + +def numerical_root(p): + lo, hi = 0., .02 + while sum(float(n)*r*math.expm1(hi*math.log(p['m']/r)) + for r, n in p['histogram'].items()) < float(p['delta']): + hi *= 2 + for _ in range(85): + a = (lo+hi)/2 + excess = math.fsum(float(n)*r*math.expm1(a*math.log(p['m']/r)) + for r, n in p['histogram'].items()) + if excess < float(p['delta']): + lo = a + else: + hi = a + return lo + + +def moment(p, a, bit=False): + m, W = p['m'], p['W'] + good = sum((n*r/(W*m)*exp_upper(a*log_upper(Q(m, r))) + for r, n in p['histogram'].items()), Q(0)) + extra = (BAD*32*m*m*p['edge_count']/(W*m)*exp_upper(a*log_upper(Q(m)))) if bit else Q(0) + return dict(saving=a, ideal_moment_upper=good, bad_moment_upper=extra, + strict_gap_lower=1-good-extra, + strict_gap_lower_decimal=float(1-good-extra)) + + +def select(p, bit=False): + root = numerical_root(p) + ticks = int(root*SELECT_GRID) + while True: + result = moment(p, Q(ticks, SELECT_GRID), bit) + if result['strict_gap_lower'] > 0: + break + ticks -= 1 + result['numerical_root_for_discovery_only'] = root + result['counts'] = p + if bit: + assert Q(2*p['m']**3, 2**80) < BAD + a = result['saving'] + edge = a/(1+a-OLD) + beta = Q(edge.numerator*10**12//edge.denominator+1, 10**12) + effective = (1-beta)*a+beta*OLD + assert effective < beta < 1-effective + result.update(atom_exponent=beta, ordinary_leaf_saving=OLD, + effective_saving=effective, + effective_saving_decimal=float(effective)) + return result + + +def construction_receipts(cdata, bdata, bit_lifts, proof): + """Reject a raw modular screen and bind the selected constructive proofs.""" + checks = cdata['contract_checks'] + for name in ('all_fresh_columns_equal_identity', + 'source_controls_at_paid_parity_frames', + 'original_source_V_before_all_controls', + 'controls_before_original_K', 'all_centers_in_phase1', + 'all_target_cap_reads_in_phase2', 'target_chains_nested'): + assert checks[name] is True, name + assert checks['checked_source_columns'] == checks['checked_target_rows'] == cdata['v'] + assert cdata['scalar_denominator_lcm'] == '2' + assert cdata['terminal_sink_substitutions'] == 0 + cp = Path(cdata['exact_lift_certificate_path']) + if not cp.is_file(): + cp = HERE.parent / cp + assert cp.is_file(), 'The exact complex lift certificate must be present' + assert sha256(cp.read_bytes()).hexdigest() == cdata['exact_lift_certificate_sha256'] + low = bdata['source_aligned_rewrite'] + assert low['exact_high_boundary_and_suffix_unchanged'] is True + assert low['exact_rank3_resource_counts_unchanged'] is True + chosen = bdata['combined_fixed_boundary_profile'] + assert chosen['paired_donors_deleted'] == 0 + assert chosen['retained_gauges'] == 3960 and chosen['retained_pairs'] == 1760 + assert chosen['child_histogram']['60'] == 2200 + lifts = json.loads(bit_lifts.read_text()) + assert lifts['source_commit'] == 'fd25adb7fbaa12ee761d02c733c54d1d2a7687ee' + assert lifts['instances'] == 2640 + assert all(value is True for value in lifts['checks'].values()) + proof_paths = (proof, HERE/'COMMON_FRAME_LIFT_AND_GLOBAL_CONTRACT.txt', + HERE.parent/'bit/SOURCE_ALIGNED_BIT_WORD.txt', bit_lifts) + def label(path): + try: + return str(path.resolve().relative_to(HERE.parent)) + except ValueError: + return path.name + return dict( + status='Constructive exact flow and fixed-boundary proofs; literal globally renumbered program/replay remains a downstream integration task', + complex_lift_certificate_sha256=cdata['exact_lift_certificate_sha256'], + complex_endpoint_checks=checks, + bit_high_boundary_sha256=low['high_boundary_and_suffix_sha256'], + bit_low_instances_sha256=lifts['instance_sha256'], + bit_low_checks=lifts['checks'], + proof_sha256={label(p):sha256(p.read_bytes()).hexdigest() + for p in proof_paths}) + + +def assemble(c, b, source, proof): + # The finite bridge is deliberately overcharged. Its derivation is in + # FINITE_BRIDGE.txt; the integers below are exact powers, not estimates. + assert proof.is_file(), 'The physical/finite bridge proof must be present' + assert c['counts']['m'] <= 72 and b['counts']['m'] <= 72 + assert c['counts']['W'] < 10**7 and b['counts']['W'] < 10**7 + assert 2*c['counts']['maxchild'] < c['counts']['m'] + coefficient, degree = 20161, 10**6 + bridge = dict( + proof=proof.name, + representation='Exact powers of two with proved dominating bounds', + semantic=dict(G=dict(base=2, exponent=30000), + E=dict(base=2, exponent=100000), + B_upper=dict(base=2, exponent=100001), + C0=dict(base=2, exponent=210000), C1=1, + strict_literal_gap=1, induction_gap_lower=1), + rows=dict(coefficient=coefficient, degree=degree, + suffix_slope=4*degree, + degree_gap=Q(degree)-Q(51*coefficient,25))) + eta, stop = Q(1,10**8), Q(1,10**9) + a = min(b['effective_saving'], (1-stop)*c['saving']-Q(1,SELECT_GRID)) + q = a*(1-2*eta) + minimum = (1-eta)*q/(1+q) + kappa = Q(minimum.numerator*SELECT_GRID//minimum.denominator, SELECT_GRID) + if kappa == minimum: + kappa -= Q(1, SELECT_GRID) + ap = source / 'scripts/paired_cube_assembly.py' + spec = importlib.util.spec_from_file_location('retained_balanced_assembly', ap) + module = importlib.util.module_from_spec(spec) + spec.loader.exec_module(module) + out = module.assembly(a,c['saving'],bridge,kappa,eta=eta,beta=stop) + assert len(out['strict_constraints']) == 47 and len(out['margins']) == 7 + assert out['minimum_margin'] == minimum + return dict(finite_bridge=bridge, assembly=out, + kappa=kappa, kappa_decimal=float(kappa), + reviewed_baseline=BASE, fixed_doubling_target=2*BASE, + ratio_to_reviewed_baseline=kappa/BASE, + ratio_to_reviewed_baseline_decimal=float(kappa/BASE), + doubling_achieved=kappa >= 2*BASE, + assembly_source_sha256=sha256(ap.read_bytes()).hexdigest()) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--complex', type=Path, required=True) + parser.add_argument('--bit', type=Path, required=True) + parser.add_argument('--source', type=Path, default=PIN) + parser.add_argument('--proof', type=Path, default=HERE/'FINITE_BRIDGE.txt') + parser.add_argument('--bit-lifts', type=Path, default=HERE.parent/'bit/source_aligned_lifts.json') + parser.add_argument('--output', type=Path, default=HERE/'global_certificate.json') + parser.add_argument('--moments-only', action='store_true') + args = parser.parse_args() + paths = dict(complex=args.complex,bit=args.bit) + data = {kind: json.loads(path.read_text()) for kind,path in paths.items()} + profiles = {kind: normalize(value) for kind,value in data.items()} + c,b = select(profiles['complex']),select(profiles['bit'],True) + out = dict(author='GPT-6 Astra', + status='Exact arithmetic; construction and finite bridge are explicit proof dependencies', + complex=c,bit=b, + source_sha256={kind:sha256(path.read_bytes()).hexdigest() for kind,path in paths.items()}, + arithmetic='32-term rational logarithm enclosure; rational exponential majorant; upward 2^120 rounding') + if not args.moments_only: + out['construction_receipts'] = construction_receipts(data['complex'],data['bit'],args.bit_lifts,args.proof) + out.update(assemble(c,b,args.source,args.proof)) + args.output.parent.mkdir(parents=True,exist_ok=True) + args.output.write_text(json.dumps(serial(out),indent=2)+'\n') + summary = dict(complex_saving=float(c['saving']), + complex_gap=c['strict_gap_lower_decimal'], + bit_coarse_saving=float(b['saving']), + bit_gap=b['strict_gap_lower_decimal'], + bit_effective_saving=b['effective_saving_decimal']) + if not args.moments_only: + summary.update(kappa=out['kappa_decimal'], + ratio=out['ratio_to_reviewed_baseline_decimal'], + doubling_achieved=out['doubling_achieved']) + print(json.dumps(summary,indent=2)) + + +if __name__ == '__main__': + main() diff --git a/research/composed-diagonal-bit-bootstrap/references/pr194/certificate.json b/research/composed-diagonal-bit-bootstrap/references/pr194/certificate.json new file mode 100644 index 0000000000..344976a1eb --- /dev/null +++ b/research/composed-diagonal-bit-bootstrap/references/pr194/certificate.json @@ -0,0 +1,577 @@ +{ + "assembly": { + "arithmetic": "PR184 assemble_profiles: 32-term rational logarithm enclosure; rational exponential majorant; upward 2^120 rounding", + "assembly": { + "absorption_gap": "252613160861230973365700389/4169449492628652010667996046250000000", + "margins": { + "Gaussian_arithmetic": "356203720907863262581885385603163/533689535056467457365503493920000000", + "balanced_prefix": "2226294102921608534396837/3335559594102921608534396837", + "bulk_exposure": "133575648846809489/200000000000000000000", + "compact_phase_layer": "222626074732566750518075165603163/333555959410292160853439683700000000", + "coordinate_movement": "133575648846809489/200000000000000000000", + "dimension": "3333333300000000000000000000/3335559594102921608534396837", + "scalar_work": "1781031946777692724595861065603163/2668447675282337286827517469600000000" + }, + "minimum_margin": "222626074732566750518075165603163/333555959410292160853439683700000000", + "parameters": { + "C0": { + "base": 2, + "exponent": 210000 + }, + "C1": 1, + "a_bit": "133575648846809489/200000000000000000000", + "a_complex": "219037/312500000", + "alpha_squared_power": "445255485024727603957758865603163/667111918820584321706879367400000000", + "beta": "1/1000000000", + "c": "6678807308764825603190511/10000000000000000000000000000", + "delta": "1/800000000", + "epsilon": "3333333300000000000000000000/3335559594102921608534396837", + "eta": "1/100000000", + "kappa": "1668581/2500000000", + "lambda_": "19986642435248894699946809489/20000000000000000000000000000", + "lambda_prime": "9993321217691235174396809489/10000000000000000000000000000", + "q": "6678782308764825603190511/10000000000000000000000000000", + "sigma": "312280963/312500000", + "tau": "199866424351153190511/200000000000000000000" + }, + "recurrence": { + "internal": "199866424351153190511/200000000000000000000", + "leaf": "312280963000219037/312500000000000000", + "reservations": "9993321192691235174396809489/10000000000000000000000000000" + }, + "strict_constraints": { + "Gaussian_arithmetic_above_kappa": "254208780131498816213930968999/66711191882058432170687936740000000000", + "K_dominates_log": "222626908065891750518075165603163/333555959410292160853439683700000000", + "K_geometry": "2502226269102921608534396837/333555959410292160853439683700000000", + "alpha_below_one": "666666663335559594102921608534396837/667111918820584321706879367400000000", + "alpha_below_one_fourth": "166332724220121352822762082984396837/667111918820584321706879367400000000", + "alpha_positive": "445255485024727603957758865603163/667111918820584321706879367400000000", + "artificial_boundary": "18680914772265377076928904582403190511/2668447675282337286827517469600000000", + "balanced_prefix_above_kappa": "83894216174295502160091321703/8338898985257304021335992092500000000", + "beta_below_one": "999999999/1000000000", + "beta_positive": "1/1000000000", + "bit_positive": "133575648846809489/200000000000000000000", + "bulk_exposure_above_kappa": "89168846809489/200000000000000000000", + "c_below_one": "9993321192691235174396809489/10000000000000000000000000000", + "c_positive": "6678807308764825603190511/10000000000000000000000000000", + "cell_above_band": "666666656664440405897078391465603163/1334223837641168643413758734800000000", + "compact_leaf": "330401684225990396809489/10000000000000000000000000000", + "compact_phase_layer_above_kappa": "252613160861230973365700389/4169449492628652010667996046250000000", + "compact_reservations": "1/400000000", + "complex_above_bit": "6608031153190511/200000000000000000000", + "complex_below_one_over32": "2386647/78125000", + "coordinate_movement_above_kappa": "89168846809489/200000000000000000000", + "delta_below_one_eighth": "99999999/800000000", + "delta_positive": "1/800000000", + "dimension_above_kappa": "8327767598636912152959510067591321703/8338898985257304021335992092500000000", + "epsilon_below_one": "2226294102921608534396837/3335559594102921608534396837", + "epsilon_positive": "3333333300000000000000000000/3335559594102921608534396837", + "gamma_sublinear": "1/200000000", + "guard_width": "2226294102921608534396837/3335559594102921608534396837", + "lambda_above_internal": "133575648846809489/20000000000000000000000000000", + "lambda_above_sigma": "660803248894699946809489/20000000000000000000000000000", + "lambda_above_tau": "133575648846809489/20000000000000000000000000000", + "lambda_prime_above_lambda": "133575648846809489/20000000000000000000000000000", + "lambda_prime_below_one": "6678782308764825603190511/10000000000000000000000000000", + "leaf_saving_above_bit": "6608031013006831/200000000000000000000", + "literal_scalar_guard": "1", + "phase_boundary": "356203720907863262581885385603163/533689535056467457365503493920000000", + "phase_local": "1781031946777692724595861065603163/2668447675282337286827517469600000000", + "prime_interval_packing": "2226294102921608534396837/3335559594102921608534396837", + "q_below_internal": "133575648846809489/10000000000000000000000000000", + "q_below_leaf": "330401684225990396809489/10000000000000000000000000000", + "q_below_reservations": "1/400000000", + "q_positive": "6678782308764825603190511/10000000000000000000000000000", + "record_suffix": "2226294102921608534396837/3335559594102921608534396837", + "row_product_gap": "23971789/25", + "scalar_work_above_kappa": "587764739541790977067370652699/66711191882058432170687936740000000000", + "short_record_fallback": "666221110462950501752035473151478503999536813707/667111918820584321706879367400000000000000000000", + "small_field_exposure": "1/100000000" + } + }, + "assembly_source_sha256": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c", + "bit": { + "atom_exponent": "133575649/200000000000", + "bad_moment_upper": "89247857896954790902471195679381717922243/27355615999190739360912919910496075776000000000000000", + "counts": { + "W": "21074", + "delta": "1936", + "edge_count": "297560", + "histogram": { + "1": "127290", + "10": "2544", + "11": "1266", + "12": "4158", + "13": "1578", + "14": "3426", + "15": "1170", + "16": "3006", + "17": "1032", + "18": "1614", + "19": "648", + "2": "59368", + "20": "5280", + "21": "13698", + "22": "9312", + "3": "30726", + "4": "9108", + "5": "7686", + "6": "3936", + "60": "2200", + "7": "3762", + "8": "2808", + "9": "1944" + }, + "m": 72, + "mass": "1515392", + "maxchild": 60 + }, + "effective_saving": "133575648846809489/200000000000000000000", + "effective_saving_decimal": "6.678782442340e-04", + "ideal_moment_upper": "168072904686372575392663389853985508233749/168072904699027902633448979930087889567744", + "ordinary_leaf_saving": "384599/10000000000", + "saving": "6682989/10000000000", + "strict_gap_lower": "5911615430598974531639452298701600939983271/82066847997572218082738759731488227328000000000000000", + "strict_gap_lower_decimal": "7.203414746444e-11" + }, + "bit_source": "research/paired-cube-twin-local-168/certificate.json bit.profile (PR189)", + "complex": { + "bad_moment_upper": "0", + "counts": { + "W": "12052", + "delta": "1320", + "edge_count": "213147", + "histogram": { + "1": "87534", + "10": "2790", + "11": "1062", + "12": "3591", + "13": "381", + "14": "2226", + "15": "5637", + "16": "264", + "17": "243", + "18": "7959", + "19": "501", + "2": "39834", + "20": "66", + "3": "29769", + "4": "12627", + "5": "5850", + "6": "4815", + "7": "2118", + "8": "4593", + "9": "1287" + }, + "m": 66, + "mass": "794112", + "maxchild": 20 + }, + "ideal_moment_upper": "8009927901769221530141375505975603941953/8009927902599903050118341345249356414976", + "saving": "219037/312500000", + "strict_gap_lower": "830681519976965839273752473023/8009927902599903050118341345249356414976", + "strict_gap_lower_decimal": "1.037064915038e-10" + }, + "construction_receipts": { + "complex_endpoint_checks": { + "all_centers_in_phase1": true, + "all_fresh_columns_equal_identity": true, + "all_target_cap_reads_in_phase2": true, + "arithmetic": "integers, endpoint scaled by 6", + "checked_source_columns": 1320, + "checked_target_rows": 1320, + "controls_before_original_K": true, + "original_source_V_before_all_controls": true, + "positive_target_data_histogram": { + "1": 3960, + "18": 1320 + }, + "read_counts": { + "center": 22, + "deferred": 2310, + "side": 3135 + }, + "source_controls_at_paid_parity_frames": true, + "target_chains_nested": true, + "target_data_histogram": { + "0": 6270, + "1": 3960, + "18": 1320 + } + }, + "complex_lift_certificate_sha256": "1d81a79bda88b8a0ef64b7ae815c0d20cf1eee7f4714053530805bbb39e89ef2" + }, + "finite_bridge": { + "proof": "FINITE_BRIDGE.txt", + "representation": "Exact powers of two with proved dominating bounds", + "rows": { + "coefficient": 20161, + "degree": 1000000, + "degree_gap": "23971789/25", + "suffix_slope": 4000000 + }, + "semantic": { + "B_upper": { + "base": 2, + "exponent": 100001 + }, + "C0": { + "base": 2, + "exponent": 210000 + }, + "C1": 1, + "E": { + "base": 2, + "exponent": 100000 + }, + "G": { + "base": 2, + "exponent": 30000 + }, + "induction_gap_lower": 1, + "strict_literal_gap": 1 + } + }, + "kappa": "1668581/2500000000", + "kappa_decimal": "6.674324000000e-04", + "source_sha256": { + "bit_certificate": "a781a738228609937165cfbc50d2eb9bfb0ecca2a28084d4deef6fb4f3bc9139", + "complex": "7374c75b7d6eaec051d0a451fbc1487acf443ecc3f6c39424af5ebcf0ee8f0cb" + }, + "status": "Exact arithmetic; construction and finite bridge are explicit proof dependencies" + }, + "binding_supplier": "bit", + "bit_effective_saving": "133575648846809489/200000000000000000000", + "complex_gain_over_pr184": "13701/205336", + 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No frozen large cache is required.", + "scalar_coefficients": [ + [ + -2, + 1 + ], + [ + -1, + 1 + ], + [ + -1, + 2 + ], + [ + 1, + 2 + ], + [ + 1, + 1 + ], + [ + 2, + 1 + ] + ], + "scalar_denominator_lcm": "2", + "signature": "GPT-6 Astra", + "source_data_histogram": { + "1": 1320, + "18": 1320, + "2": 1320 + }, + "status": "Exact local invertible flow, exact all-column fresh identity, paid source controls, target read chains, and integer histogram certified. 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Not an exact supplier certificate.", + "v": 1320, + "vectors": 26200 + }, + "gain_over_pr186": "2773425370201/330942774629799", + "gain_over_pr191": "48017/6626307", + "gain_over_pr193": "6613/1661968", + "kappa": "1668581/2500000000", + "lift": { + "all_actual_coefficients_dyadic": true, + "certificate_path": "research/source-assisted-v4/.work/lift.certificate.json.gz", + "certificate_sha256": "1d81a79bda88b8a0ef64b7ae815c0d20cf1eee7f4714053530805bbb39e89ef2", + "checker_path": "research/source-assisted/decision/exact_complex_flow_lift.py", + "checker_sha256": "9d841bcfdc7c9c19b31791e8d7cfebd223d80d5e9ecd376d26257244f5323f2e", + "coefficient_numerator_lcm": "2", + "coefficients": [ + [ + -2, + 1 + ], + [ + -1, + 1 + ], + [ + -1, + 2 + ], + [ + 1, + 2 + ], + [ + 1, + 1 + ], + [ + 2, + 1 + ] + ], + "denominator_lcm": "2", + "exact_scalar_program_sha256": "3b4e671d7c6630570b04788bb2c81629e2c52f8dc2fcc5805952f0b403921027", + "inverse_elementary_gates": 58165, + "kernel_reuses": 0, + "max_abs_numerator": "2", + "max_denominator": "2", + "nodes": 18532, + "physical_R": 9412, + "signature": "GPT-6 Astra", + "source_control_vertices": 0, + "source_erasures": 0, + "status": "Exact rational local lifts and inverse gate programs verified; monotone flow and zero-fresh kernel reuse DAG verified.", + "witness_path": "research/source-assisted-v4/.work/flow.witness.json", + "witness_sha256": "51da02c6cd844276ca26608f1b714ab07d476ec25634ad1a9b461ccda2fbe457" + }, + "lift_certificate_sha256": "1d81a79bda88b8a0ef64b7ae815c0d20cf1eee7f4714053530805bbb39e89ef2", + "scope": "PR184 contract and finite bridge unchanged; the bit supplier is PR189 (verified by its own verify.py); the complex supplier is PR184's source-parity local word and frame flow on PR168 v4's query modules and physical layer, with donor/recipient pairs that avoid parity purification. No new flattened bit transcript or full Clifford/router replay, as in PR184.", + "status": "PASS conditional finite witness", + "witness_sha256": "51da02c6cd844276ca26608f1b714ab07d476ec25634ad1a9b461ccda2fbe457" +} diff --git a/research/composed-diagonal-bit-bootstrap/verify.py b/research/composed-diagonal-bit-bootstrap/verify.py new file mode 100644 index 0000000000..a4ada96de4 --- /dev/null +++ b/research/composed-diagonal-bit-bootstrap/verify.py @@ -0,0 +1,188 @@ +#!/usr/bin/env python3 +"""Verify the composed diagonal-bit bootstrap record. + + python3 -B research/composed-diagonal-bit-bootstrap/verify.py + +Checks, in order: every pinned byte against SOURCE.json; an exact regeneration of +certificate.json from the vendored inputs; two published cross-checks (the +depth-0 value against PR200's announced value for this composition, and PR184's +grid legacy leaf against PR200's published atom-wrapper value); the standing +claim; the bit branch's own ceiling; the finite-leaf tolls; the adjacent final +grid; and the corruption controls. The physical words are inherited pins and are +not replayed here. +""" +import hashlib +import importlib.util +import json +import subprocess +import sys +from fractions import Fraction as Q +from pathlib import Path + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +WORK = HERE / ".work" +GRID = 10 ** 10 +OLD = Q(384599, GRID) + +# Published references, quoted from the open pull requests. +PR197_KAPPA = Q(135216063303877, 200000000000000000) # #197 packed bit: standing claim +PR200_LEGACY_KAPPA = Q(6768823, GRID) # #200's own value for this composition +PR200_THETA = Q(677340914792209011107, 10 ** 24) # #200 README atom-wrapper exponent +PR200_A0 = Q(677773948354561, 10 ** 18) # #200 README bit coarse saving +PR194_KAPPA = Q(1668581, 2500000000) # #194 as published + + +def sha(path): + return hashlib.sha256(Path(path).read_bytes()).hexdigest() + + +def load(path, name): + spec = importlib.util.spec_from_file_location(name, path) + module = importlib.util.module_from_spec(spec) + sys.modules[name] = module + spec.loader.exec_module(module) + return module + + +def rejects(name, operation, errors=(AssertionError, ValueError, KeyError)): + try: + operation() + except errors: + return name + raise AssertionError("control accepted: " + name) + + +def tolls(coarse, leaf): + """compose.py's own guard, mirrored so the control exercises that condition.""" + assert Q(leaf) < Q(coarse) < 1 - Q(leaf), "strict paid tolls" + + +def main(): + assert not sys.flags.optimize, "refusing -O" + if hasattr(sys, "set_int_max_str_digits"): + sys.set_int_max_str_digits(0) + + # 1. Every pinned byte. + manifest = json.loads((HERE / "SOURCE.json").read_text()) + drift = sorted(rel for rel, digest in manifest["files"].items() + if sha(ROOT / rel) != digest) + assert not drift, ("pinned byte drift", drift) + print("[pins] {} package and input files match SOURCE.json".format(len(manifest["files"]))) + + # 2. Regenerate the certificate from the vendored inputs alone. + WORK.mkdir(exist_ok=True) + regenerated = WORK / "certificate.json" + if regenerated.exists(): + regenerated.unlink() + subprocess.run([sys.executable, "-B", str(HERE / "compose.py"), "--out", str(regenerated)], + check=True, stdout=subprocess.DEVNULL) + record = json.loads(regenerated.read_text()) + assert record == json.loads((HERE / "certificate.json").read_text()), \ + "regenerated certificate differs from the committed one" + print("[regenerate] certificate.json reproduced exactly from the vendored pins") + + pr184 = load(HERE / "references/pr184/assemble_profiles.py", "verify_pr184") + bit_cert = json.loads((HERE / "inputs/pr200-bit-certificate.json").read_text()) + complex_cert = json.loads((HERE / "references/pr194/certificate.json").read_text()) + row = bit_cert["bit"]["profile"] + coarse = Q(record["bit_coarse_saving"]) + legacy = Q(record["legacy_leaf"]) + depths = record["depths"] + best_depth = max(depths, key=lambda d: Q(depths[d]["kappa"])) + best = Q(depths[best_depth]["kappa"]) + + # 3. The suppliers are the ones the certificate names. + assert Q(record["complex_supplier"]["saving"]) == Q(complex_cert["complex_saving"]) + assert Q(complex_cert["kappa"]) == PR194_KAPPA, "PR194 reference" + assert all(depths[d]["binding"] == "bit" for d in depths), "the bit branch must bind" + assert all(Q(depths[d]["kappa"]) <= best for d in depths), "best is not the maximum" + print("[pins] complex saving = {} (PR194 as published, kappa {}), binding branch = bit at " + "every depth".format(record["complex_supplier"]["saving"], PR194_KAPPA)) + + # 4. The depth-0 row must equal what PR200 announced for this composition. + assert Q(depths["0"]["kappa"]) == PR200_LEGACY_KAPPA, "PR200 announced legacy value" + assert depths["0"]["binding"] == "bit" + print("[cross-check] depth 0 kappa = {} equals PR200's announced value for this " + "composition".format(PR200_LEGACY_KAPPA)) + + # 5. PR184's grid legacy leaf against PR200's published atom wrapper. The two + # suppliers define the same wrapper at different precision, so the control is + # what the difference does to the price: exactly one grid step at depth 0, and + # nothing at all once the wrapper is bootstrapped. PR184's select() is the + # pricing path the record's assembly is defined with, so the record uses it. + complex_row = pr184.select(pr184.normalize(complex_cert["complex_profile"])) + bit_row = pr184.select(pr184.normalize(row), True) + assert Q(bit_row["saving"]) == coarse and Q(bit_row["effective_saving"]) == legacy + + def price(leaf): + boot = dict(bit_row) + boot["effective_saving"] = Q(leaf) + return Q(pr184.assemble(complex_row, boot, HERE / "references/pr168-v4", + HERE / "references/pr184/FINITE_BRIDGE.txt")["kappa"]) + + published_leaf = (1 - PR200_THETA) * PR200_A0 + PR200_THETA * OLD + assert 0 < published_leaf - legacy < Q(1, GRID), "legacy leaf disagreement" + assert price(published_leaf) - price(legacy) == Q(1, GRID), "one grid step at depth 0" + alternative = [published_leaf] + for _ in range(int(best_depth)): + alternative.append((1 - coarse) * coarse + coarse * alternative[-1]) + assert price(alternative[-1]) == best, "the bootstrapped price must not depend on the start" + print("[cross-check] PR184 legacy leaf {:.15g} vs PR200 published {:.15g} (delta {:.3g}): " + "one grid step at depth 0, identical at depth {}".format( + float(legacy), float(published_leaf), float(published_leaf - legacy), best_depth)) + + # 6. The standing claim, the ceiling, and the exhaustion of pricing. + assert best > PR197_KAPPA, "does not beat the standing claim" + assert best > PR200_LEGACY_KAPPA, "does not beat the unbootstrapped composition" + assert best > PR194_KAPPA + ceiling = Q(record["ceiling"]) + assert best <= ceiling < best + Q(1, GRID), "not within one grid unit of the ceiling" + assert Q(depths["1"]["kappa"]) < best == Q(depths["2"]["kappa"]), "depth 2 is not the claim" + print("[claim] kappa = {} ({:.15g}) at depth {}; vs #197 {:+.4f}%, vs PR200 announced " + "{:+.4f}%".format(best, float(best), best_depth, + float(best / PR197_KAPPA - 1) * 100, + float(best / PR200_LEGACY_KAPPA - 1) * 100)) + print("[ceiling] C/(1+C) = {:.15g}; the claim sits {:.3g} below it, under one grid unit " + "({:.1g})".format(float(ceiling), float(ceiling - best), 1 / GRID)) + + # 7. The finite-leaf tolls, recomputed independently in closed form. + assert legacy < coarse < 1 - coarse, "coarse saving must be a strict leaf toll" + chain = [legacy] + for _ in range(int(best_depth)): + chain.append((1 - coarse) * coarse + coarse * chain[-1]) + assert chain[-1] == coarse - coarse ** int(best_depth) * (coarse - legacy) + for i in range(1, len(chain)): + assert chain[i - 1] < chain[i] < coarse < 1 - chain[i], "strict paid tolls" + assert Q(depths[best_depth]["leaf"]) == chain[-1], "recorded leaf" + print("[tolls] a_0 < a_1 < ... < a_{} < C < 1 - a_{}".format(best_depth, best_depth)) + + # 8. The assembly's minimum margin must be that closed form, and the next grid + # point must lie beyond it, so no finer leaf can buy another grid step. + eta, stop = Q(1, 10 ** 8), Q(1, 10 ** 9) + q = chain[-1] * (1 - 2 * eta) + minimum = (1 - eta) * q / (1 + q) + assert Q(depths[best_depth]["minimum_margin"]) == minimum, "recorded minimum margin" + assert minimum < best + Q(1, GRID), "the next grid point is inside the minimum margin" + print("[adjacent grid] minimum margin = {:.15g} lies in (kappa, kappa + 1e-10)".format( + float(minimum))) + + # 9. Corruption controls, each of which must be refused. + def accept_only_a_better_composition(): + assert PR200_LEGACY_KAPPA > best, "the unbootstrapped value must not reach the claim" + + rejected = [ + rejects("bit profile with a perturbed W", + lambda: pr184.normalize(dict(row, W_per_vertex=row["W_per_vertex"] + 1))), + rejects("leaf at or above the coarse saving", + lambda: tolls(coarse, coarse + Q(1, GRID))), + rejects("unbootstrapped depth-0 value offered as the claim", + accept_only_a_better_composition), + ] + print("[controls] rejected: " + ", ".join(rejected)) + print("PASS composed-diagonal-bit-bootstrap kappa = {} at depth {}; 47 strict constraints " + "and 7 margins per depth".format(best, best_depth)) + + +if __name__ == "__main__": + main() From f07f5215b451458e70b476bc4304e99741a156d0 Mon Sep 17 00:00:00 2001 From: maxime-fleury Date: Fri, 9 Oct 2026 17:20:42 +0200 Subject: [PATCH 2/9] Model the packing lever on this word and check the model against three published values Banking a word's rank-60 exterior corrections is the only validated way to raise a bit coarse saving materially, and this word has the same 2,200 of them per copy that PR197 banked. levers.py solves the paid-moment inequality exactly over the rationals and models that transformation as the accounting PR197 validated: drop the rank-60 entries, keep the per-copy deficit, let the stock fall to what the row identity requires. The model reproduces PR187's unpacked row, PR197's independently certified banked row, and PR200's unpacked row to 1e-13 relative or better, so it is checked on a word it was not fitted to. Applied here it predicts kappa = 6.83061299e-4, +0.8484% over this package's claim, and pins the falsifiable target for whoever builds the banks: total stock 56,402 over three copies, per-copy deficit unchanged at 1,936, no rank-60 child remaining. levers.json records the MODELLED, NOT CONSTRUCTED status and verify.py enforces it. --- .../composed-diagonal-bit-bootstrap/README.md | 50 +++- .../SOURCE.json | 7 +- .../levers.json | 54 ++++ .../composed-diagonal-bit-bootstrap/levers.py | 157 ++++++++++++ .../references/pr187/certificate.json | 231 ++++++++++++++++++ .../composed-diagonal-bit-bootstrap/verify.py | 23 ++ 6 files changed, 519 insertions(+), 3 deletions(-) create mode 100644 research/composed-diagonal-bit-bootstrap/levers.json create mode 100644 research/composed-diagonal-bit-bootstrap/levers.py create mode 100644 research/composed-diagonal-bit-bootstrap/references/pr187/certificate.json diff --git a/research/composed-diagonal-bit-bootstrap/README.md b/research/composed-diagonal-bit-bootstrap/README.md index 63183dc505..31aabc5931 100644 --- a/research/composed-diagonal-bit-bootstrap/README.md +++ b/research/composed-diagonal-bit-bootstrap/README.md @@ -61,6 +61,46 @@ constructions on #200's graph rather than a recomposition: Because the bit branch binds, complex-side work is worthless here until a bit coarse saving passes the complex word's `7.009184e-4`. +## Where the next gain is, measured + +The bit branch's coarse saving is the largest `a` whose paid moment is below 1, +and the row identity `m*W - sum_r n_r*r = D` means two words with the same `D` +differ only through the child ledger. `levers.py` solves that inequality exactly +over the rationals and models the one lever that has already been validated on a +word of this family: PR197's banking of the rank-60 exterior corrections, which +drops those entries from the ledger and leaves the stock at what the identity +requires. + +The model is checked against the three published values it can be checked on, all +to `1e-13` relative or better: + +| row | model | published | source | +| --- | --- | --- | --- | +| PR187's word, unpacked | 6.70899981048782e-4 | 6.70899981048852e-4 | PR187's certificate | +| PR187's word, banked | 6.76537710350471e-4 | 6.76537710350481e-4 | PR197's **certified** packed word | +| PR200's word, unpacked | 6.77773948354529e-4 | 6.77773948354561e-4 | PR200's certificate | + +The second row is the meaningful one: the model reproduces, from the unpacked +ledger alone, the value PR197 certified after building the banks. + +Applied to this package's bit word, banking its 2,200 rank-60 exterior +corrections (132,000 of 1,483,712 rank mass, 8.90% of the child ledger) leaves +`W_per_vertex = 56402/3`, `D = 1936` and a ledger with no child above rank 22, and +gives + +| | coarse saving | kappa ceiling | +| --- | --- | --- | +| this package's word, as certified | 6.77773948354529e-4 | 6.77314882e-4 | +| the same word, banked | 6.83528191056250e-4 | **6.83061299e-4** (**+0.8484%**) | + +**This is a prediction, not a claim.** The bank construction on PR200's word is +not built here, and the package's `levers.json` records that status literally. +What the model does give is a falsifiable target for whoever builds it: over the +three copies, a bank allocation must reach a total stock of `56,402` roles with +the per-copy deficit unchanged at `1,936` and no rank-60 child remaining. The +other known lever is an order of magnitude smaller: PR198's endpoint-frame +descent bought `+0.0090%` of coarse saving on PR189's word. + ## Cross-checks against published numbers The harness is independent of the numbers it is asked to confirm, and this package @@ -104,7 +144,15 @@ python3 -B research/composed-diagonal-bit-bootstrap/verify.py `SOURCE.json`, reproduces `certificate.json` from the pins, re-checks the two published cross-checks above, requires the claim to beat #197, requires it to sit inside one grid step of the word's ceiling, re-derives the leaf tolls in closed -form, and refuses three corruption controls. +form, refuses three corruption controls, and re-runs the lever model, requiring it +to reproduce its three published references and to keep its `MODELLED, NOT +CONSTRUCTED` status. + +```bash +python3 -B research/composed-diagonal-bit-bootstrap/levers.py +``` + +prints the lever table on its own. ## Credits diff --git a/research/composed-diagonal-bit-bootstrap/SOURCE.json b/research/composed-diagonal-bit-bootstrap/SOURCE.json index ac91144c31..d442a729d4 100644 --- a/research/composed-diagonal-bit-bootstrap/SOURCE.json +++ b/research/composed-diagonal-bit-bootstrap/SOURCE.json @@ -24,9 +24,12 @@ }, "files": { "research/composed-diagonal-bit-bootstrap/compose.py": "5122db672a30e3119e5004a873354d608dfe34f0c8b15731c683e624c0f71c76", - "research/composed-diagonal-bit-bootstrap/verify.py": "e54e071f9b9b8b3941932009ddea291d5c1403e2b4cdf632a1ac7dccba11a880", + "research/composed-diagonal-bit-bootstrap/verify.py": "d2b7a6ccbb3439df84f4125c38f613a06b1a099c69d10a409a8e61be62b33246", + "research/composed-diagonal-bit-bootstrap/levers.py": "38146e6e5420f4d649d9aed9f8c6fb71625a457744d3d0c6297de231cc9f6a29", + "research/composed-diagonal-bit-bootstrap/levers.json": "68506f14fc56882a667a813bf257501d7dbb6627a584fd01ba8771394fb279ab", + "research/composed-diagonal-bit-bootstrap/references/pr187/certificate.json": "0cfcb896c86c2e1de759f0518176ba6c606036b9f515eac045d3962cc4a00073", "research/composed-diagonal-bit-bootstrap/certificate.json": "0a844fb88811af915ae5198aab07b79f61c29cc9c68b1752733d30a4c189cfc4", - "research/composed-diagonal-bit-bootstrap/README.md": "a9bb09620cc78ce58a6be787f1f44cd610e246dadbf956f34d71650c72f0d3b2", + "research/composed-diagonal-bit-bootstrap/README.md": "1b2ce63d42a70ecc00bfebfd9bab9b32c928b86f519ef87ee2b3fc17b5371696", "research/composed-diagonal-bit-bootstrap/NOTICE.md": "d3127dcacf595f645e64e8b4cdb3f63e17c3785f9dbc65c08653aabdd25c38d1", "research/composed-diagonal-bit-bootstrap/references/pr168-v4/scripts/paired_cube_assembly.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c", "research/composed-diagonal-bit-bootstrap/references/pr184/assemble_profiles.py": "c56d0638d4bc1ac3f70c78778ea824f3a2ba23c31f7eeff3c93cf17df3f2e0de", diff --git a/research/composed-diagonal-bit-bootstrap/levers.json b/research/composed-diagonal-bit-bootstrap/levers.json new file mode 100644 index 0000000000..1c01f78e95 --- /dev/null +++ b/research/composed-diagonal-bit-bootstrap/levers.json @@ -0,0 +1,54 @@ +{ + "claim": { + "kappa": "1693287/2500000000", + "kappa_decimal": 0.0006773148 + }, + "gain_vs_claim": 0.00848423716990898, + "method": "paid moment < 1 solved by exact rational bisection; row identity m*W - mass = D", + "pr200_banked": { + "W_per_vertex": "56402/3", + "W_per_vertex_decimal": 18800.666666666668, + "ceiling": "12608869607580293/18459352943317131909", + "ceiling_decimal": 0.0006830612994018895, + "coarse": "12608869607580293/18446744073709551616", + "coarse_decimal": 0.0006835281910562501, + "coarse_grid": "6835281/10000000000", + "deficit": "1936", + "ledger_share_of_rank60": 0.08896605271103826, + "rank60_children": 2200, + "rank60_mass": 132000 + }, + "pr200_unpacked": { + "ceiling": "1750181695508965114231795558893973528100349394234672187145591606720205276769314124060694002029121326599864046548156415/2584000059782417554770150967561905847857806142223458185017804948147367827293610508753706047282166952762503036019295649791", + "ceiling_decimal": 0.000677314881972695, + "coarse": "1750181695508965114231795558893973528100349394234672187145591606720205276769314124060694002029121326599864046548156415/2582249878086908589655919172003011874329705792829223512830659356540647622016841194629645353280137831435903171972747493376", + "coarse_decimal": 0.0006777739483545289 + }, + "status": "MODELLED, NOT CONSTRUCTED: the banked row is validated against PR197's certified word, but the bank construction on PR200's word is not built here and no claim is made about it.", + "validations": [ + { + "model": "1732431394271726204013639367611885929592629709917136084815878663780536905188533693636152527452580181879924855209459711/2582249878086908589655919172003011874329705792829223512830659356540647622016841194629645353280137831435903171972747493376", + "model_decimal": 0.0006708999810487818, + "name": "PR187 unpacked row", + "published": "167724995262213/250000000000000000", + "published_decimal": 0.000670899981048852, + "relative_error": 1.0456759220263077e-13 + }, + { + "model": "12479917999048577/18446744073709551616", + "model_decimal": 0.0006765377103504708, + "name": "PR187 banked row (PR197)", + "published": "676537710350481/1000000000000000000", + "published_decimal": 0.000676537710350481, + "relative_error": 1.5029354620039682e-14 + }, + { + "model": "1750181695508965114231795558893973528100349394234672187145591606720205276769314124060694002029121326599864046548156415/2582249878086908589655919172003011874329705792829223512830659356540647622016841194629645353280137831435903171972747493376", + "model_decimal": 0.0006777739483545289, + "name": "PR200 unpacked row", + "published": "677773948354561/1000000000000000000", + "published_decimal": 0.000677773948354561, + "relative_error": 4.7256075751084084e-14 + } + ] +} diff --git a/research/composed-diagonal-bit-bootstrap/levers.py b/research/composed-diagonal-bit-bootstrap/levers.py new file mode 100644 index 0000000000..34df4d6915 --- /dev/null +++ b/research/composed-diagonal-bit-bootstrap/levers.py @@ -0,0 +1,157 @@ +#!/usr/bin/env python3 +"""Where the next gain is on this word, modelled exactly. + +The bit branch's coarse saving is the largest `a` whose paid moment is below 1: + + sum_r n_r * r * (m/r)^a + BAD * 32 m^2 * edges * m^a < W * m, + +with `m*W - sum n_r r = D` the row identity. Because the moment is increasing in +`a`, two words with the same `D` differ only through the child ledger. + +PR197 lowered a word's ledger by *banking* the rank-60 exterior corrections: the +2,200 rank-60 children (one per selected gauge) are replaced by shared banks, so +the rank-60 entries leave the ledger and the stock falls to what the identity +requires. This script models that transformation exactly -- drop the rank-60 +entries, keep `D`, set `W = (mass + D)/m` -- and validates the model against the +three published values it can be checked on, then applies it to this package's +bit word. + +The model is accounting, validated on another word of the same family. On PR200's +word it is a *prediction*: realizing it needs the bank construction itself, which +this package does not build. + + python3 -B levers.py [--out levers.json] +""" +import argparse +import json +import sys +from fractions import Fraction as Q +from pathlib import Path + +HERE = Path(__file__).resolve().parent +BAD = Q(1, 10 ** 16) +RANK60 = 60 +CLAIM = Q(1693287, 2500000000) +GRID = 10 ** 10 + +# Published values the model is checked against. +PR187_COARSE = Q(167724995262213, 250000000000000000) +PR187_PACKED = Q(676537710350481, 10 ** 18) # PR197's certified packed word +PR200_COARSE = Q(677773948354561, 10 ** 18) # PR200's certified bit word +PR200_PACKED_EXCLUDED = None + + +def row(profile): + m = int(profile["m"]) + W = Q(profile["W_per_vertex"] if "W_per_vertex" in profile else profile["W"]) + D = Q(profile["deficit_per_vertex"] if "deficit_per_vertex" in profile else profile["N"]) + key = "child_multiplicities" if "child_multiplicities" in profile else "child_histogram" + hist = {int(r): int(n) for r, n in profile[key].items() if n} + assert m * W - sum(r * n for r, n in hist.items()) == D, "row identity" + return m, W, D, hist + + +def paid_root(m, W, D, hist): + """The largest a with paid moment below 1, on exact rationals.""" + fallback = BAD * 32 * m * m * sum(hist.values()) + + def excess(a): + return (sum(Q(n * r) * pow(Q(m, r), a) for r, n in hist.items()) + + fallback * pow(Q(m), a)) + + target = W * m + assert excess(0) < target, "zero-saving rank contraction" + lo, hi = Q(0), Q(1) + assert excess(hi) > target, "upper bracket" + for _ in range(400): + mid = (lo + hi) / 2 + if excess(mid) < target: + lo = mid + else: + hi = mid + return lo + + +def banked(m, W, D, hist): + """PR197's accounting: the rank-60 exterior corrections become banked roles.""" + assert hist.get(RANK60), "no rank-60 exterior corrections to bank" + trimmed = {r: n for r, n in hist.items() if r != RANK60} + mass = sum(r * n for r, n in trimmed.items()) + packed_W = (mass + D) / m + assert packed_W < W, "the stock must fall" + return packed_W, trimmed + + +def check(name, model, published): + rel = abs(model / published - 1) + assert rel < Q(1, 10 ** 11), (name, float(rel)) + return dict(name=name, published=str(published), published_decimal=float(published), + model=str(model), model_decimal=float(model), relative_error=float(rel)) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--out", type=Path, default=HERE / "levers.json") + args = parser.parse_args() + if hasattr(sys, "set_int_max_str_digits"): + sys.set_int_max_str_digits(0) + assert not sys.flags.optimize, "assertions must stay enabled" + + validations = [] + pr187 = json.loads((HERE / "references/pr187/certificate.json").read_text()) + m1, W1, D1, hist1 = row(pr187["profile"]) + a1 = paid_root(m1, W1, D1, hist1) + validations.append(check("PR187 unpacked row", a1, PR187_COARSE)) + packed_W1, trimmed1 = banked(m1, W1, D1, hist1) + packed_a1 = paid_root(m1, packed_W1, D1, trimmed1) + validations.append(check("PR187 banked row (PR197)", packed_a1, PR187_PACKED)) + + bit = json.loads((HERE / "inputs/pr200-bit-certificate.json").read_text()) + m2, W2, D2, hist2 = row(bit["bit"]["profile"]) + a2 = paid_root(m2, W2, D2, hist2) + validations.append(check("PR200 unpacked row", a2, PR200_COARSE)) + + packed_W2, trimmed2 = banked(m2, W2, D2, hist2) + packed_a2 = paid_root(m2, packed_W2, D2, trimmed2) + ceiling_now, ceiling_packed = a2 / (1 + a2), packed_a2 / (1 + packed_a2) + grid = lambda x: Q(int(x * GRID), GRID) + for v in validations: + print("[validated] {name}: model {model_decimal:.15g} vs published " + "{published_decimal:.15g} (rel {relative_error:.1e})".format(**v)) + print("[PR200 now] coarse {:.15g} (grid {:.10g}) -> ceiling {:.10g}".format( + float(a2), float(grid(a2)), float(ceiling_now))) + print("[PR200 banked] W_per_vertex {} -> coarse {:.15g} (grid {:.10g}) -> ceiling " + "{:.10g}".format(packed_W2, float(packed_a2), float(grid(packed_a2)), + float(ceiling_packed))) + print("[lever] banking the rank-60 exterior corrections is worth {:.4f}% of " + "kappa ({:.10g} -> {:.10g})".format(100 * (ceiling_packed / ceiling_now - 1), + float(ceiling_now), float(ceiling_packed))) + print("[vs the claim] {} ({:.10g}) -> {:.4f}%".format( + CLAIM, float(CLAIM), 100 * (ceiling_packed / CLAIM - 1))) + + out = dict( + status="MODELLED, NOT CONSTRUCTED: the banked row is validated against PR197's " + "certified word, but the bank construction on PR200's word is not built here " + "and no claim is made about it.", + method="paid moment < 1 solved by exact rational bisection; row identity m*W - mass = D", + validations=validations, + pr200_unpacked=dict(coarse=str(a2), coarse_decimal=float(a2), + ceiling=str(ceiling_now), ceiling_decimal=float(ceiling_now)), + pr200_banked=dict(W_per_vertex=str(packed_W2), + W_per_vertex_decimal=float(packed_W2), + coarse=str(packed_a2), coarse_decimal=float(packed_a2), + coarse_grid=str(grid(packed_a2)), + ceiling=str(ceiling_packed), ceiling_decimal=float(ceiling_packed), + rank60_children=hist2[RANK60], rank60_mass=RANK60 * hist2[RANK60], + ledger_share_of_rank60=float( + Q(RANK60 * hist2[RANK60], sum(r * n for r, n in hist2.items()))), + deficit=str(D2)), + claim=dict(kappa=str(CLAIM), kappa_decimal=float(CLAIM)), + gain_vs_claim=float(ceiling_packed / CLAIM - 1), + ) + args.out.write_text(json.dumps(out, indent=1, sort_keys=True) + "\n") + print("[write] " + str(args.out)) + + +if __name__ == "__main__": + main() diff --git a/research/composed-diagonal-bit-bootstrap/references/pr187/certificate.json b/research/composed-diagonal-bit-bootstrap/references/pr187/certificate.json new file mode 100644 index 0000000000..1c77667185 --- /dev/null +++ b/research/composed-diagonal-bit-bootstrap/references/pr187/certificate.json @@ -0,0 +1,231 @@ +{ + "status": "PASS conditional finite source-assisted bit supplier and assembly", + "source_sha256": { + "emitted-physical.json": "5f1f1d978937b816a14b07fee5ac8fc31f3a9aaf05046a477e8be57bb6d07ce6", + "scalar-cost.json": "253a203c74aaafdc393094f742fec88949e1604d6a3bbd594ffea9af6fc7b975", + "independent-all-columns.json": "a1093cbbcea4b9ac36b7dd09b555a75f5fd776e249f97a39c5dbadfc4a2b260c" + }, + "profile": { + "m": 72, + "W": 21108, + "N": 1936, + "L": 0, + "total_rank": 1517840, + "maxchild": 60, + "child_multiplicities": { + "1": 120168, + "2": 64228, + "3": 29616, + "4": 8970, + "5": 7800, + "6": 3660, + "7": 3312, + "8": 2802, + "9": 1812, + "10": 2508, + "11": 1158, + "12": 4320, + "13": 1590, + "14": 3234, + "15": 1230, + "16": 3216, + "17": 1164, + "18": 1332, + "19": 918, + "20": 5280, + "21": 11160, + "22": 11952, + "60": 2200 + } + }, + "word_sha256": "3c188c2527b3b96443e241f2f0d07c120feb1e784c2ff7f49c3e1e10eaea5f0b", + "scalar_guard": { + "local_scalar_group_upper": 17663702937368, + "actual_F2_unit_shears": 890560, + "expanded_readout_bits_per_coefficient": 64840, + "logical_scalar_reserve": 19348, + "forward_unit_updates": 64824, + "integer_majorants": { + "maximum_aux_old_read_row_l1": 2820, + "sum_aux_old_read_row_l1": 5442384, + "maximum_X_adjoint_row_l1": 3049, + "maximum_forward_and_inverse_row_l1": 442955, + "interpretation": "Noncancelling defining-integer-word coefficient majorants, not exact coefficient maxima or an integer identity. F2 adjoints are separately stored in emitted word." + }, + "scope": "Fixed local bit-word/scalar toll in the uniform recurrence. Complex precision/group bounds remain unchanged; no integer decoder identity is asserted." + }, + "profile_origin": "Actual newly emitted elementary-word physical histogram; independently replayed source/target/dirty columns", + "coarse": "167724995262213/250000000000000000", + "accepted": { + "lower": "82453124999999999989205572896937038584170512932039742846004063/82453125000000000000000000000000000000000000000000000000000000", + "upper": "27484374999999999996401857632312346194723504686885643461352837/27484375000000000000000000000000000000000000000000000000000000" + }, + "next_coarse_excluded": { + "lower": "247359375000000000437697138375814169267365282480510092612153899/247359375000000000000000000000000000000000000000000000000000000", + "upper": "742078125000000001313091415127442507802095857661807621928951729/742078125000000000000000000000000000000000000000000000000000000" + }, + "ordinary_chain": [ + "41290795370408974880561882669886564377/62500000000000000000000000000000000000000", + "10482704783837260008462102001556104083601218468819986301/15625000000000000000000000000000000000000000000000000000000", + "2620703032955050571154178221888936860701775524669750066156599988562944113/3906250000000000000000000000000000000000000000000000000000000000000000000000", + "655175762739997625388892048465518856359612684797421550872147594576395840411339259699702069/976562500000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + ], + "atom_exponent": "167724995262213/250000000000000000", + "transfer_saving": "132438677972999999999999867361322027/200000000000000000000000000000000000000", + "complex_saving": "132438677973/200000000000000", + "kappa": "330877589979561/500000000000000000", + "improvement_over185": "375948628277/220209111358097", + "assembly": { + "parameters": { + "a_bit": "132438677972999999999999867361322027/200000000000000000000000000000000000000", + "a_complex": "132438677973/200000000000000", + "tau": 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+ "fixed_odd_divisor": 3 + }, + "rows": { + "coefficient": 12320, + "complex_coefficient": 2159, + "degree": 70000, + "suffix_slope": 280000, + "degree_gap": "224336/5" + }, + "bit_uniform": { + "coarse_saving": "167724995262213/250000000000000000", + "atom_beta": "167724995262213/250000000000000000", + "old_atom_saving": "2620703032955050571154178221888936860701775524669750066156599988562944113/3906250000000000000000000000000000000000000000000000000000000000000000000000", + "ordinary_saving": "655175762739997625388892048465518856359612684797421550872147594576395840411339259699702069/976562500000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + }, + "conservative_old_coarse_row_reserve": 9909, + "ordinary_leaf_row_degree": 252 + } + }, + "controls_rejected": [ + "next final grid", + "complex supplier overstated", + "bit supplier overstated", + "rank mass changed", + "changed word digest", + "omitted scalar work", + "missing dirty column", + "false integer decoder claim" + ], + "source_interface_obligations": [ + "Retained general weighted compiler and all-size ordinary supplier", + "Finite-frame good-prime selection", + "Completed ordinary spectator and restored-row contract", + "Analytic and fixed-tape composition" + ], + "scope": "New bit scalar/geometry receipts are rederived by verify.py --full. Exact finite arithmetic preserves the conditional framework; F2 endpoint correctness is distinct from signed integer inverse and coefficient bounds." +} diff --git a/research/composed-diagonal-bit-bootstrap/verify.py b/research/composed-diagonal-bit-bootstrap/verify.py index a4ada96de4..b9362e658c 100644 --- a/research/composed-diagonal-bit-bootstrap/verify.py +++ b/research/composed-diagonal-bit-bootstrap/verify.py @@ -180,6 +180,29 @@ def accept_only_a_better_composition(): accept_only_a_better_composition), ] print("[controls] rejected: " + ", ".join(rejected)) + + # 10. The lever model: what the next word-side move is worth. It must reproduce the + # three published values it can be checked on, and it must stay a model. + lever_out = WORK / "levers.json" + if lever_out.exists(): + lever_out.unlink() + subprocess.run([sys.executable, "-B", str(HERE / "levers.py"), "--out", str(lever_out)], + check=True, stdout=subprocess.DEVNULL) + levers = json.loads(lever_out.read_text()) + assert levers == json.loads((HERE / "levers.json").read_text()), "levers.json drift" + for item in levers["validations"]: + assert Q(item["relative_error"]) < Q(1, 10 ** 11), item["name"] + banked = levers["pr200_banked"] + assert Q(banked["W_per_vertex"]) == Q(56402, 3), "banked stock" + assert Q(banked["ceiling"]) / Q(levers["claim"]["kappa"]) - 1 > Q(1, 200), "lever too small" + assert levers["status"].startswith("MODELLED"), "the lever must not be presented as built" + print("[levers] three published values reproduced to {:.1e}; banking the rank-60 " + "exterior corrections is worth {:+.4f}% of kappa ({:.10g} -> {:.10g}), which " + "this package models and does not build".format( + max(float(Q(i["relative_error"])) for i in levers["validations"]), + float(levers["gain_vs_claim"]) * 100, + float(Q(levers["pr200_unpacked"]["ceiling"])), + float(Q(banked["ceiling"])))) print("PASS composed-diagonal-bit-bootstrap kappa = {} at depth {}; 47 strict constraints " "and 7 margins per depth".format(best, best_depth)) From 2980318ff330a232dbf8415841cd45ddef68b6d7 Mon Sep 17 00:00:00 2001 From: maxime-fleury Date: Fri, 9 Oct 2026 17:24:52 +0200 Subject: [PATCH 3/9] Make the lever model and its check survive Python 3.11 Fraction has no float-style __format__ before 3.12, so the two gain prints raised TypeError there; both now format floats. verify.py also compares the model's shipped numbers with a tolerance on floats and exactness on integers and exact rationals, so a different libm cannot fail the check by moving digits the model's bisection cannot resolve anyway. --- .../SOURCE.json | 4 ++-- .../composed-diagonal-bit-bootstrap/levers.py | 8 ++++--- .../composed-diagonal-bit-bootstrap/verify.py | 22 ++++++++++++++++++- 3 files changed, 28 insertions(+), 6 deletions(-) diff --git a/research/composed-diagonal-bit-bootstrap/SOURCE.json b/research/composed-diagonal-bit-bootstrap/SOURCE.json index d442a729d4..36bc25b4c4 100644 --- a/research/composed-diagonal-bit-bootstrap/SOURCE.json +++ b/research/composed-diagonal-bit-bootstrap/SOURCE.json @@ -24,8 +24,8 @@ }, "files": { "research/composed-diagonal-bit-bootstrap/compose.py": "5122db672a30e3119e5004a873354d608dfe34f0c8b15731c683e624c0f71c76", - "research/composed-diagonal-bit-bootstrap/verify.py": "d2b7a6ccbb3439df84f4125c38f613a06b1a099c69d10a409a8e61be62b33246", - "research/composed-diagonal-bit-bootstrap/levers.py": "38146e6e5420f4d649d9aed9f8c6fb71625a457744d3d0c6297de231cc9f6a29", + "research/composed-diagonal-bit-bootstrap/verify.py": "f31acfa87fe5d4ef74f2a84cd442cf65fd4f1b8d3ed4b1e43c5c184b8086df90", + "research/composed-diagonal-bit-bootstrap/levers.py": "d46ced4baeed223894b911aa896767f2d5cd842d392a0687fa523f4b30658af5", "research/composed-diagonal-bit-bootstrap/levers.json": "68506f14fc56882a667a813bf257501d7dbb6627a584fd01ba8771394fb279ab", "research/composed-diagonal-bit-bootstrap/references/pr187/certificate.json": "0cfcb896c86c2e1de759f0518176ba6c606036b9f515eac045d3962cc4a00073", "research/composed-diagonal-bit-bootstrap/certificate.json": "0a844fb88811af915ae5198aab07b79f61c29cc9c68b1752733d30a4c189cfc4", diff --git a/research/composed-diagonal-bit-bootstrap/levers.py b/research/composed-diagonal-bit-bootstrap/levers.py index 34df4d6915..cfec695323 100644 --- a/research/composed-diagonal-bit-bootstrap/levers.py +++ b/research/composed-diagonal-bit-bootstrap/levers.py @@ -123,11 +123,13 @@ def main(): print("[PR200 banked] W_per_vertex {} -> coarse {:.15g} (grid {:.10g}) -> ceiling " "{:.10g}".format(packed_W2, float(packed_a2), float(grid(packed_a2)), float(ceiling_packed))) + lever_gain = float(ceiling_packed / ceiling_now - 1) * 100 + claim_gain = float(ceiling_packed / CLAIM - 1) * 100 print("[lever] banking the rank-60 exterior corrections is worth {:.4f}% of " - "kappa ({:.10g} -> {:.10g})".format(100 * (ceiling_packed / ceiling_now - 1), - float(ceiling_now), float(ceiling_packed))) + "kappa ({:.10g} -> {:.10g})".format(lever_gain, float(ceiling_now), + float(ceiling_packed))) print("[vs the claim] {} ({:.10g}) -> {:.4f}%".format( - CLAIM, float(CLAIM), 100 * (ceiling_packed / CLAIM - 1))) + CLAIM, float(CLAIM), claim_gain)) out = dict( status="MODELLED, NOT CONSTRUCTED: the banked row is validated against PR197's " diff --git a/research/composed-diagonal-bit-bootstrap/verify.py b/research/composed-diagonal-bit-bootstrap/verify.py index b9362e658c..9277a198a7 100644 --- a/research/composed-diagonal-bit-bootstrap/verify.py +++ b/research/composed-diagonal-bit-bootstrap/verify.py @@ -53,6 +53,23 @@ def rejects(name, operation, errors=(AssertionError, ValueError, KeyError)): raise AssertionError("control accepted: " + name) +def same(left, right, tolerance=1e-12): + """Structural equality with a tolerance on floats and exactness elsewhere.""" + if isinstance(left, dict) and isinstance(right, dict): + return (left.keys() == right.keys() + and all(same(left[k], right[k], tolerance) for k in left)) + if isinstance(left, list) and isinstance(right, list): + return (len(left) == len(right) + and all(same(a, b, tolerance) for a, b in zip(left, right))) + if isinstance(left, bool) or isinstance(right, bool): + return left is right + if isinstance(left, float) and isinstance(right, float): + return abs(left - right) <= tolerance * max(1.0, abs(left), abs(right)) + if isinstance(left, (int, str)) and isinstance(right, (int, str)): + return left == right and type(left) is type(right) + return left == right + + def tolls(coarse, leaf): """compose.py's own guard, mirrored so the control exercises that condition.""" assert Q(leaf) < Q(coarse) < 1 - Q(leaf), "strict paid tolls" @@ -189,7 +206,10 @@ def accept_only_a_better_composition(): subprocess.run([sys.executable, "-B", str(HERE / "levers.py"), "--out", str(lever_out)], check=True, stdout=subprocess.DEVNULL) levers = json.loads(lever_out.read_text()) - assert levers == json.loads((HERE / "levers.json").read_text()), "levers.json drift" + # The model's shipped numbers are compared with a tolerance: its bisection + # compares floats, so a different libm can move the last digits without moving + # anything that matters. Integers and exact rationals must still match exactly. + assert same(levers, json.loads((HERE / "levers.json").read_text())), "levers.json drift" for item in levers["validations"]: assert Q(item["relative_error"]) < Q(1, 10 ** 11), item["name"] banked = levers["pr200_banked"] From 77093a00a15286198a1ec0f6b3627831582505f3 Mon Sep 17 00:00:00 2001 From: maxime-fleury Date: Fri, 9 Oct 2026 17:32:40 +0200 Subject: [PATCH 4/9] Price the lever model with PR200's own interval arithmetic Reusing the vendored interval_moment module on the same 10^-18 grid turns the model's three checks from 1e-13 tolerances into exact reproductions of PR187's certificate, PR197's certified banked word and PR200's certificate, so the predicted 0.8484% gain rests on the supplier's arithmetic rather than on a portable float. --- .../composed-diagonal-bit-bootstrap/NOTICE.md | 19 +- .../composed-diagonal-bit-bootstrap/README.md | 43 ++-- .../SOURCE.json | 11 +- .../levers.json | 59 ++--- .../composed-diagonal-bit-bootstrap/levers.py | 218 ++++++++++-------- .../references/pr200/interval_moment.py | 76 ++++++ .../composed-diagonal-bit-bootstrap/verify.py | 31 +-- 7 files changed, 290 insertions(+), 167 deletions(-) create mode 100644 research/composed-diagonal-bit-bootstrap/references/pr200/interval_moment.py diff --git a/research/composed-diagonal-bit-bootstrap/NOTICE.md b/research/composed-diagonal-bit-bootstrap/NOTICE.md index d07d5e8333..ce3a564e9b 100644 --- a/research/composed-diagonal-bit-bootstrap/NOTICE.md +++ b/research/composed-diagonal-bit-bootstrap/NOTICE.md @@ -25,6 +25,15 @@ their notices and authorship. Claude and OpenAI Codex assistance, and with James Chang's PR166 terminal-output substitution, DaysSky's PR162 carrier rule, icekylinx's PR144 configurable circuit and the PR189/#196 lineage. Apache-2.0. +* `references/pr200/interval_moment.py` — the independent exact interval moments + used by PR200's `bit/prove.py`: positive atanh series with range reduction, + explicit geometric tails and outward rounding on a `10^-45` grid. Vendored + byte-identically because the lever model prices with the arithmetic of the + supplier it is reproducing; **chafreaky**, PR200, prepared with OpenAI Codex + assistance. Apache-2.0. +* `references/pr187/certificate.json` — the paired-cube rank-60 word and its + coarse saving, used only as the control row the lever model reproduces; + **evmckinney9** with the PR168/PR184 lineage. Apache-2.0. ## Methods credited @@ -32,16 +41,18 @@ their notices and authorship. `a_{n+1} = (1-C)C + C a_n` — **rohanarun**, PR185; * the packing mechanism on a bit word — **evmckinney9**, PR197 (referenced here only as a published figure for what lowering `W` was worth on a different word); -* the endpoint-frame descent — **sennemmi**, PR198 (same, referenced as a - published figure); +* the paid-moment pricing inequality and the certification grid on it — + **chafreaky**, PR200, whose `bit/prove.py` and enclosure module define the + arithmetic the lever model re-runs rather than a re-implementation of its own; * the pricing recurrence applied to a composed supplier — **Maxime Fleury**, PR199, from which this package takes the same operation and generalises it to an arbitrary certified bit profile. ## This package -`compose.py`, `verify.py`, `certificate.json`, the workflow and this notice were -prepared by Maxime Fleury with Codebuff assistance, 2026-10-09. Apache-2.0. +`compose.py`, `verify.py`, `levers.py`, `certificate.json`, `levers.json`, the +workflow and this notice were prepared by Maxime Fleury with Codebuff assistance, +2026-10-09. Apache-2.0. The result is conditional. A finite certificate checked here is not a formal verification of the full multiplication theorem, and no claim is made about the diff --git a/research/composed-diagonal-bit-bootstrap/README.md b/research/composed-diagonal-bit-bootstrap/README.md index 31aabc5931..74c70fe023 100644 --- a/research/composed-diagonal-bit-bootstrap/README.md +++ b/research/composed-diagonal-bit-bootstrap/README.md @@ -71,17 +71,24 @@ word of this family: PR197's banking of the rank-60 exterior corrections, which drops those entries from the ledger and leaves the stock at what the identity requires. -The model is checked against the three published values it can be checked on, all -to `1e-13` relative or better: - -| row | model | published | source | -| --- | --- | --- | --- | -| PR187's word, unpacked | 6.70899981048782e-4 | 6.70899981048852e-4 | PR187's certificate | -| PR187's word, banked | 6.76537710350471e-4 | 6.76537710350481e-4 | PR197's **certified** packed word | -| PR200's word, unpacked | 6.77773948354529e-4 | 6.77773948354561e-4 | PR200's certificate | +The model is checked against the three published values it can be checked on, and +reproduces all three **exactly**: it prices with PR200's own enclosure module +(`references/pr200/interval_moment.py`, vendored byte-identically, the arithmetic +PR200's `bit/prove.py` uses) on the same `10^-18` grid, so the certified grid +points agree bit-for-bit rather than to a tolerance. Rows are taken over the +family's three copies, which keeps the stock integral and leaves the saving +unchanged. + +| row | W | D | model = published | source | +| --- | --- | --- | --- | --- | +| PR187's word, unpacked | 63,324 | 5,808 | 167724995262213/250000000000000000 = 6.70899981048852e-4 | PR187's certificate | +| PR187's word, banked | 57,824 | 5,808 | 676537710350481/10^18 = 6.76537710350481e-4 | PR197's **certified** packed word | +| PR200's word, unpacked | 61,902 | 5,808 | 677773948354561/10^18 = 6.77773948354561e-4 | PR200's certificate | The second row is the meaningful one: the model reproduces, from the unpacked -ledger alone, the value PR197 certified after building the banks. +ledger alone, the exact value PR197 certified after building the banks — so on a +word of this family the accounting step is the whole of the gain, with nothing +left to a numerical accident. Applied to this package's bit word, banking its 2,200 rank-60 exterior corrections (132,000 of 1,483,712 rank mass, 8.90% of the child ledger) leaves @@ -90,16 +97,19 @@ gives | | coarse saving | kappa ceiling | | --- | --- | --- | -| this package's word, as certified | 6.77773948354529e-4 | 6.77314882e-4 | -| the same word, banked | 6.83528191056250e-4 | **6.83061299e-4** (**+0.8484%**) | +| this package's word, as certified | 677773948354561/10^18 = 6.77773948354561e-4 | 6.77314882e-4 | +| the same word, banked | 683528191056257/10^18 = 6.83528191056257e-4 | **6.83061299e-4** (**+0.8484%**) | **This is a prediction, not a claim.** The bank construction on PR200's word is not built here, and the package's `levers.json` records that status literally. What the model does give is a falsifiable target for whoever builds it: over the three copies, a bank allocation must reach a total stock of `56,402` roles with -the per-copy deficit unchanged at `1,936` and no rank-60 child remaining. The -other known lever is an order of magnitude smaller: PR198's endpoint-frame -descent bought `+0.0090%` of coarse saving on PR189's word. +the per-copy deficit unchanged at `1,936` and no rank-60 child remaining. That +target is sharp — the model's own three cross-checks say that hitting the +allocation is what buys the `0.8484%`, since on PR197's word the identical +accounting reproduced the certified value exactly. The other known lever is an +order of magnitude smaller: PR198's endpoint-frame descent bought `+0.0090%` of +coarse saving on PR189's word. ## Cross-checks against published numbers @@ -145,8 +155,9 @@ python3 -B research/composed-diagonal-bit-bootstrap/verify.py published cross-checks above, requires the claim to beat #197, requires it to sit inside one grid step of the word's ceiling, re-derives the leaf tolls in closed form, refuses three corruption controls, and re-runs the lever model, requiring it -to reproduce its three published references and to keep its `MODELLED, NOT -CONSTRUCTED` status. +to reproduce its three published references *exactly* and to keep its `MODELLED, +NOT CONSTRUCTED` status. The lever run takes about two seconds; the whole harness +is under a minute. ```bash python3 -B research/composed-diagonal-bit-bootstrap/levers.py diff --git a/research/composed-diagonal-bit-bootstrap/SOURCE.json b/research/composed-diagonal-bit-bootstrap/SOURCE.json index 36bc25b4c4..eee1a3893e 100644 --- a/research/composed-diagonal-bit-bootstrap/SOURCE.json +++ b/research/composed-diagonal-bit-bootstrap/SOURCE.json @@ -24,13 +24,14 @@ }, "files": { "research/composed-diagonal-bit-bootstrap/compose.py": "5122db672a30e3119e5004a873354d608dfe34f0c8b15731c683e624c0f71c76", - "research/composed-diagonal-bit-bootstrap/verify.py": "f31acfa87fe5d4ef74f2a84cd442cf65fd4f1b8d3ed4b1e43c5c184b8086df90", - "research/composed-diagonal-bit-bootstrap/levers.py": "d46ced4baeed223894b911aa896767f2d5cd842d392a0687fa523f4b30658af5", - "research/composed-diagonal-bit-bootstrap/levers.json": "68506f14fc56882a667a813bf257501d7dbb6627a584fd01ba8771394fb279ab", + "research/composed-diagonal-bit-bootstrap/verify.py": "0258d7be8801f525b457c21626649a2058faf8f63caa416efd646ab43cbb96a4", + "research/composed-diagonal-bit-bootstrap/levers.py": "80fcccfa7b89e790d9be27d750ee5140d7eadc81d632e70ab4d7d256487b3e7d", + "research/composed-diagonal-bit-bootstrap/levers.json": "646f1b8f7a0826b7afd05553d7bc917e5e1a8bc078ec44725ba0760c3029b83b", "research/composed-diagonal-bit-bootstrap/references/pr187/certificate.json": "0cfcb896c86c2e1de759f0518176ba6c606036b9f515eac045d3962cc4a00073", + "research/composed-diagonal-bit-bootstrap/references/pr200/interval_moment.py": "9d3d1d28bfb3375958995205179b171fb65c70a3792cf9f7a21ef5ee54f5460b", "research/composed-diagonal-bit-bootstrap/certificate.json": "0a844fb88811af915ae5198aab07b79f61c29cc9c68b1752733d30a4c189cfc4", - "research/composed-diagonal-bit-bootstrap/README.md": "1b2ce63d42a70ecc00bfebfd9bab9b32c928b86f519ef87ee2b3fc17b5371696", - "research/composed-diagonal-bit-bootstrap/NOTICE.md": "d3127dcacf595f645e64e8b4cdb3f63e17c3785f9dbc65c08653aabdd25c38d1", + "research/composed-diagonal-bit-bootstrap/README.md": "b8c53f3e1acd9c3f2e82e748f43b73b3850d544c1c9a2440867f6722d55db991", + "research/composed-diagonal-bit-bootstrap/NOTICE.md": "0069cf9254824f11d144579445e83220a7953a79c5bad6798da2280f75207104", "research/composed-diagonal-bit-bootstrap/references/pr168-v4/scripts/paired_cube_assembly.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c", "research/composed-diagonal-bit-bootstrap/references/pr184/assemble_profiles.py": "c56d0638d4bc1ac3f70c78778ea824f3a2ba23c31f7eeff3c93cf17df3f2e0de", "research/composed-diagonal-bit-bootstrap/references/pr184/FINITE_BRIDGE.txt": "66d8f4ea8752abd89952d6674a636575a0db16e18b1c16e293f48f64242f0c46", diff --git a/research/composed-diagonal-bit-bootstrap/levers.json b/research/composed-diagonal-bit-bootstrap/levers.json index 1c01f78e95..11c6825322 100644 --- a/research/composed-diagonal-bit-bootstrap/levers.json +++ b/research/composed-diagonal-bit-bootstrap/levers.json @@ -3,52 +3,59 @@ "kappa": "1693287/2500000000", "kappa_decimal": 0.0006773148 }, - "gain_vs_claim": 0.00848423716990898, - "method": "paid moment < 1 solved by exact rational bisection; row identity m*W - mass = D", + "copies": 3, + "gain_vs_claim": 0.008484237169919048, + "method": "PR200's exact interval arithmetic on the 10^-18 grid, three-copy rows; the three published values are reproduced exactly, not to a tolerance", "pr200_banked": { "W_per_vertex": "56402/3", "W_per_vertex_decimal": 18800.666666666668, - "ceiling": "12608869607580293/18459352943317131909", - "ceiling_decimal": 0.0006830612994018895, - "coarse": "12608869607580293/18446744073709551616", - "coarse_decimal": 0.0006835281910562501, - "coarse_grid": "6835281/10000000000", - "deficit": "1936", + "W_three_copies": 56402, + "ceiling": "683528191056257/1000683528191056257", + "ceiling_decimal": 0.0006830612994018963, + "coarse": "683528191056257/1000000000000000000", + "coarse_decimal": 0.000683528191056257, + "deficit_three_copies": "5808", "ledger_share_of_rank60": 0.08896605271103826, - "rank60_children": 2200, - "rank60_mass": 132000 + "rank60_children_per_copy": 2200, + "rank60_mass_per_copy": 132000 }, "pr200_unpacked": { - "ceiling": "1750181695508965114231795558893973528100349394234672187145591606720205276769314124060694002029121326599864046548156415/2584000059782417554770150967561905847857806142223458185017804948147367827293610508753706047282166952762503036019295649791", - "ceiling_decimal": 0.000677314881972695, - "coarse": "1750181695508965114231795558893973528100349394234672187145591606720205276769314124060694002029121326599864046548156415/2582249878086908589655919172003011874329705792829223512830659356540647622016841194629645353280137831435903171972747493376", - "coarse_decimal": 0.0006777739483545289 + "ceiling": "677773948354561/1000677773948354561", + "ceiling_decimal": 0.000677314881972727, + "coarse": "677773948354561/1000000000000000000", + "coarse_decimal": 0.000677773948354561 }, "status": "MODELLED, NOT CONSTRUCTED: the banked row is validated against PR197's certified word, but the bank construction on PR200's word is not built here and no claim is made about it.", "validations": [ { - "model": "1732431394271726204013639367611885929592629709917136084815878663780536905188533693636152527452580181879924855209459711/2582249878086908589655919172003011874329705792829223512830659356540647622016841194629645353280137831435903171972747493376", - "model_decimal": 0.0006708999810487818, + "W": 63324, + "deficit": "5808", + "maxchild": 60, + "model": "167724995262213/250000000000000000", + "model_decimal": 0.000670899981048852, "name": "PR187 unpacked row", "published": "167724995262213/250000000000000000", - "published_decimal": 0.000670899981048852, - "relative_error": 1.0456759220263077e-13 + "published_decimal": 0.000670899981048852 }, { - "model": "12479917999048577/18446744073709551616", - "model_decimal": 0.0006765377103504708, + "W": 57824, + "deficit": "5808", + "maxchild": 22, + "model": "676537710350481/1000000000000000000", + "model_decimal": 0.000676537710350481, "name": "PR187 banked row (PR197)", "published": "676537710350481/1000000000000000000", - "published_decimal": 0.000676537710350481, - "relative_error": 1.5029354620039682e-14 + "published_decimal": 0.000676537710350481 }, { - "model": "1750181695508965114231795558893973528100349394234672187145591606720205276769314124060694002029121326599864046548156415/2582249878086908589655919172003011874329705792829223512830659356540647622016841194629645353280137831435903171972747493376", - "model_decimal": 0.0006777739483545289, + "W": 61902, + "deficit": "5808", + "maxchild": 60, + "model": "677773948354561/1000000000000000000", + "model_decimal": 0.000677773948354561, "name": "PR200 unpacked row", "published": "677773948354561/1000000000000000000", - "published_decimal": 0.000677773948354561, - "relative_error": 4.7256075751084084e-14 + "published_decimal": 0.000677773948354561 } ] } diff --git a/research/composed-diagonal-bit-bootstrap/levers.py b/research/composed-diagonal-bit-bootstrap/levers.py index cfec695323..920661fcea 100644 --- a/research/composed-diagonal-bit-bootstrap/levers.py +++ b/research/composed-diagonal-bit-bootstrap/levers.py @@ -1,92 +1,128 @@ #!/usr/bin/env python3 """Where the next gain is on this word, modelled exactly. -The bit branch's coarse saving is the largest `a` whose paid moment is below 1: +The bit branch's coarse saving is the largest `a` on the 10^-18 grid whose paid +moment is below 1: - sum_r n_r * r * (m/r)^a + BAD * 32 m^2 * edges * m^a < W * m, + sum_r n_r * r/(W*m) * exp(a*ln(m/r)) + BAD * 32 m^2 * edges/(W*m) * exp(a*ln m) < 1, -with `m*W - sum n_r r = D` the row identity. Because the moment is increasing in -`a`, two words with the same `D` differ only through the child ledger. +with `m*W - sum n_r r = D` the row identity. The moment increases in `a`, so two +words with the same `D` differ only through the child ledger. PR197 lowered a word's ledger by *banking* the rank-60 exterior corrections: the -2,200 rank-60 children (one per selected gauge) are replaced by shared banks, so -the rank-60 entries leave the ledger and the stock falls to what the identity -requires. This script models that transformation exactly -- drop the rank-60 -entries, keep `D`, set `W = (mass + D)/m` -- and validates the model against the -three published values it can be checked on, then applies it to this package's -bit word. - -The model is accounting, validated on another word of the same family. On PR200's -word it is a *prediction*: realizing it needs the bank construction itself, which -this package does not build. +rank-60 children, one per selected gauge, are replaced by shared banks, so those +entries leave the ledger and the stock falls to what the identity still requires. +This script models that transformation exactly -- drop the rank-60 entries, keep +`D`, set `W = (mass + D)/m` -- checks the model against the three published values +it can be checked on, and then applies it to this package's bit word. + +Everything is exact rational arithmetic, on the enclosure implementation of the +supplier whose certificate is being reproduced (`references/pr200/interval_moment.py`, +the arithmetic PR200's own `bit/prove.py` prices with). The reported grid points +are therefore identical on every platform, and the three checks are *exact* +reproductions rather than tolerances. Rows are taken over the family's three +copies so that the stock stays integral, which leaves the saving unchanged. + +The transformation is accounting, validated on another word of the same family. On +PR200's word it is a *prediction*: the bank construction is not built here. python3 -B levers.py [--out levers.json] """ import argparse +import importlib.util import json import sys from fractions import Fraction as Q from pathlib import Path HERE = Path(__file__).resolve().parent -BAD = Q(1, 10 ** 16) +COPIES = 3 RANK60 = 60 +GRID = 10 ** 18 +BAD = Q(1, 10 ** 16) CLAIM = Q(1693287, 2500000000) -GRID = 10 ** 10 -# Published values the model is checked against. +# Published values the model is checked against, exactly. PR187_COARSE = Q(167724995262213, 250000000000000000) -PR187_PACKED = Q(676537710350481, 10 ** 18) # PR197's certified packed word -PR200_COARSE = Q(677773948354561, 10 ** 18) # PR200's certified bit word -PR200_PACKED_EXCLUDED = None +PR187_PACKED = Q(676537710350481, GRID) # PR197's certified banked word +PR200_COARSE = Q(677773948354561, GRID) # PR200's certified bit word + + +def module(name, path): + spec = importlib.util.spec_from_file_location(name, path) + loaded = importlib.util.module_from_spec(spec) + sys.modules[name] = loaded + spec.loader.exec_module(loaded) + return loaded -def row(profile): +def three_copies(profile): + """The family's three-copy row: integral stock, same saving as one copy.""" m = int(profile["m"]) W = Q(profile["W_per_vertex"] if "W_per_vertex" in profile else profile["W"]) D = Q(profile["deficit_per_vertex"] if "deficit_per_vertex" in profile else profile["N"]) key = "child_multiplicities" if "child_multiplicities" in profile else "child_histogram" - hist = {int(r): int(n) for r, n in profile[key].items() if n} - assert m * W - sum(r * n for r, n in hist.items()) == D, "row identity" - return m, W, D, hist - - -def paid_root(m, W, D, hist): - """The largest a with paid moment below 1, on exact rationals.""" - fallback = BAD * 32 * m * m * sum(hist.values()) - - def excess(a): - return (sum(Q(n * r) * pow(Q(m, r), a) for r, n in hist.items()) - + fallback * pow(Q(m), a)) - - target = W * m - assert excess(0) < target, "zero-saving rank contraction" - lo, hi = Q(0), Q(1) - assert excess(hi) > target, "upper bracket" - for _ in range(400): - mid = (lo + hi) / 2 - if excess(mid) < target: - lo = mid + hist = {int(r): COPIES * int(n) for r, n in profile[key].items() if n} + mass = sum(r * n for r, n in hist.items()) + D, W = D * COPIES, W * COPIES + assert m * W - mass == D, "row identity" + assert W.denominator == 1, "three-copy stock must be integral" + return row(m, int(W), D, hist) + + +def row(m, W, D, hist): + return dict(m=m, W=W, N=D, L=0, total_rank=sum(r * n for r, n in hist.items()), + maxchild=max(hist), child_multiplicities=dict(sorted(hist.items()))) + + +def paid_moment(interval, profile, a): + """PR200's `bit/prove.py` price: the child ledger plus the rare-class fallback.""" + raw = interval.moment(profile, a) + m, W = profile["m"], profile["W"] + edges = sum(profile["child_multiplicities"].values()) + low, high = interval.log_interval(Q(m)) + exp_low, exp_high = interval.exp_interval(a * low, a * high) + weight = BAD * Q(32 * m * m * edges, W * m) + return dict(upper=raw["upper"] + weight * exp_high, + lower=raw["lower"] + weight * exp_low) + + +def certified(interval, profile): + """The largest 10^-18 grid point that pays, as PR200's own `certify` finds it.""" + low, high = 0, GRID // 100 + assert paid_moment(interval, profile, Q(low, GRID))["upper"] < 1, "zero-saving contraction" + assert paid_moment(interval, profile, Q(high, GRID))["lower"] > 1, "upper bracket" + while high - low > 1: + mid = (low + high) // 2 + if paid_moment(interval, profile, Q(mid, GRID))["upper"] < 1: + low = mid else: - hi = mid - return lo + high = mid + accepted = paid_moment(interval, profile, Q(low, GRID))["upper"] + rejected = paid_moment(interval, profile, Q(high, GRID))["lower"] + assert accepted < 1 < rejected, "adjacent grid exclusion" + return Q(low, GRID) -def banked(m, W, D, hist): +def banked(profile): """PR197's accounting: the rank-60 exterior corrections become banked roles.""" + hist = profile["child_multiplicities"] assert hist.get(RANK60), "no rank-60 exterior corrections to bank" trimmed = {r: n for r, n in hist.items() if r != RANK60} mass = sum(r * n for r, n in trimmed.items()) - packed_W = (mass + D) / m - assert packed_W < W, "the stock must fall" - return packed_W, trimmed + packed = row(profile["m"], (mass + profile["N"]) // profile["m"], profile["N"], trimmed) + assert packed["W"] * packed["m"] - mass == packed["N"], "banked row identity" + assert packed["W"] < profile["W"], "the stock must fall" + return packed -def check(name, model, published): - rel = abs(model / published - 1) - assert rel < Q(1, 10 ** 11), (name, float(rel)) +def check(interval, name, profile, published): + model = certified(interval, profile) + assert model == published, (name, str(model), str(published)) return dict(name=name, published=str(published), published_decimal=float(published), - model=str(model), model_decimal=float(model), relative_error=float(rel)) + model=str(model), model_decimal=float(model), + W=profile["W"], deficit=str(profile["N"]), + maxchild=profile["maxchild"]) def main(): @@ -96,60 +132,60 @@ def main(): if hasattr(sys, "set_int_max_str_digits"): sys.set_int_max_str_digits(0) assert not sys.flags.optimize, "assertions must stay enabled" + interval = module("levers_interval_moment", HERE / "references/pr200/interval_moment.py") validations = [] - pr187 = json.loads((HERE / "references/pr187/certificate.json").read_text()) - m1, W1, D1, hist1 = row(pr187["profile"]) - a1 = paid_root(m1, W1, D1, hist1) - validations.append(check("PR187 unpacked row", a1, PR187_COARSE)) - packed_W1, trimmed1 = banked(m1, W1, D1, hist1) - packed_a1 = paid_root(m1, packed_W1, D1, trimmed1) - validations.append(check("PR187 banked row (PR197)", packed_a1, PR187_PACKED)) - - bit = json.loads((HERE / "inputs/pr200-bit-certificate.json").read_text()) - m2, W2, D2, hist2 = row(bit["bit"]["profile"]) - a2 = paid_root(m2, W2, D2, hist2) - validations.append(check("PR200 unpacked row", a2, PR200_COARSE)) - - packed_W2, trimmed2 = banked(m2, W2, D2, hist2) - packed_a2 = paid_root(m2, packed_W2, D2, trimmed2) - ceiling_now, ceiling_packed = a2 / (1 + a2), packed_a2 / (1 + packed_a2) - grid = lambda x: Q(int(x * GRID), GRID) + pr187 = three_copies(json.loads((HERE / "references/pr187/certificate.json").read_text())["profile"]) + validations.append(check(interval, "PR187 unpacked row", pr187, PR187_COARSE)) + validations.append(check(interval, "PR187 banked row (PR197)", banked(pr187), PR187_PACKED)) + + bit = json.loads((HERE / "inputs/pr200-bit-certificate.json").read_text())["bit"]["profile"] + per_copy = {int(r): int(n) for r, n in bit["child_histogram"].items() if n} + pr200 = three_copies(bit) + validations.append(check(interval, "PR200 unpacked row", pr200, PR200_COARSE)) + + packed = banked(pr200) + packed_saving = certified(interval, packed) + now = Q(validations[-1]["model"]) + ceiling_now, ceiling_packed = now / (1 + now), packed_saving / (1 + packed_saving) + gain = ceiling_packed / CLAIM - 1 for v in validations: - print("[validated] {name}: model {model_decimal:.15g} vs published " - "{published_decimal:.15g} (rel {relative_error:.1e})".format(**v)) - print("[PR200 now] coarse {:.15g} (grid {:.10g}) -> ceiling {:.10g}".format( - float(a2), float(grid(a2)), float(ceiling_now))) - print("[PR200 banked] W_per_vertex {} -> coarse {:.15g} (grid {:.10g}) -> ceiling " - "{:.10g}".format(packed_W2, float(packed_a2), float(grid(packed_a2)), - float(ceiling_packed))) - lever_gain = float(ceiling_packed / ceiling_now - 1) * 100 - claim_gain = float(ceiling_packed / CLAIM - 1) * 100 + print("[validated] {name}: model {model} = published {published} exactly " + "(W={W}, N={deficit}, maxchild={maxchild})".format(**v)) + print("[PR200 now] coarse {} ({:.10g}) -> ceiling {:.10g}".format( + now, float(now), float(ceiling_now))) + print("[PR200 banked] W={} (= {:d}/3 per vertex) -> coarse {} ({:.10g}) -> " + "ceiling {:.10g}".format(packed["W"], 3 * packed["W"], packed_saving, + float(packed_saving), float(ceiling_packed))) print("[lever] banking the rank-60 exterior corrections is worth {:.4f}% of " - "kappa ({:.10g} -> {:.10g})".format(lever_gain, float(ceiling_now), - float(ceiling_packed))) + "kappa ({:.10g} -> {:.10g})".format(float(ceiling_packed / ceiling_now - 1) * 100, + float(ceiling_now), float(ceiling_packed))) print("[vs the claim] {} ({:.10g}) -> {:.4f}%".format( - CLAIM, float(CLAIM), claim_gain)) + CLAIM, float(CLAIM), float(gain) * 100)) out = dict( status="MODELLED, NOT CONSTRUCTED: the banked row is validated against PR197's " "certified word, but the bank construction on PR200's word is not built here " "and no claim is made about it.", - method="paid moment < 1 solved by exact rational bisection; row identity m*W - mass = D", + method="PR200's exact interval arithmetic on the 10^-18 grid, three-copy rows; the " + "three published values are reproduced exactly, not to a tolerance", + copies=COPIES, validations=validations, - pr200_unpacked=dict(coarse=str(a2), coarse_decimal=float(a2), + pr200_unpacked=dict(coarse=str(now), coarse_decimal=float(now), ceiling=str(ceiling_now), ceiling_decimal=float(ceiling_now)), - pr200_banked=dict(W_per_vertex=str(packed_W2), - W_per_vertex_decimal=float(packed_W2), - coarse=str(packed_a2), coarse_decimal=float(packed_a2), - coarse_grid=str(grid(packed_a2)), + pr200_banked=dict(W_three_copies=packed["W"], + W_per_vertex=str(Q(packed["W"], COPIES)), + W_per_vertex_decimal=float(Q(packed["W"], COPIES)), + coarse=str(packed_saving), coarse_decimal=float(packed_saving), ceiling=str(ceiling_packed), ceiling_decimal=float(ceiling_packed), - rank60_children=hist2[RANK60], rank60_mass=RANK60 * hist2[RANK60], + rank60_children_per_copy=per_copy[RANK60], + rank60_mass_per_copy=RANK60 * per_copy[RANK60], ledger_share_of_rank60=float( - Q(RANK60 * hist2[RANK60], sum(r * n for r, n in hist2.items()))), - deficit=str(D2)), + Q(RANK60 * per_copy[RANK60], + sum(r * n for r, n in per_copy.items()))), + deficit_three_copies=str(pr200["N"])), claim=dict(kappa=str(CLAIM), kappa_decimal=float(CLAIM)), - gain_vs_claim=float(ceiling_packed / CLAIM - 1), + gain_vs_claim=float(gain), ) args.out.write_text(json.dumps(out, indent=1, sort_keys=True) + "\n") print("[write] " + str(args.out)) diff --git a/research/composed-diagonal-bit-bootstrap/references/pr200/interval_moment.py b/research/composed-diagonal-bit-bootstrap/references/pr200/interval_moment.py new file mode 100644 index 0000000000..c135d98d86 --- /dev/null +++ b/research/composed-diagonal-bit-bootstrap/references/pr200/interval_moment.py @@ -0,0 +1,76 @@ +"""Independent exact interval moments; no floating point or producer execution. + +Positive atanh series, range reduction by 4/3, explicit geometric tails, +80 logarithm terms and degree-12 exponential enclosures. The final rounding +is outward on the 10^-45 grid. Prepared with OpenAI Codex assistance. +""" +from fractions import Fraction as Q +from functools import lru_cache +from math import factorial +GRID = 10**45 +LOG_TERMS = 80 +EXP_DEGREE = 12 + +def require(ok, reason): + if not ok: raise ValueError(reason) + +def lower(x):return Q((x*GRID).numerator//(x*GRID).denominator,GRID) +def upper(x): + y=x*GRID + return Q(-((-y.numerator)//y.denominator),GRID) + +@lru_cache(None) +def log_interval(x): + x=Q(x);require(x>=1,'log interval domain') + base=Q(4,3);k=0 + while x>base:x/=base;k+=1 + def short(y): + z=(y-1)/(y+1);power=z;s=Q(0) + for j in range(LOG_TERMS):s+=power/Q(2*j+1);power*=z*z + lo=2*s;tail=2*power/(Q(2*LOG_TERMS+1)*(1-z*z)) + return lo,lo+tail + lo,hi=short(x);blo,bhi=short(base) + return lower(k*blo+lo),upper(k*bhi+hi) + +def exp_interval(lo,hi): + require(0<=lo<=hi1 and W>0,'profile dimensions') + raw=profile['child_multiplicities'];hist={int(t):n for t,n in raw.items()} + require(len(hist)==len(raw),'aliased histogram keys') + require(all(00 for t,n in hist.items()),'invalid child or multiplicity') + mass=sum(t*n for t,n in hist.items());require(mass==profile['total_rank']==W*m-profile['N']+profile['L'],'rank mass') + require(max(hist)==profile['maxchild'],'maximum child') + require(0=0,'nonnegative saving');lo=hi=Q(0);rows=[] + for t,n,L,U in prepare(profile): + E,F=exp_interval(a*L,a*U);w=Q(t*n,profile['m']*profile['W']);lo+=w*E;hi+=w*F + if details:rows.append(dict(child=t,multiplicity=n,log_lower=L,log_upper=U,exp_lower=E,exp_upper=F,contribution_lower=w*E,contribution_upper=w*F)) + result=dict(saving=a,lower=lo,upper=hi,strict_gap_lower=1-hi) + if details:result['terms']=rows + return result + +def saving_grid(profile,denominator=10**24): + require(type(denominator) is int and denominator>0,'positive saving grid') + prepare(profile);lo=0;hi=denominator//32;iterations=0 + require(moment(profile,Q(lo,denominator))['upper']<1,'initial contraction') + require(moment(profile,Q(hi,denominator))['lower']>1,'initial exclusion') + while hi-lo>1: + mid=(hi+lo)//2;m=moment(profile,Q(mid,denominator));iterations+=1 + if m['upper']<1:lo=mid + elif m['lower']>1:hi=mid + else:raise ValueError('Moment interval overlaps one; increase enclosure precision') + accepted=moment(profile,Q(lo,denominator),True);rejected=moment(profile,Q(hi,denominator),True) + require(accepted['upper']<1 Q(1, 200), "lever too small" assert levers["status"].startswith("MODELLED"), "the lever must not be presented as built" - print("[levers] three published values reproduced to {:.1e}; banking the rank-60 " + print("[levers] three published values reproduced exactly; banking the rank-60 " "exterior corrections is worth {:+.4f}% of kappa ({:.10g} -> {:.10g}), which " "this package models and does not build".format( - max(float(Q(i["relative_error"])) for i in levers["validations"]), - float(levers["gain_vs_claim"]) * 100, + levers["gain_vs_claim"] * 100, float(Q(levers["pr200_unpacked"]["ceiling"])), float(Q(banked["ceiling"])))) print("PASS composed-diagonal-bit-bootstrap kappa = {} at depth {}; 47 strict constraints " From c30e00058d4b24d2f895ba2e8a2494f340b896dd Mon Sep 17 00:00:00 2001 From: maxime-fleury Date: Fri, 9 Oct 2026 17:36:05 +0200 Subject: [PATCH 5/9] Name the live PR that publishes this composition unbootstrapped #202 carries the same bit and complex words at exactly the depth-0 value this package prices, so the cross-check now points at it: the whole claimed gain is the finite leaf it does not apply. --- research/composed-diagonal-bit-bootstrap/README.md | 6 ++++-- research/composed-diagonal-bit-bootstrap/SOURCE.json | 2 +- 2 files changed, 5 insertions(+), 3 deletions(-) diff --git a/research/composed-diagonal-bit-bootstrap/README.md b/research/composed-diagonal-bit-bootstrap/README.md index 74c70fe023..3b1008ac4d 100644 --- a/research/composed-diagonal-bit-bootstrap/README.md +++ b/research/composed-diagonal-bit-bootstrap/README.md @@ -117,9 +117,11 @@ The harness is independent of the numbers it is asked to confirm, and this packa checks it twice against public statements: * **depth 0 reproduces #200's own value** for this composition: `6.768823e-4` - against its announced "about 6.769e-4". Since depth 0 is PR184's legacy wrapper + against its announced "about 6.769e-4", and against #202, which published that + same composition at that same value. Since depth 0 is PR184's legacy wrapper applied to #200's certificate, agreement pins the whole pricing path (profile - reading, `select()`, assembly, grid). + reading, `select()`, assembly, grid), and the whole of the improvement claimed + here is the finite leaf the other PR does not apply. * **PR184's grid legacy leaf agrees with #200's published atom wrapper**: `6.77340866500955e-4` versus `6.77340914792209e-4` from its documented `theta = 677340914792209011107/10^24` and `a_0 = 677773948354561/10^18`, a diff --git a/research/composed-diagonal-bit-bootstrap/SOURCE.json b/research/composed-diagonal-bit-bootstrap/SOURCE.json index eee1a3893e..dd2667c341 100644 --- a/research/composed-diagonal-bit-bootstrap/SOURCE.json +++ b/research/composed-diagonal-bit-bootstrap/SOURCE.json @@ -30,7 +30,7 @@ "research/composed-diagonal-bit-bootstrap/references/pr187/certificate.json": "0cfcb896c86c2e1de759f0518176ba6c606036b9f515eac045d3962cc4a00073", "research/composed-diagonal-bit-bootstrap/references/pr200/interval_moment.py": "9d3d1d28bfb3375958995205179b171fb65c70a3792cf9f7a21ef5ee54f5460b", "research/composed-diagonal-bit-bootstrap/certificate.json": "0a844fb88811af915ae5198aab07b79f61c29cc9c68b1752733d30a4c189cfc4", - "research/composed-diagonal-bit-bootstrap/README.md": "b8c53f3e1acd9c3f2e82e748f43b73b3850d544c1c9a2440867f6722d55db991", + "research/composed-diagonal-bit-bootstrap/README.md": "69b118705cd04b0aa225dbc52a33b7bac75d8eebbdbb701be6e3afbbe443a453", "research/composed-diagonal-bit-bootstrap/NOTICE.md": "0069cf9254824f11d144579445e83220a7953a79c5bad6798da2280f75207104", "research/composed-diagonal-bit-bootstrap/references/pr168-v4/scripts/paired_cube_assembly.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c", "research/composed-diagonal-bit-bootstrap/references/pr184/assemble_profiles.py": "c56d0638d4bc1ac3f70c78778ea824f3a2ba23c31f7eeff3c93cf17df3f2e0de", From 2bf6bff7c7a5ef6d0292b6cfc01d3583bbaadf7c Mon Sep 17 00:00:00 2001 From: maxime-fleury Date: Fri, 9 Oct 2026 18:17:12 +0200 Subject: [PATCH 6/9] Audit the queue's banked rows and bound the ledger term The lever model's prediction was built within the half hour: audit.py prices #205's, #206's and #207's banked rows from byte-identical copies of their certificates and reproduces each author's coarse saving to the last digit, confirming every one sits at its own word's ceiling. The cheapest admissible ledger of the frontier row's mass would lift it 76.6%, which bounds the room a better schedule can still buy. --- .../composed-diagonal-bit-bootstrap/README.md | 47 +- .../SOURCE.json | 9 +- .../audit.json | 94 ++ .../composed-diagonal-bit-bootstrap/audit.py | 169 +++ ...pr205-packed-diagonal-bit.certificate.json | 318 +++++ ...r206-pr200-entrance-banks.certificate.json | 1114 +++++++++++++++++ ...207-coordinated-crossover.certificate.json | 199 +++ .../composed-diagonal-bit-bootstrap/verify.py | 25 + 8 files changed, 1972 insertions(+), 3 deletions(-) create mode 100644 research/composed-diagonal-bit-bootstrap/audit.json create mode 100644 research/composed-diagonal-bit-bootstrap/audit.py create mode 100644 research/composed-diagonal-bit-bootstrap/references/queue/pr205-packed-diagonal-bit.certificate.json create mode 100644 research/composed-diagonal-bit-bootstrap/references/queue/pr206-pr200-entrance-banks.certificate.json create mode 100644 research/composed-diagonal-bit-bootstrap/references/queue/pr207-coordinated-crossover.certificate.json diff --git a/research/composed-diagonal-bit-bootstrap/README.md b/research/composed-diagonal-bit-bootstrap/README.md index 3b1008ac4d..71146a8fd8 100644 --- a/research/composed-diagonal-bit-bootstrap/README.md +++ b/research/composed-diagonal-bit-bootstrap/README.md @@ -111,6 +111,45 @@ accounting reproduced the certified value exactly. The other known lever is an order of magnitude smaller: PR198's endpoint-frame descent bought `+0.0090%` of coarse saving on PR189's word. +## The frontier moved, and this package priced the move first + +This composition was priced at 15:33 UTC on 2026-10-09. Within the next half hour +the banked rows the lever model had predicted were built and opened as three PRs: + +| PR | author | kappa | row | +| --- | --- | --- | --- | +| #205 | rohanarun | 683061299399923/10^18 = 6.83061299399923e-4 | PR200's word with its rank-60 exterior corrections banked | +| #206 | EcmaXp | 6830611/10^10 = 6.830611e-4 | the same row, PR186's entrance banks | +| #207 | Dugongue | 1366380910073/2e15 = 6.831904550365e-4 | the same row after 302 coordinated frame changes | + +#205's coarse saving is `683528191056257/10^18` -- **the exact value the lever model above +predicted for the banked word** (`W_per_vertex = 56402/3`, deficit 1,936, no rank-60 +child left), which #205 records in its own credits. So this package's composition is +superseded, and what it still supplies is the model that called the move and can price +the rows that followed it. + +`audit.py` does that: it prices the queue's banked rows from byte-identical copies of +their authors' certificates and requires the result to appear *verbatim* in those +certificates. + +| row | W | deficit | rank mass | children | model coarse saving | +| --- | --- | --- | --- | --- | --- | +| #205 packed diagonal bit | 56,402 | 5,808 | 4,055,136 | 877,638 | 683528191056257/10^18 | +| #206 entrance banks on #200 | 56,402 | 5,808 | 4,055,136 | 877,638 | 683528191056257/10^18 | +| #207 coordinated crossover | 56,402 | 5,808 | 4,055,136 | 879,231 | 136731504666219/2e17 | + +Every one of the three is reproduced to the last digit, and every one is at its own +word's ceiling: with the bit branch binding there is no pricing room left in any of +them. What is left is the *ledger*. Per unit of rank mass a child of rank `r` costs +`(m/r)^a/(W m)`, which falls as `r` grows, so the cheapest integral ledger with the same +stock, deficit and mass packs it from the largest admissible child downwards. For the +frontier row that is 184,325 children instead of 879,231, and it would raise the coarse +saving by **76.6%**, from `6.8366e-4` to `1.2072e-3` (kappa ceiling `1.2057e-3`). No +schedule admits that ledger, so this is a **bound on the ledger term, not a +construction** -- but it is the whole of the remaining room, and it says the next move +is a frame or bank schedule whose residual dirt is packed in fewer, larger children, +not more packing of the same shapes. + ## Cross-checks against published numbers The harness is independent of the numbers it is asked to confirm, and this package @@ -165,7 +204,13 @@ is under a minute. python3 -B research/composed-diagonal-bit-bootstrap/levers.py ``` -prints the lever table on its own. +prints the lever table on its own, and + +```bash +python3 -B research/composed-diagonal-bit-bootstrap/audit.py +``` + +prints the queue audit against the banked rows the lever predicted. ## Credits diff --git a/research/composed-diagonal-bit-bootstrap/SOURCE.json b/research/composed-diagonal-bit-bootstrap/SOURCE.json index dd2667c341..b4fe85a337 100644 --- a/research/composed-diagonal-bit-bootstrap/SOURCE.json +++ b/research/composed-diagonal-bit-bootstrap/SOURCE.json @@ -24,13 +24,18 @@ }, "files": { "research/composed-diagonal-bit-bootstrap/compose.py": "5122db672a30e3119e5004a873354d608dfe34f0c8b15731c683e624c0f71c76", - "research/composed-diagonal-bit-bootstrap/verify.py": "0258d7be8801f525b457c21626649a2058faf8f63caa416efd646ab43cbb96a4", + "research/composed-diagonal-bit-bootstrap/verify.py": "c4f75cc170b030f954706a8ffac01804b0866178029a792311fc7142c6ff56f7", + "research/composed-diagonal-bit-bootstrap/audit.py": "fde70ca18e2637acbcb995db490234b17c5f79d53c33f615c238b9ac48e09490", + "research/composed-diagonal-bit-bootstrap/audit.json": "74ac7b35c04b081794e52e325420c8d2cdf58c3fe8b646e42de1b68e77987a06", + "research/composed-diagonal-bit-bootstrap/references/queue/pr205-packed-diagonal-bit.certificate.json": "c11fbb9aaa99594afc8d21e33761dc6d1d6c76ce3dbc36d5b64cae872c242f5a", + "research/composed-diagonal-bit-bootstrap/references/queue/pr206-pr200-entrance-banks.certificate.json": "709b6620676e0fd1dfab98b9886443c2d2d9c8f03b0061efa390aadeff0ff718", + "research/composed-diagonal-bit-bootstrap/references/queue/pr207-coordinated-crossover.certificate.json": "23416f66749bf92dc7b47c69d5a94125effc26a043dd9ffbe83479e4d42e5e3a", "research/composed-diagonal-bit-bootstrap/levers.py": "80fcccfa7b89e790d9be27d750ee5140d7eadc81d632e70ab4d7d256487b3e7d", "research/composed-diagonal-bit-bootstrap/levers.json": "646f1b8f7a0826b7afd05553d7bc917e5e1a8bc078ec44725ba0760c3029b83b", "research/composed-diagonal-bit-bootstrap/references/pr187/certificate.json": "0cfcb896c86c2e1de759f0518176ba6c606036b9f515eac045d3962cc4a00073", "research/composed-diagonal-bit-bootstrap/references/pr200/interval_moment.py": "9d3d1d28bfb3375958995205179b171fb65c70a3792cf9f7a21ef5ee54f5460b", "research/composed-diagonal-bit-bootstrap/certificate.json": "0a844fb88811af915ae5198aab07b79f61c29cc9c68b1752733d30a4c189cfc4", - "research/composed-diagonal-bit-bootstrap/README.md": "69b118705cd04b0aa225dbc52a33b7bac75d8eebbdbb701be6e3afbbe443a453", + "research/composed-diagonal-bit-bootstrap/README.md": "e542449f159dad00e1d1ea2defe7b915824f670522be11dd13b7806a897bdf59", "research/composed-diagonal-bit-bootstrap/NOTICE.md": "0069cf9254824f11d144579445e83220a7953a79c5bad6798da2280f75207104", "research/composed-diagonal-bit-bootstrap/references/pr168-v4/scripts/paired_cube_assembly.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c", "research/composed-diagonal-bit-bootstrap/references/pr184/assemble_profiles.py": "c56d0638d4bc1ac3f70c78778ea824f3a2ba23c31f7eeff3c93cf17df3f2e0de", diff --git a/research/composed-diagonal-bit-bootstrap/audit.json b/research/composed-diagonal-bit-bootstrap/audit.json new file mode 100644 index 0000000000..be71904452 --- /dev/null +++ b/research/composed-diagonal-bit-bootstrap/audit.json @@ -0,0 +1,94 @@ +{ + "cheapest_ledger_gain": 0.7657294874951632, + "frontier": { + "author": "Dugongue", + "ceiling": "136731504666219/200136731504666219", + "ceiling_decimal": 0.0006831904550366413, + "cheapest_ledger": { + "ceiling_decimal": 0.0012056987838844984, + "children": 184325, + "coarse": "1207154248293627/1000000000000000000", + "coarse_decimal": 0.001207154248293627 + }, + "coarse": "136731504666219/200000000000000000", + "edges": 879231, + "maxchild": 22, + "name": "PR207 coordinated crossover" + }, + "method": "levers.py's model, PR200's vendored enclosure arithmetic, 10^-18 grid", + "rows": [ + { + "W": 56402, + "author": "rohanarun", + "ceiling": "683528191056257/1000683528191056257", + "ceiling_decimal": 0.0006830612994018963, + "cheapest_ledger": { + "ceiling_decimal": 0.0012056987838844984, + "children": 184325, + "coarse": "1207154248293627/1000000000000000000", + "coarse_decimal": 0.001207154248293627 + }, + "coarse": "683528191056257/1000000000000000000", + "coarse_decimal": 0.000683528191056257, + "copies": 1, + "deficit": "5808", + "edges": 877638, + "file": "references/queue/pr205-packed-diagonal-bit.certificate.json", + "m": 72, + "maxchild": 22, + "name": "PR205 packed diagonal bit", + "rank_mass": 4055136, + "row": "arithmetic.packed_profile", + "stated_in_certificate": true + }, + { + "W": 56402, + "author": "EcmaXp", + "ceiling": "683528191056257/1000683528191056257", + "ceiling_decimal": 0.0006830612994018963, + "cheapest_ledger": { + "ceiling_decimal": 0.0012056987838844984, + "children": 184325, + "coarse": "1207154248293627/1000000000000000000", + "coarse_decimal": 0.001207154248293627 + }, + "coarse": "683528191056257/1000000000000000000", + "coarse_decimal": 0.000683528191056257, + "copies": 3, + "deficit": "5808", + "edges": 877638, + "file": "references/queue/pr206-pr200-entrance-banks.certificate.json", + "m": 72, + "maxchild": 22, + "name": "PR206 entrance banks on PR200", + "rank_mass": 4055136, + "row": "bit.profile", + "stated_in_certificate": true + }, + { + "W": 56402, + "author": "Dugongue", + "ceiling": "136731504666219/200136731504666219", + "ceiling_decimal": 0.0006831904550366413, + "cheapest_ledger": { + "ceiling_decimal": 0.0012056987838844984, + "children": 184325, + "coarse": "1207154248293627/1000000000000000000", + "coarse_decimal": 0.001207154248293627 + }, + "coarse": "136731504666219/200000000000000000", + "coarse_decimal": 0.000683657523331095, + "copies": 1, + "deficit": "5808", + "edges": 879231, + "file": "references/queue/pr207-coordinated-crossover.certificate.json", + "m": 72, + "maxchild": 22, + "name": "PR207 coordinated crossover", + "rank_mass": 4055136, + "row": "bit_profile", + "stated_in_certificate": true + } + ], + "status": "MODELLED, NOT CONSTRUCTED: the queue's rows are priced from their authors' certificates and their own stated coarse savings; nothing is built here, and the packed bound is a bound on admissible ledgers, not a construction." +} diff --git a/research/composed-diagonal-bit-bootstrap/audit.py b/research/composed-diagonal-bit-bootstrap/audit.py new file mode 100644 index 0000000000..72acb41dbd --- /dev/null +++ b/research/composed-diagonal-bit-bootstrap/audit.py @@ -0,0 +1,169 @@ +#!/usr/bin/env python3 +"""Price the top of the queue with this package's model, exactly. + +`levers.py` turns a certified bit row into the largest `a` on the `10^-18` grid +whose paid moment is below 1, and `kappa = a/(1+a)` is what the balanced assembly +reaches on that word once the finite ordinary leaf is bootstrapped. This script +runs that model over the banked bit rows now in the queue -- #205's packed +diagonal-bit word, #206's entrance-bank word (the same row) and #207's +coordinated-crossover word -- and reports, for each, the model's coarse saving +beside the value the author's own certificate states. + +The rows are vendored byte-identically under `references/queue/`; the model +reproduces every one of them exactly, so a mismatch here would be a real +disagreement rather than a grid artefact. Each row's ceiling is compared with the +`10^-18` floor the same word's ledger leaves (`ln(m/22)` per rank-mass unit if the +residual dirt could be packed at the largest admissible child), which is a bound +on how much a future schedule change can still buy and not a construction. + + python3 -B audit.py [--out audit.json] +""" +import argparse +import importlib.util +import json +import sys +from fractions import Fraction as Q +from pathlib import Path + +HERE = Path(__file__).resolve().parent +GRID = 10 ** 18 + +# Vendored queue certificates and the priced row inside each. +SOURCES = [ + ("PR205 packed diagonal bit", "pr205-packed-diagonal-bit.certificate.json", + ("arithmetic", "packed_profile"), "rohanarun"), + ("PR206 entrance banks on PR200", "pr206-pr200-entrance-banks.certificate.json", + ("bit", "profile"), "EcmaXp"), + ("PR207 coordinated crossover", "pr207-coordinated-crossover.certificate.json", + ("bit_profile",), "Dugongue"), +] + + +def module(name, path): + spec = importlib.util.spec_from_file_location(name, path) + loaded = importlib.util.module_from_spec(spec) + sys.modules[name] = loaded + spec.loader.exec_module(loaded) + return loaded + + +def dig(data, keys): + for key in keys: + data = data[key] + return data + + +def copies_row(profile): + """The family's three-copy row, whichever form the certificate stores.""" + m = int(profile["m"]) + hist_key = "child_multiplicities" if "child_multiplicities" in profile else "child_histogram" + hist = {int(r): int(n) for r, n in profile[hist_key].items() if n} + for key in ("W_per_vertex", "W"): + if key in profile: + W = Q(str(profile[key])) + break + for key in ("deficit_per_vertex", "N", "deficit"): + if key in profile: + D = Q(str(profile[key])) + break + for copies in (1, 3): + w, d = W * copies, D * copies + packed = {r: copies * n for r, n in hist.items()} + mass = sum(r * n for r, n in packed.items()) + if w.denominator == 1 and m * w - mass == d: + return copies, m, int(w), d, packed + raise ValueError("no copy count satisfies the row identity: " + json.dumps(profile)[:200]) + + +def cheapest_ledger(m, W, D, maxchild): + """The least-paying integral ledger of the same rank mass and largest child. + + Per unit of rank mass a child of rank r costs (m/r)^a/(W*m), which falls as r + grows, so filling the mass greedily from the largest admissible rank downwards + minimises the paid moment and therefore maximises the coarse saving over all + admissible ledgers -- an upper bound on the saving, not an arrangement any + schedule has to admit. + """ + mass = m * W - D + hist, remaining = {}, mass + for rank in range(maxchild, 1, -1): + count, remaining = divmod(remaining, rank) + if count: + hist[rank] = int(count) + assert not remaining, "mass must be packable into admissible children" + return hist + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--out", type=Path, default=HERE / "audit.json") + args = parser.parse_args() + if hasattr(sys, "set_int_max_str_digits"): + sys.set_int_max_str_digits(0) + assert not sys.flags.optimize, "assertions must stay enabled" + interval = module("audit_interval_moment", HERE / "references/pr200/interval_moment.py") + levers = module("audit_levers", HERE / "levers.py") + + rows, frontier = [], None + for name, filename, keys, author in SOURCES: + path = HERE / "references/queue" / filename + text = path.read_text() + profile = dig(json.loads(text), keys) + copies, m, W, D, hist = copies_row(profile) + mass = sum(r * n for r, n in hist.items()) + word = levers.row(m, W, D, hist) + coarse = levers.certified(interval, word) + assert levers.paid_moment(interval, word, coarse)["upper"] < 1 < \ + levers.paid_moment(interval, word, coarse + Q(1, GRID))["lower"], name + ceiling = coarse / (1 + coarse) + bound_hist = cheapest_ledger(m, W, D, max(hist)) + bound = levers.certified(interval, levers.row(m, W, D, bound_hist)) + rows.append(dict( + name=name, author=author, file="references/queue/" + filename, + row=".".join(keys), copies=copies, m=m, W=W, deficit=str(D), rank_mass=mass, + edges=sum(hist.values()), maxchild=max(hist), coarse=str(coarse), + coarse_decimal=float(coarse), ceiling=str(ceiling), ceiling_decimal=float(ceiling), + stated_in_certificate=str(coarse) in text, + cheapest_ledger=dict(children=sum(bound_hist.values()), coarse=str(bound), + coarse_decimal=float(bound), + ceiling_decimal=float(bound / (1 + bound))))) + if frontier is None or coarse > Q(frontier["coarse"]): + frontier = rows[-1] + + out = dict( + status="MODELLED, NOT CONSTRUCTED: the queue's rows are priced from their authors' " + "certificates and their own stated coarse savings; nothing is built here, and " + "the packed bound is a bound on admissible ledgers, not a construction.", + method="levers.py's model, PR200's vendored enclosure arithmetic, 10^-18 grid", + rows=rows, + frontier=dict(name=frontier["name"], author=frontier["author"], + coarse=frontier["coarse"], ceiling=frontier["ceiling"], + ceiling_decimal=frontier["ceiling_decimal"], + edges=frontier["edges"], maxchild=frontier["maxchild"], + cheapest_ledger=frontier["cheapest_ledger"]), + cheapest_ledger_gain=float(Q(frontier["cheapest_ledger"]["coarse"]) / Q(frontier["coarse"]) - 1), + ) + args.out.write_text(json.dumps(out, indent=1, sort_keys=True) + "\n") + + for item in rows: + print("[{stated}] {name} ({author}): W={W} D={deficit} mass={rank_mass} edges={edges} " + "maxchild={maxchild}".format( + stated="stated" if item["stated_in_certificate"] else "UNSTATED", **item)) + print(" model coarse = {coarse} = {coarse_decimal:.15g}; ceiling kappa = " + "{ceiling} = {ceiling_decimal:.15g}".format(**item)) + print("[frontier] {name}: coarse {coarse} -> kappa ceiling {ceiling}".format(**frontier)) + bound = frontier["cheapest_ledger"] + print("[bounds] the frontier's ledger has {edges} children down to rank 1; the cheapest " + "admissible ledger of the same stock, deficit and rank mass has {children} from rank " + "{maxchild} downwards and would lift its coarse saving {gain:.4f}%, from {now} to " + "{coarse} (ceiling kappa {ceiling:.15g}). That bounds what a better schedule can still " + "buy and is not a construction.".format( + edges=frontier["edges"], now=frontier["coarse_decimal"], + children=bound["children"], maxchild=frontier["maxchild"], + gain=out["cheapest_ledger_gain"] * 100, coarse=bound["coarse"], + ceiling=bound["ceiling_decimal"])) + print("[write] " + str(args.out)) + + +if __name__ == "__main__": + main() diff --git a/research/composed-diagonal-bit-bootstrap/references/queue/pr205-packed-diagonal-bit.certificate.json b/research/composed-diagonal-bit-bootstrap/references/queue/pr205-packed-diagonal-bit.certificate.json new file mode 100644 index 0000000000..5d81d4d857 --- /dev/null +++ b/research/composed-diagonal-bit-bootstrap/references/queue/pr205-packed-diagonal-bit.certificate.json @@ -0,0 +1,318 @@ +{ + "arithmetic": { + "after_packing": { + "assembly": { + "absorption_gap": 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"109385155514905442426418537664349652181461624755757237/160000000000000000000000000000000000000000000000000000000", + "21877040740002110769946254600167413306868853489797819501857050278676903/32000000000000000000000000000000000000000000000000000000000000000000000000", + "4375408149318106538866216854671930632866706725794304565219529058788314814256861959639757/6400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000" + ], + "scope": "Conditional finite supplier certificate; retained all-size interfaces and analytic assumptions", + "status": "PASS_EXACT_47_CONSTRAINT_ASSEMBLY" +} diff --git a/research/composed-diagonal-bit-bootstrap/verify.py b/research/composed-diagonal-bit-bootstrap/verify.py index 5783fccdcb..d159085be4 100644 --- a/research/composed-diagonal-bit-bootstrap/verify.py +++ b/research/composed-diagonal-bit-bootstrap/verify.py @@ -204,6 +204,31 @@ def accept_only_a_better_composition(): levers["gain_vs_claim"] * 100, float(Q(levers["pr200_unpacked"]["ceiling"])), float(Q(banked["ceiling"])))) + # 11. The queue audit: the model must price the banked rows now in the queue to exactly + # the coarse savings their own certificates state, and the frontier must be the + # banked row this package's lever predicted. + audit_out = WORK / "audit.json" + if audit_out.exists(): + audit_out.unlink() + subprocess.run([sys.executable, "-B", str(HERE / "audit.py"), "--out", str(audit_out)], + check=True, stdout=subprocess.DEVNULL) + audit = json.loads(audit_out.read_text()) + assert audit == json.loads((HERE / "audit.json").read_text()), "audit.json drift" + for item in audit["rows"]: + assert item["stated_in_certificate"], ( + "the model must reproduce " + item["name"] + " to the last digit") + queue_best = max(audit["rows"], key=lambda item: Q(item["coarse"])) + assert queue_best["name"] == audit["frontier"]["name"], "frontier row" + assert Q(audit["frontier"]["ceiling"]) > best, "the banked rows must now stand above this claim" + assert audit["cheapest_ledger_gain"] > Q(1, 2), "the ledger must be where the room is" + assert audit["status"].startswith("MODELLED"), "the audit must not present a construction" + print("[audit] {} banked rows priced to their own certificates exactly; the frontier is " + "{} at {:.15g}, and its cheapest admissible ledger would reach {:.10g} ({:+.1f}%), " + "a bound rather than a construction".format( + len(audit["rows"]), audit["frontier"]["name"], + float(Q(audit["frontier"]["ceiling"])), + float(Q(audit["frontier"]["cheapest_ledger"]["coarse"])), + audit["cheapest_ledger_gain"] * 100)) print("PASS composed-diagonal-bit-bootstrap kappa = {} at depth {}; 47 strict constraints " "and 7 margins per depth".format(best, best_depth)) From 624d95a442ebdc7a6cd7315def08a81070848c6c Mon Sep 17 00:00:00 2001 From: maxime-fleury Date: Fri, 9 Oct 2026 18:18:18 +0200 Subject: [PATCH 7/9] Pin the queue snapshot to the bytes the checkout produces PR207's certificate is stored with CRLF upstream, so the committed blob is the LF-normalised copy while the working tree kept the Windows line endings; the pin now records the digest a clean Linux checkout produces. --- research/composed-diagonal-bit-bootstrap/SOURCE.json | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/research/composed-diagonal-bit-bootstrap/SOURCE.json b/research/composed-diagonal-bit-bootstrap/SOURCE.json index b4fe85a337..fb957bc965 100644 --- a/research/composed-diagonal-bit-bootstrap/SOURCE.json +++ b/research/composed-diagonal-bit-bootstrap/SOURCE.json @@ -29,7 +29,7 @@ "research/composed-diagonal-bit-bootstrap/audit.json": "74ac7b35c04b081794e52e325420c8d2cdf58c3fe8b646e42de1b68e77987a06", "research/composed-diagonal-bit-bootstrap/references/queue/pr205-packed-diagonal-bit.certificate.json": "c11fbb9aaa99594afc8d21e33761dc6d1d6c76ce3dbc36d5b64cae872c242f5a", "research/composed-diagonal-bit-bootstrap/references/queue/pr206-pr200-entrance-banks.certificate.json": "709b6620676e0fd1dfab98b9886443c2d2d9c8f03b0061efa390aadeff0ff718", - "research/composed-diagonal-bit-bootstrap/references/queue/pr207-coordinated-crossover.certificate.json": "23416f66749bf92dc7b47c69d5a94125effc26a043dd9ffbe83479e4d42e5e3a", + "research/composed-diagonal-bit-bootstrap/references/queue/pr207-coordinated-crossover.certificate.json": "f4e30cca369fb014b729df870ca3716cc0f1e2297b9f265341492cba85a14aeb", "research/composed-diagonal-bit-bootstrap/levers.py": "80fcccfa7b89e790d9be27d750ee5140d7eadc81d632e70ab4d7d256487b3e7d", "research/composed-diagonal-bit-bootstrap/levers.json": "646f1b8f7a0826b7afd05553d7bc917e5e1a8bc078ec44725ba0760c3029b83b", "research/composed-diagonal-bit-bootstrap/references/pr187/certificate.json": "0cfcb896c86c2e1de759f0518176ba6c606036b9f515eac045d3962cc4a00073", From bf9b943a480c632a3951d2fe1e42b77182cdb45c Mon Sep 17 00:00:00 2001 From: maxime-fleury Date: Fri, 9 Oct 2026 18:31:04 +0200 Subject: [PATCH 8/9] Price the ladder of ledger moves that can still raise kappa The assembly takes the smaller branch budget, so the complex word caps the frontier at +2.52% and the bit word's 377,316 rank-1 children -- dirt the banks refuse -- are enough to reach it. Soaking both rows' small children buys +16% to +76% on the 10^-10 grid; every rung is a target, not a construction, and the calculator is checked against PR184's own assemble() and against PR205's and PR207's published kappa. --- .../composed-diagonal-bit-bootstrap/README.md | 52 +++- .../SOURCE.json | 6 +- .../targets.json | 162 ++++++++++++ .../targets.py | 238 ++++++++++++++++++ .../composed-diagonal-bit-bootstrap/verify.py | 29 +++ 5 files changed, 484 insertions(+), 3 deletions(-) create mode 100644 research/composed-diagonal-bit-bootstrap/targets.json create mode 100644 research/composed-diagonal-bit-bootstrap/targets.py diff --git a/research/composed-diagonal-bit-bootstrap/README.md b/research/composed-diagonal-bit-bootstrap/README.md index 71146a8fd8..635f8736c7 100644 --- a/research/composed-diagonal-bit-bootstrap/README.md +++ b/research/composed-diagonal-bit-bootstrap/README.md @@ -150,6 +150,50 @@ construction** -- but it is the whole of the remaining room, and it says the nex is a frame or bank schedule whose residual dirt is packed in fewer, larger children, not more packing of the same shapes. +## New ways to raise kappa, priced with the assembly's own formula + +PR184's unchanged assembly takes `a = min(bit leaf, (1-1e-9)*C_complex - 1e-10)` and +returns `kappa = a/(1+a)` on the `10^-10` grid, so **the smaller branch is the whole +constraint** and a gain on the stronger side is worth nothing until the other side +catches up. Today the bit branch binds at `6.831904e-4`, while the complex side caps +at `7.004273e-4`: **+2.52% is available with no complex-side work at all**, as soon as +the bit word's coarse saving reaches `7.009184e-4` instead of `6.836575e-4`. + +`targets.py` prices the ladder of moves that can get there. For a fixed stock and +deficit the coarse saving is `C = (1 - mass/(W m)) / L` with `L` the rank-mass-weighted +mean of `ln(m/r)`, so the lever is `L`: a ledger whose residual dirt sits in fewer, +larger children. Soaking every child of rank at or below a threshold into the largest +admissible child gives, on the queue's own two rows: + +| soak | bit coarse saving | complex coarse saving | kappa | gain | binds | +| --- | --- | --- | --- | --- | --- | +| today | 136731504666219/2e17 | 350459221139329/5e17 | 6.831904e-4 | — | bit | +| bit only, rank-1 | 792978386838687/10^18 | — | 7.004273e-4 | +2.52% | complex | +| both, rank-1 | 792978386838687/10^18 | 814442339516203/10^18 | 7.923515e-4 | +15.98% | bit | +| both, rank-2 | 898167154125293/10^18 | 918515942111545/10^18 | 8.973611e-4 | +31.35% | bit | +| both, rank-3 | 981391149202381/10^18 | 1041436537175764/10^18 | 9.804289e-4 | +43.51% | bit | +| both, rank-4 | 1015042828910707/10^18 | 1112905588874264/10^18 | 1.014014e-3 | +48.42% | bit | +| both, rank-8 | 1096975618911405/10^18 | 1243672552482743/10^18 | 1.095774e-3 | +60.39% | bit | +| both, rank-16 | 1178908992537918/10^18 | 1367642974340202/10^18 | 1.177521e-3 | +72.36% | bit | +| cheapest ledgers | 1207154248293627/10^18 | 1391081382485139/10^18 | 1.205699e-3 | +76.48% | — | + +The first rung is the cheapest and it is a single identifiable population: the bit +word's 377,316 rank-1 children, 9.3% of its rank mass, are dirt the banks currently +refuse -- #207's own note lists alias recipients, source births, deleted terminals and +spectator fields as excluded from fresh bank allocation. Letting the banks absorb +those, so that the ledger entry is a completed child rather than a singleton, takes the +bit coarse saving from `6.836575e-4` to `7.929784e-4` (+16%) and clears the complex cap +in one step. The complex word's own 87,534 rank-1 children (11% of its mass) do the +same for its side, `7.009184e-4` to `8.144423e-4` (+16.2%), which is what the second +rung needs. + +**All of this is MODELLED, NOT CONSTRUCTED.** No ledger is built here: each rung is a +shape the assembly would price this way, computed from the queue's certified rows. The +calculator is checked two ways -- it equals PR184's own `assemble()` on the vendored +pair, and it reproduces #205's and #207's published kappa to within one grid step -- +so a rung is a usable target rather than a guess, in the same way the lever model's +banked row was. + ## Cross-checks against published numbers The harness is independent of the numbers it is asked to confirm, and this package @@ -210,7 +254,13 @@ prints the lever table on its own, and python3 -B research/composed-diagonal-bit-bootstrap/audit.py ``` -prints the queue audit against the banked rows the lever predicted. +prints the queue audit against the banked rows the lever predicted, and + +```bash +python3 -B research/composed-diagonal-bit-bootstrap/targets.py +``` + +prints the ladder of what each next ledger move on the two suppliers would be worth. ## Credits diff --git a/research/composed-diagonal-bit-bootstrap/SOURCE.json b/research/composed-diagonal-bit-bootstrap/SOURCE.json index fb957bc965..e1ccb27434 100644 --- a/research/composed-diagonal-bit-bootstrap/SOURCE.json +++ b/research/composed-diagonal-bit-bootstrap/SOURCE.json @@ -24,7 +24,9 @@ }, "files": { "research/composed-diagonal-bit-bootstrap/compose.py": "5122db672a30e3119e5004a873354d608dfe34f0c8b15731c683e624c0f71c76", - "research/composed-diagonal-bit-bootstrap/verify.py": "c4f75cc170b030f954706a8ffac01804b0866178029a792311fc7142c6ff56f7", + "research/composed-diagonal-bit-bootstrap/verify.py": "5f098bddcdcd7bff435ad121cb0c0b2b6397f61a0150db1c544b894509a78d9a", + "research/composed-diagonal-bit-bootstrap/targets.py": "4209112d8eb1cc615c09e053b4bcdda30a70be27ccd373ad6cecf271eb19c786", + "research/composed-diagonal-bit-bootstrap/targets.json": "031b623f9969ed451189de6b7ee42aad5f1f4ef261475231367daab1544a3f07", "research/composed-diagonal-bit-bootstrap/audit.py": "fde70ca18e2637acbcb995db490234b17c5f79d53c33f615c238b9ac48e09490", "research/composed-diagonal-bit-bootstrap/audit.json": "74ac7b35c04b081794e52e325420c8d2cdf58c3fe8b646e42de1b68e77987a06", "research/composed-diagonal-bit-bootstrap/references/queue/pr205-packed-diagonal-bit.certificate.json": "c11fbb9aaa99594afc8d21e33761dc6d1d6c76ce3dbc36d5b64cae872c242f5a", @@ -35,7 +37,7 @@ "research/composed-diagonal-bit-bootstrap/references/pr187/certificate.json": "0cfcb896c86c2e1de759f0518176ba6c606036b9f515eac045d3962cc4a00073", "research/composed-diagonal-bit-bootstrap/references/pr200/interval_moment.py": "9d3d1d28bfb3375958995205179b171fb65c70a3792cf9f7a21ef5ee54f5460b", "research/composed-diagonal-bit-bootstrap/certificate.json": "0a844fb88811af915ae5198aab07b79f61c29cc9c68b1752733d30a4c189cfc4", - "research/composed-diagonal-bit-bootstrap/README.md": "e542449f159dad00e1d1ea2defe7b915824f670522be11dd13b7806a897bdf59", + "research/composed-diagonal-bit-bootstrap/README.md": "b5a5b1dd68eb73e17a2ce9601b40b3451d50c9b363e29097540c2463a504a2ef", "research/composed-diagonal-bit-bootstrap/NOTICE.md": "0069cf9254824f11d144579445e83220a7953a79c5bad6798da2280f75207104", "research/composed-diagonal-bit-bootstrap/references/pr168-v4/scripts/paired_cube_assembly.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c", "research/composed-diagonal-bit-bootstrap/references/pr184/assemble_profiles.py": "c56d0638d4bc1ac3f70c78778ea824f3a2ba23c31f7eeff3c93cf17df3f2e0de", diff --git a/research/composed-diagonal-bit-bootstrap/targets.json b/research/composed-diagonal-bit-bootstrap/targets.json new file mode 100644 index 0000000000..b0f4dfa3a2 --- /dev/null +++ b/research/composed-diagonal-bit-bootstrap/targets.json @@ -0,0 +1,162 @@ +{ + "assembly_replica_check": "1693287/2500000000", + "bit_ladder": { + "1": { + "binding": "complex", + "gain": "1777/70432", + "kappa": "7004273/10000000000" + }, + "12": { + "binding": "complex", + "gain": "1777/70432", + "kappa": "7004273/10000000000" + }, + "16": { + "binding": "complex", + "gain": "1777/70432", + "kappa": "7004273/10000000000" + }, + "2": { + "binding": "complex", + "gain": "1777/70432", + "kappa": "7004273/10000000000" + }, + "3": { + "binding": "complex", + "gain": "1777/70432", + "kappa": "7004273/10000000000" + }, + "4": { + "binding": "complex", + "gain": "1777/70432", + "kappa": "7004273/10000000000" + }, + "6": { + "binding": "complex", + "gain": "1777/70432", + "kappa": "7004273/10000000000" + }, + "8": { + "binding": "complex", + "gain": "1777/70432", + "kappa": "7004273/10000000000" + } + }, + "both_soaked": { + "1": { + "binding": "bit", + "gain": "272899/1707976", + "kappa": "15847/20000000" + }, + "12": { + "binding": "bit", + "gain": "4563611/6831904", + "kappa": "2279103/2000000000" + }, + "16": { + "binding": "bit", + "gain": "4943303/6831904", + "kappa": "11775207/10000000000" + }, + "2": { + "binding": "bit", + "gain": "2141707/6831904", + "kappa": "8973611/10000000000" + }, + "3": { + "binding": "bit", + "gain": "2972385/6831904", + "kappa": "9804289/10000000000" + }, + "4": { + "binding": "bit", + "gain": "3308231/6831904", + "kappa": "2028027/2000000000" + }, + "6": { + "binding": "bit", + "gain": "1908885/3415952", + "kappa": "5324837/5000000000" + }, + "8": { + "binding": "bit", + "gain": "4125831/6831904", + "kappa": "2191547/2000000000" + } + }, + "cheapest_ledger_both": { + "gain": "5225083/6831904", + "kappa": "12056987/10000000000" + }, + "complex_side_cap": { + "bit_coarse_needed": "350459170788869778860671/500000000000000000000000000", + "gain": "1777/70432", + "kappa": "7004273/10000000000", + "kappa_decimal": 0.0007004273 + }, + "frontier": { + "binding": "bit", + "bit_budget": "136731504666219/200000000000000000", + "complex_budget": "350459170788869778860671/500000000000000000000000000", + "kappa": "213497/312500000", + "kappa_decimal": 0.0006831904 + }, + "method": "PR184's unchanged assembly formula on this package's exact coarse savings", + "published_checks": { + "PR205 packed diagonal bit": { + "claimed": "683061299399923/1000000000000000000", + "coarse": "683528191056257/1000000000000000000", + "modelled": "1707653/2500000000", + "within_one_grid_step": true + }, + "PR207 coordinated crossover": { + "claimed": "1366380910073/2000000000000000", + "coarse": "136731504666219/200000000000000000", + "modelled": "213497/312500000", + "within_one_grid_step": true + } + }, + "status": "MODELLED, NOT CONSTRUCTED: these are schedules the assembly would price this way, computed from the queue's certified rows; no ledger or word is built here.", + "suppliers": { + "bit": { + "W": 56402, + "cheapest_ledger": "1207154248293627/1000000000000000000", + "coarse": "136731504666219/200000000000000000", + "deficit": "5808", + "edges": 879231, + "ladder": { + "1": "792978386838687/1000000000000000000", + "12": "5704258000893/5000000000000000", + "16": "589454496268959/500000000000000000", + "2": "898167154125293/1000000000000000000", + "3": "981391149202381/1000000000000000000", + "4": "1015042828910707/1000000000000000000", + "6": "1066102863416711/1000000000000000000", + "8": "219395123782281/200000000000000000" + }, + "m": 72, + "maxchild": 22, + "rank_mass": 4055136 + }, + "complex": { + "W": 12052, + "cheapest_ledger": "1391081382485139/1000000000000000000", + "coarse": "350459221139329/500000000000000000", + "deficit": "1320", + "edges": 213147, + "ladder": { + "1": "814442339516203/1000000000000000000", + "12": "1315101403353627/1000000000000000000", + "16": "683821487170101/500000000000000000", + "2": "183703188422309/200000000000000000", + "3": "260359134293941/250000000000000000", + "4": "139113198609283/125000000000000000", + "6": "1188483794904097/1000000000000000000", + "8": "1243672552482743/1000000000000000000" + }, + "m": 66, + "maxchild": 20, + "rank_mass": 794112 + } + } +} diff --git a/research/composed-diagonal-bit-bootstrap/targets.py b/research/composed-diagonal-bit-bootstrap/targets.py new file mode 100644 index 0000000000..5215ac2b02 --- /dev/null +++ b/research/composed-diagonal-bit-bootstrap/targets.py @@ -0,0 +1,238 @@ +#!/usr/bin/env python3 +"""What the next gains are worth, priced exactly. + +PR184's unchanged assembly takes + + a = min(bit_leaf, (1-1e-9)*C_complex - 1e-10), kappa = a/(1+a) + +to the `10^-10` grid, where `bit_leaf` is the finite ordinary leaf after PR185's +bootstrap (the fixed point of `a_{n+1} = (1-C_bit)C_bit + C_bit a_n`, so `C_bit` +itself once bootstrapped) and `C_complex` is the complex word's coarse saving. Two +consequences drive everything below: + +* the **binding branch is the smaller budget**, so a gain on the stronger side is + worth nothing until the other side catches up, and the complex budget carries a + fixed `10^-10` grid step plus `1e-9` that the bit budget does not; +* a budget is raised only by raising a word's **coarse saving** `C`, and + + C = (1 - mass/(W m)) / L, L = rank-mass-weighted mean of ln(m/r), + + so at fixed stock and deficit the lever is `L`: a ledger whose residual dirt sits + in fewer, larger children. This script prices the ladder of such ledgers -- + soaking children of rank at or below a threshold into the largest admissible + child -- for both suppliers, and reports the exact `kappa` each rung buys, with + the branch that binds at every rung. + + python3 -B targets.py [--out targets.json] +""" +import argparse +import importlib.util +import json +import sys +from fractions import Fraction as Q +from pathlib import Path + +HERE = Path(__file__).resolve().parent +STOP, ETA, SELECT_GRID = Q(1, 10 ** 9), Q(1, 10 ** 8), 10 ** 10 +THRESHOLDS = (1, 2, 3, 4, 6, 8, 12, 16) + + +def module(name, path): + spec = importlib.util.spec_from_file_location(name, path) + loaded = importlib.util.module_from_spec(spec) + sys.modules[name] = loaded + spec.loader.exec_module(loaded) + return loaded + + +def assembly_kappa(budget): + """PR184's `assemble`, exactly: the minimum budget to the 10^-10 grid.""" + assert 0 < budget < 1, "budget must be a saving" + q = budget * (1 - 2 * ETA) + minimum = (1 - ETA) * q / (1 + q) + kappa = Q(minimum.numerator * SELECT_GRID // minimum.denominator, SELECT_GRID) + if kappa == minimum: + kappa -= Q(1, SELECT_GRID) + return kappa + + +def branch_budgets(bit_coarse, complex_coarse): + bit = bit_coarse # bootstrapped leaf, the fixed point + complex_ = (1 - STOP) * complex_coarse - Q(1, SELECT_GRID) + return bit, complex_, ("bit" if bit <= complex_ else "complex") + + +def rows(profile): + """The family's three-copy row, whichever form the certificate stores.""" + m = int(profile["m"]) + key = "child_multiplicities" if "child_multiplicities" in profile else "child_histogram" + hist = {int(r): int(n) for r, n in profile[key].items() if n} + W = Q(str(profile.get("W_per_vertex", profile.get("W")))) + D = Q(str(profile.get("deficit_per_vertex", + profile.get("N", profile.get("deficit"))))) + for copies in (1, 3): + w, d = W * copies, D * copies + packed = {r: copies * n for r, n in hist.items()} + if w.denominator == 1 and m * w - sum(r * n for r, n in packed.items()) == d: + return m, int(w), d, packed + raise ValueError("no copy count satisfies the row identity") + + +def soak(m, W, D, hist, threshold): + """Move all mass in children of rank <= threshold into the largest child. + + The rank mass, the stock and the deficit are unchanged: only the shape of the + ledger differs, which is what a better schedule would have to deliver. + """ + if threshold >= max(hist): + return None + kept = {r: n for r, n in hist.items() if r > threshold} + mass = m * W - D + remaining = mass - sum(r * n for r, n in kept.items()) + top = max(hist) + for rank in range(top, 1, -1): + count, remaining = divmod(remaining, rank) + if count: + kept[rank] = kept.get(rank, 0) + int(count) + assert not remaining and sum(r * n for r, n in kept.items()) == mass + return kept + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--out", type=Path, default=HERE / "targets.json") + args = parser.parse_args() + if hasattr(sys, "set_int_max_str_digits"): + sys.set_int_max_str_digits(0) + assert not sys.flags.optimize, "assertions must stay enabled" + interval = module("targets_interval_moment", HERE / "references/pr200/interval_moment.py") + levers = module("targets_levers", HERE / "levers.py") + pr184 = module("targets_pr184", HERE / "references/pr184/assemble_profiles.py") + + queue = HERE / "references/queue/pr207-coordinated-crossover.certificate.json" + newest = json.loads(queue.read_text()) + suppliers = {} + for side, key in (("bit", "bit_profile"), ("complex", "complex_profile")): + m, W, D, hist = rows(newest[key]) + ladder = {} + for threshold in THRESHOLDS: + candidate = soak(m, W, D, hist, threshold) + if candidate: + ladder[str(threshold)] = levers.certified( + interval, levers.row(m, W, D, candidate)) + cheapest = soak(m, W, D, hist, max(hist) - 1) + suppliers[side] = dict( + m=m, W=W, deficit=str(D), rank_mass=int(m * W - D), edges=sum(hist.values()), + maxchild=max(hist), coarse=levers.certified(interval, levers.row(m, W, D, hist)), + ladder=ladder, + cheapest_ledger=levers.certified(interval, levers.row(m, W, D, cheapest))) + # Soaking more mass into larger children can only raise the coarse saving. + rungs = [Q(suppliers[side]["coarse"])] + [Q(ladder[k]) for k in ladder] + assert all(left <= right for left, right in zip(rungs, rungs[1:])), side + assert Q(suppliers[side]["cheapest_ledger"]) >= rungs[-1], side + + # Validate the replica against PR184's own assembly on the vendored pair. + complex_cert = json.loads((HERE / "references/pr194/certificate.json").read_text()) + bit_cert = json.loads((HERE / "inputs/pr200-bit-certificate.json").read_text()) + complex_row = pr184.select(pr184.normalize(complex_cert["complex_profile"])) + bit_row = pr184.select(pr184.normalize(bit_cert["bit"]["profile"]), True) + bit_leaf = Q(bit_row["saving"]) # the bootstrap's fixed point + complex_coarse = Q(complex_row["saving"]) + boot = dict(bit_row) + boot["effective_saving"] = bit_leaf + real = Q(pr184.assemble(complex_row, boot, HERE / "references/pr168-v4", + HERE / "references/pr184/FINITE_BRIDGE.txt")["kappa"]) + assert real == assembly_kappa(min(*branch_budgets(bit_leaf, complex_coarse)[:2])), \ + "the replica must equal PR184's own assembly" + + # The queue's claims, each against its own row: an independent check that the + # formula reproduces what three authors certified on two different words. + packed205 = json.loads((HERE / "references/queue/pr205-packed-diagonal-bit.certificate.json").read_text()) + published = [("PR205 packed diagonal bit", packed205["arithmetic"]["packed_profile"], + Q(683061299399923, 10 ** 18)), + ("PR207 coordinated crossover", newest["bit_profile"], + Q(1366380910073, 2 * 10 ** 15))] + checks = {} + for name, profile, claimed in published: + m, W, D, hist = rows(profile) + coarse = levers.certified(interval, levers.row(m, W, D, hist)) + modelled = assembly_kappa( + branch_budgets(coarse, Q(suppliers["complex"]["coarse"]))[0]) + checks[name] = dict(claimed=str(claimed), modelled=str(modelled), + coarse=str(coarse), + within_one_grid_step=abs(modelled - claimed) <= Q(1, SELECT_GRID)) + + bit_coarse = Q(suppliers["bit"]["coarse"]) + complex_coarse = Q(suppliers["complex"]["coarse"]) + bit_budget, complex_budget, binding = branch_budgets(bit_coarse, complex_coarse) + now = assembly_kappa(min(bit_budget, complex_budget)) + complex_only = assembly_kappa(complex_budget) + # The bit coarse saving this word needs to stop binding. + needed = complex_budget + bit_soaked = {k: assembly_kappa(min(Q(v), complex_budget)) + for k, v in suppliers["bit"]["ladder"].items()} + both = {} + for threshold, bit_value in suppliers["bit"]["ladder"].items(): + complex_value = suppliers["complex"]["ladder"].get(threshold) + if complex_value: + pair_budget = min(Q(bit_value), (1 - STOP) * Q(complex_value) - Q(1, SELECT_GRID)) + both[threshold] = dict(kappa=str(assembly_kappa(pair_budget)), + binding=branch_budgets(Q(bit_value), Q(complex_value))[2], + gain=str(assembly_kappa(pair_budget) / now - 1)) + out = dict( + status="MODELLED, NOT CONSTRUCTED: these are schedules the assembly would price " + "this way, computed from the queue's certified rows; no ledger or word is " + "built here.", + method="PR184's unchanged assembly formula on this package's exact coarse savings", + assembly_replica_check=str(real), + published_checks=checks, + suppliers={k: dict(v, coarse=str(v["coarse"]), + ladder={t: str(c) for t, c in v["ladder"].items()}, + cheapest_ledger=str(v["cheapest_ledger"])) + for k, v in suppliers.items()}, + frontier=dict(binding=binding, kappa=str(now), kappa_decimal=float(now), + bit_budget=str(bit_budget), complex_budget=str(complex_budget)), + complex_side_cap=dict(kappa=str(complex_only), kappa_decimal=float(complex_only), + gain=str(complex_only / now - 1), + bit_coarse_needed=str(needed)), + bit_ladder={ + t: dict(kappa=str(k), gain=str(k / now - 1), + binding=branch_budgets(Q(v), complex_coarse)[2]) + for (t, v), k in zip(suppliers["bit"]["ladder"].items(), bit_soaked.values())}, + both_soaked=both, + cheapest_ledger_both=dict( + kappa=str(assembly_kappa(min(Q(suppliers["bit"]["cheapest_ledger"]), + (1 - STOP) * Q(suppliers["complex"]["cheapest_ledger"]) + - Q(1, SELECT_GRID)))), + gain=str(assembly_kappa(min(Q(suppliers["bit"]["cheapest_ledger"]), + (1 - STOP) * Q(suppliers["complex"]["cheapest_ledger"]) + - Q(1, SELECT_GRID))) / now - 1)), + ) + args.out.write_text(json.dumps(out, indent=1, sort_keys=True) + "\n") + + for side in ("bit", "complex"): + item = suppliers[side] + print("[{side}] m={m} W={W} deficit={deficit} rank mass={rank_mass} children={edges} " + "maxchild={maxchild}".format(side=side, **item)) + print(" coarse today = {coarse}".format(**item)) + for threshold, value in item["ladder"].items(): + print(" soak children <= {t:>2}: coarse = {v}".format(t=threshold, v=value)) + print(" cheapest ledger: coarse = " + str(item["cheapest_ledger"])) + print("[frontier] {binding} binds: kappa = {k}".format(k=now, **out["frontier"])) + print("[complex cap] kappa = {k} ({g:+.2%}), reached when the bit coarse saving is " + "{n}".format(k=complex_only, g=float(complex_only / now - 1), n=needed)) + for threshold, item in out["bit_ladder"].items(): + print("[bit soak {t:>2}] kappa = {k} ({g:+.2%}, binding {b})".format( + t=threshold, k=item["kappa"], g=float(Q(item["gain"])), b=item["binding"])) + print("[cheapest both] kappa = {k} ({g:+.2%})".format( + k=out["cheapest_ledger_both"]["kappa"], + g=float(Q(out["cheapest_ledger_both"]["gain"])))) + print("[published] " + "; ".join( + "{k}: modelled {v[modelled]} vs claimed {v[claimed]} ({ok})".format( + k=k, ok="within a grid step" if v["within_one_grid_step"] else "MISMATCH", + **{"v": v}) for k, v in checks.items())) + print("[write] " + str(args.out)) + + +if __name__ == "__main__": + main() diff --git a/research/composed-diagonal-bit-bootstrap/verify.py b/research/composed-diagonal-bit-bootstrap/verify.py index d159085be4..522a3b863a 100644 --- a/research/composed-diagonal-bit-bootstrap/verify.py +++ b/research/composed-diagonal-bit-bootstrap/verify.py @@ -229,6 +229,35 @@ def accept_only_a_better_composition(): float(Q(audit["frontier"]["ceiling"])), float(Q(audit["frontier"]["cheapest_ledger"]["coarse"])), audit["cheapest_ledger_gain"] * 100)) + # 12. The frontier calculator: what each next move on the two suppliers would be + # worth, from the queue's own rows. It must reproduce the published kappa of two + # different authors' banked rows, keep its ladder monotone, and stay a model. + targets_out = WORK / "targets.json" + if targets_out.exists(): + targets_out.unlink() + subprocess.run([sys.executable, "-B", str(HERE / "targets.py"), "--out", str(targets_out)], + check=True, stdout=subprocess.DEVNULL) + targets = json.loads(targets_out.read_text()) + assert targets == json.loads((HERE / "targets.json").read_text()), "targets.json drift" + for name, item in targets["published_checks"].items(): + assert item["within_one_grid_step"], ( + "the assembly replica must reproduce " + name + " to within a grid step") + assert targets["status"].startswith("MODELLED"), "the targets must not present a construction" + assert Q(targets["complex_side_cap"]["gain"]) > 0, "the complex side must cap the frontier" + ladder = [Q(targets["both_soaked"][key]["gain"]) + for key in sorted(targets["both_soaked"], key=int)] + assert all(left < right for left, right in zip(ladder, ladder[1:])), \ + "soaking more rank mass into larger children must buy more" + assert Q(targets["cheapest_ledger_both"]["gain"]) > Q(1, 2), "the ledger must be the room" + print("[targets] the frontier is {} at {}; taking the bit word's rank-1 children into " + "larger ones reaches the complex side's {:.10g} ({:+.2%}), and soaking both words' " + "cheap children buys {:+.2%}, rising to {:+.2%} at the cheapest admissible " + "ledgers".format( + targets["frontier"]["binding"], Q(targets["frontier"]["kappa"]), + targets["complex_side_cap"]["kappa_decimal"], + float(Q(targets["complex_side_cap"]["gain"])), + float(Q(targets["both_soaked"]["1"]["gain"])), + float(Q(targets["cheapest_ledger_both"]["gain"])))) print("PASS composed-diagonal-bit-bootstrap kappa = {} at depth {}; 47 strict constraints " "and 7 margins per depth".format(best, best_depth)) From 525ed356ec4928f4c31c7668ecb547f575278f4e Mon Sep 17 00:00:00 2001 From: maxime-fleury Date: Fri, 9 Oct 2026 18:38:10 +0200 Subject: [PATCH 9/9] Name the smallest ledger move that still raises kappa Bisecting the bit word's smallest-child population shows 57/1000 of its mass is enough to clear the complex side, so the whole +2.52% first rung is a 5.7% coarsening of one population rather than a new construction. #207's bank proof settles the packing side itself, so the README now points the next move at the word's child inventory, which is where the ledger term actually lives. --- .../composed-diagonal-bit-bootstrap/README.md | 27 ++++++++----- .../SOURCE.json | 8 ++-- .../targets.json | 5 +++ .../targets.py | 38 +++++++++++++++++++ .../composed-diagonal-bit-bootstrap/verify.py | 8 ++++ 5 files changed, 73 insertions(+), 13 deletions(-) diff --git a/research/composed-diagonal-bit-bootstrap/README.md b/research/composed-diagonal-bit-bootstrap/README.md index 635f8736c7..b35fb3f0c9 100644 --- a/research/composed-diagonal-bit-bootstrap/README.md +++ b/research/composed-diagonal-bit-bootstrap/README.md @@ -177,15 +177,24 @@ admissible child gives, on the queue's own two rows: | both, rank-16 | 1178908992537918/10^18 | 1367642974340202/10^18 | 1.177521e-3 | +72.36% | bit | | cheapest ledgers | 1207154248293627/10^18 | 1391081382485139/10^18 | 1.205699e-3 | +76.48% | — | -The first rung is the cheapest and it is a single identifiable population: the bit -word's 377,316 rank-1 children, 9.3% of its rank mass, are dirt the banks currently -refuse -- #207's own note lists alias recipients, source births, deleted terminals and -spectator fields as excluded from fresh bank allocation. Letting the banks absorb -those, so that the ledger entry is a completed child rather than a singleton, takes the -bit coarse saving from `6.836575e-4` to `7.929784e-4` (+16%) and clears the complex cap -in one step. The complex word's own 87,534 rank-1 children (11% of its mass) do the -same for its side, `7.009184e-4` to `8.144423e-4` (+16.2%), which is what the second -rung needs. +The cheapest step is smaller than the table suggests. The bit word needs a coarse +saving of `7.009184e-4` to stop binding, and the cheapest 5.7% of its smallest +children already delivers it: `targets.py` bisects that population and reports that +**moving 57/1000 of the mass sitting in the bit word's rank-1 children into +rank-22 children takes the bit coarse saving to `7.009717e-4`**, past the complex +word, for `kappa = 7.004273e-4` (+2.52%). The whole rank-1 population (377,316 +children, 9.3% of the rank mass) is worth +16% on its own, and the complex word's +own 87,534 rank-1 children (11% of its mass) do the same for its side, +`7.009184e-4` to `8.144423e-4` (+16.2%). + +**What has to change is the child inventory, not the packing.** #207's bank proof +settles the packing side itself: its banks tile width 72 exactly with the word's two +residual families (`6 x rank-4 + 2 x rank-24`, or `3 x rank-24`), and it states that +the current word "has exactly the 4/24 residual families and both tile 72 exactly ... +there is no new LP improvement to add". The children the moment actually charges are +the word's own retained children -- internal, source, target, center, compensating +and terminal-substitution children -- and it is their inventory, set by the weighted +compilation and by the frame schedule, that holds the `L` above `ln(m/22)`. **All of this is MODELLED, NOT CONSTRUCTED.** No ledger is built here: each rung is a shape the assembly would price this way, computed from the queue's certified rows. The diff --git a/research/composed-diagonal-bit-bootstrap/SOURCE.json b/research/composed-diagonal-bit-bootstrap/SOURCE.json index e1ccb27434..e013ae3416 100644 --- a/research/composed-diagonal-bit-bootstrap/SOURCE.json +++ b/research/composed-diagonal-bit-bootstrap/SOURCE.json @@ -24,9 +24,9 @@ }, "files": { "research/composed-diagonal-bit-bootstrap/compose.py": "5122db672a30e3119e5004a873354d608dfe34f0c8b15731c683e624c0f71c76", - "research/composed-diagonal-bit-bootstrap/verify.py": "5f098bddcdcd7bff435ad121cb0c0b2b6397f61a0150db1c544b894509a78d9a", - "research/composed-diagonal-bit-bootstrap/targets.py": "4209112d8eb1cc615c09e053b4bcdda30a70be27ccd373ad6cecf271eb19c786", - "research/composed-diagonal-bit-bootstrap/targets.json": "031b623f9969ed451189de6b7ee42aad5f1f4ef261475231367daab1544a3f07", + "research/composed-diagonal-bit-bootstrap/verify.py": "c6e3bd70a69378e1504d59d23507a8fe0642f52bf2d7158f3bdae20318f39a1e", + "research/composed-diagonal-bit-bootstrap/targets.py": "9a1ff251249d81b5b28128cbfaf9f14455ebbba48e8a1d8a74af4c93773fba54", + "research/composed-diagonal-bit-bootstrap/targets.json": "75677790fac04f3d450916cec989572d8eee2f75edbd674b26f5c491d485ede7", "research/composed-diagonal-bit-bootstrap/audit.py": "fde70ca18e2637acbcb995db490234b17c5f79d53c33f615c238b9ac48e09490", "research/composed-diagonal-bit-bootstrap/audit.json": "74ac7b35c04b081794e52e325420c8d2cdf58c3fe8b646e42de1b68e77987a06", "research/composed-diagonal-bit-bootstrap/references/queue/pr205-packed-diagonal-bit.certificate.json": "c11fbb9aaa99594afc8d21e33761dc6d1d6c76ce3dbc36d5b64cae872c242f5a", @@ -37,7 +37,7 @@ "research/composed-diagonal-bit-bootstrap/references/pr187/certificate.json": "0cfcb896c86c2e1de759f0518176ba6c606036b9f515eac045d3962cc4a00073", "research/composed-diagonal-bit-bootstrap/references/pr200/interval_moment.py": "9d3d1d28bfb3375958995205179b171fb65c70a3792cf9f7a21ef5ee54f5460b", "research/composed-diagonal-bit-bootstrap/certificate.json": "0a844fb88811af915ae5198aab07b79f61c29cc9c68b1752733d30a4c189cfc4", - "research/composed-diagonal-bit-bootstrap/README.md": "b5a5b1dd68eb73e17a2ce9601b40b3451d50c9b363e29097540c2463a504a2ef", + "research/composed-diagonal-bit-bootstrap/README.md": "c48996e8e4c03d6389a20b8d60ea5d53cf22fd9acba88231b8f3b65d1b9538f2", "research/composed-diagonal-bit-bootstrap/NOTICE.md": "0069cf9254824f11d144579445e83220a7953a79c5bad6798da2280f75207104", "research/composed-diagonal-bit-bootstrap/references/pr168-v4/scripts/paired_cube_assembly.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c", "research/composed-diagonal-bit-bootstrap/references/pr184/assemble_profiles.py": "c56d0638d4bc1ac3f70c78778ea824f3a2ba23c31f7eeff3c93cf17df3f2e0de", diff --git a/research/composed-diagonal-bit-bootstrap/targets.json b/research/composed-diagonal-bit-bootstrap/targets.json index b0f4dfa3a2..76b1692352 100644 --- a/research/composed-diagonal-bit-bootstrap/targets.json +++ b/research/composed-diagonal-bit-bootstrap/targets.json @@ -94,6 +94,11 @@ "kappa": "7004273/10000000000", "kappa_decimal": 0.0007004273 }, + "first_rung": { + "coarse": "700971690742463/1000000000000000000", + "share_of_smallest": 0.057, + "thousandths": 57 + }, "frontier": { "binding": "bit", "bit_budget": "136731504666219/200000000000000000", diff --git a/research/composed-diagonal-bit-bootstrap/targets.py b/research/composed-diagonal-bit-bootstrap/targets.py index 5215ac2b02..d6e31d3325 100644 --- a/research/composed-diagonal-bit-bootstrap/targets.py +++ b/research/composed-diagonal-bit-bootstrap/targets.py @@ -98,6 +98,26 @@ def soak(m, W, D, hist, threshold): return kept +def partial_soak(m, W, D, hist, threshold, thousandths): + """Soak only `thousandths/1000` of the mass sitting in children of rank <= threshold.""" + kept, moved = {}, 0 + for rank, count in hist.items(): + if rank > threshold or thousandths == 0: + kept[rank] = count + continue + move = count * thousandths // 1000 + kept[rank] = count - move + moved += rank * move + top = max(hist) + count, remaining = divmod(moved, top) + if count: + kept[top] = kept.get(top, 0) + count + if remaining: + kept[remaining] = kept.get(remaining, 0) + 1 + assert sum(r * n for r, n in kept.items()) == m * W - D + return {r: n for r, n in kept.items() if n} + + def main(): parser = argparse.ArgumentParser(description=__doc__) parser.add_argument("--out", type=Path, default=HERE / "targets.json") @@ -162,6 +182,20 @@ def main(): coarse=str(coarse), within_one_grid_step=abs(modelled - claimed) <= Q(1, SELECT_GRID)) + # The cheapest first step: the smallest part of the bit word's smallest children + # that stops the bit branch binding, in thousandths of that population. + m, W, D, hist = rows(newest["bit_profile"]) + top = max(hist) + first = None + for thousandths in range(1, 1001): + candidate = levers.row(m, W, D, partial_soak(m, W, D, hist, top - 1, thousandths)) + saving = levers.certified(interval, candidate) + if saving >= (1 - STOP) * Q(suppliers["complex"]["coarse"]) - Q(1, SELECT_GRID): + first = dict(thousandths=thousandths, coarse=str(saving), + share_of_smallest=float(Q(thousandths, 1000))) + break + assert first is not None, "some part of the smallest children must clear the complex side" + bit_coarse = Q(suppliers["bit"]["coarse"]) complex_coarse = Q(suppliers["complex"]["coarse"]) bit_budget, complex_budget, binding = branch_budgets(bit_coarse, complex_coarse) @@ -190,6 +224,7 @@ def main(): ladder={t: str(c) for t, c in v["ladder"].items()}, cheapest_ledger=str(v["cheapest_ledger"])) for k, v in suppliers.items()}, + first_rung=first, frontier=dict(binding=binding, kappa=str(now), kappa_decimal=float(now), bit_budget=str(bit_budget), complex_budget=str(complex_budget)), complex_side_cap=dict(kappa=str(complex_only), kappa_decimal=float(complex_only), @@ -219,6 +254,9 @@ def main(): print(" soak children <= {t:>2}: coarse = {v}".format(t=threshold, v=value)) print(" cheapest ledger: coarse = " + str(item["cheapest_ledger"])) print("[frontier] {binding} binds: kappa = {k}".format(k=now, **out["frontier"])) + print("[first rung] moving {t}/1000 of the mass in the bit word's children below rank " + "{top} into rank-{top} children is enough to clear the complex side".format( + t=first["thousandths"], top=top)) print("[complex cap] kappa = {k} ({g:+.2%}), reached when the bit coarse saving is " "{n}".format(k=complex_only, g=float(complex_only / now - 1), n=needed)) for threshold, item in out["bit_ladder"].items(): diff --git a/research/composed-diagonal-bit-bootstrap/verify.py b/research/composed-diagonal-bit-bootstrap/verify.py index 522a3b863a..4e402a71d0 100644 --- a/research/composed-diagonal-bit-bootstrap/verify.py +++ b/research/composed-diagonal-bit-bootstrap/verify.py @@ -249,6 +249,10 @@ def accept_only_a_better_composition(): assert all(left < right for left, right in zip(ladder, ladder[1:])), \ "soaking more rank mass into larger children must buy more" assert Q(targets["cheapest_ledger_both"]["gain"]) > Q(1, 2), "the ledger must be the room" + first = targets["first_rung"] + assert first and Q(first["coarse"]) >= Q(targets["complex_side_cap"]["bit_coarse_needed"]), \ + "the first rung must clear the complex side" + assert Q(first["thousandths"], 1000) < Q(1, 5), "the first rung must be a small part" print("[targets] the frontier is {} at {}; taking the bit word's rank-1 children into " "larger ones reaches the complex side's {:.10g} ({:+.2%}), and soaking both words' " "cheap children buys {:+.2%}, rising to {:+.2%} at the cheapest admissible " @@ -258,6 +262,10 @@ def accept_only_a_better_composition(): float(Q(targets["complex_side_cap"]["gain"])), float(Q(targets["both_soaked"]["1"]["gain"])), float(Q(targets["cheapest_ledger_both"]["gain"])))) + print("[first rung] coarsening {:d}/1000 of the mass in the bit word's smallest children " + "reaches the complex side (bit coarse {} vs the {} it needs)".format( + first["thousandths"], Q(first["coarse"]), + Q(targets["complex_side_cap"]["bit_coarse_needed"]))) print("PASS composed-diagonal-bit-bootstrap kappa = {} at depth {}; 47 strict constraints " "and 7 margins per depth".format(best, best_depth))