From 9b6ad038f8690206c14ed8f28fb90ec6b3a79ae1 Mon Sep 17 00:00:00 2001 From: Chafik Boukhalfa Date: Fri, 9 Oct 2026 21:31:17 +0400 Subject: [PATCH] A frame-layout ceiling for #200's bit word: coarse < 6.964e-4 banked, kappa < 6.959e-4 (no new kappa) Adds research/bit-frame-ceiling-200 and one workflow. DaysSky's #192 frame-floor method carried to the physical bit word shared by #200, #205, #206 and #207: joint frame bounds through both registers of every operation, exact per-slot dynamic programme, Lagrangian coupling, exact integer arithmetic with rational logarithm bounds. The eight pinned #200 files are carried in baseline-pr200.tar.gz with sha256 pins to a1175449. Prepared by Chafik Boukhalfa with substantial Anthropic Claude assistance. --- .github/workflows/bit-frame-ceiling.yml | 25 + research/bit-frame-ceiling-200/NOTICE | 28 + research/bit-frame-ceiling-200/PROOF.md | 131 ++++ research/bit-frame-ceiling-200/README.md | 42 ++ research/bit-frame-ceiling-200/SOURCE.json | 18 + .../baseline-pr200.tar.gz | Bin 0 -> 1405363 bytes research/bit-frame-ceiling-200/ceiling.py | 577 ++++++++++++++++++ research/bit-frame-ceiling-200/expected.json | 25 + 8 files changed, 846 insertions(+) create mode 100644 .github/workflows/bit-frame-ceiling.yml create mode 100644 research/bit-frame-ceiling-200/NOTICE create mode 100644 research/bit-frame-ceiling-200/PROOF.md create mode 100644 research/bit-frame-ceiling-200/README.md create mode 100644 research/bit-frame-ceiling-200/SOURCE.json create mode 100644 research/bit-frame-ceiling-200/baseline-pr200.tar.gz create mode 100644 research/bit-frame-ceiling-200/ceiling.py create mode 100644 research/bit-frame-ceiling-200/expected.json diff --git a/.github/workflows/bit-frame-ceiling.yml b/.github/workflows/bit-frame-ceiling.yml new file mode 100644 index 0000000000..7224b6ba29 --- /dev/null +++ b/.github/workflows/bit-frame-ceiling.yml @@ -0,0 +1,25 @@ +name: bit-frame-ceiling + +on: + pull_request: + paths: + - 'research/bit-frame-ceiling-200/**' + - '.github/workflows/bit-frame-ceiling.yml' + push: + paths: + - 'research/bit-frame-ceiling-200/**' + - '.github/workflows/bit-frame-ceiling.yml' + +jobs: + ceiling: + runs-on: ubuntu-latest + strategy: + matrix: + python-version: ['3.11', '3.14'] + steps: + - uses: actions/checkout@v4 + - uses: actions/setup-python@v5 + with: + python-version: ${{ matrix.python-version }} + - name: Bit frame-layout ceiling of #200's word, compared with expected.json + run: python3 research/bit-frame-ceiling-200/ceiling.py --check diff --git a/research/bit-frame-ceiling-200/NOTICE b/research/bit-frame-ceiling-200/NOTICE new file mode 100644 index 0000000000..46d459338c --- /dev/null +++ b/research/bit-frame-ceiling-200/NOTICE @@ -0,0 +1,28 @@ +Prepared by Chafik Boukhalfa with substantial Anthropic Claude assistance. +Apache-2.0. Inherited files retain their original notices and assistance +disclosures. This package claims no exclusive priority over concurrent work +and reports no new exponent. + +Method and lineage: +- DaysSky: PR192 (research/kappa-ceiling), the frame-layout ceiling of #168's + complex word: the moment-root bound a < D/C, the subadditive chain bound, + joint frame bounds through both registers of an operation, the exact + per-slot dynamic programme and the Lagrangian coupling. ceiling.py carries + that method, with the same structure and rigorous arithmetic, to the physical + bit word; the rational logarithm bounds and the archive/pin layout follow + PR192 directly. PR201 supplies the design ceiling cited in README.md. +- romainhedouin: PR183, the closed-form acceptance ceiling of the assembly. +- icekylinx PR144 and eumemic PR117/155/157/161/168: the paired-cube bit word, + its exact integer checker check_paired_cube_bit.py (pinned here byte for + byte from PR200's vendored copy of PR168 v4) and the physical ledger whose + chains ceiling.py mirrors. +- jamesyc / James Chang: PR166 terminal-output accumulation, whose bit form in + PR200 (bit/terminal.py) fixes the sink substitution used here. +- The word itself: Chafik Boukhalfa, PR200 at + a1175449f34d39ff933d9d8ab23ced1f32b290ec (research/paired-cube-diagonal-bit-168), + with Anthropic Claude and OpenAI Codex assistance. The eight files read are + pinned in SOURCE.json and carried in baseline-pr200.tar.gz. +- The banked ledger priced alongside is the completed-entrance-bank accounting + of Dugongue PR186, Evan McKinney PR197, Rohan Arun PR205, EcmaXp PR206 and + Dugongue PR207 on this word; their bank constructions are not re-verified + here and the ceiling does not depend on them. diff --git a/research/bit-frame-ceiling-200/PROOF.md b/research/bit-frame-ceiling-200/PROOF.md new file mode 100644 index 0000000000..36846873aa --- /dev/null +++ b/research/bit-frame-ceiling-200/PROOF.md @@ -0,0 +1,131 @@ +# A frame-layout ceiling for #200's physical bit word + +This note proves an upper bound on the coarse bit saving, and hence on κ, that any choice of operation frames for +the physical bit word of #200 can certify, and applies it to the two ledgers in use on that word: #200's own and the +completed-entrance-bank ledger of #205, #206 and #207. It makes no κ claim and changes no existing file. The method +is DaysSky's #192 (`research/kappa-ceiling`), carried from #168's complex word to this bit word; the facts below +restate #192's with the bit ledger in place of the complex one. `ceiling.py` evaluates every bound with exact +integers and checks its own model against #200's certified ledger child for child. + +## Setting + +A shared-core bit supplier is described per group vertex by `W` roles, `m = 3h`, and a multiset of children: `n_r` +children of width `r`, `0 < r < m`. Its rank mass telescopes, `Σ_r r·n_r = W·m − D` with `D = 2v − 3ℓ` +(`v` ports, `ℓ` the copied-centre loss). Write `f(r) = r·ln(m/r)` and `C = Σ_r n_r·f(r)`. The repository certifies a +coarse saving `a` when an exact upper bound on the paid moment `Σ n_r·(r/(W·m))·(m/r)^a` plus the positive bad-class +term is below 1 (`bit/prove.py`, `arithmetic/interval_moment.py` in #200). So a certified `a` satisfies + + Σ_r n_r·r·(m/r)^a < W·m. (∗) + +**Fact 1 (moment root, #192 Lemma 1).** If (∗) holds then `a < D/C`, since `(m/r)^a ≥ 1 + a·ln(m/r)`. On #200 the +certified coarse saving lies 0.088% below `D/C` (`ceiling.py`, fact 1). + +**Fact 2 (assembly and bootstrap).** #183 (romainhedouin) gives the balanced assembly's acceptance region in closed +form: κ below `G_η(a) = a(1−2η)(1−η)/(1 + a(1−2η))`, increasing in `a` and decreasing in `η`, so `κ < a/(1+a)` for +every `η > 0`. The ordinary-leaf wrapper gives `A_B = (1−θ)·a + θ·a_old < a`. The finite stopped-leaf bootstrap of +#185/#197/#207 produces `a_j = (1−c)·c + c·a_{j−1} < c` at every level from the coarse saving `c`. Hence every κ +built on this word by any of these assemblies satisfies `κ < G(min(bit, complex)) < G(bit coarse) ≤ G(D/C)` with the +bit ledger's `D` and `C`. + +**Fact 3 (chains, #192 Lemma 3).** `f` is strictly subadditive on `(0, m)`, so a chain of steps of total width `t` +costs at least `f(t)`; splitting a frame climb into more steps only costs more. + +## Fact 4: the frame floor of the fixed word + +The certified bit ledger (`scripts/paired_cube_bit_physical.py` of PR168 v4, re-counted by #200's `bit/word.py` and +`bit/terminal.py`) consists of, per vertex: + +- three times the steps of every physical slot's frame chain, where a slot starts at 0, at its source line `⟨χ_S⟩` + or at its gauge `σ`, passes the frame of each of its operations in execution order, its root frame if it is a root, + and ends at the full space; a recipient continues its donor's slot through the exact step into its gauge; +- three times the source-injection children of width 1 and the copied-centre children (width `dim` of the centre); +- three times the partner-chain (source data) steps, fixed by the partner chronology `kchron`; +- three times the target-chain steps, fixed by the gauges' targets and read order, the side-root frames and the + partner deliveries; +- one child of width `3·dim σ` per gauged first occupant that is not a recipient (the entrance tails); +- `2v` children of width 2. + +`ceiling.py` rebuilds this multiset from the word with #200's own operation frames and checks that it equals +`overridden_profile.child_histogram` of #200's certificate exactly (W 20,668; rank 1,486,160), and that subtracting +the terminal record gives `profile.child_histogram`. + +Fix the word: its DAG, operations and execution order, sources and source frames, gauges and read chronology, reuse +pairs, partner chronology, root frames and terminal sinks. The free choice is the frame `F_i` of each operation. An +admissible layout satisfies, as checked by the retained physical checker before the terminal record is applied: +`span(x_i) ⊆ F_i`; both registers of operation `i` are at `F_i` while it runs; every slot's frames nest along its +chain; a donor's last frame lies inside its recipient's gauge; a root is read at its root frame. + +**Lemma 4a (joint bounds).** Every admissible layout has `L_i ⊆ F_i ⊆ U_i`, where `L_i = span(x_i) + L_prev(a) + +L_prev(b)` runs forward in execution order from the registers' entrance frames and `U_i = U_next(a) ∩ U_next(b)` runs +backward from root frames, recipients' gauges (for donors) and the full space. *Proof.* Both registers sit at `F_i`, +so `F_i` contains everything below either register's previous frame and lies inside everything above either +register's next frame; the ends of every chain are fixed. ∎ Values only move between registers through operations, +whose shared frame links both chains, so this backward pass already carries every root constraint reachable from +`x_i`. `ceiling.py` checks that #200's layout, and #207's 302-frame layout when given, satisfy every bound. + +**Lemma 4b (slot floor).** For each slot, take the minimum of `Σ f(steps)` over nondecreasing dimension sequences with +`d_i ∈ [dim(cumulative L), dim(cumulative U)]` at each event; exact events (gauge of a recipient, root frame) are +fixed; the sequence starts at the entrance dimension and ends at `h`. The sum over slots is at most the slots' cost in +every admissible layout. *Proof.* As in #192: only the coupling between the two registers of an operation and the +subspace structure are dropped. ∎ + +**Lemma 4c (coupling).** For any integer prices `λ_i`, adding `+λ_i·d` to the destination register's cost and `−λ_i·d` +to the control register's cost at operation `i` keeps the sum of per-slot minima a lower bound, since both registers +share `d = dim F_i` in any admissible layout. ∎ `ceiling.py` runs subgradient rounds on the prices, keeps the best +round and asserts every round's total lies below #200's own layout cost. + +**The terminal record.** #200's `bit/terminal.py` (the bit form of #166) deletes each sink register and copies its +rank increments to a pivot target; the certified substitution removes, per sink and stage, exactly the sink's last +step (root frame to full space, width `h − dim root = 3`, present in every layout since the root frame is fixed) and +one target child of width 21 (the pivot's cap read, fixed by the gauges and roots), and keeps every other step +charged. `ceiling.py` checks this against the certificate's `child_delta` (−102 of width 3, −102 of width 21) and the +pre/post target histograms, so the floor of the terminal ledger is the pre-sink floor minus this fixed cost. #207 +audits the same −102/−102 substitution on its layout. + +**The two ledgers.** `C_own` includes the entrance tails `3·dim σ`; `C_banked` omits them, which is the only ledger +change the completed-entrance-bank construction of #205/#206/#207 makes to the children (their `W` changes do not +enter `D/C`). Both floors share the slot floor and the fixed parts. Hence, for every admissible frame layout of this +word, + + coarse_own < D / C_own,floor and coarse_banked < D / C_banked,floor, + +and `κ < G(·)` of each. + +**Arithmetic.** Every logarithm is a rational lower bound (partial sums of `2·atanh`, nonnegative terms, truncation +below `3^-80`), every `f(r)` is rounded down on the grid `2^-64`, and all sums, the dynamic programme and the prices +are exact integers. The printed ceilings are rounded up on the `10^-7` grid. + +## Result + +`ceiling.py --check` (1,200 Lagrangian rounds, about 2.5 minutes, stdlib only) on the pinned files of #200 gives: + +| Ledger | Floor on C | Coarse saving ceiling | κ ceiling | Certified layout | +|---|---:|---:|---:|---| +| #200's own (entrance tails charged) | 2,804,210 | **6.904e-4** | 6.900e-4 | #200's coarse 6.7777e-4 is 98.2% of the ceiling | +| completed entrance banks (#205/#206/#207) | 2,780,144 | **6.964e-4** | **6.959e-4** | #207's bit coarse 6.8366e-4 (D/C 6.8427e-4) is 98.2% of it | +| without coupling the two registers of an operation | | 7.056e-4 / 7.118e-4 | | | + +The deficit is `D = 2v − 3ℓ = 1,936` (`v = 1,760`, `ℓ = 528`, `h = 24`, `m = 72`); the word has 41,288 operations, +18,908 roles, 1,760 reuse pairs and 34 sinks. `--overrides` on #207's `frames/opframe-bases.json` confirms that its +302-frame layout lies inside every joint bound and above the floor. + +Consequences. + +- Every frame refinement still possible on this word is worth at most +1.8% on the bit side under either ledger. +- The complex supplier used with this word (#202's source-assisted word, coarse 7.00918e-4, itself within 0.01% of + #192's 7.010e-4 ceiling for its own frames) can never become the binding branch: the bit ceiling 6.964e-4 lies below + it. So every κ assembled from this bit word and any complex word at or below that ceiling stays below 6.959e-4, no + matter how the bit frames are chosen. Going further needs a different bit word (circuit, reuse, gauges or sinks), + a bank construction that removes other children, or a different design (DaysSky's #201 bounds the design at + 2.5592e-3). + + +## Scope and limits + +- The ceiling covers one word: the DAG, operations, sources, gauges, reuse pairs, partner chronology and 34 sinks of + #200 at `a1175449`. #205, #206 and #207 keep all of these (#207 changes 302 operation frames), so it covers their + rows. It does not bound constructions that change the word, the pairs, the gauges or the sinks, nor a different + bank construction that removes other children. +- Fact 2 uses only that every retained assembly accepts κ below `a/(1+a)` of the binding supplier and that the + bootstrap stays below its coarse saving. It does not re-verify any assembly or bank construction. +- The proofs are elementary and not machine-checked beyond the script's exact arithmetic and self-tests. diff --git a/research/bit-frame-ceiling-200/README.md b/research/bit-frame-ceiling-200/README.md new file mode 100644 index 0000000000..7299ce76e0 --- /dev/null +++ b/research/bit-frame-ceiling-200/README.md @@ -0,0 +1,42 @@ +# bit-frame-ceiling-200 + +A rigorous ceiling on the bit coarse saving, and hence on κ, for every operation-frame layout of #200's physical bit +word, the word shared by #200, #205, #206 and #207. **No new κ; no existing file changes.** The method is DaysSky's +#192 (`research/kappa-ceiling`), carried from #168's complex word to this bit word. + +## Result + +For every admissible choice of operation frames on this word (its DAG, operations, sources, gauges, 1,760 reuse pairs, +partner chronology and 34 sinks fixed, as in #200, #205, #206 and #207): + + bit coarse saving < 6.904e-4 under #200's own ledger, + bit coarse saving < 6.964e-4 under the completed-entrance-bank ledger of #205/#206/#207, + +and hence κ < 6.900e-4, respectively κ < 6.959e-4, for any assembly built on it. #207's bit side (coarse 6.8366e-4, +κ = 6.8319e-4) is 98.2% of its ceiling, so frame work on this word is worth at most +1.8% more. The ceiling sits +below the complex supplier those PRs use (7.009e-4), so that complex word can never become the binding branch on +this bit word. Going further needs a different bit word, a bank construction that removes other children, or a +different design. [PROOF.md](PROOF.md) has the statements, proofs and the full table. + + +## Verify + + python3 research/bit-frame-ceiling-200/ceiling.py --check # stdlib only, about 2.5 minutes; -O is refused + +The script rebuilds the eight pinned files of #200 it reads (frozen physical bit word, frames, partner chronology, +graph, profile, sinks, certificate and the retained PR168-v4 exact integer checker) in a temporary directory from +`baseline-pr200.tar.gz` after checking the archive's and every file's sha256 against `SOURCE.json`, whose hashes are +those of commit `a1175449`. Reviewers can confirm the pins with `git show a1175449: | sha256sum`, or rebuild +the archive byte for byte with `git archive --format=tar a1175449 | gzip -n -9`. A tampered archive is +rejected. `--tree PATH` runs on a checkout of #200 instead. `--overrides FILE` prices another layout of the same +word, for instance #207's `frames/opframe-bases.json`, and checks it against the bounds and the floor. + +Self-tests: #200's layout lies inside every derived frame bound; its slot chains reproduce #200's certified pre-sink +ledger child for child and the terminal substitution; every per-slot floor and every Lagrangian round lies below the +actual cost. All bounds use exact integers with rounded-down logarithms, so the printed ceilings are upper bounds. + +## Files + +- `ceiling.py`: the computation; `PROOF.md`: statements and proofs; `expected.json`: the results `--check` compares. +- `SOURCE.json`, `baseline-pr200.tar.gz`: the pinned inputs. +- `.github/workflows/bit-frame-ceiling.yml` runs `--check` on Python 3.11 and 3.14. diff --git a/research/bit-frame-ceiling-200/SOURCE.json b/research/bit-frame-ceiling-200/SOURCE.json new file mode 100644 index 0000000000..c6a9c56931 --- /dev/null +++ b/research/bit-frame-ceiling-200/SOURCE.json @@ -0,0 +1,18 @@ +{ + "archive": "baseline-pr200.tar.gz", + "archive_sha256": "316aa6942a7a027112a8c38c472c59db025c964021abf2d8b3d8fd0e90b7b075", + "commit": "a1175449f34d39ff933d9d8ab23ced1f32b290ec", + "files": { + "research/paired-cube-diagonal-bit-168/certificate.json": "853afa75980e11ce16b333c28311c4f635e84065867c049fda9916c2419091ed", + "research/paired-cube-diagonal-bit-168/references/pr168-v4/research/paired-cube-bit/check_paired_cube_bit.py": "4d7c86cd999a1519e0dfb6dcf33a8f26e442a353c3665a0f06881216a260fbf3", + "research/paired-cube-diagonal-bit-168/selected/bit/frames_p12.json.gz": "ad8e2705652b68476713d7647a8592505e222f2b3ccd1728dedce153aac6d462", + "research/paired-cube-diagonal-bit-168/selected/bit/graph_p12.json": "31a09a55920e64c8bfbac8b845dc01754c112aa6e207812e2fd1f4939d8f64cb", + "research/paired-cube-diagonal-bit-168/selected/bit/kchron_p12.json": "0fab548e84cf5ca7c04e8bd19b5810850463f36e0f92180efe73aeff17105e39", + "research/paired-cube-diagonal-bit-168/selected/bit/profile_p12.json": "c44ef8640cbcbcc9bac3a30e13373bd79efddde55d7cea514354ca2cdb60d66d", + "research/paired-cube-diagonal-bit-168/selected/bit/sinks.json": "c00ff70c564829d4b97740f92796fc6ce14fbcd5ca519663828650552b80249d", + "research/paired-cube-diagonal-bit-168/selected/bit/word_p12.json.gz": "1cb7e8ed45cf542e304fddc4b12247dbb248a0dc84dedbd832f336b2d172793a" + }, + "note": "The exact files of #200 that ceiling.py reads (the frozen physical bit word, frames, partner chronology, graph, profile, terminal sinks, certificate and the retained PR168-v4 exact integer checker), byte for byte from commit a1175449; reproducible with: git archive --format=tar a1175449 | gzip -n -9", + "pr": 200, + "repository": "CrocSwap/integer-mult-bounds" +} \ No newline at end of file diff --git a/research/bit-frame-ceiling-200/baseline-pr200.tar.gz b/research/bit-frame-ceiling-200/baseline-pr200.tar.gz new file mode 100644 index 0000000000000000000000000000000000000000..cc62d8e44195a014b59b7473fb3c39841a1549d4 GIT binary patch literal 1405363 zcmbSx(|a5a&~@0@Xl%1>Y&5p9abv3+8;u&XvAx;YXspKA*xuOA`};1w+xOy~=UmJm zFmvWS=L}^GGR*%gIQY|bqj-wZM0y*eDKOPfk*;gxc;t8@Q|IP7U9{6Pwpu;9`Vlsr z8aW0b`AT~9=N_=ga6{$D^HJqYdGWFI;;kJ0w;TW6{`IxfZ1drb&G)B+yQ~PX)8?9= zyXVWv`ITqjOCaFQolN$<u99zj-$G 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mode 100644 index 0000000000..b20986da4f --- /dev/null +++ b/research/bit-frame-ceiling-200/ceiling.py @@ -0,0 +1,577 @@ +#!/usr/bin/env python3 +"""Rigorous ceiling on the bit saving, and hence on kappa, for every operation-frame layout of #200's physical bit +word (Python stdlib only; no -O). The method is DaysSky's #192 (research/kappa-ceiling), carried from #168's complex +word to the bit word that #200, #205, #206 and #207 share. + +For a shared-core bit profile with children n_r (0 < r < m), W roles per vertex, deficit D = W m - sum r n_r and +cost C = sum n_r r ln(m/r): + + 1. every coarse saving a certified by the paid moment test satisfies a < D / C (e^x >= 1 + x); + 2. the balanced assembly accepts kappa only below a (1 - 2 eta)(1 - eta) / (1 + a (1 - 2 eta)) < a / (1 + a) + (#183, romainhedouin), and the finite ordinary-leaf bootstrap of #185/#197/#207 stays below the coarse saving + it starts from (a_j = (1 - c) c + c a_(j-1) < c); + 3. a chain of frame steps of total rank t costs at least f(t) = t ln(m/t) (f is subadditive); + 4. for the fixed word (DAG, operations and their order, sources, gauges, reuse pairs, partner chronology and terminal + sinks), every admissible choice of operation frames has C >= C_floor, where C_floor propagates frame bounds + jointly through both registers of every operation, minimises each physical slot's chain exactly by dynamic + programming over frame dimensions, and couples the two registers of each operation by Lagrangian prices. + +Hence coarse < D / C_floor and kappa < G(D / C_floor) for every frame layout of the word. Two ledgers are priced: +#200's own (gauged first occupants pay 3 dim sigma) and the completed-entrance-bank ledger of #205/#206/#207 (those +children removed, nothing else changed), so the ceiling also covers the banked rows built on this word. + +All costs are exact integers in units of 2^-64 with every logarithm replaced by a rational lower bound, so the printed +ceilings are true upper bounds, rounded up. By default the script rebuilds the eight pinned files of #200 it reads +(the frozen physical bit word, frames, partner chronology, graph, profile, sinks, certificate and the retained +PR168-v4 exact integer checker) in a temporary directory from baseline-pr200.tar.gz after checking every sha256 +against SOURCE.json (commit a1175449). Nothing outside the temporary directory is read or written. + +Usage: python3 research/bit-frame-ceiling-200/ceiling.py [--check] [--tree PATH] [--rounds N] [--overrides FILE] + --check compare the results with expected.json + --tree run on a checkout of #200 (its root or research/paired-cube-diagonal-bit-168) instead of the archive + --overrides also test another layout of the same word, given as #207's frames/opframe-bases.json ([op, rows]...) +""" +import argparse +import hashlib +import importlib.util +import io +import json +import math +import sys +import tarfile +import tempfile +import time +from collections import Counter, defaultdict +from fractions import Fraction as Q +from pathlib import Path + +if sys.flags.optimize: + raise SystemExit('Assertions must remain enabled: run without -O') +sys.set_int_max_str_digits(0) +sys.dont_write_bytecode = True + +HERE = Path(__file__).resolve().parent +PKG = 'research/paired-cube-diagonal-bit-168' +SCALE = 64 # costs are integers in units of 2^-64, rounded down +T0 = time.time() + + +def log(*a): + print('[%4.0fs]' % (time.time() - T0), *a, flush=True) + + +# ---------------------------------------------------------------------------------------------- rigorous logarithms +def log_lower(x): + """A rational lower bound on ln x for rational x >= 1: k ln 2 + ln y with y in [1, 2), each from partial sums of + 2 atanh((y-1)/(y+1)), whose terms are all nonnegative. The truncation error is below 3^-80.""" + assert x >= 1 + def series(y): + z = (y - 1) / (y + 1) + return 2 * sum((z ** (2 * j + 1) / (2 * j + 1) for j in range(40)), Q(0)) + k = 0 + while x >= 2: + x /= 2 + k += 1 + return k * series(Q(2)) + series(x) + + +def cost_table(m): + """f(r) = r ln(m/r), as integers rounded down in units of 2^-SCALE, for 0 <= r < m.""" + out = [0] * m + for r in range(1, m): + val = r * log_lower(Q(m, r)) + out[r] = (val.numerator << SCALE) // val.denominator + return out + + +def G(a): + """Every acceptance region used by the retained assemblies lies below a/(1+a) (#183: q(1-eta)/(1+q) with + q = a(1-2 eta), increasing in a and decreasing in eta; the limit eta -> 0 is the weakest bound).""" + return a / (1 + a) + + +def ceil7(x): + return -((-x.numerator * 10**7) // x.denominator) # round up on the 10^-7 grid + + +# ---------------------------------------------------------------------------------------------- the pinned files +def rebuild(dest): + """Write the pinned #200 files into dest after checking the archive and every file against SOURCE.json.""" + src = json.loads((HERE / 'SOURCE.json').read_text()) + data = (HERE / src['archive']).read_bytes() + if hashlib.sha256(data).hexdigest() != src['archive_sha256']: + raise SystemExit('baseline archive differs from SOURCE.json') + with tarfile.open(fileobj=io.BytesIO(data), mode='r:gz') as archive: + members = [x for x in archive.getmembers() if x.isfile()] + if sorted(x.name for x in members) != sorted(src['files']): + raise SystemExit('baseline archive lists other files than SOURCE.json') + for x in members: + part = Path(x.name) + if part.is_absolute() or '..' in part.parts: + raise SystemExit('unsafe path in baseline archive: ' + x.name) + body = archive.extractfile(x).read() + if hashlib.sha256(body).hexdigest() != src['files'][x.name]: + raise SystemExit('baseline file differs from SOURCE.json: ' + x.name) + (dest / part).parent.mkdir(parents=True, exist_ok=True) + (dest / part).write_bytes(body) + return src['commit'] + + +def read(p): + import gzip + raw = p.read_bytes() + return json.loads(gzip.decompress(raw) if p.suffix == '.gz' else raw) + + +def load(tree): + """The retained exact integer checker on #200's frozen bit word, with its geometry (frames, decoder supports, + coordinate rows, target covectors) prepared, plus the sinks and the certified bit record.""" + pkg = tree if (tree / 'selected/bit').exists() else tree / PKG + path = pkg / 'references/pr168-v4/research/paired-cube-bit/check_paired_cube_bit.py' + spec = importlib.util.spec_from_file_location('check_paired_cube_bit', path) + backend = importlib.util.module_from_spec(spec) + spec.loader.exec_module(backend) + C = backend.Checker.__new__(backend.Checker) + C.mut = None + B = pkg / 'selected/bit' + C.g, C.prof, C.w, C.fr, C.k = (read(B / n) for n in ('graph_p12.json', 'profile_p12.json', 'word_p12.json.gz', + 'frames_p12.json.gz', 'kchron_p12.json')) + C.h, C.v = C.g['h'], C.g['v'] + C.frames() + C.decoder() + C.geometry() + sinks = json.loads((B / 'sinks.json').read_text()) + cert = json.loads((pkg / 'certificate.json').read_text()) + return dict(C=C, backend=backend, sinks=sinks, cert=cert['bit'], kappa=cert.get('kappa'), pkg=pkg) + + +# ---------------------------------------------------------------------------------------------- the word's chains +class Word: + """Mirrors the role, partner and target chains of the retained physical checker (PR168 v4 + scripts/paired_cube_bit_physical.py), and derives the joint frame bounds of #192, Lemma 4a.""" + + def __init__(self, T): + C, backend = T['C'], T['backend'] + self.C, self.mod = C, backend + w, h = C.w, C.h + self.w, self.h, self.m, self.v = w, h, 3 * h, C.v + self.ops = [tuple(o) for o in w['ops']] + self.opf = list(w['op_frame']) + assert len(self.opf) == len(self.ops) + self.ids = {tuple(B): f for f, B in C.B.items()} + phase = set(w['phase1']) + self.order = sorted(phase) + [i for i in range(len(self.ops)) if i not in phase] + self.position = {i: p for p, i in enumerate(self.order)} + self.cut = len(phase) + self.sources = {int(x): s for x, s in w['sources'].items()} + self.R = 1 + max(max(max(a, b) for a, b, _ in self.ops), max(w['rootroles']), max(self.sources.values())) + self.start = {s: w['source_frame'][x] for x, s in self.sources.items()} + self.gauge = {z['role']: z for z in w['gauges']} + for s, z in self.gauge.items(): + assert s not in self.start + self.start[s] = z['frame'] + self.rootframe = {s: w['root_frame'][j] for j, s in enumerate(w['rootroles'])} + self.full = w['full_frame'] + self.zero = self.register([]) + self.role_ops = defaultdict(list) + for i in self.order: + for s in self.ops[i][:2]: + self.role_ops[s].append(i) + self.pairs = [(int(a), int(b)) for a, b in w.get('pairs', [])] + self.recipient_of = {a: b for a, b in self.pairs} + self.donor_of = {b: a for a, b in self.pairs} + reads = {int(s): t for s, t in w.get('reads', {}).items()} + self.when = {} + for k, z in enumerate(reversed(w['gauges'])): + self.when[z['role']] = (reads.get(z['role'], self.cut), k) + self.sinkroles = {w['rootroles'][e['root']] for e in T['sinks']} + assert len(self.sinkroles) == len(T['sinks']) + assert not self.sinkroles & (set(self.donor_of) | set(self.recipient_of) | set(self.gauge) | set(self.sources.values())) + + # exact linear algebra over the h coordinates, through the retained checker + def register(self, rows): + C, mod = self.C, self.mod + B, _ = mod.reduce_rows(rows, self.h) + B = tuple(sorted(map(tuple, B), key=lambda r: next(i for i, x in enumerate(r) if x))) + if B in self.ids: + return self.ids[B] + f = max(C.B) + 1 + A, _ = mod.kernel(B, self.h) + C.B[f], C.A[f], C.dimf[f] = B, A, len(B) + self.ids[B] = f + return f + + def join(self, *fs): + return self.register([row for f in fs for row in self.C.B[f]]) + + def meet(self, *fs): + rows, _ = self.mod.kernel([row for f in fs for row in self.C.A[f]], self.h) + return self.register(rows) + + def dim(self, f): + return self.C.dimf[f] + + def sub(self, f, g): + return self.C.sub(f, g) + + def span(self, x): + bits, rows = self.C.sup[x], [] + while bits: + b = bits & -bits + bits -= b + rows.append(self.C.chi[b.bit_length() - 1]) + return self.register(rows) + + def bounds(self): + """Lemma 4a: L_i = span(x_i) + previous frames of both registers; U_i = next frames of both registers. + Sink registers take part: every admitted layout is first admitted as a complete pre-sink layout, and the + terminal record then substitutes fixed children (see run).""" + live = lambda r: True + cur = {s: self.start.get(s, self.zero) for s in range(self.R)} + lo = [None] * len(self.ops) + for i in self.order: + a, b, x = self.ops[i] + F = self.span(x) + for r in (a, b): + if live(r): + F = self.join(F, cur[r]) + lo[i] = F + for r in (a, b): + if live(r): + cur[r] = F + cur = {s: self.rootframe.get(s, self.gauge[self.recipient_of[s]]['frame'] if s in self.recipient_of else self.full) + for s in range(self.R)} + hi = [None] * len(self.ops) + for i in reversed(self.order): + a, b, x = self.ops[i] + U = cur[a] if live(a) else self.full + if live(b): + U = self.meet(U, cur[b]) + hi[i] = U + for r in (a, b): + if live(r): + cur[r] = U + for i in range(len(self.ops)): + assert self.sub(lo[i], hi[i]), 'joint bounds infeasible at op %d' % i + self.lo, self.hi = lo, hi + return lo, hi + + def inside(self, opf): + return all(self.sub(self.lo[i], opf[i]) and self.sub(opf[i], self.hi[i]) for i in range(len(self.ops))) + + def slots(self): + """Physical slots with their events (lo, hi, tag): a recipient continues its donor's slot through the exact + step into its gauge; a root is read at its root frame; the chain ends at the full space.""" + live = lambda r: True + out = [] + for s in range(self.R): + if s in self.donor_of: + continue + events = [] + lives = [s] + ([self.recipient_of[s]] if s in self.recipient_of else []) + for k, u in enumerate(lives): + if k > 0: + g = self.gauge[u]['frame'] + events.append((g, g, None)) + for i in self.role_ops[u]: + a, b, _ = self.ops[i] + tag = (i, 1 if a == u else -1) if live(a) and live(b) else None + events.append((self.lo[i], self.hi[i], tag)) + if u in self.rootframe: + events.append((self.rootframe[u], self.rootframe[u], None)) + if not events and s not in self.start: + continue + out.append((s, self.start.get(s, self.zero), events, s in self.sinkroles)) + return out + + def chain_dims(self, s, opf): + """The actual frame dimensions along slot s under layout opf (the checker's chain(s), spliced at a pair).""" + seq = [self.start.get(s)] + lives = [s] + ([self.recipient_of[s]] if s in self.recipient_of else []) + for k, u in enumerate(lives): + if k > 0: + seq.append(self.gauge[u]['frame']) + seq += [opf[i] for i in self.role_ops[u]] + if u in self.rootframe: + seq.append(self.rootframe[u]) + seq.append(self.full) + d0, steps = (0 if seq[0] is None else self.dim(seq[0])), [] + for f in seq[1:]: + d = self.dim(f) + assert d >= d0 + if d > d0: + steps.append(d - d0) + d0 = d + return steps + + def fixed_children(self): + """The children that no layout changes: source injections, copied centres, partner (source data) chains, + target chains (gauge reads, side caps, partner deliveries), gauged first occupants and the 2v data children.""" + C, w, h, v = self.C, self.w, self.h, self.v + dim = self.dim + injections = sum(1 for s in self.sources.values() if s not in self.gauge) + centres = [dim(w['root_frame'][j]) for j, r in enumerate(C.g['roots']) if r['kind'] == 'center'] + source = Counter() + for e in C.k['entries']: + c, d = e['carrier'], e['passive'] + for ch in ((w['source_frame'][c], e['mix_frame'], e['deliver_frame'], self.full), + (w['source_frame'][d], e['mix_frame'], self.full)): + for f1, f2 in zip(ch, ch[1:]): + assert self.sub(f1, f2) + source[dim(f2) - dim(f1)] += 1 + events = defaultdict(list) + for s in sorted(self.when, key=self.when.get): + for t in self.gauge[s]['targets']: + events[t].append(self.gauge[s]['frame']) + deliveries = defaultdict(list) + for e in C.k['entries']: + deliveries[e['deliver_after_root']].append(e) + for j, r in enumerate(C.g['roots']): + if r['kind'] == 'side': + for t in r['targets']: + events[t].append(w['root_frame'][j]) + for e in deliveries.get(j, ()): + for t in e['receivers']: + events[t].append(e['deliver_frame']) + target = Counter() + for t in range(v): + prev, d0 = None, 0 + for f in events[t]: + assert prev is None or self.sub(prev, f) + if dim(f) > d0: + target[dim(f) - d0] += 1 + prev, d0 = f, dim(f) + assert d0 <= h - 1 + if d0 < h - 1: + target[h - 1 - d0] += 1 + tails = Counter(dim(z['frame']) for s, z in self.gauge.items() if s not in self.donor_of) + return dict(injections=injections, centres=centres, source=source, target=target, tails=tails) + + +# ---------------------------------------------------------------------------------------------- the slot floor +def slot_bounds(W, start, events): + n = len(events) + lo, acc = [0] * n, start + for i, ev in enumerate(events): + acc = W.join(acc, ev[0]) + lo[i] = W.dim(acc) + hi, acc = [0] * n, W.full + for i in reversed(range(n)): + acc = W.meet(acc, events[i][1]) + hi[i] = W.dim(acc) + assert all(l <= u for l, u in zip(lo, hi)), 'infeasible slot' + return lo, hi + + +def slot_dp(d_start, lo, hi, tags, h, F, price): + """min over nondecreasing dimensions d_i in [lo_i, hi_i] of sum f(d_i - d_(i-1)) + f(h - d_last) + + sum sign * price[op] * d_i (the Lagrangian term of coupled events). Exact integers. Returns (cost, dims).""" + best, back = {d_start: 0}, [] + for i in range(len(lo)): + w = 0 + if tags[i] is not None: + w = tags[i][1] * price.get(tags[i][0], 0) + nxt, arg = {}, {} + for d in range(lo[i], hi[i] + 1): + c, p = None, None + for d0, c0 in best.items(): + if d0 <= d and (c is None or c0 + F[d - d0] < c): + c, p = c0 + F[d - d0], d0 + if c is not None: + nxt[d], arg[d] = c + w * d, p + best = nxt + back.append(arg) + d = min(best, key=lambda e: best[e] + F[h - e]) + cost = best[d] + F[h - d] + dims = [0] * len(lo) + for i in reversed(range(len(lo))): + dims[i] = d + d = back[i][d] + return cost, dims + + +# ---------------------------------------------------------------------------------------------- main +def main(): + ap = argparse.ArgumentParser(description=__doc__, formatter_class=argparse.RawDescriptionHelpFormatter) + ap.add_argument('--tree', type=Path, default=None) + ap.add_argument('--check', action='store_true') + ap.add_argument('--rounds', type=int, default=1200, help='Lagrangian rounds (default 1200)') + ap.add_argument('--overrides', type=Path, default=None, help='another layout of the word ([op, rows] list)') + a = ap.parse_args() + if a.tree is not None: + return run(a, a.tree.resolve()) + with tempfile.TemporaryDirectory(prefix='bit-frame-ceiling-pr200-') as d: + commit = rebuild(Path(d)) + log('rebuilt the pinned files of #200 (commit %s) from baseline-pr200.tar.gz; hashes match SOURCE.json' % commit[:7]) + return run(a, Path(d).resolve()) + + +def run(a, tree): + T = load(tree) + W = Word(T) + h, v, m = W.h, W.v, W.m + cert = T['cert'] + pre, post = cert['overridden_profile'], cert['profile'] + loss = pre['loss'] + D = 2 * v - 3 * loss + assert pre['deficit_per_vertex'] == post['deficit_per_vertex'] == D and pre['m'] == post['m'] == m + F = cost_table(m) + unit = Q(1, 1 << SCALE) + out = dict(package=PKG, h=h, v=v, loss=loss, D=D, m=m, operations=len(W.ops), roles=W.R, reuse_pairs=len(W.pairs), + sinks=len(W.sinkroles)) + log('#200 bit word: h %d, v %d, centre loss %d, deficit D = 2v - 3 loss = %d, %d operations, %d roles, %d reuse pairs, %d sinks' + % (h, v, loss, D, len(W.ops), W.R, len(W.pairs), len(W.sinkroles))) + + # fact 1, numerically: D/C of the certified profile against its certified coarse saving + f = lambda r: r * math.log(m / r) + Hpost = {int(r): n for r, n in post['child_histogram'].items() if n} + C_post = math.fsum(n * f(r) for r, n in Hpost.items()) + coarse = Q(cert['coarse']['coarse_saving']) + log('fact 1: certified coarse saving %.7e < D/C = %.7e (gap %.3f%%)' % (float(coarse), D / C_post, 100 * (1 - float(coarse) / (D / C_post)))) + assert coarse < Q(D) / Q(C_post) + + # the slot model: with #200's own frames it reproduces the certified ledger child for child + W.bounds() + assert W.inside(W.opf), 'the certified layout lies outside the joint bounds' + slots = W.slots() + fixed = W.fixed_children() + local, prepared, actual_total = Counter(), [], 0 + for s, start, ev, is_sink in slots: + steps = W.chain_dims(s, W.opf) + local.update(steps) + lo, hi = slot_bounds(W, start, ev) + tags = [e[2] for e in ev] + own, _ = slot_dp(W.dim(start), lo, hi, tags, h, F, {}) + assert own <= sum(F[r] for r in steps), 'floor above the actual chain of slot %d' % s + if is_sink: + assert steps[-1] == h - W.dim(W.rootframe[s]), 'sink chain ends with the root-to-full step' + prepared.append((W.dim(start), lo, hi, tags)) + actual_total += sum(F[r] for r in steps) + # the terminal record: per sink and stage, the sink's last step (root frame to full space, width h - dim root, + # present in every layout) and one target child (the pivot's cap read, width fixed by the gauges and roots) + # disappear; the sink's other steps are copied to the pivot and stay charged (research/paired-cube-diagonal-bit-168 + # bit/terminal.py; #207 audits the same -102/-102 substitution on its layout) + delta = Counter({int(r): n for r, n in cert['terminal']['child_delta'].items()}) + sink_steps = Counter({r: -n // 3 for r, n in delta.items()}) + assert all(-n == 3 * sink_steps[r] for r, n in delta.items()) and sum(sink_steps.values()) == 2 * len(W.sinkroles) + last = Counter(h - W.dim(W.rootframe[s]) for s in W.sinkroles) + assert sink_steps[next(iter(last))] >= last[next(iter(last))] and len(last) == 1 + other = [r for r in sink_steps if r != next(iter(last))] or [next(iter(last))] + pre_t = {int(r): n for r, n in pre['physical_target_histogram'].items()} + post_t = {int(r): n for r, n in post['physical_target_histogram'].items()} + assert all(pre_t.get(r, 0) - post_t.get(r, 0) >= sink_steps[r] - last.get(r, 0) for r in other), 'removed target children' + local[1] += fixed['injections'] + for r in fixed['centres']: + local[r] += 1 + children = Counter() + for part in (local, fixed['source'], fixed['target']): + for r, n in part.items(): + if r and n: + children[r] += 3 * n + for d, n in fixed['tails'].items(): + children[3 * d] += n + children[2] += 2 * v + assert dict(children) == {int(r): n for r, n in pre['child_histogram'].items() if n}, 'slot model differs from the certified pre-sink ledger' + assert 2 * v + W.R - len(W.pairs) == pre['W_per_vertex'] and sum(r * n for r, n in children.items()) == pre['rank_per_vertex'] + less = Counter(children) + for r, n in sink_steps.items(): + less[r] -= 3 * n + assert +less == Counter(Hpost), 'the certified sink record is not one [r] and one [h - r] per sink and stage' + assert dict(Counter({int(r): n for r, n in cert['terminal']['child_delta'].items()})) == {r: -3 * n for r, n in sink_steps.items()} + log('self-test: #200\'s layout lies inside every derived frame bound; its slot chains reproduce the certified ' + 'pre-sink ledger exactly (W %d, rank %d); the terminal record substitutes [%s] per sink and stage; every slot floor is below its actual chain' + % (pre['W_per_vertex'], pre['rank_per_vertex'], ', '.join('%d' % r for r in sorted(sink_steps)))) + + # fact 4: Lagrangian coupling; each round's total is a valid floor (price terms cancel on any common-frame layout) + price, best, step, independent = {}, None, (3 << SCALE) // 10, None + for k in range(a.rounds + 1): + total, grad = 0, defaultdict(int) + for d0, lo, hi, tags in prepared: + c, dims = slot_dp(d0, lo, hi, tags, h, F, price) + total += c + for tg, d in zip(tags, dims): + if tg is not None: + grad[tg[0]] += tg[1] * d + assert total <= actual_total, 'Lagrangian floor above the certified layout' + if best is None or total > best: + best = total + if k == 0: + independent = total + for i, g in grad.items(): + if g: + price[i] = price.get(i, 0) + step * g + step = step * 995 // 1000 + sink_cost = 3 * sum(F[r] * n for r, n in sink_steps.items()) # fixed in every layout (see the terminal record above) + fixed_cost = 3 * (fixed['injections'] * F[1] + sum(F[r] for r in fixed['centres']) + + sum(F[r] * n for r, n in fixed['source'].items() if r) + + sum(F[r] * n for r, n in fixed['target'].items() if r)) + 2 * v * F[2] + tails_cost = sum(F[3 * d] * n for d, n in fixed['tails'].items()) + results = {} + for name, extra in (('own', tails_cost), ('banked', 0)): + C_floor = (3 * best + fixed_cost + extra - sink_cost) * unit + C_ind = (3 * independent + fixed_cost + extra - sink_cost) * unit + C_act = (3 * actual_total + fixed_cost + extra - sink_cost) * unit + results[name] = dict(C_floor=float(C_floor), C_certified_layout=float(C_act), + coarse_ceiling='%d/10^7' % ceil7(Q(D) / C_floor), coarse_ceiling_uncoupled='%d/10^7' % ceil7(Q(D) / C_ind), + kappa_ceiling='%d/10^7' % ceil7(G(Q(D) / C_floor))) + out.update(results=results, rounds=a.rounds, certified_coarse=str(coarse), + certified_kappa=str(T['kappa']) if T['kappa'] is not None else None) + Hpre = {int(r): n for r, n in pre['child_histogram'].items() if n} + Hbank = dict(Hpost) + for d, n in fixed['tails'].items(): + Hbank[3 * d] -= n + Hbank = {r: n for r, n in Hbank.items() if n} + log('fact 4, #200\'s own ledger: certified C = %.0f, floor C >= %.0f; coarse < %s = %.7e (certified %.7e is %.1f%% of it); kappa < %s' + % (C_post, results['own']['C_floor'], results['own']['coarse_ceiling'], ceil7(Q(D) / Q(results['own']['C_floor'])) / 1e7, + float(coarse), 100 * float(coarse) / (ceil7(Q(D) / Q(results['own']['C_floor'])) / 1e7), results['own']['kappa_ceiling'])) + C_bank = math.fsum(n * f(r) for r, n in Hbank.items()) + log('fact 4, banked ledger (#205/#206/#207 accounting on this word): D/C of #200\'s layout = %.7e; floor C >= %.0f; coarse < %s; kappa < %s' + % (D / C_bank, results['banked']['C_floor'], results['banked']['coarse_ceiling'], results['banked']['kappa_ceiling'])) + log('without coupling the two registers of an operation: coarse < %s (own), %s (banked)' + % (results['own']['coarse_ceiling_uncoupled'], results['banked']['coarse_ceiling_uncoupled'])) + + if a.overrides is not None: # another layout of the same word, e.g. #207's 302 changed frames + opf = list(W.opf) + changes = json.loads(a.overrides.read_text()) + for i, rows in changes: + opf[i] = W.register([tuple(int(z) for z in r) for r in rows]) + assert W.inside(opf), 'the override layout lies outside the joint bounds' + total_over, loc = 0, Counter() + for s, start, ev, is_sink in slots: + steps = W.chain_dims(s, opf) + loc.update(steps) + total_over += sum(F[r] for r in steps) + if is_sink: + assert steps[-1] == h - W.dim(W.rootframe[s]) + assert best <= total_over, 'floor above the override layout' + Hov = Counter() + loc[1] += fixed['injections'] + for r in fixed['centres']: + loc[r] += 1 + for part in (loc, fixed['source'], fixed['target']): + for r, n in part.items(): + if r and n: + Hov[r] += 3 * n + Hov[2] += 2 * v + for r, n in sink_steps.items(): + Hov[r] -= 3 * n + C_ov = math.fsum(n * f(r) for r, n in Hov.items() if n) + out['overrides'] = dict(file=str(a.overrides), changed=len(changes), inside_bounds=True, + banked_DC=D / C_ov, own_DC=D / (C_ov + math.fsum(n * f(3 * d) for d, n in fixed['tails'].items()))) + log('override layout %s: %d changed frames, inside every bound, above the floor; banked D/C = %.7e (%.1f%% of the banked ceiling)' + % (a.overrides.name, len(changes), D / C_ov, 100 * (D / C_ov) / (ceil7(Q(D) / Q(results['banked']['C_floor'])) / 1e7))) + + if a.check: + expected = json.loads((HERE / 'expected.json').read_text()) + keys = ('h', 'v', 'loss', 'D', 'm', 'operations', 'roles', 'reuse_pairs', 'sinks', 'rounds', 'certified_coarse') + got = {k: out[k] for k in keys} + got['results'] = {n: {k: r[k] for k in ('coarse_ceiling', 'coarse_ceiling_uncoupled', 'kappa_ceiling')} for n, r in results.items()} + exp = {k: expected[k] for k in keys} + exp['results'] = {n: {k: r[k] for k in ('coarse_ceiling', 'coarse_ceiling_uncoupled', 'kappa_ceiling')} for n, r in expected['results'].items()} + assert got == exp, 'results differ from expected.json' + log('PASS results equal expected.json') + print(json.dumps(out, indent=1, sort_keys=True)) + + +if __name__ == '__main__': + main() diff --git a/research/bit-frame-ceiling-200/expected.json b/research/bit-frame-ceiling-200/expected.json new file mode 100644 index 0000000000..e315d2ff88 --- /dev/null +++ b/research/bit-frame-ceiling-200/expected.json @@ -0,0 +1,25 @@ +{ + "D": 1936, + "certified_coarse": "677773948354561/1000000000000000000", + "h": 24, + "loss": 528, + "m": 72, + "operations": 41288, + "results": { + "banked": { + "coarse_ceiling": "6964/10^7", + "coarse_ceiling_uncoupled": "7118/10^7", + "kappa_ceiling": "6959/10^7" + }, + "own": { + "coarse_ceiling": "6904/10^7", + "coarse_ceiling_uncoupled": "7056/10^7", + "kappa_ceiling": "6900/10^7" + } + }, + "reuse_pairs": 1760, + "roles": 18908, + "rounds": 1200, + "sinks": 34, + "v": 1760 +} \ No newline at end of file