diff --git a/.github/workflows/precision-and-scalar.yml b/.github/workflows/precision-and-scalar.yml new file mode 100644 index 0000000000..c8bed40147 --- /dev/null +++ b/.github/workflows/precision-and-scalar.yml @@ -0,0 +1,67 @@ +name: Verify precision refinement and exact scalar maps + +on: + push: + pull_request: + workflow_dispatch: + +permissions: + contents: read + +jobs: + verify: + runs-on: ubuntu-24.04 + timeout-minutes: 20 + strategy: + fail-fast: false + matrix: + python-version: ['3.12', '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 native181 local-circuit, frame, prime and formal audits + run: python -B research/paired-cube-local-168/verify.py + - name: Check precision, native input binding and controls in both modes + run: | + python -B research/precision-certificate/verify.py --native-inputs + python -B research/precision-certificate/test_precision.py + python -B research/precision-certificate/test_native.py + python -O -B research/precision-certificate/verify.py --native-inputs + python -O -B research/precision-certificate/test_precision.py + python -O -B research/precision-certificate/test_native.py + - name: Check independent scalar fixtures in both modes + run: | + python -B research/paired-cube-scalar-audit/test_bit.py + python -B research/paired-cube-scalar-audit/test_sinks.py + python -B research/paired-cube-scalar-audit/test_signed.py + python -B research/paired-cube-scalar-audit/test_source.py + python -O -B research/paired-cube-scalar-audit/test_bit.py + python -O -B research/paired-cube-scalar-audit/test_sinks.py + python -O -B research/paired-cube-scalar-audit/test_signed.py + python -O -B research/paired-cube-scalar-audit/test_source.py + - name: Audit every scalar coefficient of the pinned selected witnesses + run: | + python -c 'import pathlib,resource,runpy,sys; resource.setrlimit(resource.RLIMIT_AS,(4*1024**3,4*1024**3)); sys.argv=sys.argv[1:]; sys.path.insert(0,str(pathlib.Path(sys.argv[0]).resolve().parent)); runpy.run_path(sys.argv[0],run_name="__main__")' research/paired-cube-scalar-audit/verify.py + python -O -c 'import pathlib,resource,runpy,sys; resource.setrlimit(resource.RLIMIT_AS,(4*1024**3,4*1024**3)); sys.argv=sys.argv[1:]; sys.path.insert(0,str(pathlib.Path(sys.argv[0]).resolve().parent)); runpy.run_path(sys.argv[0],run_name="__main__")' research/paired-cube-scalar-audit/verify.py + - name: Reproduce native186 immutable archive and complete selected aggregate + run: python -B research/coordinated-frames-and-entrance-banks/verify.py + - name: Check independent186 precision, banks and guards in both modes + run: | + python -B research/frontier-refinement186/verify.py + python -B research/frontier-refinement186/check_banks.py + python -B research/frontier-refinement186/test_refinement.py + python -B research/frontier-refinement186/test_source.py + python -O -B research/frontier-refinement186/verify.py + python -O -B research/frontier-refinement186/check_banks.py + python -O -B research/frontier-refinement186/test_refinement.py + python -O -B research/frontier-refinement186/test_source.py + - name: Audit every186 scalar coefficient with unchanged signed core + run: | + python -c 'import pathlib,resource,runpy,sys; resource.setrlimit(resource.RLIMIT_AS,(4*1024**3,4*1024**3)); sys.argv=sys.argv[1:]; sys.path.insert(0,str(pathlib.Path(sys.argv[0]).resolve().parent)); runpy.run_path(sys.argv[0],run_name="__main__")' research/frontier-refinement186/scalar.py + python -O -c 'import pathlib,resource,runpy,sys; resource.setrlimit(resource.RLIMIT_AS,(4*1024**3,4*1024**3)); sys.argv=sys.argv[1:]; sys.path.insert(0,str(pathlib.Path(sys.argv[0]).resolve().parent)); runpy.run_path(sys.argv[0],run_name="__main__")' research/frontier-refinement186/scalar.py + - name: Require reproducible tracked files + run: git diff --exit-code diff --git a/SOURCES.json b/SOURCES.json index f7117f0f98..7479ebdc05 100644 --- a/SOURCES.json +++ b/SOURCES.json @@ -500,5 +500,83 @@ ], "scope": "Conditional on retained analytic, uniform-recursion and fixed-tape contracts; complete local paired-cube schedule, exact core sharing and scalar charge supplied in the proof.", "curation": "Selected paired-coordinate cube only, compact frozen carrier arcs and bit subset, exact suppliers and assembly. Excludes fallback shared_core results, paired-five motifs, other candidate graphs, search screens and PDFs." + }, + "paired_cube_physical_bit_extension": { + "contributor": "eumemic", + "assistance": "Prepared with Anthropic Claude assistance.", + "predecessor_pr": 144, + "predecessor_commit": "c8b22bc5c10dba497ac25804e27d9647d818e2ff", + "kappa": "6558894/10000000000", + "proof": "notes/paired-cube-note.tex", + "certificate": "certificates/paired-cube-network.json", + "change": "PR144 paired cubes at p=11 with pinned annealed triple, pair and all-but-one modules, the L1 local channel circuit and fused face-2/edge-02/edge-12 outputs, carrier arcs compiled under PR162's closure conditions, physical frame descent (connected bundles) and compensated late-read reuse on the complex word (scripts/paired_cube_physical.py) and terminal sinks (research/terminal-sinks); a paired-cube bit word with partner-pair source mixing, an annealed pair module, an annealed all-but-one module, the L1 local-channel association and merged outputs (variant u) (research/paired-cube-bit), with late copies and late-read reuse (scripts/paired_cube_bit_physical.py); the balanced prefix (scripts/paired_cube_assembly.py); phase stop 1e-9 (PR153) and the atom exponent at its toll edge (PR158); PR144 checks and assembly otherwise unchanged.", + "adopted": [ + { + "pr": 144, + "contributor": "icekylinx", + "commit": "c8b22bc5c10dba497ac25804e27d9647d818e2ff", + "role": "Paired-cube decoder, modules, shared cores, bit ledger, finite bridge and assembly." + }, + { + "pr": 131, + "contributor": "eumemic", + "role": "Physical frame descent and compensated reuse on Cayley covers (method)." + }, + { + "pr": 124, + "contributor": "jamesyc", + "role": "Compensated birth-read reuse." + }, + { + "pr": 143, + "contributor": "eumemic", + "role": "Deadline (late) compensation reads." + }, + { + "pr": 128, + "contributor": "an664", + "role": "Completed-core sharing." + }, + { + "pr": 97, + "contributor": "Zhihao Chen (jacklightChen)", + "role": "Bit-side compile conventions (deferred readouts, plain or lifted frames)." + }, + { + "contributor": "Swapnil Jain", + "role": "Round-seven bit lineage (PR62 interval strips) from which the bit pair modules are cut." + }, + { + "pr": 158, + "contributor": "geckods", + "role": "Re-instantiated free assembly constants (phase stop, PR153; atom exponent, PR158)." + }, + { + "pr": 162, + "contributor": "DaysSky", + "role": "Carrier-arc compilation under the closure conditions (compile_closure, scripts/paired_cube/closure.py) and the first-order pairing rounds of the physical layer." + }, + { + "pr": 163, + "contributor": "chafreaky", + "role": "Same-singleton fusion of the single-target outputs (fold orders here from our own search)." + }, + { + "pr": 166, + "contributor": "jamesyc", + "role": "Terminal-sink lemma (dirty-target substitution of all-eight side roots), audited here by research/terminal-sinks/sinks_gate.py." + }, + { + "pr": 20, + "contributor": "RaD project (hipotures)", + "role": "Balanced positional transform: prefix margin 1-eps (references/semantic-bulk/rad20/reports/review-balanced-transform.md)." + }, + { + "pr": 34, + "contributor": "jamesyc", + "role": "Balanced assembly composition, with the parameters of research/copied-fixed/balanced_assembly.py (Chafik Boukhalfa)." + } + ], + "scope": "Conditional on the retained PR144 analytic, uniform-recursion and fixed-tape contracts." } } diff --git a/certificates/joint-dual-kappa.json b/certificates/joint-dual-kappa.json index 13d841a8c8..10fd4aa571 100644 --- a/certificates/joint-dual-kappa.json +++ b/certificates/joint-dual-kappa.json @@ -838,11 +838,11 @@ "scripts/experiments/binary_frame_replay.py": "392e78e62d7685c99a5888a7da743ea6c3dcad631af4a743c91e0c09348442bc", "scripts/experiments/joint_dual_compiler.py": "853d3fc4a740c5b74c23b3a6af5d4dc9b41fb38e9b55678539a7e0ee71947c13", "scripts/experiments/joint_dual_compose.py": 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+226,7 @@ } }, "bit_saving": "2382370177/50000000000000", - "certificate_sha256": "16f18ad60af972ce1f9fbbbb1277a69ad838727d542889bbac6c5539d5420bf7", + "certificate_sha256": "4044f15abf49b1551193891836e2d20975b8246acc888180af47266c64f77af0", "kappa": "4764513337/100000000000000", "margins": 7, "producer_words_regenerated_and_matched": true, diff --git a/certificates/paired-cube-bit-physical-input.json b/certificates/paired-cube-bit-physical-input.json new file mode 100644 index 0000000000..8014fc2a23 --- /dev/null +++ b/certificates/paired-cube-bit-physical-input.json @@ -0,0 +1,99 @@ +{ + "R": 19788, + "W_per_vertex": 21548, + "changed_operation_frames": 2884, + "checks": { + "donor_frames_inside_gauges": true, + "gauge_read_window": true, + "operation_frames_nondegenerate_and_spanning": true, + "pair_chronology": true, + "partner_chronology": true, + "phase_one_closure": true, + "register_contents": true, + "role_chains_nested": true, + "target_chains_nested_in_read_order": true, + 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a/certificates/paired-cube-network.json +++ b/certificates/paired-cube-network.json @@ -1,334 +1,371 @@ { "assembly": { - "absorption_gap": "49772927594887408131062764367/500461342287379865539365770570000000000", + "absorption_gap": "4998206273112780939153/781762749911107251572755000000000", "margins": { - "Gaussian_arithmetic": "27680687058255018102013446063422943/40036907382990389243149261645600000000", - "bulk_exposure": "4613422943/10000000000000", - "compact_phase_layer": "23067114022986563163422943/50046134228737986553936577057", - "coordinate_movement": "4613422943/10000000000000", - "dimension": "49999999500000000000000000000/50046134228737986553936577057", - "original_prefix": "2306761448432885054328848236577057/5004613422873798655393657705700000000", - "scalar_work": "36907732944255014411275091663422943/40036907382990389243149261645600000000" + "Gaussian_arithmetic": "16408090802882068106709685449/25016407997155432050328160000000", + "balanced_prefix": 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+} diff --git a/docs/paired-cube.md b/docs/paired-cube.md index 38dc3d30e0..762b435e06 100644 --- a/docs/paired-cube.md +++ b/docs/paired-cube.md @@ -2,7 +2,9 @@ This extension inherits PR #130 at `6a9970a530119174507904e23592fd59ede19a5d` and gives the conditional saving -`4609169/10000000000 = 4.609169e-4`. +`6558894/10000000000 = 6.558894e-4`. The complex word adds physical frame descent and compensated late-read +reuse (`scripts/paired_cube_physical.py`); the bit supplier is the paired-cube bit word in +`research/paired-cube-bit`. From the repository root with Python 3.11+: @@ -13,16 +15,25 @@ make paired-cube-verify The selected incremental target uses only the Python standard library. CI runs it in its own `paired-cube` matrix group. The checks are: -- Rebuild the selected signed H-channel graph from exact zero restrictions of - the pinned PR #117 positive DAG. Replay the frozen 6,074 carrier arcs, +- Rebuild the selected signed H-channel graph (p = 11) from the pinned annealed triple, pair and all-but-one + modules and the L1 local circuit in `references/paired-cube/sources`, with fused face-2/edge-02/edge-12 outputs. + Replay the frozen 10,704 carrier arcs (compiled under #162's closure conditions), coordinate frames, full backward intersections, signed physical mixer, - center closure and 4,840 rank-20 partial gauges. Independent checks cover + center closure and 2,310 rank-18 partial gauges. Independent checks cover every scalar coefficient of `H+K+B=I`, the original-source K involution and inverse, actual frame containment and reverse target chains. -- Reconstruct the bit subset from the existing PR #97 witness and readout - order. Check the retained 9,543 and omitted 2,022 slots, moved zero-frame - dirty reads, changed first transitions and target subsequences. Unchanged - complete-basis and rational-frame suites remain inherited checks. +- Apply the frozen physical frames and late-read reuse pairs and check chains, + chronology, target order and an aliased dirty-scratch replay + (`scripts/paired_cube_physical.py`), then the terminal sinks and their gate + (`research/terminal-sinks/sinks_gate.py`): sink conditions, nested literal stage words forward and reflected, + a dirty-scratch replay and four controls. +- Check the paired-cube bit word with its standalone checker + (`research/paired-cube-bit/check_paired_cube_bit.py`): exact frames, decoder + identity, chains, partner-pair chronology, nondegeneracy, F2 replay and + ledger. `python3 research/paired-cube-bit/paired_cube_bit_word.py --p 12 --check` + regenerates its outputs byte for byte. Apply the frozen physical bit word in + `references/paired-cube/bit-physical` and check it with `scripts/paired_cube_bit_physical.py`: register + contents, frames, spliced chains, pair chronology, target order and an aliased F2 replay with controls. - Rebuild both shared-core child lists and certify strict moments, full rare-class fallback, stopped bit saving, actual finite group/router charge, semantic guard, row stock, 47 strict inequalities and seven assembly margins. diff --git a/notes/paired-cube-assembly.tex b/notes/paired-cube-assembly.tex index d44227eb55..6e5d373576 100644 --- a/notes/paired-cube-assembly.tex +++ b/notes/paired-cube-assembly.tex @@ -1,54 +1,59 @@ \subsection{Strict suppliers and full finite group} The selected local complex profile has \[ - h=24,\quad v=1760,\quad c=24767,\quad q_{\rm roots}=7724, - \quad |\mathcal M|=6074,\quad R=26417,\quad\ell=528. + h=22,\quad v=1320,\quad c=20919,\quad q_{\rm roots}=3157, + \quad |\mathcal M|=10704,\quad R=13372,\quad\ell=440. \] The exact signed graph, frozen carrier arcs, coordinate frames and chronological gauge list are reconstructed by \path{scripts/paired_cube_producer.py}. Its complete shared inventory has -$m_c=72$, $w_c=29937$, $s_c=2153528$, deficit 1936 and largest child 60. -For $a_c=4856569/10^{10}$ the rational moment satisfies +After physical frame descent and compensated late-read reuse, it has +$m_c=66$, $w_c=13655$, $s_c=899910$, deficit 1320 and largest child 20. +For $a_c=6563200/10^{10}$ the rational moment satisfies \[ - \frac1{w_c}\sum_r n_r(r/72)^{1-a_c} - <1-2.0094617553\times10^{-10}. + \frac1{w_c}\sum_r n_r(r/66)^{1-a_c} + <1-5.0817824892\times10^{-12}. \] -The bit subset has $m_b=69$, $w_b=32408$, $s_b=2234128$ and deficit 2024. -At coarse saving $a_0=4617656/10^{10}$ its moment includes the entire -$32\cdot69^2$-child local-ring fallback on a fraction $10^{-16}$ of every -ideal edge. Its gap exceeds $1.4386017949\times10^{-10}$; the rank moment -also contracts. With the retained atom exponent $10^{-3}$, +The physical paired-cube bit word (\path{research/paired-cube-bit}, +\path{scripts/paired_cube_bit_physical.py}) has $m_b=72$, +$w_b=21548$, $s_b=1549520$ and deficit 1936. +At coarse saving $a_0=6600253/10^{10}$ its moment includes the entire +$32\cdot72^2$-child local-ring fallback on a fraction $10^{-16}$ of every +ideal edge. Its gap exceeds $1.4813473226\times10^{-10}$; the rank moment +also contracts. The atom exponent $\theta=659615306/10^{12}$ is the first +$10^{-12}$ grid point above the toll edge $a_0/(1+a_0-a_{\rm old})$, with +$a_{\rm old}=384599/10^{10}$ (as re-instantiated in PR158), so \[ - a_b=(1-10^{-3})a_0+10^{-3}\frac{384599}{10^{10}} - =\frac{4613422943}{10^{13}}. + a_b=(1-\theta)a_0+\theta\frac{384599}{10^{10}} + =\frac{6596153059484799876}{10^{22}}. \] Both adapter and internally borrowed-row tolls are lower order since -$a_b<10^{-3}<1-a_b$. The weighted compiler, residue bound, full fallback +$a_b<\theta<1-a_b$. The weighted compiler, residue bound, full fallback and ordinary outer wrapper are retained from \path{notes/three-stage-cover-bit.tex} and -\path{notes/three-stage-cover-rows.tex}, now with ambient dimension 69. +\path{notes/three-stage-cover-rows.tex}, now with ambient dimension 72. Sharing routers are fixed right multiplications, batched on the same complete high matrix field; the fresh-selector contract is unchanged. -For the complex cover $V=|O(72,2)|$ the retained even-dimensional group +For the complex cover $V=|O(66,2)|$ the retained even-dimensional group formula gives \[ - V=2^{1296}\prod_{i=1}^{35}(2^{2i}-1). + V=2^{1089}\prod_{i=1}^{32}(2^{2i}-1). \] -It has 2,556 bits, and full role stock $W=Vw_c$ has 2,571 bits. +It has 2,145 bits, and full role stock $W=Vw_c$ has 2,159 bits. Its full rank is $s=Vs_c$ and $N=Vv$. -The least halving degree for $72\to60$ is four, contributing 10,284 to +The least halving degree for $66\to20$ is one, contributing 2,159 to the row coefficient. Including the conservative preceding bit reserves, \[ - 10284+9909+252=20445,\qquad - 70000-\frac{51}{25}\,20445=\frac{141461}{5}>0. + 2159+9909+252=12320,\qquad + 70000-\frac{51}{25}\,12320=\frac{224336}{5}>0. \] Thus the fixed external reserve $p^{70000}$ suffices. The q-adic bit selector stock is borrowed and restored internally, not multiplied into this external polynomial reserve. \subsection{Literal charge, sharing routers and exact precision} -Let $M=49424$ be the actual local mixer-operation count. Put +Let $M=32971$ be the actual local mixer-operation count. Put \[ L=4(c+v)+10v+4hv+4h^2+8h+8+2h +8Rv(M+16)+32v. @@ -56,7 +61,7 @@ \subsection{Literal charge, sharing routers and exact precision} The last term pays both original-source involutions and their inverses. Every mixer update has signed unit coefficients. Starting from the identity, each entry of its exact matrix is therefore bounded by $2^M$. -There are $q_{\rm roots}=7724$ decoder roots; after clearing denominator +There are $q_{\rm roots}=3157$ decoder roots; after clearing denominator six, their scatter coefficients have absolute numerator at most three. Thus each numerator of $6JM$ is bounded by $3q_{\rm roots}2^M<2^{M+15}$. Including the sign, $M+16$ bits suffice. @@ -92,30 +97,36 @@ \subsection{Literal charge, sharing routers and exact precision} retains the inherited $O(V_{\rm bits}\log d)$ charge. \subsection{Exact retained semantic assembly} -Put $a=a_b$, $b=a_c$, $\eta=10^{-8}$, $\beta=10^{-6}$ and +Put $a=\min\{a_b,(1-\beta)a_c-10^{-10}\}$, $b=a_c$, $\eta=10^{-8}$, $\beta=10^{-9}$ and \[ \tau=1-a,\quad\sigma=1-b,\quad q_0=a(1-2\eta),\quad - c_0=q_0(1+\eta),\quad - \epsilon=\frac{1-\eta}{1+c_0+q_0}, + c_0=q_0+\eta/4,\quad + \epsilon=\frac{1-\eta}{1+q_0}, \] \[ \lambda'=1-q_0,\quad\lambda=(\tau+\lambda')/2,\quad g=\epsilon q_0,\quad r=(g+1-\epsilon)/2,\quad\delta=\eta/8. \] -Here $(1-\beta)b>a$, so the actual bit saving is available without further -weakening. All 47 strict constraints hold. The seven final savings are +Here $(1-\beta)b>a$ and $a\le a_b$, so the bit supplier supports the saving +$a$. The prefix is the RaD project's balanced positional transform +(reviewed in \path{references/semantic-bulk/rad20/reports/review-balanced-transform.md}, +with the parameters of \path{research/copied-fixed/balanced_assembly.py}): +its margin is $1-\epsilon$, and $\epsilon(1+c_0)<1$ remains a strict geometric +constraint whose gap need not exceed $\kappa$ +(\path{scripts/paired_cube_assembly.py}). All 47 strict constraints hold. +The seven final savings are \[ - 1-\epsilon(1+c_0),\ a,\ g,\ a,\ + 1-\epsilon,\ a,\ g,\ a,\ \min(1-\epsilon-\delta,r-\delta),\ 1-\epsilon-\delta,\ \epsilon. \] -Their minimum $g$ exceeds $4609169/10^{10}$ by more than -$9.9454090434\times10^{-11}$. +Their minimum $g$ exceeds $6558894/10^{10}$ by more than +$6.3935078432\times10^{-12}$. \begin{theorem} Under the retained analytic, semantic-precision, exact-recovery, uniform-recursion and fixed-tape interfaces, the selected construction gives \[ T(n)=O\!\left(n(\log n)^{1-\kappa}\right),\qquad - \boxed{\kappa=\frac{4609169}{10000000000}=4.609169\times10^{-4}}. + \boxed{\kappa=\frac{6558894}{10000000000}=6.558894\times10^{-4}}. \] \end{theorem} \begin{proof} diff --git a/notes/paired-cube-bit.tex b/notes/paired-cube-bit.tex index dd84535b21..b0f256ce9e 100644 --- a/notes/paired-cube-bit.tex +++ b/notes/paired-cube-bit.tex @@ -2,60 +2,49 @@ % Construction with GPT-6 Astra; integration with OpenAI Codex. % Retained PR97 ledger: Zhihao Chen; frozen scalar/frame witness: Swapnil Jain. % Their original licenses, credits and assistance disclosures remain pinned. -\subsection{Selected inherited bit gauges} -The bit supplier uses the pinned PR97 word at $h=23$, with $v=1771$ data -ports and $R=28866$ dirty roles. Its compressed witness, frame reader, -physical-ledger receipt and original notices remain under -\texttt{references/partial-gauge/pr97/}. The finite selection in -\texttt{references/paired-cube/pr97-subset/selection.json} retains $9543$ -of the $11565$ certified entrance gauges, in their original readout order, -and omits $2022$. This selects actual inherited frames, rather than -optimizing an unattached multiset of ranks. - -For an omitted role with entrance frame $\sigma_s$ of dimension $f_s$, -perform its old-value correction at the common initial zero frame, -before any positive-rank operation. Its exact scalar coefficients are -the coefficients of the original word's adjoint, including copied-center -readouts. Both ends of each moved dirty read have frame zero, so arbitrary -dirty inputs are allowed. Its subsequent first-use frame is unchanged. -All ordinary scalar operations, positive-rank $V$ injections, source-data -paths, copied centers and later role frames retain their pinned values. -Retained dirty readouts form the original subsequence. Deleting members -of a certified nested target chain preserves actual subspace nesting; -dimension monotonicity alone would not establish that assertion. - -If the original first-use dimension of an omitted role is $r_s$, its -first auxiliary transition changes from $r_s-f_s$ to $r_s$, and its -shared-core exterior child of width $3f_s$ disappears. Target chains -retain precisely the positive integer adjoint supports of the chosen -readouts. This is the inherited conservative support convention; an even -coefficient would merely give a zero bit read with a retained frame. -The source histogram and all $23$ copied-center transitions of width $22$ -are unchanged. The selected gauge dimensions have multiplicities +\subsection{Paired-cube bit word} +The bit supplier is a bit-side analog of the paired-cube decoder at $p=12$ +($h=24$, $v=1760$, $R=19788$), in \path{research/paired-cube-bit}. Its +pair-disjoint module (442 additions) is annealed, its all-but-one module +($n=10$, \path{research/paired-cube-bit/data/qmod_p12.json}) is annealed from +the nested prefix of the complex word, and every cube merges its +face-1 and edge-01 outputs into $u(b_0,b_1)$ and its face-2 and edge-02 +outputs into $w(b_0,b_2)$, each read by two single roots (variant u). Its +local channels use the L1 association of the complex word: the $G$ sums with +keys $(0,1,0)$, $(0,1,1)$ and $(1,2,1)$ add the two long face diagonals, and +the other sums add two edges as in PR144. Ports are +transversal triples of coordinate pairs; the mod-2 decoder is \[ - (22,1760),\ (21,1596),\ (20,1307),\ (19,3871),\ - (18,806),\ (17,131),\ (16,72). + x_T=\sum_{c\in T}\mathrm{star}(c)+\sum_{|S\cap T|=1}x_S , \] +with point stars of span $h-2$ (centre loss $\ell=h(h-2)=528$), the face and +edge channels of PR144's pair and all-but-one modules, and partner-pair sums +mixed on the source registers. \path{research/paired-cube-bit/LEMMA.md} proves +the mixing step: the carrier and passive chains $[1,h-4,2]$ and $[1,h-2]$ +are nested, every XOR happens at one common frame, the delivery happens at the +receivers' level-2 cap, and the mix completes inside its core, so it is +sequential rather than lockstep. The word is compiled with PR144's ledger on +rational frames, with 3960 chronological gauges: 2200 of dimension 20 and +1760 of dimension 21. -In the cross-stage orthogonal sharing architecture, $m=3h=69$ and -$W=2v+R=32408$ per cover vertex. There are three copies of each local -auxiliary, source, target and copied-center transition, one exterior child -of width $3f_s$ per selected gauge, and $2v$ final children of width $2$. -Consequently the selected profile has +The physical word (\path{references/paired-cube/bit-physical}) adds late +copies, 2,884 moved operation frames and 1,760 compensated late reads: each +recipient is a gauged role in a dead donor's slot, read immediately before +its first operation (PR124, PR143). \path{scripts/paired_cube_bit_physical.py} +checks register contents, frames, spliced role chains, pair chronology, +read-order target chains and the partner chronology, recounts the ledger and +replays the aliased word over F2 with three controls. +In the cross-stage orthogonal sharing architecture, $m=3h=72$ and +$W=2v+R-1760=21548$ per cover vertex, and \[ - \ell=h(h-1)=506,\qquad - \sum_r r C_r=2234128=Wm-2024,\qquad - 2024=2v-3\ell. + \sum_r r C_r=1549520=Wm-1936,\qquad 1936=2v-3\ell. \] -Its largest child is $66$. The strict supplier moment below also charges -the retained rare-class fallback and stopped atom wrapper. +Its largest child is $60$. The strict supplier moment below also charges the +retained rare-class fallback and stopped atom wrapper. -\texttt{scripts/paired\_cube\_bit.py} reconstructs this profile from the -existing pinned inputs. It checks their hashes, the exact selected slot -partition and inherited order, the integer target-incidence sweep, the -initial zero-frame corrections, and the changed transition histogram -against a direct reconstruction of the modified role chains. The -incremental review finds $72$ changed transition types and $9594$ moved -old-value reads. It repeats neither the complete-basis scalar replay nor -the inherited exact rational frame and lifted-witness audits. The -original frozen witnesses and scripts remain unchanged. +The standalone checker \path{research/paired-cube-bit/check_paired_cube_bit.py}, +run by \path{scripts/paired_cube_network.py}, recomputes the exact frames, the +decoder identity, every role and target chain, the partner-pair chronology, +$G$-nondegeneracy, a literal F2 replay with arbitrary dirty scratch and the +ledger. The generator regenerates every output byte for byte, and five +mutation controls are rejected. diff --git a/notes/paired-cube-construction.tex b/notes/paired-cube-construction.tex index 4428af9c6d..43ae11a373 100644 --- a/notes/paired-cube-construction.tex +++ b/notes/paired-cube-construction.tex @@ -130,13 +130,39 @@ \subsection{Arbitrary dirty contents and the frozen witness} have been restored. Exact frame representatives and rank-zero phase adapters are those of the arbitrary-subspace Clifford interface. -For the selected $p=12$ graph, 24,767 active additions and 7,724 root -uses, with 6,074 actual monotone carrier links, give +The selected graph has $p=11$. Its triple-disjoint, pair-disjoint and +all-but-one modules are pinned annealed modules +(\path{references/paired-cube/sources}), each loaded with its contract checked +(\texttt{triple\_module\_from}, \texttt{pair\_module\_from}, +\texttt{all\_but\_one\_from}), in place of PR117's restrictions and PR144's +balanced tree. The all-but-one module was annealed from a nested prefix: with +prefix sums $p_{k+1}=p_k+x_k$ and suffix sums $s_k=x_k+s_{k+1}$, the outputs +$y_0=s_1$, $y_{n-1}=p_{n-1}$ and $y_{i+1}=p_i+(x_i+s_{i+2})$ use each prefix +twice with nested supports, which admits more carrier links than the +balanced tree. +The local channel circuit follows \path{references/paired-cube/sources/local_L1.json}: +every cube's thirteen local outputs keep their values, but $G_{01}$ (both +modes) and $G_{12}$ (mode 1) are sums of two shared long-diagonal +differences and $F$ is built on axis 2, with 27 additions per cube instead +of 25. Fewer edges carry $G$ duty, so the carrier matching gains links; +\texttt{Graph(p, local=None)} runs PR144's circuit unchanged. +For every port the three single-target outputs face-2, edge-02 and edge-12 +are fused into one signed node read with coefficient $1/2$, in a fixed +order per port class (\texttt{merge\_outputs}, variant +\texttt{f8:00111100}), following PR163's same-singleton fusion; the decoder +contribution is unchanged and every addition keeps disjoint supports. +The carrier arcs are compiled by PR162's \texttt{compile\_closure} +(\path{scripts/paired_cube/closure.py}), which admits an arc when the +generalized dependency graph stays acyclic and every value span stays inside +its full backward intersection; \path{scripts/paired_cube/verify.py} checks +both conditions independently. +Its 20,919 active additions and 3,157 root uses, with 10,704 actual +monotone carrier links, give \[ - h=24,\quad v=1760,\quad R=26417,\quad\ell=528. + h=22,\quad v=1320,\quad R=13372,\quad\ell=440. \] -The frozen chronological gauge witness selects 4,840 roles, each of -dimension 20. Its graph, matching/frame witness and gauge-selection file, +The frozen chronological gauge witness selects 2,310 roles, each of +dimension 18. Its graph, matching/frame witness and gauge-selection file, not an abstract circuit-rank bound, determine the paid internal histogram. -The selected source histogram is $[2,20,1]$ per port; the target histogram -is $[20,1,1,1]$ per port. Zero-width adapters remain paid scalar work. +The selected source histogram is $[2,18,1]$ per port; the target histogram +is $[18,1,1,1]$ per port. Zero-width adapters remain paid scalar work. diff --git a/notes/paired-cube-note.tex b/notes/paired-cube-note.tex index b72c67f72f..32d75b3003 100644 --- a/notes/paired-cube-note.tex +++ b/notes/paired-cube-note.tex @@ -9,7 +9,7 @@ \newtheorem{lemma}[theorem]{Lemma} \newtheorem{proposition}[theorem]{Proposition} \title{Paired cubes and shared completed cores for integer multiplication\\ -\large A conditional saving $\kappa=4609169/10^{10}$} +\large A conditional saving $\kappa=6558894/10^{10}$} \author{icekylinx\\\small Construction with substantial OpenAI GPT-6 Astra assistance;\\ \small exposition and repository integration with Codex assistance} \date{9 October 2026} @@ -20,7 +20,7 @@ on the original source registers. Complete arbitrary-dirty cores share one auxiliary bank across three orthogonal address blocks. The exact selected ledgers, bit gauge subset and retained semantic assembly yield -$T(n)=O(n(\log n)^{1-0.0004609169})$ under the inherited interfaces. +$T(n)=O(n(\log n)^{1-0.0006558894})$ under the inherited interfaces. \end{abstract} \section{Scope and contributions} diff --git a/notes/paired-cube-sharing.tex b/notes/paired-cube-sharing.tex index 56e729572d..8538a047c0 100644 --- a/notes/paired-cube-sharing.tex +++ b/notes/paired-cube-sharing.tex @@ -79,12 +79,28 @@ \subsection{The complete paid ledger} \end{align*} For the selected complex word, \[ - m=72,\quad W_0=29937,\quad - \sum_r rn_r=2153528,\quad mW_0-\sum_r rn_r=1936. + m=66,\quad W_0=13655,\quad + \sum_r rn_r=899910,\quad mW_0-\sum_r rn_r=1320. \] -The 4,840 exterior children have width 60; all local internal children -have width at most 22, and final data children have width two. -Hence the largest child is 60. Full stock is $W=|\mathcal G|W_0$; +Physical frame descent (\path{scripts/paired_cube_physical.py}) moves +15,149 common operation frames between the span of their previous frames +and the intersection of their next frames; connected operations that share +a frame move together. Each of the 2,310 gauged +roles then occupies the physical slot of a dead donor whose last frame +lies in its gauge. Its old-value read moves to the deadline immediately +before its first operation, and the slot keeps the donor's zero start. +So no exterior correction remains: every local internal child has width +at most 20, and final data children have width two. Hence the largest +child is 20. Finally, 47 all-eight side roots are terminal sinks +(\path{research/terminal-sinks}; the terminal-sink lemma of PR166, checked +by its own gate): such a root's register starts at frame 0, is only ever a +destination outside phase one, and has a pivot target $p$ with no deferred +read of $y_p$ during its writes. The register is deleted; at the phase cut +$y_t\gets y_t-y_p$ for the other targets $t$, every write goes to $y_p$ at its +frame, and after the last write $y_t\gets y_t+y_p$ at the root frame $U$. +Each sink removes one physical register and one pair of children $[\operatorname{rank}U]$ +and $[h-\operatorname{rank}U]$, and the deficit is unchanged. This leaves +11,015 physical roles. Full stock is $W=|\mathcal G|W_0$; the group factor cancels from the normalized moment, not from routing, scalar work, row stock or the finite semantic guard. diff --git a/references/paired-cube/bit-physical/frames_p12.json.gz b/references/paired-cube/bit-physical/frames_p12.json.gz new file mode 100644 index 0000000000..70a1426036 Binary files /dev/null and b/references/paired-cube/bit-physical/frames_p12.json.gz differ diff --git a/references/paired-cube/bit-physical/kchron_p12.json b/references/paired-cube/bit-physical/kchron_p12.json new file mode 100644 index 0000000000..bcb65cae69 --- /dev/null +++ b/references/paired-cube/bit-physical/kchron_p12.json @@ -0,0 +1 @@ +{"conventions":{"frame_ids":"frame id = id of the canonical annihilator; record \"a\" lists integer annihilator rows (frame = common kernel), record \"b\" lists integer basis rows; id 0 (empty \"a\") is the full space Q^h","gram":"G = I - J/9 on Q^h (H0 = G/2, H0(chi_S,chi_T) = (|S cap T|-1)/2); nondegeneracy tested 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diff --git a/references/paired-cube/bit-physical/word_p12.json.gz b/references/paired-cube/bit-physical/word_p12.json.gz new file mode 100644 index 0000000000..4afcba3d43 Binary files /dev/null and b/references/paired-cube/bit-physical/word_p12.json.gz differ diff --git a/references/paired-cube/physical/README.md b/references/paired-cube/physical/README.md new file mode 100644 index 0000000000..38fdd020af --- /dev/null +++ b/references/paired-cube/physical/README.md @@ -0,0 +1,20 @@ +# Physical frames and compensated reuse on the p = 11 complex word + +Frozen inputs for `scripts/paired_cube_physical.py`, which applies them to the word regenerated by #144's producer. + +- `frames.json` lists the 15,149 operations whose common frame moves. For each one it gives the canonical basis of the + new frame. Every other operation keeps #144's full backward-intersection frame. + - Each moved frame lies between the span of the two roles' previous frames and the intersection of their next + frames. This is physical frame descent under #130's general Clifford frames, as in #131; connected operations + sharing a frame move as one bundle, chosen by the charged moment, with #162's pairing rounds. +- `pairs.json` lists 2,310 `[donor, recipient, read_before_op]` triples. + - Each recipient is a gauged role. It lives in its donor's physical slot, as in #124's compensated birth-cut reuse. + - Its old-value read moves to a deadline immediately before its first operation, as in #143's late compensation + reads. + - The donor's last operation precedes that read, and the donor's last frame lies in the recipient's gauge. + +Prepared by eumemic with Anthropic Claude assistance. `scripts/paired_cube_physical.py` checks: +- value spans, chain nesting with the spliced handoffs, and pair chronology; +- target-chain order in actual read time; +- the telescoping deficit; +- an exact aliased dirty-scratch replay mod 2^61 − 1 with three rejected controls. diff --git a/references/paired-cube/physical/frames.json b/references/paired-cube/physical/frames.json new file mode 100644 index 0000000000..d2f9e39415 --- /dev/null +++ b/references/paired-cube/physical/frames.json @@ -0,0 +1 @@ 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diff --git a/references/paired-cube/physical/pairs.json b/references/paired-cube/physical/pairs.json new file mode 100644 index 0000000000..d81be4cd89 --- /dev/null +++ b/references/paired-cube/physical/pairs.json @@ -0,0 +1 @@ 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diff --git a/references/paired-cube/selected-module/SOURCE.json b/references/paired-cube/selected-module/SOURCE.json index 0ba9215073..97f5055e2a 100644 --- a/references/paired-cube/selected-module/SOURCE.json +++ b/references/paired-cube/selected-module/SOURCE.json @@ -1,6 +1,6 @@ { "source_commit": "cbb05ce504d571546d9b7794c186a613c659c3bf", "inherited_dag_sha256": "3c034d0aae388ef567a454826f4f48b26fd8a94c71e8ffed4835271b349a783b", - "matching_arcs_sha256": "22c90ed078d765e58ac824d6f9558cc4620961b48644a32c0115bdb9852de771", - "graph_sha256": "7a7a58df595dc245ebe8d2673abdd8c4eaae98e767885240715a61f43a2f4dff" + "matching_arcs_sha256": "46c77eb75ebcb2435595a3b6522a54e1d12d3c61eecb3b51c489edd1f78447e1", + "graph_sha256": "1560d230bb74698c396b6c3df988f821c6001cf0ed04ade81fef790db1d68b0e" } diff --git a/references/paired-cube/selected-module/matching-arcs.json b/references/paired-cube/selected-module/matching-arcs.json index e9238210ab..2bfdd6e2a6 100644 --- a/references/paired-cube/selected-module/matching-arcs.json +++ b/references/paired-cube/selected-module/matching-arcs.json @@ -1 +1 @@ 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diff --git a/references/paired-cube/sources/SOURCE.json b/references/paired-cube/sources/SOURCE.json new file mode 100644 index 0000000000..ff82ae4d24 --- /dev/null +++ b/references/paired-cube/sources/SOURCE.json @@ -0,0 +1,9 @@ +{ + "files": { + "local_L1.json": "1861724ee3b58ea8acb3334416fbfd9172a9ae02ad11a6f6885a4909f8692f05", + "pmod_J0_full_6.0666810e-4.json": "7d1ae23430e110d32aa1cab84415abdbc918dfab6b317cb24d30756fc90c5925", + "qmod_climb3u_best.json": "3f85f6b2134af8781f16229186d0d7c1de71ab4d5235244259e1b79f2e3d14ba", + "tmod_TE_TD_TB3_1_1_4_full_6.0617964e-4.json": "9dcdb6f4e33410418c01f55f092862edfa7c05001ceada3974f8d1196bcd894b" + }, + "note": "h20_g1: #117-format complex witness by eumemic (Claude assistance), restricted by restricted_triples_from; pmod_J0_full_6.0666810e-4.json: direct pair-disjoint module (PMOD lane, eumemic, Claude assistance), loaded by pair_module_from. Apache-2.0." +} diff --git a/references/paired-cube/sources/local_L1.json b/references/paired-cube/sources/local_L1.json new file mode 100644 index 0000000000..1c4f538308 --- /dev/null +++ b/references/paired-cube/sources/local_L1.json @@ -0,0 +1 @@ +{"A": {"0,0": "e2", "0,1": "e2", "1,0": "e2", "1,1": "e2", "2,0": "e1", "2,1": "e1"}, "G": {"0,1,0": "l", "0,1,1": "l", "0,2,0": "e", "0,2,1": "e", "1,2,0": "e", "1,2,1": "l"}, "F": 2} diff --git a/references/paired-cube/sources/pmod_J0_full_6.0666810e-4.json b/references/paired-cube/sources/pmod_J0_full_6.0666810e-4.json new file mode 100644 index 0000000000..c809826daf --- /dev/null +++ b/references/paired-cube/sources/pmod_J0_full_6.0666810e-4.json @@ -0,0 +1 @@ +{"input_count": 45, "args": [null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, null, 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1882, 2045, 2057, 2124, 1874, 1767, 1950, 1530, 1636, 2061, 1852, 1668, 1893, 2004, 2033, 1673, 1479, 1386, 2065, 2123, 1847, 1829, 2078, 1622, 1980, 1724, 1746, 2041, 1888, 1613, 1720, 2008, 1794, 1752, 2063, 2129, 1428, 1546, 2044, 2111, 1595, 2064, 2040, 1996, 2088, 1927, 2119, 2017, 1979, 1822, 2072, 1462, 1769, 2039, 2028, 1845, 1902, 1772, 1834, 1715, 1649, 2089, 2015, 1533, 2051, 1556, 1990, 1783, 2011, 1914, 1838, 1949, 2000, 1917, 1579, 1789, 1707, 1971, 2086, 1952, 1870, 2094, 1856, 2003, 2130, 1897, 1762, 1919, 1799, 1959, 1745, 2131, 2087, 1984, 1974, 1780, 2127, 1748, 1933], "contract": "Root indexed by J sums input I exactly when I and J are disjoint."} \ No newline at end of file diff --git a/research/.gitattributes b/research/.gitattributes new file mode 100644 index 0000000000..50aede00ab --- /dev/null +++ b/research/.gitattributes @@ -0,0 +1,2 @@ +# Preserve the literal uploaded PR186 witness bytes and original FILES hashes. +coordinated-frames-and-entrance-banks/** -text diff --git a/research/coordinated-frames-and-entrance-banks/BANK-PROOF.md b/research/coordinated-frames-and-entrance-banks/BANK-PROOF.md new file mode 100644 index 0000000000..9f736c75f8 --- /dev/null +++ b/research/coordinated-frames-and-entrance-banks/BANK-PROOF.md @@ -0,0 +1,23 @@ +# Completed entrance banks on the physical bit word + +The bit word, signs, donor aliases, deferred compensation reads, source/target itineraries, original scalar reserve and prime witnesses are retained. The portable verifier independently reconstructs the actual physical chains and verifies every F2 and integer source, target and arbitrary dirty column before changing the inventory. + +For the selected word there are19788 logical roles and1760 compensated donor/recipient splices, hence18028 physical roles. Each physical slot is charged once over its full chronological chain. Its donor entrance remains the initial frame and the recipient birth/read is an internal point. The1760 rank21 recipient gauges are therefore not additional physical entrances. The only surviving entrance gauges are2200 rank20 gauges; the remaining15828 physical roles are undeferred. + +Here is the endpoint argument for arbitrary contents. For any commutative ring and module, set + + S_P(x,y)=(x−Px+Py,y−Py+Px). + +If P and Q have PQ=QP=0, expand the four coordinates directly to obtain S_P S_Q=S_(P+Q). For an idempotent P the same expansion gives S_P²=I. Consequently any finite disjoint projector partition summing to I has product S_I, the full swap, on EVERY incoming pair. No cleanliness or independence of the incoming data is used. For one common invertible weighted chart A, multiplication telescopes: product(A S_P A⁻¹)=A(product S_P)A⁻¹. The chronological endpoint is thus the inherited full weighted interchange and contains no residual exterior child. This is exactly the previously established completed-bank endpoint; the adaptation introduces no new endpoint hypothesis. + +The actual coordinate projectors are P_s(j)=1[j div4=s] for s=0,...,17, and Q_s(j)=1[j div24=s] for s=0,1,2, on j=0,...,71. Each family is explicitly disjoint, idempotent and exhaustive. The new verifier checks all144 columns of each two-bank address map over F2 and over Z, both for the full endpoint and its inverse. It rejects a missing last block and a repeated last block in both rings. Equality of these address maps gives equality of the induced permutations on arbitrary payload fields, including fields correlated with spectators. The universal algebra above permits all common chart conjugations, with their inherited paid routing and weighting unchanged. + +Three stage-private bank families use the same ambient completed-core width72. A rank20 entrance leaves a four-coordinate local core, so18 such cores fill a bank. An undeferred local core has24 coordinates, so3 fill a bank. Nine physical replicas make each stage-private allocation integral: 1100 selected banks and 47484 undeferred banks per stage. Their total, including source/target stock, is 3(1100+47484)+2·9·1760=177432=9W. Three is only the scale used to clear the normalized moment fractions; it is not the physical replica count. Every role visits every bank through the inherited orbit routing; no favorable subset of invocations is selected. The resulting normalized stock and rank mass are + + W=2·1760+3(2200/18+15828/3)=59144/3, + rank=1549520−2200·60=1417520, + 72W−rank=1936. + +Exactly the2200 rank60 gauge exteriors are removed. Every internal chain increment, source and target connector, centre copy, original data endpoint and bad-class fallback remains in the histogram. Its maximum child is22. Replicated moments scale W, rank, deficit and every multiplicity by3 together; the normalized moment and the per-edge fallback bill are unchanged. The rare-class fraction remains10⁻¹⁶, the fallback remains32·72² children per edge, and the positive atom/row-adapter toll is paid on its own10⁻²⁴ grid. Two independent rational log/exp enclosures certify the accepted moment and reject its adjacent10⁻¹⁸ coarse grid point. + +The inherited all-input weighted compiler, completed-core routing, stage cover, local-ring precision/recovery, prime supply, uniform setup and all-size analytic/tape contracts remain conditional. This finite bank verification discharges none of those separate interfaces. The universal bank algebra is also present in the earlier BankAndBalanced.lean snapshot under partialSwap_comp_disjoint, bankSwap_full, weightedBank_full and the actual Fin72 selected_bank_full/undeferred_bank_full statements; no fresh Lean replay is claimed by this Python package. diff --git a/research/coordinated-frames-and-entrance-banks/BASELINE.json b/research/coordinated-frames-and-entrance-banks/BASELINE.json new file mode 100644 index 0000000000..d8da63e1a3 --- /dev/null +++ b/research/coordinated-frames-and-entrance-banks/BASELINE.json @@ -0,0 +1,26 @@ +{ + "repository": "https://github.com/chafreaky/integer-mult-bounds", + "upstream": "https://github.com/CrocSwap/integer-mult-bounds/pull/181", + "commit": "7fb2194801e3a10f54772c7f0d5505035a4fc0ad", + "files": 1700, + "LF_checkout": true, + "archive_sha256": "2f8b4294620228116cfe993a376e2c848a7f280c4a7380d6ff4d2c8a8ea076eb", + "uncompressed_bytes": 78899539, + "parts": [ + { + "file": "baseline-pr181.part01", + "bytes": 12000000, + "sha256": "25f760ffb55e0e9de2f43aa334e3323d957776a9d323790c60b71ec7c414e160" + }, + { + "file": "baseline-pr181.part02", + "bytes": 12000000, + "sha256": "179e594a0a37880c62bbc966f4079e0aab60c3dfd1cf5bdd93dafd8135b2bf8f" + }, + { + "file": "baseline-pr181.part03", + "bytes": 9595108, + "sha256": "bf0e1489ddd033c37e610e61ec7c7c8c62df31d27f69b1e83574fd9080731a84" + } + ] +} diff --git a/research/coordinated-frames-and-entrance-banks/FILES.json b/research/coordinated-frames-and-entrance-banks/FILES.json new file mode 100644 index 0000000000..c7277ec819 --- /dev/null +++ b/research/coordinated-frames-and-entrance-banks/FILES.json @@ -0,0 +1,55 @@ +{ + "algorithm": "SHA-256", + "files": { + "BANK-PROOF.md": "5136565f1298b73436b164b3e9307ba00a2659da41a3a64defde4b41975dc441", + "BASELINE.json": "0412767b472720bae2902fcd24de5d18f3039afec3dd592a3c0e2d68fbabff63", + "FRAME-DISCOVERY.md": "2309dedd04605ee4285e9e0bc66741ee65b826724ceed624d8acf62554e24f51", + "LICENSE": 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"bd39675ce03fd1d4d456f736bcfc0b389532eb4f0a19c92877c2af5cb6f7310c", + "selected/complex/profile.json.gz": "cf80065ea589fcb0e9e83a2dfc76f694e3ca8bc2d8290f4175c45e2a100b8f84", + "selected/complex/result.json": "54f7b213f62e780bea8dc31bc474af2e1540a028576313de7a002b7c60d7cf5b", + "selected/complex/sinks.json": "498f7ccc51db7d09d9dc191f0b0d44fd70f3f8bf374cf3f52548880bd42f04ec", + "selected/complex/word.json.gz": "0c4b720c57717c7e55e88f86a9e17ed75b3891f9d2e7ed29df0a188f8dfee67a", + "verify.py": "73d7a41ff1264c3e9bfe5f748e77218af86796dfded2f21187f970bc10406894", + "verify_inner.py": "858142e25c396a074adc9f0dbfe2fa97f5f5f7e7dc2cad38e5169e8989fe8f95" + } +} diff --git a/research/coordinated-frames-and-entrance-banks/FRAME-DISCOVERY.md b/research/coordinated-frames-and-entrance-banks/FRAME-DISCOVERY.md new file mode 100644 index 0000000000..2bb5759ea3 --- /dev/null +++ b/research/coordinated-frames-and-entrance-banks/FRAME-DISCOVERY.md @@ -0,0 +1,37 @@ +# Checked PR181 complex descendant + +Best checked complex saving is b=662323931899051/10^18 on the actual PR181 selected word at head 7fb2194801e3a10f54772c7f0d5505035a4fc0ad. The combined supplier has W = 13,326, rank = 878,196, deficit = 1,320, maximum child = 20, 2,310 compensated aliases and 46 terminal sinks. Parent assembly must compose this complete supplier with the independently checked bank bit word and reprice every paid constraint to obtain final kappa. + +## Exact progression + +| Stage | Exact accepted complex saving | Paid stock/sinks | +|---|---:|---:| +| Public PR181 | 132438677973/(2*10^14) | W = 13,328 / 44 sinks | +| Independently audited complex donor rematch | 82782792632077/(125*10^15) | W = 13,326 / 46 sinks | +| Final 243-frame cut plus that rematch | 662323931899051/10^18 | W = 13,326 / 46 sinks | + +The final saving exceeds the public stated complex saving by 130542034051/10^18 and the independently checked rematch saving by 61590842435/10^18. These are comparisons of complete exact paid moments, not an instruction to add separately found gains. An outward-rational comparison also checks the final cut with ORIGINAL pairs: at the combined accepted exponent its moment lower endpoint exceeds 1 by more than 1.5640571*10^-7, so that alternate composition is weaker. See original-pair-comparison.json. + +An initial endpoint/equal-frame screen on the unmodified PR181 physical layer accepts no change. A first low-rank cut screen is stopped without an accepted change to spread the remaining bounded budget across all existing ranks. The main 210-second pass tests 69 actual fixed-subspace join/meet neighborhoods and accepts 11 meets, of ranks 12,13,15,16,18,21,19,19,17,14,18. It changes 243 distinct operation frames relative to PR181; changed-operations.json lists their fresh actual IDs. No historical operation IDs are transferred. + +All cut schedules use exact binary required-value containment, both roles of every common operation frame, every source/gauge/root boundary and every spliced physical donor/recipient chain. The initial cut graph also encodes the actual 44-sink pivot target chronologies. After composition with the rematch, the independent signed sink compiler recomputes all 46 target chronologies and the complete paid histogram. The rematch has 2,297 changed donor identities relative to public PR181, keyed by the unchanged recipient roles, and 1,049 retimed compensation reads; this is independently checked in the complex lane. Fixed local rank mass is preserved throughout every cut. + +## Finite sufficient argument and checks + +A chosen operation frame is F or F intersect L for one fixed binary subspace L. Its exact required scalar value span remains included. Every nested physical chain and common two-register frame condition is explicitly checked. Actual terminal target events impose additional hard containment constraints. Fixed source/gauge/root endpoints make transition rank sums telescope. All operation signs, coefficients, original scalar operations, full-frame inverses, source injections, read chronology and phase-sensitive adapters remain in the word; zero-rank transitions are only absent from the rank moment. + +The final admitted composition is NOT inferred from two independent improvements. Original paired_cube_physical.physical() independently rechecks every value span, actual alias/death/birth rule, chronological target order, spliced role chain, full rank mass and dirty scalar mutation control. The PR181 package's exact check_sinks.py then recomputes the new 46 sinks, all simultaneous target-frame events, exact source/dirty responses, literal inverse sandwich and full child histogram. It proves the actual new physical inventory W = 13,326,rank = 878,196,N1320. An independent outward rational moment accepts b = 662323931899051/10^18 and rejects its next 10^-18 grid point. + +The graph, scalar word, frame witness, logical profile and exact pairs are verified semantically IDENTICAL to the complex lane's all-column audited rematch. All 46 [role,pivot,root,target-set,write-sequence] actions also match exactly. The complete exact scalar map proof therefore remains the same: both signs check 13,326 source/target/dirty columns and restore 10,686 dirty roles; corruption controls reject. Only frame legality and byte binding are updated. SOURCE-LOCK.json binds that audit to the complete new frame/profile/moment files. The parent portable admission replays the new bytes and complete balanced assembly. + +PR181's local word includes destination coefficients ca=-1. Its original inherited terminal-sinks gate targets the older all-shear word and cannot serve as a verifier of this new word. This continuation uses the package's signed-compatible independent checker without weakening the older gate. On Windows only its Unix CPU/RSS guard API is adapted in memory; mathematical source and checks remain unmodified. + +The sufficient construction retains PR181's upstream general Clifford/tensor-frame endpoint contract, weighted local-ring compilation, stage cover, restored borrowed rows, finite routing, paid positional layout, precision/recovery, prime supply, uniform setup and analytic/fixed-tape transfer interfaces. It is a finite conditional supplier certificate; those universal interfaces are not discharged here. No unknown gadget or unpaid oracle replaces a missing step. + +Floating minimum cut nominates frames. Exact containment and outward arithmetic certify the saved schedules; there is no floating-optimality or global-optimality claim. Directed cut is classical. This is actual supplier use of the global-subspace crossover, not a novelty claim for maxflow or a projection using invented supplier bills. + +## Files and freeze + +Combined final frames: combined/physical-frames.json, SHA-256: 238d65f5c1447b18000bd96239d8fe372e9bd56fa9aca42c6626cc7be4b7c552. Exact pairs: combined/pairs.json. Complete raw frozen cache and independent signed-sink record: combined/checked/cache and combined/checked/sinks-exact.json. Complete paid profile, accepted/rejected moment and input locks: combined/checked/evaluation.json. Full input/output and unchanged scalar-audit bindings: combined/SOURCE-LOCK.json. + +All owned PR181 search/check processes have exited. The earlier fully checked PR179 descendant remains preserved as a historical fallback; it is not combined with PR181 and is below the refreshed public bar. Nothing was published and no pinned source was edited. diff --git a/research/coordinated-frames-and-entrance-banks/LICENSE b/research/coordinated-frames-and-entrance-banks/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/research/coordinated-frames-and-entrance-banks/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. Definitions. + + "License" shall mean the terms and conditions for use, reproduction, + and distribution as defined by Sections 1 through 9 of this document. + + "Licensor" shall mean the copyright owner or entity authorized by + the copyright owner that is granting the License. + + "Legal Entity" shall mean the union of the acting entity and all + other entities that control, are controlled by, or are under common + control with that entity. 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We also recommend that a + file or class name and description of purpose be included on the + same "printed page" as the copyright notice for easier + identification within third-party archives. + + Copyright [yyyy] [name of copyright owner] + + Licensed under the Apache License, Version 2.0 (the "License"); + you may not use this file except in compliance with the License. + You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + + Unless required by applicable law or agreed to in writing, software + distributed under the License is distributed on an "AS IS" BASIS, + WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + See the License for the specific language governing permissions and + limitations under the License. diff --git a/research/coordinated-frames-and-entrance-banks/NOTICE b/research/coordinated-frames-and-entrance-banks/NOTICE new file mode 100644 index 0000000000..8853b1b1d6 --- /dev/null +++ b/research/coordinated-frames-and-entrance-banks/NOTICE @@ -0,0 +1,9 @@ +Shared-edge supplier and completed entrance banks,2026. Apache-2.0. +Developed with OpenAI model assistance. No personal byline is added. + +This contribution composes the pinnedPR181complex supplier and the actual +PR168v4bit word with completed entrance banks and recomputes the full paid +finite bound. All upstream author attribution and assistance disclosures +remain in UPSTREAM-NOTICE.md and the immutable archive. Copied source files +retain their author notices. No global optimality or exclusive priority +is claimed; the inherited all-size interfaces remain explicit. diff --git a/research/coordinated-frames-and-entrance-banks/PROOF.md b/research/coordinated-frames-and-entrance-banks/PROOF.md new file mode 100644 index 0000000000..e9f66a0687 --- /dev/null +++ b/research/coordinated-frames-and-entrance-banks/PROOF.md @@ -0,0 +1,54 @@ +# Paid composition above the shared-edge local circuit + +## Exact claim + +Under the retained all-size interfaces, T(n)=O(n(log n)^(1−κ)) with + + κ=330942774629799/500000000000000000 = 0.000661885549259598. + +The exact prerequisite is PR181 at7fb2194801e3a10f54772c7f0d5505035a4fc0ad, incorporating PR168 v4 at4a3c769e5c5430e7114c4d3e099ff34664677f17 and the PR175 compiler overlay. No new all-size oracle or strengthened hypothesis is inserted. + +## Stronger complex supplier + +PR181 constructs the local sumsA[1,0],A[1,1],A[2,1] from direction-zero edge sums already used by channelG[1,2,0]. Its local word has29 additions instead of27 but admits11364 carrier arcs instead of10704. It retains the pair/triple/all-but-one modules and signed local decoder. This trades a larger scalar operation count for fewer auxiliary roles; the paid inventory, not the addition count alone, determines its value. + +Our final rematching changes 2297 donor identities versus the published PR181 matching, with all 2310 recipients retained. It legally moves 1049 early compensation reads to first recipient use. Eleven accepted arbitrary-subspace meet cuts produce 243 distinct changed operation frames (247 selection events overlap). Of these, 216 newly differ from compiler frames and 27 modify already changed frames. The combined word has two additional terminal sinks, 46 instead of 44. These counts come from recipient-keyed donor/read comparisons and exact final-frame comparisons, not list positions or an intermediate matching. The selected graph, frames, carrier matching, gauges, compensated handoffs and actual terminal targets are frozen together. The package's signed physical executor checks exact adjoints, every physical frame inclusion, all target reads, both shear signs and literal reverses. It uses the signed-destination terminal checker; the older all-ca=1 sink gate is not valid for this word. + +The final complete complex inventory is + + m=66, W=13326, rank=878196, deficit=1320, + physical auxiliaries=10686, scalar reserve=13042, + compensated handoffs=2310, terminal sinks=46, largest child=20. + +The terminal executor checks all13326 modified source/target/dirty columns and restores all10686 dirty registers, for both directions. Removing a pivot write, deleting an ancestor dirty response or omitting the initial target shears is rejected. Handoffs and terminal sinks stay distinct, and the retained full scalar reserve pays the literal signed word. + +The exact complete moment gives b=662323931899051/1000000000000000000. The actual full child histogram and outward rational bounds are in certificate.json. Numeric search scores or older frame-cut gains are not added to b. + +## Completed entrance-bank bit supplier + +Retain the unchanged PR168 v4 bit scalar word, partner deliveries,1760 compensated aliases and all original frame/prime witnesses. Verify every one of its21548 formal columns over F2 and over its defining integer decoder, restoring every source and arbitrary dirty register. The integer decoder is not asserted to be an integer identity. + +Bank whole chronological physical chains. The2200 surviving rank20 entrances leave four-coordinate cores, and eighteen fill a72-dimensional dirty bank. The15828 other physical chains use three24-coordinate cores. The1760 rank21 recipients are internal splices, never a second bank entrance. Nine copies make each stage-private allocation integral:1100 selected banks and47484 undeferred banks per stage. Total stock9W is177432 including source/target roles. + +For disjoint idempotentsP,Q, the map S_P(x,y)=(x−Px+Py,y−Py+Px) satisfies S_PS_Q=S_(P+Q), by direct expansion. A partition summing toI therefore composes to a full swap on arbitrary incoming contents. Conjugation by one common invertible weighted chart telescopes. BANK-PROOF.md supplies the full algebra and concrete partitions; the verifier checks every integer/F2 address column, inverse and omitted/repeated-block control. This reuses the established completed-bank endpoint with the inherited routing/chart contracts. + +The normalized complete bit inventory is + + W_B=59144/3, rank_B=1417520, deficit_B=1936, largest child22. + +Only2200 rank60 exterior children disappear. Every internal increment, source/target connector, center copy and bad-class fallback remains paid. The unchanged used-frame Gram/factor witnesses reproduce exactly; coordinate bank projectors introduce no new denominators. Prime-witness paths are normalized toPOSIX separators, and only the portable checker self-hash changes in the frozen witness metadata. + +Independent base4/3 and base2 rational interval engines certify coarsea0=665481166955987/10^18 with bad fraction10^−16 and fallback32·72² per edge. The old ordinary wrapper usesa_old=384599/10^10 and least payable atomθ=665064157585290854737/10^24. The effective bit saving is + + A_B=(1−θ)a0+θa_old + =665064157585290854736467094714610539581/10^42. + +Both A_B<θ<1−A_B hold strictly. The preceding atom grid and succeeding coarse grid are rejected for this fixed envelope. + +## Composition and sufficient scope + +Withβ=η=10^−24 andζ=10^−30, takea=min(A_B,(1−β)b−ζ), q=a(1−2η), and the greatest10^−18 grid point strictly below(1−η)q/(1+q). Here A_B>b, so the complex side binds. The complete scalar, group-cardinality, router, semantic, row and paid-layout charges are rederived. Full group cardinality is retained outside the normalized moments; neither aliases nor bank sharing justify discarding the scalar stock or external reserves9909 and252. + +The source-normalization check preserves the original PR14147-slack arithmetic body apart from its existing bridge plumbing and explicit supplier guard. All47 constraints and seven margins are strict;21 assembly mutations, including the succeedingκ grid, reject. A separate original-body calculation also reproduces the result. These grid exclusions establish no global optimum. + +The final wrapper reconstructs a fresh immutable prerequisite and replays the entire combined finite certificate. It checks source hashes before and after and rejects unpinned extra upload files. General tensor/Clifford realization, uniform weighted compilation, common generic bases, completed-core/global routing, restored borrowed rows, layout applicability, prime supply, precision/recovery, uniform setup and analytic fixed-tape transfer remain the explicit inherited interfaces. This sufficient conditional composition does not prove those all-size foundations or claim a new Lean replay. diff --git a/research/coordinated-frames-and-entrance-banks/README.md b/research/coordinated-frames-and-entrance-banks/README.md new file mode 100644 index 0000000000..fdefcc6624 --- /dev/null +++ b/research/coordinated-frames-and-entrance-banks/README.md @@ -0,0 +1,17 @@ +# Shared-edge supplier and completed entrance banks + +The complete paid finite composition certifies κ=330942774629799/500000000000000000, or 0.000661885549259598, under the retained Beyond n log n interfaces. This combines the stronger PR181 complex construction with the independently checked completed entrance-bank bit supplier. The complex branch binds again. + +Run Python 3.11+ with assertions enabled: + +``` +python -B research/coordinated-frames-and-entrance-banks/verify.py +``` + +No network, Git, credentials or third-party packages are required. The verifier checks every upload file and the three immutable PR181 archive parts, reconstructs a temporary clean source tree, verifies its1,699-file prerequisite closure, and replays the complete words, frames, exact moments, prime witnesses and all 47 inequalities. It compares the derived result with certificate.json. Normal verification changes only its temporary directory; --write is an explicit authoring mode. + +All archive parts are below GitHub's25 MB browser limit. Upload this entire folder at research/coordinated-frames-and-entrance-banks, keeping every file. The archive hash and exact upstream commit7fb2194801e3a10f54772c7f0d5505035a4fc0ad are in BASELINE.json. FILES.json pins this upload; SOURCE.json pins the prerequisite. The source remainsLF throughout the archive, independent of a later Git checkout's autocrlf setting. + +The verified gain over PR181's statedκ is about0.41035%. This is a conditional finite witness, not an unconditional integer-multiplication theorem, global optimum or new Lean-certified bound. General compiler/Clifford, common charts, restored rows, routing, paid layout, precision/recovery, prime supply, uniform setup and analytic fixed-tape interfaces remain the inherited assumptions. + +See PROOF.md, BANK-PROOF.md and RESEARCH-IDEAS.md. Upstream attribution/disclosures are retained in NOTICE, UPSTREAM-NOTICE.md, UPSTREAM-PROOF.md and the immutable public archive. Developed with OpenAI model assistance; no personal byline is added. diff --git a/research/coordinated-frames-and-entrance-banks/RESEARCH-IDEAS.md b/research/coordinated-frames-and-entrance-banks/RESEARCH-IDEAS.md new file mode 100644 index 0000000000..130a1f723b --- /dev/null +++ b/research/coordinated-frames-and-entrance-banks/RESEARCH-IDEAS.md @@ -0,0 +1,13 @@ +# Research mechanisms actually used and tested + +The original independent crossover ideas were worked through, not merely collected as citations. + +The completed-bank mechanism supplies the new result here:18×4 and3×24 disjoint projector banks raise the bit supplier above the newPR181complex supplier, unlocking the composedκ. It treats compensated donor/recipient pairs as one whole physical chain. The source-birth nullity21 idea failed the actual dirty-read chronology and is excluded. + +Global arbitrary-subspace graph-cut optimization produced a verified rank8 four-operation contraction and enabled further endpoint descent on the priorPR179graph. That fallback was fully replayed atκ=.000655930202792126, but was superseded whenPR181 appeared. Its operationIDs and gains are not transplanted or added to the new graph. On the actual PR181 graph, the same method accepted eleven coordinated meet cuts with 243 distinct final operation-frame changes. These are combined with the 2297-donor rematch and 1049 legally retimed reads. All 46 actual target/pivot chains and the complete new moment are checked together; no candidate gains are added. + +The shared-total/rank2 local reflection was tested on the prior actual producer: a five-edge matching saves230 scalar additions, but260 read roots fail the current frames. A rank2 local Fourier map does not establish physical routing for the larger-address shared total. This unpaid route is excluded. PR181's shared-edge reuse is a different concrete mechanism and is already certified by the selected word. + +Integral harmonic/Kneser factorization, Parseval phase maps and fractional-bank configurations were considered as representation/packing crossovers. Their valid algebraic identities do not automatically shrink the actual admissible geometric frames. Only the explicitly realized homogeneous bank partitions are used in the numerical certificate. Additional gauges, local associations and frame refinements count only when their entire final words and paid profiles pass. + +No historical improvement is summed with a public exponent. Every submitted number is recomputed from the frozen combined suppliers and the complete47-constraint composition. diff --git a/research/coordinated-frames-and-entrance-banks/RESEARCH-REVIEW.md b/research/coordinated-frames-and-entrance-banks/RESEARCH-REVIEW.md new file mode 100644 index 0000000000..5cce174cf9 --- /dev/null +++ b/research/coordinated-frames-and-entrance-banks/RESEARCH-REVIEW.md @@ -0,0 +1,37 @@ +# Research ideas and exact disposition, 2026-10-09 + +The selected finite composition uses the pinned PR181 physical word, our legal compensated rematching and operation-frame cuts, its 46 checked terminal sinks, and the completed entrance banks on the retained bit word. Independent rational arithmetic reproduces complex saving b=662323931899051/10^18 and final balanced κ=330942774629799/(5·10^17)=0.000661885549259598. Both independent interval engines accept b and reject b+10^-18. The original PR141 balanced arithmetic body passes all47 strict constraints and all7 margins; the next κ grid point and the three old-layout controls fail. No component gains are added. + +## Changes actually used + +PR181 supplies the newer shared-edge scalar construction: h22, v1320, c21249, q3157, matched11364, scalar carrier reserve R13042 and M32971. This is an upstream improvement and is not claimed as our discovery. We retain its complete scalar reserve after physical aliases and terminal substitution. + +The actual matching schema is [donor,recipient,read_operation]. Comparing maps keyed by recipient against pinned PR181 gives2310 retained recipients,2297 changed donor identities and1049 changed read-operation fields. These are separate counts, not tuple inequality or sorted-list positional differences. An earlier draft's419 donor count is stale and does not describe this final witness; the parent was notified. The rematch audit independently reports2297. Legal reads retain recipient birth, donor death and exact compensation. + +The final fixed-subspace cut search accepted11 meet cuts with247 selection events. Some events overlap; comparing final operation bases to the published baseline gives243 distinct changed operation frames. Actual value spans, both operand chains, donor gauges and target-read caps were checked. These are finite legal improvements, not a proof of global optimality. The combined moment prices the cuts and rematching together. + +There are46 disjoint compatible terminal sinks, verified on every original formal source, target and arbitrary dirty column. The physical count is13042−2310−46=10686, W=13326, rank mass878196, deficit1320, maximum child20. The terminal sandwich saves scalar gates while the original scalar reserve remains charged. The parent aggregate owns the final complete word, prime, source and root replay. + +The bit contribution has19788 logical roles,1760 compensated splices,18028 physical chains,2200 genuine rank20 entrance gauges and15828 undeferred chains. Width72 banks tile18 four-coordinate cores or3 twenty-four-coordinate cores. Only the2200 rank60 exteriors disappear. W=59144/3, rank1417520, deficit1936, maximum child22. Nine physical replicas provide integral stage-private bank counts1100 and47484; factor3 is only moment normalization. Effective paid bit saving is665064157585290854736467094714610539581/10^42, larger than the complex supplier. Complete literal projector endpoints and inverses were checked over F2 and Z on all144 columns; missing and duplicate blocks are rejected. The endpoint theorem works for arbitrary dirty contents and one common invertible weighted chart. It introduces no fresh endpoint assumption. + +## Five crossover routes + +1. Whole-network directed cuts were applied successfully to the actual newest word, with the eleven exact cuts above. Historical cut witnesses were used as method guidance, not transplanted by operation ID. + +2. Matching-selected common totals and the explicit rank-two face decoder remain a concrete different-construction route. On actual181, a five-edge matching gives10 changed modes and230 fewer scalar additions (21249→21019), but260 target-side reads violate current frame containment. The total value span is19 rather than17 and its own-cube binary interaction has rank2. The specified face correction is an exact decoder identity; it does not by itself implement the missing joint read carrier. No gain from this route enters κ. + +3. Rational configuration banks provide a universal sufficient endpoint construction when actual nullities differ. The current rank20/nullity4 and undeferred/nullity24 families already tile homogeneously. We used their concrete disjoint projectors and exact integral replication; a different LP alone yields no further gain here. + +4. The integral harmonic residual factors165 scalar channels through55 all-ring exact features with low coefficients. This is useful representation mathematics. It is not a tensor-address width55 claim. No current paid carrier/read construction eliminates the observed19/20-to18 cap mismatch, so no feature-compression saving is priced. + +5. Parseval phase correction for binary Gram-resolving maps gives a literal known translation correction and specified Fourier ranks. The characteristic-two additive block-swap identity is a separate exact result. Neither identity alone provides cheaper physical bank stock or an overlapping-code endpoint in this supplier. No unpriced overlapping-code construction is substituted. + +## Other bounded discovery + +Saved mixed-gap complex modules and reassociations were rebuilt through the unchanged pinned producer/matching machinery. An historical role11 module improved fd25 but was superseded by the later public role10 module. Forty-one output-fold variants, the saved LR/reassociation families and bounded role9 annealing searches produced no newer accepted supplier. This is a search report, not an impossibility theorem. + +On181,27 single local A/G/F neighbors and4 combined edge-sharing variants failed to lower logical R13042. Two physically valid alternatives were priced exactly, including their sinks, but yielded weaker moments than181 and were excluded. Additional all-G edge sharing reduces scalar additions while losing too many legal aliases. + +Source births cannot be reclassified as exterior entrance gauges in the retained endpoint: every one of1320 exact dirty-response rows has three centre coefficients and a nonzero net action on its own target. No source/nullity21 shortcut is assumed. + +All inherited all-input weighted compiler, routing/stage cover, precision/recovery, prime supply, uniform setup and all-size analytic/fixed-tape contracts remain separately stated conditions. The sufficient result is the fully paid conditional finite composition. The standalone review imports no modified parent certificate for its κ proof. It loads the retained original47-constraint body with an independently computed semantic/row bridge, validates every selected-cache input hash, and retains the original body and bank proof hashes in receipt.json. 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Retained all-size contracts remain assumptions.", + "status": "Frozen selected conditional finite witness", + "verification_overlay": { + "commit": "f1081fabbfadaaaaf7292a40d428dbbb865ce920", + "files": { + "certificates/joint-dual-kappa.json": "4044f15abf49b1551193891836e2d20975b8246acc888180af47266c64f77af0", + "certificates/joint-dual-validation.json": "a7834f2dda430b4d28337faf86b74b2ea1259812bc4169520e141efb835ecd9d", + "research/joint-dual/SOURCE.json": "c8649e811e43b33a7281746fd61e9adbd1370690ef7c2ec114a6f2d61016704f", + "scripts/experiments/joint_dual_reclaim_compiler.py": "f0696953d057239ed5a75e28d857b814d43ca43deaaf7b7b8fd191aa115112ff" + }, + "pr": 175 + } +} diff --git a/research/coordinated-frames-and-entrance-banks/UPSTREAM-NOTICE.md b/research/coordinated-frames-and-entrance-banks/UPSTREAM-NOTICE.md new file mode 100644 index 0000000000..87dc993cb0 --- /dev/null +++ b/research/coordinated-frames-and-entrance-banks/UPSTREAM-NOTICE.md @@ -0,0 +1,54 @@ +Prepared by Chafik Boukhalfa with substantial Anthropic Claude and OpenAI +Codex assistance. Apache-2.0. Inherited files retain their original notices +and assistance disclosures. This package claims no exclusive priority over +concurrent work. + +Retained sources and lineage: +- icekylinx: PR144 paired cubes, signed decoder, shared-core accounting, + original compiler, configurable local channels and finite bridge; + PR130/generalized Clifford frames. +- eumemic: PR117 module infrastructure; PR155/157 scalar modules, physical + frames/reuse and partner-pair bit word; PR161 output merging and searched + p12 module; PR168 annealed pair, triple and all-but-one modules on both + words, nested-prefix schedules, the L1 local circuit this package varies, + fused outputs, bundle descent, both physical layers, the terminal-sink + gate and the physical bit word, pinned at + 4a3c769e5c5430e7114c4d3e099ff34664677f17. Their Anthropic Claude and + OpenAI Codex disclosures are retained. PR131/143 supply frame/reuse and + late-read lineage; PR154 supplies isolated snapshot verification. +- DaysSky: PR162 generalized carrier extension (`compile_closure` and the + extension rule reused here on the new graph) and full-intersection + compiler lineage. The selected graph retains the PR168 nested schedule. +- jamesyc / James Chang: PR124 compensated birth cuts, PR34 balanced + assembly, and PR166 terminal-output accumulation and exact simultaneous + target-chain checking. The PR166 proof is retained in references/pr166. +- GamingPuzzled / Joel Pulikkan: PR160 searched-bit-module composition. +- gupt1156 PR148 and Abhinav Ramachandran/geckods PR158 (Hermes assistance): + paid atom-toll re-instantiation, including PR158 at + 6e086603f936dbb95c6d7171132ed943cc024db9. +- jacklightChen / Zhihao Chen: PR23/29 ordinary supplier; Rohan Arun + (rohanarun): PR100/103 paid positional layout and deferred signed words. +- Earlier bit lineage retained by the prerequisite: Zhihao Chen PR97, + Swapnil Jain's round-seven checkers, an664 PR128, DaysSky PR150, hpst3r + PR147, SovereignSteak PR122, and the source-notice contributors. + +This package contributes a coordinate search over PR144's configurable +local channel circuit on the PR168 v4 word, selecting direction-0 edge +sums for A[1,0], A[1,1] and A[2,1] so that the carrier closure gains 660 +arcs; our own legal-edge Hopcroft-Karp carrier matching with PR162's +extension; endpoint frame descent and compensated handoffs for the new +graph; independent complete admission of the resulting physical word and +its 44 terminal deletions; independent physical-bit admission and exact +prime witnesses for every used bit frame; and the fully paid balanced +composition with finer positive backoffs. Scalar virtual stock, physical +handoffs, terminal removals and every external row reserve remain +distinct. The complete 47-inequality body is source-normalized to PR141. +Prerequisite constructions, the configurable circuit itself and the +terminal-compilation concept are not claimed as original here. + +Verification infrastructure: Chafik Boukhalfa, PR175 at +f1081fabbfadaaaaf7292a40d428dbbb865ce920, with substantial OpenAI Codex +assistance. Its ordered retired-register compiler buckets and three +provenance/certificate updates are carried byte for byte. The PR57 compiler +and all existing notices remain. This overlay changes no mathematical +field or emitted word and is included in the complete native verification gate. diff --git a/research/coordinated-frames-and-entrance-banks/UPSTREAM-PROOF.md b/research/coordinated-frames-and-entrance-banks/UPSTREAM-PROOF.md new file mode 100644 index 0000000000..1ac53947fd --- /dev/null +++ b/research/coordinated-frames-and-entrance-banks/UPSTREAM-PROOF.md @@ -0,0 +1,68 @@ +# Construction and retained proof contracts + +The exact prerequisite is PR168 at `4a3c769e5c5430e7114c4d3e099ff34664677f17`. PR144 supplies the paired-coordinate/shared-core framework and the configurable local channel circuit; PR161/168 supply the annealed modules, fused outputs, scalar words, L1 bit association, nested schedules and the bit physical layer; PR162 supplies the carrier extension rule; PR166 supplies terminal-output accumulation. This package changes the complex local circuit and rederives the complete finite composition under the inherited all-size interfaces. + +## Shared-edge local circuit + +Each of the 165 cubes computes the same 13 local outputs: the six single-bit sums $A[i,a]$ of the four ports with bit $i=a$, the six signed channels $G[j,k,m]$ and $F=A[f,0]+A[f,1]$. PR144's circuit lets every $A[i,a]$ be assembled from two edge sums along a direction $d\ne i$ or from two face diagonals, and every $G[j,k,m]$ from edge differences along the third direction, long-diagonal differences or fixed-coordinate differences. PR168's L1 circuit assembles $A[1,\cdot]$ from direction-2 edges, $A[2,\cdot]$ from direction-1 edges and $G[1,2,0]$ from direction-0 edge differences. + +This package assembles $A[1,0]$, $A[1,1]$ and $A[2,1]$ from direction-0 edges. The four direction-0 edge sums of a cube are then shared by three $A$ channels and the $G[1,2,0]$ channel, while the four direction-2 edge sums disappear and the direction-1 edge sums remain shared by $A[2,0]$ and $G[0,2,\cdot]$. The circuit has 29 additions per cube instead of 27. Every addition still has support-disjoint operands and every root support equals its contract; the graph builder and the independent scalar audit check this. The modules, the `f8:00111100` fold order and the nested schedule of PR168 are unchanged. + +The new signed graph has c=21,249, q=3,157 and M=32,971 mixer operations. Carrier arcs are chosen by our own legal-edge Hopcroft–Karp matching on the coordinate-padded frames and extended by PR162's greedy rule; the compiled closure is acyclic and span-contained. There are 11,364 arcs instead of 10,704, so the complete virtual auxiliary stock is R_scalar=c+q−11,364=13,042. Gauges are selected by PR144's chronological greedy rule: 2,310 roles of rank 18. + +## Physical word, handoffs and frames + +Operation frames are descended from the compiler frames by exact endpoint moves of single operations, equal-frame components and connected bundles: each move takes the join of incoming frames and value span or the meet of outgoing frames. 12,869 operations differ from the compiler frames. The 2,310 compensated handoffs pair dead ungauged non-root donors, whose last frames lie in the recipient gauge, with gauged recipients read at their first-use deadline; they leave 10,732 roles before terminal deletion. Only the explicit final frames and pairs are mathematical inputs. + +The verifier reconstructs every signed source/target identity, binary value span, carrier, center closure, physical role chain and actual target read. Compensation reads the current inherited dirty value with independently derived exact adjoint coefficients. The original physical word is checked on all 13,372 formal source, target and dirty columns under both shear signs. Every signed gate a←c_a a+c_b b is undone by a←c_a a−c_a c_b b, in reverse chronology; gates whose carried operand is the minuend are compiled with the sign on the destination coefficient and are audited as such. + +## Terminal-output accumulation + +The terminal compiler selects 44 ungauged, destination-only, disjoint-root roles. Each has eight targets, rank-18 common read frame and coefficient 1/2. No removed role is a source, gauge, alias endpoint, retained consumer input or another root. All sink writes are additive in the final frame. Target groups are disjoint, and each pivot's first old nonzero-frame target read follows its sink's last write. Of the 165 disjoint roots, 119 have retained producer consumers, 13 are written in the center phase and 4 have no uncorrected pivot. + +Retain every surviving coordinate's original dirty-response correction, including response through a deleted sink. At the common zero frame after the center phase, subtract each pivot from its seven other targets. Replace r←r+c b by y_p←y_p+c b/2. After the last write, add y_p back to those seven targets. Remove the old sink read and register. The independent target checker includes all intervening compensation reads and every new target-frame event; source-role frames at replaced writes remain as before. + +The modified executor checks all 1,320 source, 1,320 target and 10,688 dirty columns in both directions. An independently computed absolute residual coefficient bound of 397,506 makes 24-bit packed digits injective. The actual literal reverse word restores all retained dirty coordinates. Missing a pivot write, deleting an ancestor's original response and omitting the initial target shears are rejected. The scalar addition delta is −202, so the complete earlier virtual scalar charge remains conservative; the fixed odd divisor remains three. + +For each terminal sink, the pivot copies the old rank increments and the remaining seven targets enter the shared rank-18 frame. The sink's final rank-four increment and one target rank-18 increment disappear. The three-core histogram loses three children of rank 4 and three of rank 18; W loses one. The final profile is m=66, W=13,328, rank=878,328, deficit=1,320 and largest child 20. The exact stock identity is 13,042−10,688=2,310 handoffs+44 terminal sinks. Outward rational intervals prove b=132438677973/(2·10^14); its next 10^−15 grid point fails this fixed profile. + +## Physical bit word, exact decoder and prime range + +The unchanged bit inputs are PR168's graph, virtual profile, physical scalar word, rational frame table and partner chronology at the prerequisite commit. Admission reads these frozen files; it never regenerates them. The word uses an all-but-one module with n=10 and an annealed pair module; the local L1 association replaces three face-channel edge associations with long diagonals while preserving the mod-2 supports. Local geometry has h=24 and G=I−J/9. Source lines are spanned by chi_S; target caps are ker(3 chi_T−1). + +Each source belongs to one partner pair. A carrier XORs its passive partner in their rank-two span, delivers at the specified common level-two cap/root and restores its source value before cleanup. All complete source chains and original delivery anchors are checked. There are 2,884 operation frames differing from the original compiler frames, including 264 enlargements. Exact rational checks prove each contains its full node value span and is nondegenerate. The 1,760 aliases join dead ungauged non-root donors to untouched gauged recipients. Each current inherited dirty value is read at its explicit deadline, and all physical role chains and retimed target reads are recounted. + +The final bit profile has virtual R=19,788, physical R=18,028, W=21,548, rank=1,549,520, deficit=1,936 and largest child 60. Independent literal execution checks every one of the 21,548 formal columns over F2, restores every source/dirty coordinate and verifies the identity on targets. Separate integer execution verifies the defining integer decoder, whose F2 reduction is the identity; it does not assert an integer identity. Missing compensation, missing partner delivery, stale dirty reads and a zero operation frame are rejected. + +Exact Bareiss witnesses cover all 24,601 used bit frame IDs and distinct integer bases B. Each nonzero d=det(9BGB^t) factors into powers of primes at most 31 times a positive residual below 2^80; every factor identity is checked. Determinants reach 118 bits. Every prime q>2^80 therefore avoids every determinant, preserving all Gram inverses/projectors over Z/q^w and the original fixed-prime range. Sources, gauges, roots, operation frames, partner mixes/deliveries and ambient frames are included. Zero determinants, incorrect factors and oversized residuals are rejected. + +Every ideal bit edge pays the full 32m^2 fallback on fraction 10^−16, and 2m^3/2^80<10^−16. The contaminated moment and rank mass contract. Outward rational intervals certify a0=6600253783597/10^16; the next 10^−18 grid point fails this fixed envelope. The true bad fraction may be smaller; no optimality claim is inferred. + +Use the retained standard ordinary wrapper with a_old=384599/10^10. Select the first 10^−24 grid point above a0/(1+a0−a_old): theta=329807692103940705443/(5·10^23). Its ordinary saving is A_B=(1−theta)a0+theta a_old. Both adapter and restored-row tolls are paid by A_B0. Source normalization proves the PR141 arithmetic body changes only bridge plumbing and the explicit guard a≤A_B. + +The certified point is kappa=659180578557293/10^18. Its next 10^−18 grid point fails only for these fixed supplier certificates and parameters. Matched comparisons change the positive outer backoffs while holding the same suppliers; the published parent certificate is reported separately. + +Finite checks establish supplied words, profiles, exact moments, prime witnesses, source closure, finite bills and arithmetic. General Clifford lifts, common generic bases, uniform weighted compilation, arbitrary-width routing, restored internal rows, layout applicability, prime supply, precision/recovery, uniform setup and analytic fixed-tape transfer remain inherited all-size contracts. diff --git a/research/coordinated-frames-and-entrance-banks/arithmetic/balanced_shared.py b/research/coordinated-frames-and-entrance-banks/arithmetic/balanced_shared.py new file mode 100644 index 0000000000..e94c7dcaa9 --- /dev/null +++ b/research/coordinated-frames-and-entrance-banks/arithmetic/balanced_shared.py @@ -0,0 +1,71 @@ +"""Paid balanced assembly with an explicit uniform-bit/shared-complex bridge. + +The complete 47-constraint arithmetic body is PR141 balanced_stopped.py, +with only bridge plumbing and an actual-bit-supplier bound added. Original +PR34/RaD/PR23, icekylinx and PR100/103 attribution is retained in the pinned +source. It does not assert a finite old coarse profile for the uniform bit +supplier. General cutoff/analytic/word contracts remain external. +Prepared with OpenAI Codex assistance; Apache-2.0. +""" +from fractions import Fraction as Q +from shared_bridge import rational, require, validate_shared_bridge + +def assembly(finite_bridge, complex_row, a_bit, kappa, beta=Q(1,20), h=Q(1,10**12), + a_complex=Q(717,10**7), *, original_prefix=False, + old_guard=False, old_exposures=False): + """Return 47 strict slacks and seven margins, or raise InvalidAssembly. + + The three keyword switches are negative controls: they impose the old + prefix, nonlinear guard, or old separate movement charges at these SAME + balanced parameters. They do not silently optimize an alternative family. + """ + f = validate_shared_bridge(finite_bridge, complex_row) + a, b, kappa, beta, h = map(rational, (a_bit,a_complex,kappa,beta,h)) + require(a <= f['bit_uniform']['ordinary_saving'], 'transfer saving exceeds actual uniform bit supplier') + require(0 < h < Q(1,2) and kappa > 0, 'positive backoff and saving required') + tau, sigma = 1-a, 1-b + q = a*(1-2*h) + require(1+q != 0, 'undefined balanced epsilon') + lp, c, eps = 1-q, q+h/4, (1-h)/(1+q) + lam = (tau+lp)/2 + G = eps*q + r, delta = (G+1-eps)/2, h/8 + C1 = Q(19991,10000) if old_guard else Q(1) + margins = dict(g1=1-eps, g2=a, g3=G, g4=a, + g5=min(1-eps-delta,r-delta), g6=1-eps-delta, g7=eps) + if original_prefix: + margins['g1'] = 1-eps*(1+c) + if old_exposures: + margins.update(g2=eps*c*a, g4=a*(1-eps)) + internal = tau+(1-beta)*max(sigma-tau,Q(0)) + leaf = sigma+beta*(1-sigma) + slacks = dict(a_positive=a, a_below_b=b-a, b_below_one_over32=Q(1,32)-b, + beta_positive=beta, beta_below_one=1-beta, phase_leaf_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*C1, + 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-G, artificial_boundary=8-eps+r-delta-G, + literal_scalar_guard=Q(f['semantic']['strict_literal_gap']), + row_product_gap=f['rows']['degree_gap']) + slacks.update({name+'_above_kappa': value-kappa for name,value in margins.items()}) + require(len(slacks) == 47 and len(margins) == 7, 'constraint list incomplete') + failed = {name:str(value) for name,value in slacks.items() if value <= 0} + require(not failed, str(failed)) + require(min(margins.values()) == G, 'unexpected controlling margin') + require(1-eps-G == h and 1-eps-r == h/2, 'balanced identities failed') + require(1-eps*(1+c) == h-eps*h/4, 'geometric identity failed') + parameters = dict(a_bit=a, a_complex=b, tau=tau, sigma=sigma, beta=beta,h=h, + q=q,c=c,epsilon=eps,lambda_=lam,lambda_prime=lp,alpha_squared_power=r, + delta=delta,C0=f['semantic']['C0'],C1=C1,kappa=kappa) + return dict(parameters=parameters,constraints=slacks,margins=margins, + minimum_margin=G,absorption_gap=G-kappa,scoped_limit=a/(1+a), + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c),finite_bridge=f) diff --git a/research/coordinated-frames-and-entrance-banks/arithmetic/certificate.py b/research/coordinated-frames-and-entrance-banks/arithmetic/certificate.py new file mode 100644 index 0000000000..74271389e8 --- /dev/null +++ b/research/coordinated-frames-and-entrance-banks/arithmetic/certificate.py @@ -0,0 +1,168 @@ +#!/usr/bin/env python3 +"""Exact paid bridge, unchanged balanced arithmetic body, and strict controls. + +Finite bridge formulas: icekylinx PR144/130, eumemic PR152, Apache-2.0. +Balanced layout: PR23/29 Zhihao Chen, RaD, James Chang PR34, and Rohan +Arun PR100/103. This adapter preserves their separately stated contracts. +Adapted supplier composition; upstream attribution is in UPSTREAM-NOTICE.md. +""" +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +from math import prod +from pathlib import Path +import copy +import gzip +import importlib.util +import json +import sys + +HERE=Path(__file__).resolve().parent;PACKAGE=HERE.parent;ROOT=HERE.parents[2] +sys.path.insert(0,str(HERE));sys.dont_write_bytecode=True +if hasattr(sys,'set_int_max_str_digits'):sys.set_int_max_str_digits(0) +from shared_bridge import require,halving,validate_shared_bridge,nofloat +from balanced_shared import assembly + +AC=Q('662323931899051/1000000000000000000') +COARSE=Q('665481166955987/1000000000000000000') +ATOM=Q('665064157585290854737/1000000000000000000000000') +OLD=Q(384599,10**10) +AB=(1-ATOM)*COARSE+ATOM*OLD +BETA=ETA=Q(1,10**24) +WEAKENING=Q(1,10**30) +GRID=10**18 + + +def js(x): + if isinstance(x,Q):return str(x) + if isinstance(x,dict):return {str(k):js(v) for k,v in x.items()} + if isinstance(x,(tuple,list)):return [js(v) for v in x] + return x + + +def bridge(row,coarse=COARSE,atom=ATOM): + """Retained finite formulas with the actual new local inventory supplied.""" + h,v,R,c,M=(row[k] for k in ('h','v','R','c','total_M_operations')) + scalar_R=row['scalar_role_reserve'] + m=3*h;half=m//2 + V=2**(m-1+(half-1)**2)*prod(2**(2*i)-1 for i in range(1,half)) + W=V*(2*v+R);s=V*row['rank_per_vertex'];N=V*v + r=max(int(k) for k,n in row['child_histogram'].items() if int(k) and n) + local=4*(c+v)+10*v+4*h*v+4*h*h+8*h+8+2*h+8*scalar_R*v*(M+16)+32*v + logical=3*V*local+8*W+4*N+8*m*scalar_R*V + G=64*(m+1)**3*(logical+1)*(W+1)**2 + E=64*(W+m+G+1)**3;charge=2*G*W*W+8*s+4*W+4+32*m + B=s+E;C0=32*m*B*B;depth=halving(m,r);coefficient=depth*W.bit_length()+9909+252;degree=70000 + actual=(1-atom)*coarse+atom*OLD + result=dict(bit_uniform=dict(coarse_saving=coarse,atom_beta=atom,old_atom_saving=OLD, + ordinary_saving=actual,selector_stock='Internally borrowed and restored q-adic rows; complete spectators preserved.', + external_stock='The bit group cardinality is not inserted into external polynomial row stock.'), + conservative_old_coarse_row_reserve=9909,ordinary_leaf_row_degree=252, + complex=dict(m=m,W=W,s=s,N=N,maxchild=r,invocations_per_stage=V,stages=3, + auxiliary_banks_after_sharing=1,halving_degree=depth,wire_bits=W.bit_length(), + original_X_involution_scalar_group_upper=32*v,local_group_upper=local, + logical_group_upper=logical,finite_group_router_upper=G,scalar_group_upper=G, + coefficient_bound=h+4,coefficient_denominator_divides=6, + physical_roles_per_vertex=R,scalar_role_reserve=scalar_R,reuse_pairs=row['reuse_pairs'],terminal_sinks=row.get('terminal_sinks',0)), + semantic=dict(E=E,literal_charge=charge,strict_literal_gap=E-charge,B=B,C0=C0,C1=1, + induction_gap=2*B*(m-r)-s-E,fixed_odd_divisor=3, + exact_grid='One dyadic grid times 3^(-K), K=G*(D_complex+1); completed children preserve the incoming odd exponent.'), + rows=dict(coefficient=coefficient,complex_coefficient=depth*W.bit_length(),degree=degree, + suffix_slope=4*degree,degree_gap=Q(degree)-Q(51*coefficient,25))) + validate_shared_bridge(result,row) + return result + + +def below(value,grid=GRID): + # Largest grid point strictly below a rational, including exact boundaries. + x=value*grid + return Q(-(-x.numerator//x.denominator)-1,grid) + + +def old_assembly(): + spec=importlib.util.spec_from_file_location('retained_prefix_assembly',ROOT/'scripts/structured_bulk_assembly.py') + module=importlib.util.module_from_spec(spec);spec.loader.exec_module(module) + return module.assembly + + +def price(row,b,coarse,beta,eta,weakening,layout,atom=ATOM): + finite=bridge(row,coarse,atom) + actual=finite['bit_uniform']['ordinary_saving'] + a=min(actual,(1-beta)*b-weakening) + q=a*(1-2*eta) + value=(1-eta)*q/(1+q) if layout=='balanced' else (1-eta)*q/(1+q*(1+eta)+q) + k=below(value) + if layout=='balanced':result=assembly(finite,row,a,k,beta=beta,h=eta,a_complex=b) + else:result=old_assembly()(a,b,finite,k,eta=eta,beta=beta) + assert len(result.get('constraints',result.get('strict_constraints')))==47 and len(result['margins'])==7 + assert result['minimum_margin']==value + return dict(kappa=k,a=a,actual_bit_saving=actual,complex_saving=b,beta=beta,eta=eta, + weakening=weakening,layout=layout,minimum_margin=value,assembly=result,finite_bridge=finite) + + +def normalized_body_check(): + source=(PACKAGE/'references/pr141/balanced_stopped.py').read_text() + old=source[source.index('def assembly('):source.index('\n\ndef cutoffs(')].rstrip() + body=(HERE/'balanced_shared.py').read_text();body=body[body.index('def assembly('):].rstrip() + body=body.replace('def assembly(finite_bridge, complex_row, a_bit, kappa,','def assembly(finite_bridge, ordinary_leaf, a_bit, kappa,',1) + body=body.replace('f = validate_shared_bridge(finite_bridge, complex_row)','f = validate_bridge(finite_bridge, ordinary_leaf)',1) + body=body.replace(" require(a <= f['bit_uniform']['ordinary_saving'], 'transfer saving exceeds actual uniform bit supplier')\n",'',1) + require(body==old,'The retained 47-slack body changed outside bridge plumbing and supplier support') + + +def certificate(row,physical): + nofloat(row);normalized_body_check() + final=price(row,AC,COARSE,BETA,ETA,WEAKENING,'balanced') + require(final['kappa']==Q('330942774629799/500000000000000000'),'Selected final kappa differs') + counts=physical['scalar_bound'] + require(counts['terminal_sinks']==row['terminal_sinks']==physical['terminal_compiler']['eligible_count'],'Terminal sink inventory mismatch') + require(counts['terminal_scalar_gate_delta']<=0 and counts['terminal_original_scalar_reserve_retained'],'Terminal compiler must fit the retained scalar reserve') + require(final['finite_bridge']['complex']['local_group_upper']==counts['local_group_upper'],'Scalar bill detached from physical word') + for key,field in (('physical_R','R'),('logical_R','scalar_role_reserve'),('handoffs','reuse_pairs'),('c','c'),('q','q'),('M_operations','total_M_operations')): + require(counts[key]==row[field],'Physical scalar inventory mismatch '+key) + require(counts['fixed_odd_divisor']==3 and counts['scalar_denominators_divide']==6,'Exact odd-grid contract') + require(sha256((ROOT/'notes/general-clifford-frames.tex').read_bytes()).hexdigest() in physical['source_sha256'].values(),'Frame theorem source drift') + parent_path=ROOT/'certificates/paired-cube-network.json' + require(sha256(parent_path.read_bytes()).hexdigest()=='05b253a21dc526b6039f56d1068162a19a8a4f29291ad94eb892656b88e9142d','Published prerequisite certificate changed') + parent=json.loads(parent_path.read_text()) + published_parent=dict(source_commit='4a3c769e5c5430e7114c4d3e099ff34664677f17',certificate_sha256=sha256(parent_path.read_bytes()).hexdigest(),kappa=parent['kappa'],ordinary_saving=parent['bit']['effective_saving']) + rows=[('Same suppliers with earlier positive outer backoffs',row,AC,COARSE,Q(1,10**9),Q(1,10**8),Q(1,10**10),'balanced',ATOM), + ('Same suppliers with finer positive outer backoffs',row,AC,COARSE,BETA,ETA,WEAKENING,'balanced',ATOM)] + controls_table=[] + for name,*args in rows: + result=price(*args);controls_table.append(dict(name=name,**{k:v for k,v in result.items() if k not in ('assembly','finite_bridge')})) + accepted=[] + def reject(name,operation): + try:operation() + except (KeyError,ValueError,AssertionError):accepted.append(name) + else:raise ValueError('Adverse control accepted: '+name) + finite=final['finite_bridge'];a=final['a'];k=final['kappa'] + def mutate(name,change): + bad=copy.deepcopy(finite);change(bad);reject(name,lambda:validate_shared_bridge(bad,row)) + mutate('full group stock replaced by local W',lambda x:x['complex'].update(W=row['W_per_vertex'])) + mutate('old ordinary reserve omitted',lambda x:x.update(ordinary_leaf_row_degree=0)) + mutate('conservative old coarse reserve omitted',lambda x:x.update(conservative_old_coarse_row_reserve=0)) + mutate('uniform supplier replaced by fictional finite profile',lambda x:(x.pop('bit_uniform'),x.update(bit_coarse={'m':529,'W':108516254}))) + mutate('actual ordinary saving overstated',lambda x:x['bit_uniform'].update(ordinary_saving=AB+Q(1,10**24))) + mutate('unpaid previous atom grid',lambda x:x['bit_uniform'].update(atom_beta=ATOM-Q(1,10**24),ordinary_saving=(1-ATOM+Q(1,10**24))*COARSE+(ATOM-Q(1,10**24))*OLD)) + mutate('scalar role reserve collapsed to physical stock',lambda x:x['complex'].update(scalar_role_reserve=row['R'])) + mutate('terminal removals omitted',lambda x:x['complex'].update(terminal_sinks=0)) + mutate('terminal removals counted as aliases',lambda x:x['complex'].update(reuse_pairs=row['reuse_pairs']+row['terminal_sinks'])) + mutate('odd divisor silently changed to 21',lambda x:x['semantic'].update(fixed_odd_divisor=21)) + mutate('C0 detached from scalar charge',lambda x:x['semantic'].update(C0=1)) + mutate('scalar group charge omitted',lambda x:x['complex'].update(scalar_group_upper=0)) + mutate('stale total row coefficient',lambda x:x['rows'].update(coefficient=1)) + mutate('inadequate polynomial row degree',lambda x:x['rows'].update(degree=1)) + mutate('float in otherwise unused metadata',lambda x:x['bit_uniform'].update(extra=0.5)) + mutate('noncontracting maximum child',lambda x:x['complex'].update(maxchild=row['m'])) + reject('transfer saving exceeds actual uniform supplier',lambda:assembly(finite,row,AB+Q(1,10**24),k,beta=BETA,h=ETA,a_complex=AC)) + reject('old prefix charged at balanced parameters',lambda:assembly(finite,row,a,k,beta=BETA,h=ETA,a_complex=AC,original_prefix=True)) + reject('old nonlinear scalar guard',lambda:assembly(finite,row,a,k,beta=BETA,h=ETA,a_complex=AC,old_guard=True)) + reject('old separate movement exposures',lambda:assembly(finite,row,a,k,beta=BETA,h=ETA,a_complex=AC,old_exposures=True)) + reject('next final 1e-18 kappa grid point',lambda:assembly(finite,row,a,k+Q(1,GRID),beta=BETA,h=ETA,a_complex=AC)) + return js(dict(status='PASS',kappa=k,actual_uniform_bit_saving=AB,coarse_bit_saving=COARSE, + complex_saving=AC,weakened_transfer_saving=a,beta=BETA,eta=ETA,strict_weakening=WEAKENING,atom_exponent=ATOM, + bridge=finite,assembly=final['assembly'],matched_comparisons=controls_table,published_parent=published_parent, + unchanged_47_slack_body=True,adverse_controls=accepted,adverse_control_count=len(accepted), + next_grid_scope='Rejection at these fixed certified supplier values and stated parameters; no global or true-profile optimality claim.', + scope='Conditional finite witness retaining the source-specified uniform bit, exact tensor, row-restoration, paid layout and analytic/fixed-tape contracts.')) diff --git a/research/coordinated-frames-and-entrance-banks/arithmetic/interval_moment.py b/research/coordinated-frames-and-entrance-banks/arithmetic/interval_moment.py new file mode 100644 index 0000000000..c135d98d86 --- /dev/null +++ b/research/coordinated-frames-and-entrance-banks/arithmetic/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=0 and terminal>=0 and scalar_R-R==reuse+terminal,'Physical role count must match reuse and terminal removals') + require(h>=2 and h%2==0 and min(v,R,c,M)>0,'Positive even-dimensional complex family') + m=3*h + hist={integer(k):integer(n) for k,n in row['child_histogram'].items() if integer(n)} + require(all(00 for t,n in hist.items()),'Proper positive child histogram') + r=max(hist);localW=2*v+R;localS=sum(t*n for t,n in hist.items()) + require((m,localW,localS)==tuple(integer(row[k]) for k in ('m','W_per_vertex','rank_per_vertex')),'Complex inventory totals') + require(m*localW-localS==integer(row['deficit_per_vertex'])==2*v-3*integer(row['loss']),'Shared-core deficit identity') + half=m//2 + vertices=2**(m-1+(half-1)**2)*prod(2**(2*i)-1 for i in range(1,half)) + W,s,N=vertices*localW,vertices*localS,vertices*v + original_X=32*v + local=4*(c+v)+10*v+4*h*v+4*h*h+8*h+8+2*h+8*scalar_R*v*(M+16)+original_X + logical=3*vertices*local+8*W+4*N+8*m*scalar_R*vertices + G=64*(m+1)**3*(logical+1)*(W+1)**2 + E=64*(W+m+G+1)**3 + literal=2*G*W**2+8*s+4*W+4+32*m + B=s+E;C0=32*m*B**2;depth=halving(m,r) + expected_complex=dict(m=m,W=W,s=s,N=N,maxchild=r,invocations_per_stage=vertices,stages=3, + auxiliary_banks_after_sharing=1,halving_degree=depth,wire_bits=W.bit_length(), + original_X_involution_scalar_group_upper=original_X,local_group_upper=local, + logical_group_upper=logical,finite_group_router_upper=G,scalar_group_upper=G, + coefficient_bound=h+4,coefficient_denominator_divides=6, + physical_roles_per_vertex=R,scalar_role_reserve=scalar_R,reuse_pairs=reuse,terminal_sinks=terminal) + expected_semantic=dict(E=E,literal_charge=literal,strict_literal_gap=E-literal,B=B,C0=C0,C1=1, + induction_gap=2*B*(m-r)-s-E,fixed_odd_divisor=3) + for name,expected in [('complex',expected_complex),('semantic',expected_semantic)]: + for k,value in expected.items():require(rational(bridge[name][k])==value,'Stale '+name+'/'+k) + require(E>literal and 2*B*(m-r)>=s+E and C0>2*B+18,'Completed exact-child semantic induction') + # These are conservative, retained external reserves. The varying q-adic + # group cardinality is deliberately not interpreted as an external stock. + old_coarse=integer(bridge['conservative_old_coarse_row_reserve']) + old_leaf=integer(bridge['ordinary_leaf_row_degree']) + require(old_coarse==9909 and old_leaf==252,'Retained separate external row reserves') + coeff=depth*W.bit_length()+old_coarse+old_leaf + degree=integer(bridge['rows']['degree']);gap=Q(degree)-Q(51,25)*coeff + require(degree>0 and gap>0,'Insufficient external row reserve') + expected_rows=dict(coefficient=coeff,complex_coefficient=depth*W.bit_length(), + degree=degree,suffix_slope=4*degree,degree_gap=gap) + for k,value in expected_rows.items():require(rational(bridge['rows'][k])==value,'Stale row/'+k) + u=bridge['bit_uniform'] + coarse,atom,old,actual=(rational(u[k]) for k in ('coarse_saving','atom_beta','old_atom_saving','ordinary_saving')) + require(0 2: + x /= 2 + k += 1 + lo, hi = log_unit(x) + l2, u2 = log_unit(Q(2)) + lo, hi = lo+k*l2, hi+k*u2 + # Outward rational rounding keeps later certificates compact. + return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID) + + +def exp_bounds(x): + require(0 <= x < 1, "exponential range") + term = total = Q(1) + for j in range(1, 13): + term *= x/j + total += term + tail = term*x/13/(1-x/14) + return total, total+tail + + +def moment(m, W, entries, saving): + lo = hi = Q(0) + for t, count in entries: + t, count = int(t), int(count) + require(0 < t < m and count > 0, "improper child") + l, u = log_bounds(Q(m, t)) + lower = exp_bounds(saving*l)[0] + upper = exp_bounds(saving*u)[1] + lo += Q(t*count, m*W)*lower + hi += Q(t*count, m*W)*upper + return Q((lo*GRID).__floor__(), GRID), Q((hi*GRID).__ceil__(), GRID) + diff --git a/research/coordinated-frames-and-entrance-banks/bit/base_word.py b/research/coordinated-frames-and-entrance-banks/bit/base_word.py new file mode 100644 index 0000000000..b4a40a7e05 --- /dev/null +++ b/research/coordinated-frames-and-entrance-banks/bit/base_word.py @@ -0,0 +1,202 @@ +#!/usr/bin/env python3 +"""Reusable independent formal checks for a physical partner-pair bit word. + +The supplied frozen inputs are source-pinned. This never runs their producer. +The Z check is of the defining integer decoder; only its F2 reduction is I. +Prepared with OpenAI Codex assistance; Apache-2.0. +""" +from collections import Counter, defaultdict +import importlib.util +import json +from pathlib import Path +import sys +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[2] +BASE = ROOT / 'research/paired-cube-bit' +P = 12 +if sys.flags.optimize: raise SystemExit('refusing -O') + + +def need(ok, msg): + if not ok: + raise ValueError(msg) + +class Candidate: + def exact_frames(self): + C = self.C + C.decoder(); C.geometry() + for i in self.changed_frames: + f = self.opframe[i]; x = self.ops[i][2]; bits = C.sup[x] + need(C.nondeg(f), 'replacement operation frame nondegenerate') + while bits: + low = bits&-bits; s=low.bit_length()-1; bits-=low + need(C.in_frame(C.chi[s],f), 'value span in replacement operation frame') + for b, d in self.pairs: + need(C.sub(self.endframe[d], self.gauge[b]['frame']), 'exact Q donor-to-birth containment') + need(C.nondeg(self.endframe[d]) and C.nondeg(self.gauge[b]['frame']), 'handoff endpoints nondegenerate') + + def register(self, rows): + C = self.C + B,_ = self.module.reduce_rows(rows,self.h if hasattr(self,'h') else C.h) + B = tuple(sorted(map(tuple,B),key=lambda r:next(i for i,x in enumerate(r) if x))) + if not hasattr(self,'frame_ids'): + self.frame_ids = {} + if B in self.frame_ids: return self.frame_ids[B] + f=max(C.B)+1; A,_=self.module.kernel(B,C.h) + C.B[f],C.A[f],C.dimf[f]=B,A,len(B);self.frame_ids[B]=f + return f + + + def row(self): + C,h,v=self.C,self.h,self.v + _,baseline_Y,src,_=C.chains() + seq=defaultdict(list) + for i,(a,b,x) in enumerate(self.ops): + seq[a].append(self.opframe[i]);seq[b].append(self.opframe[i]) + for j,s in enumerate(self.w['rootroles']):seq[s].append(self.w['root_frame'][j]) + start={b:self.w['source_frame'][x] for x,b in self.source.items()} + start.update({b:z['frame'] for b,z in self.gauge.items()}) + recipient={d:b for b,d in self.pairs} + H=Counter() + for s in range(self.R): + if s in self.donor:continue + chain=list(seq[s]) + if s in recipient: + b=recipient[s];chain += [self.gauge[b]['frame']]+seq[b] + chain.append(self.w['full_frame']) + prev=start.get(s);dp=0 if prev is None else C.dimf[prev] + if s in self.source.values():H[1]+=1 + for f in chain: + need(prev is None or C.sub(prev,f),'physical role chain nested') + d=C.dimf[f] + if d>dp:H[d-dp]+=1 + prev,dp=f,d + for j,r in enumerate(self.g['roots']): + if r['kind']=='center':H[C.dimf[self.w['root_frame'][j]]]+=1 + Y=Counter();current=[None]*v + def read(t,f): + old=current[t];d=0 if old is None else C.dimf[old] + need(old is None or C.sub(old,f),'actual target frame chronology') + if C.dimf[f]>d:Y[C.dimf[f]-d]+=1 + current[t]=f + for b in sorted(self.order,key=lambda b:self.readtime[b]): + for t in self.gauge[b]['targets']:read(t,self.gauge[b]['frame']) + deliveries=defaultdict(list) + for e in self.k['entries']:deliveries[e['deliver_after_root']].append(e) + for j,r in enumerate(self.g['roots']): + if r['kind']!='center': + for t in r['targets']:read(t,self.w['root_frame'][j]) + for e in deliveries[j]: + for t in e['receivers']:read(t,e['deliver_frame']) + for t,f in enumerate(current): + need(f is not None and all(self.module.dot(C.cov[t],b)==0 for b in C.B[f]),'final target cap') + gap=h-1-C.dimf[f] + if gap:Y[gap]+=1 + need(sum(r*n for r,n in Y.items())==v*(h-1),'target rank mass') + hist=Counter() + for part in (H,Y,src): + for r,n in part.items(): + if r and n:hist[r]+=3*n + for b,z in self.gauge.items(): + if b not in self.donor:hist[3*z['dim']]+=1 + hist[2]+=2*v + hist={r:n for r,n in sorted(hist.items()) if n} + need(all(00 for r,n in hist.items()),'positive proper child bins') + R=self.R-len(self.pairs);W=2*v+R;mass=sum(r*n for r,n in hist.items());m=3*h + need(W*m-mass==C.prof['deficit_per_vertex'],'reuse preserves telescoping deficit') + return dict(h=h,v=v,R=R,virtual_R=self.R,reused_registers=len(self.pairs),W_per_vertex=W,m=m, + loss=C.prof['loss'],rank_per_vertex=mass,deficit_per_vertex=W*m-mass, + child_histogram=hist,maxchild=max(hist),selected_roles=len(self.gauge)-len(self.pairs), + selected_rank_histogram=dict(Counter(z['dim'] for b,z in self.gauge.items() if b not in self.donor)), + changed_operation_frames=len(self.changed_frames), + frames_not_contained_in_original=sum(not C.sub(self.opframe[i],self.original_opframe[i]) for i in self.changed_frames), + physical_target_histogram=dict(Y),physical_internal_histogram=dict(H), + foreign_producer_replays=0) + + def adjoint(self): + adj = [dict() for _ in range(self.R)] + for r,s in zip(self.g['roots'], self.w['rootroles']): + for t in r['targets']: adj[s][t] = adj[s].get(t,0)+1 + for a,b,_ in reversed(self.ops): + for t,c in adj[a].items(): adj[b][t] = adj[b].get(t,0)+c + return adj + + def formal(self, ring, tamper=None): + """All source, target and dirty-register columns; no random sampling.""" + v, phys = self.v, self.phys + regs = sorted(set(phys.values())); index = {r:2*v+j for j,r in enumerate(regs)} + if ring == 2: + unit = lambda i: 1<=0 for x in powers.values()) + assert type(residual) is int and 00 for r,n in H.items()),'proper paid bank children') + need(9*gauges%18==0 and 9*rest%3==0,'stage-private integer bank realization') + need(3*(9*gauges//18+9*rest//3)+2*9*word.v==9*W,'nine-copy literal stock agrees') + packed=dict(row,W_per_vertex=W,rank_per_vertex=mass,deficit_per_vertex=1936,child_histogram=H,maxchild=22, + physical_roles_before_banks=row['R'],bank_roles_per_vertex=W-2*word.v, + bank=dict(entrance_rank=20,entrance_gauges=gauges,undeferred_physical_roles=rest, + selected_blocks=18,selected_width=4,undeferred_blocks=3,undeferred_width=24, + stages=3,physical_chains_spliced=True,physical_replica_count=9,moment_normalization_scale=3,selected_banks_per_stage=1100,undeferred_banks_per_stage=47484), + bank_projector_checks=bank_projectors()) + expected=json.loads((HERE/'banks.json').read_text()) + ep=expected['profile'] + need(Q(ep['W_per_vertex'])==W and ep['rank_per_vertex']==mass and ep['deficit_per_vertex']==1936,'stored packed dimensions') + need({int(r):n for r,n in ep['child_multiplicities'].items()}==H,'stored entire packed histogram') + need(expected['bank']==dict(entrance_rank=20,entrance_gauges=gauges,undeferred_physical_roles=rest),'stored actual bank role classes') + return packed + + +def independent_bank_moment(row,coarse): + from base_two_moment import moment as alternate_moment + W=int(3*row['W_per_vertex']);H=[(r,3*n) for r,n in row['child_histogram'].items()] + count=sum(n for r,n in H);fallback=32*72**2*count + _,upper=alternate_moment(72,W,H,coarse['coarse_saving']) + _,bad_upper=alternate_moment(72,W,[(1,fallback)],coarse['coarse_saving']) + gap=1-upper-Q(1,10**16)*bad_upper + need(gap>0,'independent base-two paid moment contracts') + next_saving=coarse['coarse_saving']+Q(1,coarse['coarse_grid']) + lower,_=alternate_moment(72,W,H,next_saving) + bad_lower,_=alternate_moment(72,W,[(1,fallback)],next_saving) + need(lower+Q(1,10**16)*bad_lower>1,'independent base-two adjacent paid moment exclusion') + return gap + + +def certify(row): + p=dict(m=row['m'],W=row['W_per_vertex'],N=row['deficit_per_vertex'],L=0, + total_rank=row['rank_per_vertex'],maxchild=row['maxchild'],child_multiplicities=row['child_histogram']) + # Scale three clears the normalized moment fractions; the stage-private physical realization uses nine copies. + p=dict(p,W=int(3*Q(p['W'])),N=3*p['N'],total_rank=3*p['total_rank'], + child_multiplicities={r:3*n for r,n in p['child_multiplicities'].items()}) + grid=10**18;lo=0;hi=grid//100 + need(paid_moment(p,Q(lo,grid))['upper']<1,'zero-saving rank contraction') + need(paid_moment(p,Q(hi,grid))['lower']>1,'upper bracket') + while hi-lo>1: + mid=(lo+hi)//2;r=paid_moment(p,Q(mid,grid)) + if r['upper']<1:lo=mid + elif r['lower']>1:hi=mid + else:raise ValueError('increase moment precision') + coarse=Q(lo,grid);accepted=paid_moment(p,coarse,True);rejected=paid_moment(p,Q(hi,grid),True) + need(accepted['upper']<1=0) + need(closure==set(self.phase1),'phase one is exactly centre closure') + content=[0]*self.R + for n,s in self.source.items():content[s]=1<0,'gauge dimension and complete response support') + src=Counter();members=Counter();labels=list(map(set,self.g['labels'])) + for e in self.k['entries']: + c,d,f,cap=e['carrier'],e['passive'],e['mix_frame'],e['deliver_frame'] + need(len(labels[c]&labels[d])==1,'orthogonal partner pair') + need(C.dimf[f]==2 and C.in_frame(C.chi[c],f) and C.in_frame(C.chi[d],f),'partner mix span') + need(C.sub(f,cap) and all(self.module.dot(C.cov[t],u)==0 for t in e['receivers'] for u in C.B[cap]),'partner mix delivery cap') + need(e['carrier_chain']==[w['source_frame'][c],f,cap,w['full_frame']] and e['passive_chain']==[w['source_frame'][d],f,w['full_frame']],'exact partner chains') + root=self.g['roots'][e['deliver_after_root']] + need(root['kind']=='side' and sorted(e['receivers'])==sorted(root['targets']),'partner delivery at own receiver root') + for chain in (e['carrier_chain'],e['passive_chain']): + for a,b in zip(chain,chain[1:]): + need(C.sub(a,b),'nested source chronology');src[C.dimf[b]-C.dimf[a]]+=1 + members[c]+=1;members[d]+=1 + need(all(members[s]==1 for s in range(v)),'every source in one partner pair') + return Counter(),Counter(),src,self.R diff --git a/research/coordinated-frames-and-entrance-banks/certificate.json b/research/coordinated-frames-and-entrance-banks/certificate.json new file mode 100644 index 0000000000..cd1eecca63 --- /dev/null +++ b/research/coordinated-frames-and-entrance-banks/certificate.json @@ -0,0 +1,3510 @@ +{ + "arithmetic": { + "actual_uniform_bit_saving": "665064157585290854736467094714610539581/1000000000000000000000000000000000000000000", + "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": 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b/research/coordinated-frames-and-entrance-banks/complex/check_sinks.py @@ -0,0 +1,216 @@ +#!/usr/bin/env python3 +"""Author exact finite check for target-accumulating disjoint-root deletion. + +Portability-only adaptation by Chafik Boukhalfa with OpenAI Codex assistance. +Original PR166 author James Chang. Uses frozen selected complex data; never imports upstream programs, +regenerates a source graph, searches a new producer, or computes a new kappa. +Python standard library. Copyright 2026; Apache-2.0. +""" +import argparse,gzip,hashlib,json,signal,sys,time +try: + import resource +except ImportError: + class resource: + RUSAGE_SELF=0 + RLIMIT_CPU=0 + @staticmethod + def setrlimit(*_): pass + @staticmethod + def getrusage(_): + class Usage: ru_maxrss=0 + return Usage() +from collections import Counter +from fractions import Fraction +from pathlib import Path + + +def main(): + if sys.flags.optimize:raise SystemExit('Run without -O') + ap=argparse.ArgumentParser(description=__doc__) + ap.add_argument('--candidate',type=Path,required=True) + ap.add_argument('--output',type=Path,required=True) + a=ap.parse_args();start_time=time.monotonic() + resource.setrlimit(resource.RLIMIT_CPU,(60,60));getattr(signal,"alarm",lambda _:None)(60) + pins=json.loads((a.candidate/'result.json').read_text())['pins'];data={} + for name in ['graph','word','frames','physical-frames','physical-pairs','profile-before','profile']: + name+='.json.gz';b=(a.candidate/name).read_bytes();assert hashlib.sha256(b).hexdigest()==pins[name] + data[name[:-8]]=json.loads(gzip.decompress(b)) + g,w,fw,changes,pairs,row,profile=[data[n] for n in ['graph','word','frames','physical-frames','physical-pairs','profile-before','profile']] + H,V,R=g['h'],g['v'],row['R'];assert (H,V)==(22,1320) + def basis(rows): + b={} + for x in rows: + for p,y in sorted(b.items(),reverse=True): + if x>>p&1:x^=y + if x: + p=x.bit_length()-1 + for k,y in list(b.items()): + if y>>p&1:b[k]=y^x + b[p]=x + return tuple(b[k] for k in sorted(b,reverse=True)) + def perp(rows): + rows=basis(rows);p={r.bit_length()-1:r for r in rows};out=[] + for j in range(H): + if j in p:continue + x=1<>j&1:x|=1<len(A)) + if s in sources.values():local[1]+=1 + for t in (s,donors.get(s)): + if t is not None and rkind.get(t)=='center':local[len(rframe[t])]+=1 + assert fmt(local)==profile['local_histogram'] + source=Counter({int(k):v for k,v in profile['source_data_histogram'].items()});target=Counter({int(k):v for k,v in profile['target_data_histogram'].items()}) + def children(L,T): + c=Counter({r:3*n for r,n in L.items() if r});c.update({r:3*n for r,n in T.items() if r});c.update({r:3*n for r,n in source.items() if r});c[2]+=2*V + for s,z in selected.items(): + if s not in aliases:c[3*z['rank']]+=1 + return c + oldchildren=children(local,target);assert fmt(oldchildren)==profile['child_histogram'] + rejected=Counter();eligible=[] + for j,r in enumerate(g['roots']): + if r.get('channel')!='disjoint':continue + s=w['rootroles'][j];writes=[i for i in roleops[s] if w['ops'][i][0]==s];uses=[i for i in roleops[s] if w['ops'][i][1]==s];why=[];U=rootframes[j] + if s in aliases or s in donors:why.append('alias_or_donor') + if s in sources.values():why.append('source_injection') + if s in selected:why.append('selected_gauge') + if roots_of[s]!=[j]:why.append('multiple_roots') + if uses:why.append('retained_producer_consumer') + if not writes:why.append('no_writes') + if any(w['opcoeff'][i][0]!=1 for i in writes):why.append('nonadditive_destination') + if any(not within(ofs[i],U) for i in writes):why.append('outside_read_frame') + if any(i in phase for i in writes):why.append('center_phase_touch') + available_pivots=[t for t in r['targets'] if writes and first_read[t]>max(when[i] for i in writes)] + if not available_pivots:why.append('no_uncorrected_pivot') + if why:rejected.update(why);continue + assert len(r['targets'])==8 and len(U)==18 and r['coefficients']==['1/2']*8 + # The sink's whole original trajectory is copied by only one target pivot. + # Every other target stays at0 until the common rank18 post-read. + path=[()]+[ofs[i] for i in writes]+[U];assert all(within(A,B) for A,B in zip(path,path[1:])) + prefix=[len(B)-len(A) for A,B in zip(path,path[1:]) if len(B)>len(A)] + assert sum(prefix)==18 + eligible.append(dict(root_index=j,role=s,targets=r['targets'],pivot=available_pivots[0],writes=writes,write_ranks=[len(ofs[i]) for i in writes],prefix_children=prefix,pre_at_phase_cut_after_center_before_old_reads=True,post_after_op=writes[-1],last_write_chronology=max(when[i] for i in writes),first_pivot_old_read=first_read[available_pivots[0]],first_any_old_read=min(first_read[t] for t in r['targets']))) + assert len(set(t for x in eligible for t in x['targets']))==8*len(eligible) + removed={x['role'] for x in eligible};removed_ops={i for x in eligible for i in x['writes']} + assert all(aa not in removed and bb not in removed for i,(aa,bb,n) in enumerate(w['ops']) if i not in removed_ops) + # All formal source and dirty coefficients of every selected sink are checked + # by exact adjoint pullback of its current final value through actual aliases. + # Remaining source/dirty identity follows from literal inverse cancellation + # of the unchanged retained word; no sampler or packed-digit hypothesis. + def final_form(s,stop): + c={s:1} + for i in reversed(chron[:stop+1]): + aa,bb,n=w['ops'][i];aa,bb=alias(aa),alias(bb);ca,cb=w['opcoeff'][i];v=c.get(aa,0) + if v: + c[aa]=ca*v;c[bb]=c.get(bb,0)+cb*v + if not c[bb]:del c[bb] + fresh={n-1:c[alias(s)] for n,s in sources.items() if c.get(alias(s),0)} + return c,fresh + dirtyterms=[] + for item in eligible: + s=item['role'];c,fresh=final_form(s,item['last_write_chronology']);assert c[s]==1 + assert not (set(c)&(removed-{s})) + cube={x//2 for x in g['labels'][item['targets'][0]]} + expected={n:1 for n,t in enumerate(g['labels']) if cube.isdisjoint(x//2 for x in t)} + assert fresh==expected and len(fresh)==448;dirtyterms.append(len(c)-1) + # Exact independent-target/sink/accumulation-symbol sandwich, both signs. + # Algebra includes arbitrary previous target corrections in y[t]. + for direction in (1,-1): + N=16+len(item['writes']);ys=[[Fraction(int(i==t)) for i in range(N)] for t in range(8)] + for t in range(1,8):ys[t]=[a-b for a,b in zip(ys[t],ys[0])] + # Arbitrary intervening non-pivot corrections are explicit independent + # columns. The chosen pivot has none until after its post-read. + for t in range(1,8):ys[t][8+len(item['writes'])+t]+=1 + for k,i in enumerate(item['writes']):ys[0][8+k]+=direction*Fraction(w['opcoeff'][i][1],2) + for t in range(1,8):ys[t]=[a+b for a,b in zip(ys[t],ys[0])] + for t in range(8): + expected=[Fraction(int(i==t)) if i<8 else direction*Fraction(w['opcoeff'][item['writes'][i-8]][1],2) if i<8+len(item['writes']) else Fraction(int(t>0 and i==8+len(item['writes'])+t)) for i in range(N)] + assert ys[t]==expected + # Whole simultaneous local and shared three-core ledger. + L=local.copy();T=target.copy() + for item in eligible: + L.subtract(Counter(item['prefix_children']+[4]));T[18]-=1;T.update(item['prefix_children']) + assert all(v>=0 for v in L.values()) and all(v>=0 for v in T.values()) + # Replay every target event in the actual deadline order, interleaving the + # new pivot writes and post-reads. Pre-shears are at the common zero frame + # just after the center phase and before its first compensation read. + by_write={i:item for item in eligible for i in item['writes']} + after={item['writes'][-1]:item for item in eligible} + read_at={} + for z in reversed(w['selected']): + d=deadline.get(z['role']);position=len(phase) if d is None else when[d] + read_at.setdefault(position,[]).append(z) + current=[() for _ in range(V)];actual_target=Counter();target_events=[] + def move_target(t,U,kind,index): + U=tuple(U);assert within(current[t],U),(kind,index,t,current[t],U) + actual_target[len(U)-len(current[t])]+=1 + target_events.append([kind,index,t,list(current[t]),list(U)]) + current[t]=U + for position,i in enumerate(chron): + for z in read_at.get(position,[]): + U=perp(z['annihilator']) + for t in z['targets']:move_target(t,U,'old-read',z['role']) + if i in by_write: + item=by_write[i];move_target(item['pivot'],ofs[i],'pivot-write',i) + if i in after: + item=after[i];U=rootframes[item['root_index']] + for t in item['targets']:move_target(t,U,'post-read',i) + assert all(current[t]==current[item['pivot']]==U for t in item['targets']) + for j,r in enumerate(g['roots']): + if r['kind']=='side' and w['rootroles'][j] not in removed: + for t in r['targets']:move_target(t,rootframes[j],'retained-root',j) + for t,q in enumerate(g['inputs']):move_target(t,perp((q,)),'target-finish',t) + assert fmt(Counter({r:n for r,n in actual_target.items() if r}))==fmt(Counter({r:n for r,n in T.items() if r})) + # Independent reverse of each scalar sandwich, including arbitrary inserted + # non-pivot corrections, yields the inverse rather than assuming a sign rule. + for item in eligible: + N=16+len(item['writes']);initial=[[Fraction(int(i==t)) for i in range(N)] for t in range(8)] + state=[r[:] for r in initial];events=[] + for t in range(1,8):events.append(('shear',t,0,Fraction(-1))) + for k,i in enumerate(item['writes']):events.append(('basis',0,8+k,Fraction(w['opcoeff'][i][1],2))) + for t in range(1,8):events.append(('basis',t,8+len(item['writes'])+t,Fraction(1))) + for t in range(1,8):events.append(('shear',t,0,Fraction(1))) + def apply(e,sign): + kind,t,s,c=e;c*=sign + if kind=='basis':state[t][s]+=c + else:state[t]=[a+c*b for a,b in zip(state[t],state[s])] + for e in events:apply(e,1) + for e in reversed(events):apply(e,-1) + assert state==initial + C=children(L,T);n=len(eligible);delta={str(k):C[k]-oldchildren[k] for k in C.keys()|oldchildren.keys() if C[k]!=oldchildren[k]} + assert delta==({'4':-3*n,'18':-3*n} if n else {});W=profile['W_per_vertex']-n;rank=sum(k*v for k,v in C.items());assert rank==profile['rank_per_vertex']-66*n and 66*W-rank==1320 + result=dict(status='AUTHOR_EXACT_FINITE_COMPILER_CHECK_PASS',scope='Only all-eight disjoint roots; retained full proof contracts unchanged',input_pins={k:pins[k] for k in pins if k in [n+'.json.gz' for n in data]},h=H,v=V,old_physical_R=len(live),new_physical_R=len(live)-n,old_W=profile['W_per_vertex'],new_W=W,old_rank=profile['rank_per_vertex'],new_rank=rank,deficit=1320,eligible_count=n,rejected_conditions=dict(rejected),targets_disjoint=True,simultaneous_compatible=True,all_formal_source_and_dirty_coefficients=True,formal_original_source_dirty_target_columns=2*V+len(live),remaining_formal_columns=2*V+len(live)-n,chronological_inverse_by_literal_reverse=True,full_old_physical_histogram_verified=True,all_new_target_events_replayed=True,scalar_sandwich_literal_reverse_checked=True,shared_child_delta=delta,scalar_gate_delta=-sum(len(x['writes'])+2 for x in eligible),new_odd_denominator=False,new_kappa_claimed=False,local_histogram=fmt(L),target_histogram=fmt(T),child_histogram=fmt(C),sinks=eligible,dirty_coefficient_nonzero_range=[min(dirtyterms),max(dirtyterms)],seconds=time.monotonic()-start_time,rss_kib=resource.getrusage(resource.RUSAGE_SELF).ru_maxrss) + a.output.write_text(json.dumps(result,indent=2)+'\n');print(json.dumps({k:v for k,v in result.items() if k not in ['sinks','local_histogram','target_histogram','child_histogram','input_pins']},indent=2)) +if __name__=='__main__':main() diff --git a/research/coordinated-frames-and-entrance-banks/complex/formal_sinks.py b/research/coordinated-frames-and-entrance-banks/complex/formal_sinks.py new file mode 100644 index 0000000000..703d57f386 --- /dev/null +++ b/research/coordinated-frames-and-entrance-banks/complex/formal_sinks.py @@ -0,0 +1,137 @@ +"""Independent full execution of PR166 sink substitution on our fused168. + +James Chang's PR166 compiler; fused168 source lineage in its SOURCE.json. +New full packed-column executor by Chafik Boukhalfa with OpenAI Codex. +""" +from pathlib import Path +from fractions import Fraction as Q +from collections import defaultdict +from hashlib import sha256 +import argparse,gzip,json,time,importlib.util,sys + +BASE=Path(__file__).resolve().parent +ap=argparse.ArgumentParser(description=__doc__) +ap.add_argument('--candidate',type=Path,default=BASE.parents[1]/'r13-search/fused168') +ap.add_argument('--selection',type=Path,default=BASE/'fused168-screen.json') +ap.add_argument('--formal-helper',type=Path) +ap.add_argument('--output',type=Path,default=BASE/'formal-sinks.json') +args=ap.parse_args();INPUT=args.candidate;HELPER=args.formal_helper or INPUT/'prove.py' +if sys.flags.optimize:raise SystemExit('Run without -O') +spec=importlib.util.spec_from_file_location('original_formal',HELPER) +old=importlib.util.module_from_spec(spec);spec.loader.exec_module(old) +def load(name):return json.loads(gzip.decompress((INPUT/(name+'.json.gz')).read_bytes())) +g,w,row=[load(n) for n in ['graph','word','profile-before']] +pairs=load('physical-pairs');selection=json.loads(args.selection.read_text()) +for name,digest in selection['input_pins'].items():assert sha256((INPUT/name).read_bytes()).hexdigest()==digest,name +sinks=selection['sinks'];removed={s['role'] for s in sinks};sinkroots={s['root_index'] for s in sinks} +alias={b:a for a,b,t in pairs};R=row['R'];v=g['v'] +live=[s for s in range(R) if s not in alias and s not in removed] +slot={s:i for i,s in enumerate(live)} +phys=lambda s:slot[alias.get(s,s)] +D,adj=old.adjoint(g,w,R) +ops=w['ops'];coef=w['opcoeff'];phase=w['phase1'];rest=[i for i in range(len(ops)) if i not in set(phase)] +deadlines=dict((b,t) for a,b,t in pairs);at=defaultdict(list) +for s,t in deadlines.items(): + if t is not None:at[t].append(s) +selected=[z['role'] for z in w['selected']];deferred=set(selected) +sources={int(x):s for x,s in w['sources'].items()} +bywrite={i:s for s in sinks for i in s['writes']};after={s['writes'][-1]:s for s in sinks} +cnum=[[int(6*Q(c)) for c in r['coefficients']] for r in g['roots']] +assert len(live)==selection['new_physical_R'] + +def execute(direction,bits=None,mutation=None): + # With bits=None this is an absolute coefficient L1 majorant. With bits + # supplied it is the actual signed word on an injectively packed basis. + major=bits is None; top=6; count=2*v+len(live) + def basis(i):return 6 if major else 6<<(bits*i) + def add(x,c,y):return x+abs(c)*y if major else x+c*y + def track(xs): + nonlocal top + if major:top=max(top,max(xs,default=0)) + X=[basis(i) for i in range(v)];Y=[basis(v+i) for i in range(v)];Z=[basis(2*v+i) for i in range(len(live))] + initial=Y[:];z=Z[:] + # Retain the ORIGINAL response of every retained dirty coordinate, + # including responses propagated through the deleted sinks. + virtual=[0 if s in deferred or s in alias or s in removed else Z[phys(s)] for s in range(R)] + def gate(values,i): + a,b,_=ops[i];ca,cb=coef[i] + values[a]=abs(ca)*values[a]+abs(cb)*values[b] if major else ca*values[a]+cb*values[b] + def decode(values,kind=None,skip=False): + out=[0]*v + for j,(root,s,cs) in enumerate(zip(g['roots'],w['rootroles'],cnum)): + if kind is not None and root['kind']!=kind:continue + if skip and j in sinkroots:continue + for t,c in zip(root['targets'],cs):out[t]=add(out[t],c,values[s]) + assert all(x%6==0 for x in out) + return [x//6 for x in out] + for i in range(len(ops)):gate(virtual,i) + response=decode(virtual,skip=mutation=='omit-ancestor-response') + Y=[add(y,-direction,r) for y,r in zip(Y,response)];track(Y);del virtual,response + for n,s in sources.items():z[phys(s)]=add(z[phys(s)],1,X[n-1]) + done=[] + def actualgate(i): + a,b,_=ops[i];ca,cb=coef[i];a,b=phys(a),phys(b) + z[a]=abs(ca)*z[a]+abs(cb)*z[b] if major else ca*z[a]+cb*z[b] + if major: + nonlocal top + top=max(top,z[a]) + done.append(i) + def read(s): + for t,c in D[s].items(): + assert z[phys(s)]%6==0 + Y[t]=add(Y[t],-direction*c,z[phys(s)]//6) + track(Y) + for i in phase:actualgate(i) + virtual=[0 if s in removed else z[phys(s)] for s in range(R)] + center=decode(virtual,'center');Y=[add(y,direction,c) for y,c in zip(Y,center)];track(Y);del virtual,center + for sink in sinks: + pivot=sink['pivot'] + for t in sink['targets']: + if t!=pivot and mutation!='omit-pre-shear':Y[t]=add(Y[t],-1,Y[pivot]) + track(Y) + for s in reversed(selected): + if deadlines.get(s) is None:read(s) + for i in rest: + for s in at.get(i,[]):read(s) + if i in bywrite: + sink=bywrite[i];pivot=sink['pivot'];b=phys(ops[i][1]);assert z[b]%2==0 + if mutation!='omit-first-write' or i!=sinks[0]['writes'][0]:Y[pivot]=add(Y[pivot],direction*coef[i][1],z[b]//2) + track(Y) + else:actualgate(i) + if i in after: + sink=after[i];pivot=sink['pivot'] + for t in sink['targets']: + if t!=pivot:Y[t]=add(Y[t],1,Y[pivot]) + track(Y) + virtual=[0 if s in removed else z[phys(s)] for s in range(R)] + side=decode(virtual,'side',True);Y=[add(y,direction,c) for y,c in zip(Y,side)];del virtual,side + for a in range(0,v,8): + for j,q in enumerate(g['inputs'][a:a+8]): + value=0 + for r,x in zip(g['inputs'][a:a+8],X[a:a+8]): + c=1 if (q^r).bit_count()==6 else -1 if (q^r).bit_count()==2 else 0 + value=add(value,c,x) + assert value%2==0;Y[a+j]=add(Y[a+j],direction,value//2) + track(Y) + if not major:assert Y==[y+direction*x for y,x in zip(initial,X)],'all formal output columns' + for i in reversed(done): + a,b,_=ops[i];ca,cb=coef[i];a,b=phys(a),phys(b) + z[a]=z[a]+abs(cb)*z[b] if major else ca*(z[a]-cb*z[b]) + if major:top=max(top,z[a]) + for n,s in sources.items():z[phys(s)]=add(z[phys(s)],-1,X[n-1]) + track(z) + if not major:assert z==Z,'retained arbitrary dirty columns restored' + # Include the expected map in a safe final residual bound. + return top+12 if major else dict(direction=direction,columns=count,dirty=len(live),outputs=True,restored=True) + +if __name__=='__main__': + t=time.monotonic();bound=execute(1);bits=8*((bound.bit_length()+2+7)//8);assert 2**bits>2*bound + print('majorant',bound,'digit bits',bits,flush=True) + columns=[execute(d,bits) for d in [1,-1]] + controls={} + for mutation in ['omit-first-write','omit-ancestor-response','omit-pre-shear']: + try:execute(1,bits,mutation) + except AssertionError:controls[mutation]='REJECTED' + else:raise AssertionError('accepted '+mutation) + result=dict(status='PASS full modified finite word',absolute_residual_bound=bound,digit_bits=bits,columns=columns,controls=controls,source_sha256=sha256(Path(__file__).read_bytes()).hexdigest(),input_pins={p.name:sha256(p.read_bytes()).hexdigest() for p in list(INPUT.glob('*.json.gz'))+[args.selection,HELPER]},seconds=time.monotonic()-t) + args.output.write_text(json.dumps(result,indent=2)+'\n');print(json.dumps(result)) diff --git a/research/coordinated-frames-and-entrance-banks/complex/physical.py b/research/coordinated-frames-and-entrance-banks/complex/physical.py new file mode 100644 index 0000000000..8e55fa721d --- /dev/null +++ b/research/coordinated-frames-and-entrance-banks/complex/physical.py @@ -0,0 +1,177 @@ +#!/usr/bin/env python3 +"""Exact audit of the extended-link fused PR161/162 complex physical word, including every input. + +Chafik Boukhalfa with OpenAI Codex assistance. Apache-2.0. +The scalar signed graph, binary frames and original compiler are credited to +icekylinx (PR144); searched modules and physical reuse baseline to eumemic +(PR157 and PR161), extended carrier closure by DaysSky (PR162), with the lineage retained there. New checks independently execute +all physical aliases, deadline reads and inverse cleanup on an injective +packed formal basis, using a separately derived absolute coefficient bound. +""" +from pathlib import Path +from fractions import Fraction as Q +from collections import defaultdict,Counter +from hashlib import sha256 +import argparse,gzip,json,sys,time,copy,gc +try: + import resource +except ImportError: + class resource: + RUSAGE_SELF=0 + @staticmethod + def getrusage(_): + class Usage: ru_maxrss=0 + return Usage() + + +def adjoint(g,word,R): + D=[{} for _ in range(R)] + for root,s in zip(g['roots'],word['rootroles']): + for t,c in zip(root['targets'],root['coefficients']): + c=Q(c)*6;assert c.denominator==1;D[s][t]=D[s].get(t,0)+int(c) + for (a,b,_),(ca,cb) in zip(reversed(word['ops']),reversed(word['opcoeff'])): + for t,c in D[a].items():D[b][t]=D[b].get(t,0)+cb*c + if ca<0:D[a]={t:-c for t,c in D[a].items()} + D=[{t:c for t,c in row.items() if c} for row in D] + for z in word['selected']:assert set(D[z['role']])<=set(z['targets']) + receipt=dict(nonzeros=sum(map(len,D)),max_numerator_over_6=max(abs(c) for row in D for c in row.values()),L1=sum(abs(c) for row in D for c in row.values()),gauge_supports_contained=True) + selected={z['role']:D[z['role']] for z in word['selected']} + return selected,receipt + +class Formal: + def __init__(self,g,word,row,pairs,D): + self.g,self.word,self.row,self.D=g,word,row,D;self.v=g['v'];self.R=row['R'] + self.merge={b:a for a,b,t in pairs};assert len(self.merge)==len(pairs)==len(set(self.merge.values())) + assert not set(self.merge)&set(self.merge.values()) + self.live=[s for s in range(self.R) if s not in self.merge];self.slot={s:i for i,s in enumerate(self.live)} + self.phys=[self.slot[self.merge.get(s,s)] for s in range(self.R)] + self.sources={int(x):s for x,s in word['sources'].items()} + self.selected=[z['role'] for z in word['selected']];self.deferred=set(self.selected) + self.phase=sorted(word['phase1']);pset=set(self.phase);self.rest=[i for i in range(len(word['ops'])) if i not in pset] + self.deadline={b:t for a,b,t in pairs};self.at=defaultdict(list) + for b,t in self.deadline.items(): + if t is not None:self.at[t].append(b) + self.ops=[tuple(x) for x in word['ops']];self.coef=[tuple(x) for x in word['opcoeff']] + assert all(a in (-1,1) and b in (-1,1) for a,b in self.coef) + assert all(self.phys[a]!=self.phys[b] for a,b,x in self.ops) + self.cnum=[[int(6*Q(c)) for c in r['coefficients']] for r in g['roots']] + self.bound=self.coefficient_bound() + self.width=8*((self.bound.bit_length()+2+7)//8);self.base=1<2*self.bound + def coefficient_bound(self): + # Unscaled formal variables: a physical slot has coefficients bounded + # by its absolute row sum b. Actual packed slots use 6 times the basis. + g,word,v,R=self.g,self.word,self.v,self.R + old=[int(s not in self.deferred and s not in self.merge) for s in range(R)] + for (a,b,_),(ca,cb) in zip(self.ops,self.coef):old[a]=abs(ca)*old[a]+abs(cb)*old[b] + y=[6]*v + for root,s,cs in zip(g['roots'],word['rootroles'],self.cnum): + for t,c in zip(root['targets'],cs):y[t]+=abs(c)*old[s] + b=[1]*len(self.live);top=max([6*x for x in old]+y) + for node,s in self.sources.items():b[self.phys[s]]+=1 + done=[] + def gate(i): + nonlocal top + (a,c,_),(ca,cb)=self.ops[i],self.coef[i];a,c=self.phys[a],self.phys[c] + b[a]=abs(ca)*b[a]+abs(cb)*b[c];top=max(top,6*b[a]);done.append(i) + def read(s): + for t,c in self.D[s].items():y[t]+=abs(c)*b[self.phys[s]] + for i in self.phase:gate(i) + # All root/center positive readouts may be safely bounded by their + # value after the complete M: centers are closed in phase one. + for s in reversed(self.selected): + if self.deadline.get(s) is None:read(s) + for i in self.rest: + for s in self.at.get(i,[]):read(s) + gate(i) + for root,s,cs in zip(g['roots'],word['rootroles'],self.cnum): + for t,c in zip(root['targets'],cs):y[t]+=abs(c)*b[self.phys[s]] + # K has four +/-1/2 source contributions in every output row. + y=[x+12+6 for x in y];top=max(top,max(y)) + for i in reversed(done): + (a,c,_),(ca,cb)=self.ops[i],self.coef[i];a,c=self.phys[a],self.phys[c] + b[a]=abs(ca)*b[a]+abs(ca*cb)*b[c];top=max(top,6*b[a]) + for node,s in self.sources.items():b[self.phys[s]]+=1;top=max(top,6*b[self.phys[s]]) + return top + def decode(self,z,kind=None): + out=[0]*self.v + for root,s,cs in zip(self.g['roots'],self.word['rootroles'],self.cnum): + if kind is not None and root['kind']!=kind:continue + for t,c in zip(root['targets'],cs):out[t]+=c*z[s] + assert all(x%6==0 for x in out);return [x//6 for x in out] + def run(self,direction,mutation=None): + v,R,w=self.v,self.R,self.width + X=[6<<(w*i) for i in range(v)];Y0=[6<<(w*(v+i)) for i in range(v)];Z=[6<<(w*(2*v+i)) for i in range(len(self.live))] + # Compute precisely the initial reads D[s]z_s without expanding + # nongauged D: exact transposition identity D=JM gives this cheaper + # independent algebraic evaluation. All late physical reads below + # use the explicitly computed integer adjoint rows. + old=[Z[self.phys[s]] if s not in self.deferred and s not in self.merge else 0 for s in range(R)] + for (a,b,_),(ca,cb) in zip(self.ops,self.coef):old[a]=ca*old[a]+cb*old[b] + old=self.decode(old);y=[y-direction*z for y,z in zip(Y0,old)];del old;gc.collect() + z=Z[:];done=[] + def read(s): + if mutation=='missing-read' and s==self.selected[0]:return + value=z[self.phys[s]];assert value%6==0 + for t,c in self.D[s].items():y[t]-=direction*c*(value//6) + def gate(i): + (a,b,_),(ca,cb)=self.ops[i],self.coef[i];a,b=self.phys[a],self.phys[b] + z[a]=ca*z[a]+cb*z[b];done.append(i) + for node,s in self.sources.items():z[self.phys[s]]+=X[node-1] + for i in self.phase:gate(i) + physical_virtual=[z[self.phys[s]] for s in range(R)] + center=self.decode(physical_virtual,'center');del physical_virtual + for t,c in enumerate(center):y[t]+=direction*c + del center + late=[b for b,t in self.deadline.items() if t is not None];early=late[-1] if mutation=='early-read' and late else None + for s in reversed(self.selected): + if self.deadline.get(s) is None or s==early:read(s) + for i in self.rest: + for s in self.at.get(i,[]): + if s!=early:read(s) + gate(i) + physical_virtual=[z[self.phys[s]] for s in range(R)] + side=self.decode(physical_virtual,'side');del physical_virtual + for t,c in enumerate(side):y[t]+=direction*c + del side + def K(xs): + out=[] + for a in range(0,v,8): + block=xs[a:a+8];qs=self.g['inputs'][a:a+8] + for q in qs: + value=sum((1 if (q^r).bit_count()==6 else -1 if (q^r).bit_count()==2 else 0)*x for r,x in zip(qs,block));assert value%2==0;out.append(value//2) + return out + mixed=K(X);assert K(mixed)==X + for t,x in enumerate(mixed):y[t]+=direction*x + assert y==[y+direction*x for y,x in zip(Y0,X)],'full formal output map' + for i in reversed(done): + (a,b,_),(ca,cb)=self.ops[i],self.coef[i];a,b=self.phys[a],self.phys[b] + z[a]=ca*(z[a]-cb*z[b]) + for node,s in self.sources.items():z[self.phys[s]]-=X[node-1] + assert z==Z,'all physical dirty columns restored' + return dict(direction=direction,every_formal_column=True,source_columns=v,target_columns=v,dirty_columns=len(self.live),K_and_inverse=True,all_aliases_and_deadline_reads=True,all_physical_dirty_slots_restored=True) + +def main(): + ap=argparse.ArgumentParser();ap.add_argument('--candidate',type=Path,required=True);ap.add_argument('--source',type=Path,required=True);ap.add_argument('--out',type=Path,required=True);a=ap.parse_args();sys.path.insert(0,str(a.source/'scripts')) + from verify_fused import verify + from paired_cube_physical import physical + start=time.time();pins=json.loads((a.candidate/'result.json').read_text())['pins'];data={} + for name in ['graph','baseline','frames','word','profile-before','physical-frames','physical-pairs','profile']: + p=a.candidate/(name+'.json.gz');assert sha256(p.read_bytes()).hexdigest()==pins[p.name];data[name]=json.loads(gzip.decompress(p.read_bytes())) + g,b,w,word,row=[data[n] for n in ['graph','baseline','frames','word','profile-before']] + finite=verify(g,b,w,word,row);print('PASS exact signed scalar pairs and pre-reuse complete physical frame word',flush=True) + actual=physical(g,w,word,row,data['physical-frames'],data['physical-pairs']);assert json.loads(json.dumps(actual))==data['profile'];print('PASS all descended frames, nested chains, aliases and target read chronology',flush=True) + D,adj=adjoint(g,word,row['R']);formal=Formal(g,word,row,data['physical-pairs'],D);print('PASS exact adjoint; formal coefficient bound',formal.bound,'digit bits',formal.width,flush=True) + columns=[formal.run(d) for d in (1,-1)];print('PASS every formal column under both shear signs',flush=True) + mutations={} + for tag in ['missing-read','early-read']: + try:formal.run(1,tag) + except AssertionError:mutations[tag]='REJECTED' + else:raise AssertionError('accepted mutation '+tag) + cs=[Q(c) for r in g['roots'] for c in r['coefficients']] + assert set(cs)<={Q(1,2),Q(-1,2),Q(1,3),Q(-1,6)} and 3*row['q']<2**15 + local=4*(row['c']+row['v'])+10*row['v']+4*row['h']*row['v']+4*row['h']**2+8*row['h']+8+2*row['h']+8*row['R']*row['v']*(row['total_M_operations']+16)+32*row['v'] + scalar=dict(c=row['c'],q=row['q'],M_operations=row['total_M_operations'],logical_R=row['R'],physical_R=actual['physical_R'],handoffs=actual['pairs'],scalar_denominators_divide=6,fixed_odd_divisor=3,gate_and_inverse_coefficients=[-1,1],decoder_coefficients=sorted(map(str,set(cs))),three_q_less_than_2pow15=True,binary_dirty_read_bits=row['total_M_operations']+16,local_group_upper=local,scope='Conservative inherited virtual-word bill retained after aliasing, including all compensated reads. Alias and frame route choices are finite permutations/Clifford adapters; their separate global movement bill remains an assembly obligation.') + result=dict(status='PASS exact fused physical candidate, all formal source/target/dirty columns',source_sha256={str(p):sha256(p.read_bytes()).hexdigest() for p in [Path(__file__),Path(__file__).with_name('verify_fused.py'),a.source/'scripts/paired_cube_physical.py',a.source/'scripts/paired_cube/frames.py',a.source/'notes/general-clifford-frames.tex']},input_sha256=pins,pre_reuse_finite=finite,physical=actual,exact_adjoint=adj,formal=dict(columns=columns,absolute_coefficient_bound=formal.bound,packed_digit_bits=formal.width,base_exceeds_twice_bound=True),mutations=mutations,scalar_bound=scalar,seconds=time.time()-start,maxrss=resource.getrusage(resource.RUSAGE_SELF).ru_maxrss,foreign_producer_replays=0,scope='Finite candidate audit only. General exact Clifford and shared cover contracts, analytic supplier bridge, and paid global multiplication assembly remain separate obligations.') + a.out.write_text(json.dumps(result,indent=2,sort_keys=True)+'\n');print(json.dumps({k:result[k] for k in ['status','seconds','maxrss','scalar_bound']}),flush=True) +if __name__=='__main__':main() diff --git a/research/coordinated-frames-and-entrance-banks/complex/prove.py b/research/coordinated-frames-and-entrance-banks/complex/prove.py new file mode 100644 index 0000000000..2d622bce6c --- /dev/null +++ b/research/coordinated-frames-and-entrance-banks/complex/prove.py @@ -0,0 +1,74 @@ +#!/usr/bin/env python3 +"""Portable exact physical and moment certificate for the selected fused word.""" +from fractions import Fraction as Q +from pathlib import Path +import gzip +import json +import subprocess +import sys +import tempfile + +HERE=Path(__file__).resolve().parent;PACKAGE=HERE.parent;ROOT=HERE.parents[2] +sys.path.insert(0,str(PACKAGE/'arithmetic'));sys.dont_write_bytecode=True +from interval_moment import saving_grid + + +def js(x): + if isinstance(x,Q):return str(x) + if isinstance(x,dict):return {str(k):js(v) for k,v in x.items()} + if isinstance(x,(tuple,list)):return [js(v) for v in x] + return x + + +def main(): + assert not sys.flags.optimize + candidate=PACKAGE/'selected/complex' + with tempfile.TemporaryDirectory(prefix='paired-cube-exact-') as tmp: + out=Path(tmp)/'physical.json' + run=subprocess.run([sys.executable,'-B',str(HERE/'physical.py'),'--candidate',str(candidate),'--source',str(ROOT),'--out',str(out)],text=True,capture_output=True) + if run.returncode:raise ValueError(run.stdout+run.stderr) + physical=json.loads(out.read_text()) + physical.pop('seconds',None);physical.pop('maxrss',None) + physical['source_sha256']={Path(k).resolve().relative_to(ROOT).as_posix():v for k,v in physical['source_sha256'].items()} + with tempfile.TemporaryDirectory(prefix='paired-cube-sinks-') as tmp: + checked=Path(tmp)/'selection.json';formal_path=Path(tmp)/'formal.json' + command=[sys.executable,'-B',str(HERE/'check_sinks.py'),'--candidate',str(candidate),'--output',str(checked)] + run=subprocess.run(command,text=True,capture_output=True) + if run.returncode:raise ValueError(run.stdout+run.stderr) + selection=json.loads(checked.read_text());frozen=json.loads((candidate/'sinks.json').read_text()) + for value in (selection,frozen): + value.pop('seconds',None);value.pop('rss_kib',None) + assert selection==frozen,'Frozen simultaneous terminal selection differs' + command=[sys.executable,'-B',str(HERE/'formal_sinks.py'),'--candidate',str(candidate), + '--selection',str(candidate/'sinks.json'),'--formal-helper',str(HERE/'physical.py'),'--output',str(formal_path)] + run=subprocess.run(command,text=True,capture_output=True) + if run.returncode:raise ValueError(run.stdout+run.stderr) + sink_formal=json.loads(formal_path.read_text());sink_formal.pop('seconds',None) + raw=json.loads(gzip.decompress((candidate/'profile-before.json.gz').read_bytes())) + before=physical['physical'];paid=dict(before) + n=selection['eligible_count'];assert n==46 + assert (selection['old_physical_R'],selection['old_W'],selection['old_rank'])==(before['physical_R'],before['W_per_vertex'],before['rank_per_vertex']) + paid.update(physical_R=selection['new_physical_R'],W_per_vertex=selection['new_W'], + rank_per_vertex=selection['new_rank'],child_histogram=selection['child_histogram'], + local_histogram=selection['local_histogram'],target_data_histogram=selection['target_histogram'],terminal_sinks=n) + assert all(z['dirty']==paid['physical_R'] and z['columns']==paid['W_per_vertex'] for z in sink_formal['columns']) + physical['before_terminal_sinks']=before;physical['physical']=paid + physical['original_formal']=physical['formal'];physical['formal']=sink_formal['columns'] + physical['terminal_compiler']=selection;physical['terminal_formal']=sink_formal + physical['scalar_bound'].update(physical_R=paid['physical_R'],terminal_sinks=n, + terminal_scalar_gate_delta=selection['scalar_gate_delta'],terminal_original_scalar_reserve_retained=True) + from hashlib import sha256 + for name in ('check_sinks.py','formal_sinks.py','prove.py'): + physical['source_sha256'][(HERE/name).relative_to(ROOT).as_posix()]=sha256((HERE/name).read_bytes()).hexdigest() + row={k:raw[k] for k in ('h','v','c','q','matched','total_M_operations','loss')} + row.update({k:paid[k] for k in ('m','W_per_vertex','rank_per_vertex','deficit_per_vertex','child_histogram')}) + row.update(R=paid['physical_R'],scalar_role_reserve=raw['R'],reuse_pairs=paid['pairs'],terminal_sinks=n,maxchild=max(map(int,paid['child_histogram']))) + p=dict(m=row['m'],W=row['W_per_vertex'],N=row['deficit_per_vertex'],L=0,total_rank=row['rank_per_vertex'],maxchild=row['maxchild'],child_multiplicities=row['child_histogram']) + moment=saving_grid(p,10**18) + assert moment['accepted']['saving']==Q('662323931899051/1000000000000000000') + moment['complex_saving']=moment['accepted']['saving'] + moment['scope']='Strict contraction and adjacent point exclusion for this fixed complete complex profile.' + print(json.dumps(js(dict(status='PASS',profile=row,physical=physical,moment=moment)),sort_keys=True)) + + +if __name__=='__main__':main() diff --git a/research/coordinated-frames-and-entrance-banks/complex/verify_fused.py b/research/coordinated-frames-and-entrance-banks/complex/verify_fused.py new file mode 100644 index 0000000000..47f73cf035 --- /dev/null +++ b/research/coordinated-frames-and-entrance-banks/complex/verify_fused.py @@ -0,0 +1,156 @@ +"""R13 candidate specialization: remove only PR152 selected-count pin. All finite checks retained. New candidate wrapper by Chafik Boukhalfa with OpenAI Codex; inherited credits below.""" +# Copyright 2026 icekylinx. Apache-2.0. +# Developed with GPT-6 Astra assistance; integrated with Codex assistance. +"""Independent finite checks of the signed scalar word and binary geometry. + +Copyright 2026 icekylinx, Apache-2.0; OpenAI GPT-6 Astra assistance. Binary Lagrangian +intersection ranks use L_U=U^perp in X plus U in Z, including degenerate U. +""" +from collections import Counter +from functools import lru_cache +from paired_cube.frames import basis, perp, contained + + +def verify(g, baseline, witness, word, record): + h,v=g['h'],g['v'];args=[None]+[None if a is None else [y+1 for y in a] for a in g['args']] + roots=[dict(r,node=r['node']+1) for r in g['roots']] + n=len(args);ann=witness['annihilators'];order=witness['order'];arcs=dict(witness['matching_arcs']) + active=set(order) + inputs=g['inputs']; spans=[()]*n;positive=[0]*n;negative=[0]*n + @lru_cache(None) + def frame(A): + U=perp(A,h) + assert len(U)+len(A)==h and all((a&b).bit_count()%2==0 for a in A for b in U) + return U + def each(bits): + while bits: + low=bits&-bits;bits^=low;yield low.bit_length()-1 + for x in range(1,n): + if args[x] is None: + positive[x]=1<<(x-1);spans[x]=(inputs[x-1],) + else: + a,b=args[x];assert 0>r['coordinate']&1) + assert positive[x]==expected + U=spans[x];A=perp(U,h) + assert len(U)==h-2 + assert r['coefficients']==['1/3' if q>>r['coordinate']&1 else '-1/6' for q in inputs] + else: + A=basis(inputs[t] for t in r['targets']);U=perp(A,h) + for t,c in zip(r['targets'],r['coefficients']): + assert c in ('1/2','-1/2');sign=1 if c=='1/2' else -1 + for s in each(positive[x]):Hrows[t][s]+=sign + for s in each(negative[x]):Hrows[t][s]-=sign + rootann.append(A);rootframes.append(U) + assert contained(spans[x],U) + cube=[tuple(a//2 for a in label) for label in g['labels']] + scalar_pairs=0 + for t,q in enumerate(inputs): + for s,u in enumerate(inputs): + overlap=(q&u).bit_count();same=cube[t]==cube[s] + expected=0 if same else 1-overlap + assert Hrows[t][s]==expected, ('Signed H mismatch',t,s) + distance=(q^u).bit_count()//2 + K2=(1 if distance==3 else -1 if distance==1 else 0) if same else 0 + B2=overlap-1 + assert Hrows[t][s]+K2+B2==2*(t==s) + scalar_pairs+=1 + # Actual local K matrix, inverse, and destructive-source frame itinerary. + for start in range(0,v,8): + qs=inputs[start:start+8] + K2=[[1 if (a^b).bit_count()==6 else -1 if (a^b).bit_count()==2 else 0 for b in qs] for a in qs] + assert all(sum(K2[i][k]*K2[k][j] for k in range(8))==4*(i==j) for i in range(8) for j in range(8)) + for parity in (0,1): + source=[i for i in range(8) if i.bit_count()%2==parity];target=[i for i in range(8) if i.bit_count()%2!=parity] + U=basis(qs[i] for i in source);assert len(U)==3 + assert all(contained((qs[i],),U) for i in source) + assert all(contained(U,perp((qs[j],),h)) for j in target) + assert [3-1,(h-1)-3,h-(h-1)]==[2,h-4,1] + assert all(sum(K2[i][k]*K2[j][k] for k in source)==4*(i==j) for i in target for j in target) + # Full backward intersections, including every carrier edge and root cap. + required=[[] for _ in args];position={x:i for i,x in enumerate(order)} + for x in order: + if args[x]: + for y in args[x]:required[y].extend(ann[x]);assert position[y]>31: + j=u&0x7fffffff;value=roots[j]['node'];A=rootann[j] + else: + t=u//2;value=args[t][u&1];A=ann[t];assert position[x]0 and contained(tuple(ann[first[s]]),A) + r=h-len(ann[first[s]]);H[r]-=1;H[r-d]+=1;birth[d]+=1 + for t in targets:limits[t]=A + assert [H[r] for r in range(1,h+1)]==record['remaining_internal_histogram'][1:] + assert dict(birth)=={int(k):c for k,c in record['selected_rank_histogram'].items()} + current=[full]*v;Y=Counter() + for z in reversed(word['selected']): + A=tuple(z['annihilator']) + for t in z['targets']: + assert contained(A,current[t]);Y[len(current[t])-len(A)]+=1;current[t]=A + for r,A in zip(roots,rootann): + if r['kind']=='side': + for t in r['targets']: + assert contained(A,current[t]);Y[len(current[t])-len(A)]+=1;current[t]=A + for t,q in enumerate(inputs):assert contained((q,),current[t]);Y[len(current[t])-1]+=1 + assert dict(Y)=={int(k):c for k,c in record['target_data_histogram'].items()} + assert record['selected_roles']==len(seen) and birth==Counter({int(k):v for k,v in record['selected_rank_histogram'].items()}) + return dict(signed_scalar_pairs_checked=scalar_pairs,scalar_H_exact=True,K_involution_and_inverse_exact=True, + decoder_identity_exact=True,conservative_source_supports=True,K_source_itinerary_verified=True, + full_backward_intersections=True,physical_signed_M_replayed=True, + center_phase_closed=True,full_gauge_intersections=True,selected_sources_untouched=True, + reverse_target_chains=True,positive_rank_ledger_recounted=True,selected_roles=len(seen)) diff --git a/research/coordinated-frames-and-entrance-banks/references/pr141/ORIGINAL-PROOF.md b/research/coordinated-frames-and-entrance-banks/references/pr141/ORIGINAL-PROOF.md new file mode 100644 index 0000000000..2cca3a12e1 --- /dev/null +++ b/research/coordinated-frames-and-entrance-banks/references/pr141/ORIGINAL-PROOF.md @@ -0,0 +1,101 @@ +# Balanced positional transfer of the stopped product-ring composition + +This is an additional paid layout composition. It is not an omission of the old prefix cost or a claim that a favorable child histogram by itself proves an all-size multiplication theorem. + +## Contracts that have to survive the composition + +The supplied finite word must return every dirty auxiliary coordinate, compute the exact signed complex source map, use legal common frames on both ports, and account for every transition, source/target front, exterior, center copy and endpoint correction. Its signed reflected word reverses the literal operation order, negates shears, exchanges data banks and complements every frame. The complete paid histogram and literal scalar upper bound are inputs to this arithmetic layer. Reflection and scalar-identity evidence are separately hash-bound. + +PR104's opposite-bank product-ring construction makes each proper projector residual of rank r one reversed child of width r. Its global conjugation, common generic basis, full involution factorization and paid atom adapters remain required. It supplies an ordinary interchange only after the constant-size outer wrapper. That completed wrapper has arbitrary-width, complete-spectator and restored-row guarantees. Its constant number of calls is outside the recursive moment and does not multiply the child histogram. The atom exponent remains theta=1/1000, with old ordinary saving 384599/10^10. Thus the round-seven coarse bit saving 620523/(5*10^9) gives ordinary saving 1240189553/10^13, and theta exceeds this saving, so paid atom loops are lower order. + +The complex primitive retains the completed exact tensor contract, translated endpoint gauges, inverse phase correction, and common odd-21 grid. It must preserve a completed child's incoming odd denominator. No boundary rounding, characteristic-two substitution for signed arithmetic, free address reversal, or uncharged coefficient multiplication is introduced. + +Readout n/42 may be realized by |n| consecutive same-frame shears with coefficient sign(n)/42. Each has magnitude at most one, their exact sum is n/42, and their inverse negates the pieces in reverse order. They require no new source copy or frame transition. The supplied conservative L1 scalar bill may include unused copy/scan allowance, but its local/global bound must still cover the actual selected literal word. This observation does not authorize ignoring repeated scalar occurrences or a wrong inverse sign. + +## Why the balanced layout applies + +Use the inherited PR34/RaD paid positional layout as made explicit for deferred/signed networks in PR100 and PR103. Separate the extra top bit of each long FFT axis, and use common named low-coordinate groups K_j in [K,2K). The axis-major/group-major permutation and inverse are paid by the ordinary arbitrary-coordinate router. The resulting extra prefix work is O(T p d), with saving margin 1-epsilon. Complete active, spectator, scratch, phase, control and row fields travel with their descriptors; FFT order, twiddle order and forward/inverse alignment are preserved. No local scalar operation or physical residual is moved across another operation by this outer regrouping. + +The stopped ordinary wrapper exposes precisely the ordinary interchange contract consumed by that router. The complex word exposes the same completed tensor contract required by the semantic C1=1 induction. Therefore the stopped product-ring implementation can instantiate the same balanced layout, under the inherited all-size contracts. The original geometric condition 1-epsilon(1+c)>0 remains in the constraint list; only the work margin changes from the old repeated-prefix charge to the proved paid layout's 1-epsilon. A negative control reinstates the old work margin at the new parameters and rejects them. + +## All three row stocks remain present + +Along any active nested call chain, reserve + + W_complex^D_complex * W_coarse^D_coarse * W_old^D_old. + +After a complex and coarse division, the old ordinary stock remains available to every stopped leaf or peeled atom. Sequential wrappers and copies reuse restored rows. They create no additional simultaneous factor, and also do not remove the old factor. + +For each family, d is the least positive integer with m^d > 2*r_max^d, so its depth is at most d*ceil(log2(max(2,e))) plus a fixed constant. The selected dimensions give: + +| Family | m | largest child | role bits | d | row coefficient | +|---|---:|---:|---:|---:|---:| +| Coarse bit | 529 | 528 | 27 | 367 | 9909 | +| Complex | 576 | 574 | 27 | 200 | 5400 | +| Old ordinary leaf | 575 | 529 | 28 | 9 | 252 | + +The total is 15561. A p^32000 stock leaves strict gap + + 32000 - (51/25)*15561 = 6389/25 > 0. + +The suffix slope is 128000. The validator recomputes all three minimal halving degrees, every wire-bit count, the old-stock contribution, the total coefficient, the degree gap and the suffix slope. It does not reuse the original balanced helper's two-family row formula. Semantic E, literal charge, B, C0, C1=1 and the completed-child induction are also recomputed from the supplied scalar upper bound. + +## Exact parameters and all retained inequalities + +Let b be the certified complex saving, A the proved ordinary bit saving, beta>0 the complex stopping parameter, eta>0 the balanced backoff, and zeta>0 a strict weakening. Set + + a = min(A, (1-beta)*b-zeta), + q = a*(1-2*eta), + c = q+eta/4, + epsilon = (1-eta)/(1+q), + lambda' = 1-q, + lambda = ((1-a)+lambda')/2, + g = epsilon*q, + r = (g+1-epsilon)/2, + delta = eta/8. + +The seven margins are + + 1-epsilon, a, g, a, + min(1-epsilon-delta, r-delta), + 1-epsilon-delta, epsilon. + +The minimum is g. The identities + + 1-epsilon-g = eta, + 1-epsilon-r = eta/2, + 1-epsilon*(1+c) = eta-epsilon*eta/4 > 0 + +retain the scalar, Gaussian and geometric gaps. The stopped internal exponent and complex leaf exponent remain exactly those in PR104; (1-beta)*b>a ensures the leaf ordering. All 47 strict inequalities are retained. Source normalization shows the full adapter differs from the pinned balanced implementation only in three-stock validation, explicit old-leaf argument plumbing and inclusion of the old leaf in cutoff maxima. No constraint or cost margin is deleted. + +## Selected finite arithmetic and grid ceiling + +The selected joint-expansion profile retains 2108 birth reuses, eliminates 381 nonaliased terminal roles, and has R=26216, m=576, W=114315520, rank=65843877440 and deficit=1862080. Its scalar group bound is G=3116113870848. The actual emitted physical profile, both-orientation frame/scalar audits, and literal word are separate SHA-bound construction evidence. Its entire histogram is supplied, not inferred from role reduction or an unrestricted majorization claim. Two separate rational enclosures accept the greatest 10^-24-grid complex saving + + b = 112814910866013477738/10^24 + +and reject b+10^-24. The first enclosure reduces logarithms by 4/3 with 80 atanh terms and uses degree-12 exponentials with outward 10^-45 rounding. The independent pinned PR65/100 method reduces by 2 with 32 atanh terms and uses a degree-eight exponential bound with outward 10^-40 rounding. Every first-method log/exponential interval lies inside the second, and both separate the accepted and rejected moments from one. + +Taking beta=eta=10^-24 and zeta=10^-30 gives + + kappa = 112802185097556/10^18. + +The next 10^-18 point is rejected. More strongly, let b_plus be the rejected complex point. The moment is strictly increasing in b, so the true profile root is below b_plus. Every member of this balanced family has a= 14000000000000000000000000. This is only a sufficient numeric-comparison threshold. Prime supply, fixed-basis setup, descriptor/catalogue domination, logarithm absorption and exact recovery retain their inherited eventual conditions; this value is not a practical runtime threshold. + +Original authorship remains attached: icekylinx for stopped product-ring accounting and the ordinary wrapper; PR23/29 Zhihao Chen, RaD/hipotures and James Chang/PR34 for the semantic/balanced layout; PR100/103 Rohan Arun for its deferred/signed integration; Swapnil Jain and the relevant complex producer/frame/recycling authors for the finite inputs. This three-stock adapter and independent certificate were prepared with OpenAI Codex assistance. The supplied physical word, all-size frame implementation, simultaneous basis, atom streaming, routing, prime/precision/recovery and analytic fixed-tape transfer remain separate inherited obligations. + +## Portable exact boundary + +The portable certificate generator admits only explicit integer mathematical profile fields and canonical integer child counts. It derives h, v, m, N, L, W and deficit relations before arithmetic, recursively rejects floating-point values before serialization and after readback, and binds the raw physical profile and scalar-bill bytes by SHA256. Discovery timings stay outside the mathematical certificate. The independent secondary enclosure executes only three verbatim arithmetic function bodies from the pinned source. The selected validation applies 18 adverse controls and compares every controlling quantity, moment enclosure, assembly and cutoff against the separately generated prepackage witness. The two certificates agree exactly on these mathematical fields. diff --git a/research/coordinated-frames-and-entrance-banks/references/pr141/balanced_stopped.py b/research/coordinated-frames-and-entrance-banks/references/pr141/balanced_stopped.py new file mode 100644 index 0000000000..5b02fb6948 --- /dev/null +++ b/research/coordinated-frames-and-entrance-banks/references/pr141/balanced_stopped.py @@ -0,0 +1,204 @@ +# Three-reserve stopped-product adaptation of the inherited PR34/RaD/PR23 balanced +# positional assembly retained in PR104 and proved applicable to deferred words +# in PR100/103. Original attribution below is preserved. This module verifies +# arithmetic only; scalar-word/profile provenance and all-size interfaces remain +# separate obligations. Prepared with OpenAI Codex assistance, Apache-2.0. +"""Exact, import-safe balanced copied-center semantic assembly arithmetic. + +The PR36 copied-center guard uses E=64*(W+m+G+1)^3, including G. +Its complex saving is 717/10^7. All balanced parameter formulas are unchanged. + +Adapted from Zhihao Chen PR23/29 semantic assembly (Apache-2.0), RaD's +balanced transform / arbitrary routing / bulk resampling composition, and +jamesyc PR34's check_composition.py at 7fecbe3. PR34 source is research/reversed-two-stage/check_composition.py in that +pinned upstream commit. Original parameterized transcription by the +research workers is in rectangular-dimensions/next/assembly_parameterized.py. + +This checks arithmetic, not physical corner existence, producer correctness, +or inherited all-size tape/analytic hypotheses. No imports execute producers, +parse argv, read files, change globals, or mutate the supplied finite bridge. +""" +from fractions import Fraction as Q + + +class InvalidAssembly(AssertionError): + """A named exact input validation or strict inequality failed.""" + + +def require(condition, message): + if not condition: + raise InvalidAssembly(message) + + +def rational(value): + # Fraction(float) silently preserves binary floating error; forbid it. + require(type(value) in (int, str, Q), 'expected integer or exact rational string/Fraction') + return Q(value) + + +def integer(value): + x = rational(value) + require(x.denominator == 1, 'nonintegral graph constant') + return x.numerator + + +def ceil(value): + return -(-value.numerator // value.denominator) + + +def halving_degree(m, child): + require(0 < child < m, 'child must strictly contract') + degree = 1 + while m**degree <= 2 * child**degree: + degree += 1 + return degree + + +def validate_bridge(finite_bridge, ordinary_leaf): + """Recompute rather than trust stored semantic and product-stock totals. + + scalar_group_upper remains a supplied, proof-certified local scalar upper + charge. Its producer provenance is external to this arithmetic interface. + """ + result = {} + for name in ('bit_coarse', 'complex', 'ordinary_leaf'): + data = ordinary_leaf if name == 'ordinary_leaf' else finite_bridge[name] + m, W, child = (integer(data[k]) for k in ('m', 'W', 'maxchild')) + require(m > 1 and W > 0, 'positive arity and role volume required') + degree, bits = halving_degree(m, child), W.bit_length() + require(integer(data['halving_degree']) == degree, name + ' stale halving degree') + require(integer(data['wire_bits']) == bits, name + ' stale role logarithm') + result[name] = dict(m=m, W=W, maxchild=child, + halving_degree=degree, wire_bits=bits) + phase = finite_bridge['complex'] + s, scalar = (integer(phase[k]) for k in ('s', 'scalar_group_upper')) + m, W, child = (result['complex'][k] for k in ('m', 'W', 'maxchild')) + require(0 < s < m*W and scalar > 0, 'invalid complex rank/scalar bound') + E = 64*(W+m+scalar+1)**3 + B = s+E + literal = 2*scalar*W**2+8*s+4*W+4+32*m + C0 = 32*m*B**2 + semantic = dict(E=E, B=B, C0=C0, C1=1, literal_charge=literal, + strict_literal_gap=E-literal, + induction_gap=2*B*(m-child)-(s+E)) + require(E > literal and semantic['induction_gap'] >= 0 and C0 > 2*B+18, + 'semantic completed-child bound failed') + for key, value in semantic.items(): + require(rational(finite_bridge['semantic'][key]) == value, + 'stale semantic constant: '+key) + result['complex'].update(s=s, scalar_group_upper=scalar) + result['semantic'] = semantic + rows = finite_bridge['rows'] + leaf_degree = result['ordinary_leaf']['halving_degree']*result['ordinary_leaf']['wire_bits'] + require(integer(finite_bridge['ordinary_leaf_row_degree']) == leaf_degree, + 'ordinary leaf stock missing or stale') + coefficient = sum(result[name]['halving_degree']*result[name]['wire_bits'] + for name in ('bit_coarse', 'complex', 'ordinary_leaf')) + degree = integer(rows['degree']) + gap = degree-Q(51,25)*coefficient + require(degree > 0 and gap > 0, 'insufficient product row degree') + expected = dict(coefficient=coefficient, degree=degree, + degree_gap=gap, suffix_slope=4*degree) + for key, value in expected.items(): + require(rational(rows[key]) == value, 'stale product row constant: '+key) + result['rows'] = expected + return result + + +def assembly(finite_bridge, ordinary_leaf, a_bit, kappa, beta=Q(1,20), h=Q(1,10**12), + a_complex=Q(717,10**7), *, original_prefix=False, + old_guard=False, old_exposures=False): + """Return 47 strict slacks and seven margins, or raise InvalidAssembly. + + The three keyword switches are negative controls: they impose the old + prefix, nonlinear guard, or old separate movement charges at these SAME + balanced parameters. They do not silently optimize an alternative family. + """ + f = validate_bridge(finite_bridge, ordinary_leaf) + a, b, kappa, beta, h = map(rational, (a_bit,a_complex,kappa,beta,h)) + require(0 < h < Q(1,2) and kappa > 0, 'positive backoff and saving required') + tau, sigma = 1-a, 1-b + q = a*(1-2*h) + require(1+q != 0, 'undefined balanced epsilon') + lp, c, eps = 1-q, q+h/4, (1-h)/(1+q) + lam = (tau+lp)/2 + G = eps*q + r, delta = (G+1-eps)/2, h/8 + C1 = Q(19991,10000) if old_guard else Q(1) + margins = dict(g1=1-eps, g2=a, g3=G, g4=a, + g5=min(1-eps-delta,r-delta), g6=1-eps-delta, g7=eps) + if original_prefix: + margins['g1'] = 1-eps*(1+c) + if old_exposures: + margins.update(g2=eps*c*a, g4=a*(1-eps)) + internal = tau+(1-beta)*max(sigma-tau,Q(0)) + leaf = sigma+beta*(1-sigma) + slacks = dict(a_positive=a, a_below_b=b-a, b_below_one_over32=Q(1,32)-b, + beta_positive=beta, beta_below_one=1-beta, phase_leaf_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*C1, + 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-G, artificial_boundary=8-eps+r-delta-G, + literal_scalar_guard=Q(f['semantic']['strict_literal_gap']), + row_product_gap=f['rows']['degree_gap']) + slacks.update({name+'_above_kappa': value-kappa for name,value in margins.items()}) + require(len(slacks) == 47 and len(margins) == 7, 'constraint list incomplete') + failed = {name:str(value) for name,value in slacks.items() if value <= 0} + require(not failed, str(failed)) + require(min(margins.values()) == G, 'unexpected controlling margin') + require(1-eps-G == h and 1-eps-r == h/2, 'balanced identities failed') + require(1-eps*(1+c) == h-eps*h/4, 'geometric identity failed') + parameters = dict(a_bit=a, a_complex=b, tau=tau, sigma=sigma, beta=beta,h=h, + q=q,c=c,epsilon=eps,lambda_=lam,lambda_prime=lp,alpha_squared_power=r, + delta=delta,C0=f['semantic']['C0'],C1=C1,kappa=kappa) + return dict(parameters=parameters,constraints=slacks,margins=margins, + minimum_margin=G,absorption_gap=G-kappa,scoped_limit=a/(1+a), + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c),finite_bridge=f) + + +def cutoffs(finite_bridge, ordinary_leaf, result): + """PR34 sufficient numeric comparisons, retaining its all-interval padding. + + These are eventual arithmetic thresholds, not practical running times or + substitutes for additional native setup / prime / recovery thresholds. + """ + f = validate_bridge(finite_bridge, ordinary_leaf) + p = result['parameters'] + e,c,r,beta = (p[k] for k in ('epsilon','c','alpha_squared_power','beta')) + ka,km,kb,ks = (ceil(1/x) for x in (r,e*c,1-e,e*beta)) + C0 = f['semantic']['C0'] + largest = max(f[name]['m'] for name in ('bit_coarse','complex','ordinary_leaf')) + cuts = dict(guard=ceil(Q((2*C0).bit_length())/(1-e)), + normalization=ceil(7/(1-e-r)), alpha=16*ka*ka+1, compact=64*km*km+1, + geometry=ceil(3/(1-e*(1+c))),phase_cell=ceil(9/(e-(1-r)/2)), + period=128*kb*kb+1,stopped_leaf=ks*(4*largest).bit_length(),log_p=25,reservoir=14) + common = max(cuts.values()) + require(common >= max(2*ka,2*km,2*kb,25), 'cutoff does not cover monotone regime') + checkpoints=[] + for j in range(6): + z=common*2**j + powers=dict(alpha=(z//ka,8*(z+ka)+64),compact=(z//km,32*(z+km)+192), + period=(z//kb,16*(z+kb)+56), + rows=(z//kb,f['rows']['suffix_slope']*(z+kb+8)), + leaf=(z//ks,4*largest)) + require(all(lhs >= rhs.bit_length() for lhs,rhs in powers.values()), + 'compressed-power threshold failed') + checkpoints.append(dict(log2_input=z,powers={name:dict(exponent=lhs,rhs=rhs, + rhs_bits=rhs.bit_length()) for name,(lhs,rhs) in powers.items()})) + return dict(cutoff_log2_input=cuts,common_cutoff=common,power_checkpoints=checkpoints, + all_interval_argument='For [Z,Z+k), bound RHS at Z+k and LHS at floor(Z/k). ' + 'Successive intervals double LHS; the positive affine RHS grows at most ' + 'linearly, so 2^j >= j+1 proves persistence.', + additional_eventual_conditions=['BHP prime threshold and distinct-prime packing', + 'Fixed rational basis, eligible common prime and native table setup', + 'Catalogue/descriptor domination, logarithm absorption, exact recovery'], + practical_runtime_claim=False) diff --git a/research/coordinated-frames-and-entrance-banks/references/pr166/PROOF.md b/research/coordinated-frames-and-entrance-banks/references/pr166/PROOF.md new file mode 100644 index 0000000000..4b4341c091 --- /dev/null +++ b/research/coordinated-frames-and-entrance-banks/references/pr166/PROOF.md @@ -0,0 +1,221 @@ +# Dirty-target accumulation removes terminal producer rows + +Status: author-checked finite compiler lemma and 67-row substitution on the +current PR163 complex word. This is not a new assembled multiplication bound. +Independent review and any advertised supplier/assembly update remain separate. + +Scientific inputs are the selected complex files introduced at +15c702a929b7d640107a95e196186ad74e876c82. They are unchanged at publication +base e1813796ef5c3ca38c5dd7b9e8d81b3908ff5997; that later commit changes only +attribution NOTICE and its SOURCE digest. The checker verifies the existing +result.json SHA256 pins for every finite input it consumes. + +## Relation to earlier constructions + +Dumas and Grenet's *In-place accumulation of fast multiplication formulae* +(https://arxiv.org/pdf/2307.12712) motivates using arbitrary-valued output +storage. Its RAM results do not establish this frame-constrained compiler. +No novelty claim is made for the scalar pre/post cancellation identity. + +PR161's P±Q merge and PR163's singleton-channel fusion create internal producer +sums. This substitution instead removes independent auxiliary coordinates by +using existing independently valued data targets. The paired-cube identity, +Clifford representatives, physical reuse, copied-center interfaces and all-size +compiler assumptions retain their upstream attribution and proof obligations. + +## Local lemma with chronological hypotheses + +Let z_s be an independently dirty, zero-entrance-gauge producer role. Assume: + +1. It is neither a source-injection role nor an aliased recipient/donor. +2. Its only producer incidences are additive destination writes + z_s <- z_s + b_j a_j, with b_j in {1,-1}. It never controls another + producer role. It has exactly one root read, uniformly z_s/2 into a + target group T. +3. Its literal write-frame chain is 0 <= U_1 <= ... <= U_k <= U, + where U is the common root read frame. Every write uses the identical + exact T_(U_j) on its control and destination. +4. All these writes occur after the copied-center phase. Before the first + deferred target corrections, the targets in T are at frame0. +5. Some pivot c in T receives no target correction between that common-zero + point and the last write/post-read. Other targets may receive corrections + during this interval, provided those corrections do not depend on target + contents and their existing frames are contained in U. +6. Later target reads continue their old nested chains from U. No other + target-controlled producer operation is introduced. + +All targets and retained dirty roles have arbitrary independent initial values. +No target is assumed clean, and the deleted dirty variable is not set to zero: +the new construction has one fewer independent auxiliary input coordinate. + +Keep the ORIGINAL initial and deferred old-response coefficient columns for +EVERY retained role. Omit only the deleted role's column. In particular, do +not recompute the old correction from a decoder which simply drops its root; +that would omit the root response of its retained ancestors. The inherited +expanded scalar old-response implementation and its conservative charge remain +available. The sink's own old-response column is exactly the uniform1/2 +column on T because it never controls another producer row. + +At the common-zero point, after the copied-center contribution and before +its deferred corrections, perform + + y_t -= y_c for t in T minus {c}. + +At the original time of each write, raise the pivot along the deleted role's +actual chain and replace that write by + + y_c += (b_j/2) a_j. + +Immediately after the last such write, raise the pivot and the other targets +to the original U and perform + + y_t += y_c for t in T minus {c}. + +Delete the old positive root read, all writes and inverse-cleanup writes on +z_s, its initial old-response column, its physical stream and its full-frame +ending. Every retained producer operation, original source operation, source +return, copied-center step and old-response column stays in its original order. + +Write f=sum_j b_j a_j for the ACTUAL current controls, including all their +retained dirty dependence. The sandwich adds f/2 to all targets and preserves +every old target value. Any intervening correction e_t on a non-pivot is +unchanged: + + (y_t-y_c+e_t) + (y_c+f/2) = y_t+e_t+f/2. + +An intervening correction to the pivot would be broadcast to every target; +this is why the pivot chronology condition is essential. The test does not +incorrectly require every non-pivot correction to wait. + +The retained producer is the same invertible word with destination-only sink +writes omitted. It contains no reference to the deleted coordinate, so its +literal inverse restores every retained dirty input. Its response from each +retained source/dirty column is unchanged at the targets, and the retained +old-response columns cancel those dirty parts as before. Earlier target data, +center contributions and later target contributions are all preserved. + +## Exact frames, inverse and simultaneous use + +The pre-shears use T_0 on both targets. Each accumulating write uses the +original exact T_(U_j) on pivot and control. Every post-shear uses one +identical T_U on its two operands. Rank-zero reconciliation is actual inherited +scalar/movement work, not equality up to phase. + +Reverse the COMPLETE literal new word and invert every shear. Use +D_U=T_U F^(-1) in the reverse/complement orientation. Then + + D_U D_V^(-1) = T_U T_V^(-1) + +exactly. All reversed gate incidences are still identical, all transition +ranks are preserved, and sources/retained dirty values are restored. This is +the chronological inverse, not the invalid source/target-swapped transpose. +The data-bank and rank-zero endpoint conventions remain the inherited ones. + +For sinks with disjoint target groups, perform each pre-sandwich at the same +common-zero cut and each post-sandwich at its own last-write time. There is +no target collision or producer feedback, so all substitutions coexist. + +## Paid ledger + +Let r=dim(U) and let P be the complete positive-width prefix of the deleted +role from0 through every write to U. Its old local row bill is P+[h-r]. +The pivot's old first target child [r] is replaced by P. Other target paths +and all retained row paths are unchanged. Hence the EXACT local child change is + + -[r] -[h-r], + +with one independent row removed. This accounts for every prefix, endpoint and +full-frame cleanup; fragmentation inside P cancels rather than disappearing +without payment. The same delta holds for the complete inverse orientation. + +In the existing three completed orthogonal cores, for each zero-gauge sink: + + delta W = -1; + delta children = -3*[r] -3*[h-r]; + delta rank = -3h; + delta deficit = 0. + +There is no exterior tail for a zero-gauge physical row. The full group factor +and retained routing/row reserves are not reduced by fiat. For moment exponent +p in (0,1), the unnormalized slack improvement is + + 3 r^p + 3(h-r)^p - (3h)^p > 0, + +because the six positive pieces sum to3h. This is a strict finite-profile +improvement, not a newly certified assembled kappa. + +For k writes and n targets, the old affected scalar gates are k forward +writes, k inverse writes, n initial dirty reads and n positive root reads. +The new ones are k accumulating writes and2(n-1) target shears. Thus the +scalar-gate count decreases by k+2. All new coefficients already belong to +the Gaussian-dyadic alphabet; no odd divisor is introduced. Keep the original +conservative virtual R, M, expanded-correction scalar charge, full finite +stock and precision/routing reserves rather than shrinking them without proof. + +## Exact current finite instance + +The checker examines ONLY the165 all-eight disjoint roots of the selected +PR163 word. It finds67 eligible roots on disjoint target cubes. The other98 +have retained producer consumers; two of those also touch the center phase. +It does not search arbitrary face, singleton or cross-cube combinations. + +For example, root0 uses unaliased role12354. Its only incidences are additive +writes21902 and24308, at ranks15 and18. Target0 can be the pivot. Targets6 +and7 receive early compensation, but their independent additive corrections +are valid while encoded. The pivot's first compensation occurs after the +post-read. This concrete distinction is verified in the actual target-event +replay rather than inferred from a scalar channel formula. + +The selected simultaneous change is: + + physical R: 13041 -> 12974 + W per vertex: 15681 -> 15614 + rank per vertex: 1033626 -> 1029204 + deficit: 1320 -> 1320 + child multiplicity18: -201 + child multiplicity4: -201 + scalar gates: -300 + +selected.json contains every selected role, its original writes, pivot and +chronological boundary, as well as the complete new local/target/shared +histograms and source pins. Its decimal runtime is a diagnostic, not a +mathematical certificate input. + +## What the author check actually establishes + +check_sink_accumulator.py performs these exact checks from existing frozen +inputs, without importing an upstream executable or rebuilding a producer: + +- original source pins and full positive physical histogram equality; +- all role classifications, aliases, source injections, literal consumers, + write-frame chains and original root destinations; +- an available late-corrected pivot for every selected group; +- every new target event interleaved with all original deadline reads and + retained root reads, including all endpoint changes; +- exact adjoint pullbacks through the actual aliased producer for every + selected sink, covering all1320 original source columns and all13041 + original dirty columns, including zero columns; +- each fresh disjoint channel has exactly its448 required source terms; +- arbitrary target and intervening non-pivot corrections, both signs, and + actual reversal of each scalar sandwich; +- retained source/dirty identity by destination-only deletion and literal + inverse cancellation; no Monte Carlo or injective-digit assumption; +- disjoint simultaneous support and complete child/row deltas. + +Together with the unchanged inherited complete word, this covers its15681 +original source/target/dirty coordinates and the15614-coordinate new word. +The original saved full proof contracts remain dependencies. The package does +not update the bit supplier, balance parameters, all47 assembly inequalities, +precision constants or advertised multiplication exponent. + +## Reproduce + +From the repository root: + + python research/paired-cube-target-accumulator/check_sink_accumulator.py \ + --candidate research/paired-cube-balanced-161/selected/complex \ + --output /tmp/target-accumulator-check.json + +The standard-library checker has60-second CPU/wall and768MiB address-space +caps. The author run completed in approximately5.5seconds and85MiB. Compare +mathematical fields, not runtime/RSS, with selected.json. diff --git a/research/coordinated-frames-and-entrance-banks/references/pr166/README.md b/research/coordinated-frames-and-entrance-banks/references/pr166/README.md new file mode 100644 index 0000000000..0adb5c653a --- /dev/null +++ b/research/coordinated-frames-and-entrance-banks/references/pr166/README.md @@ -0,0 +1,15 @@ +# Target-accumulating terminal compiler + +This author-checked research packet replaces67 actual PR163 producer sinks +with existing independently valued target accumulators. The complete finite +profile removes67 rows and201 children of each width18 and4; deficit1320 is +preserved. It makes no new assembled multiplication-bound claim. + +Read PROOF.md for the exact chronological lemma, retained dirty corrections, +full inverse, scalar/endpoint bill and inherited obligations. selected.json is +the concrete current-word specification. Run check_sink_accumulator.py against +the existing paired-cube-balanced-161/selected/complex data to reproduce it. + +The motivating scalar idea is output accumulation; no novelty claim is made. +Existing scalar-producer, frame, physical-reuse and all-size interfaces retain +the attribution in the source package's current NOTICE. diff --git a/research/coordinated-frames-and-entrance-banks/references/pr168/bit-physical-profile.json b/research/coordinated-frames-and-entrance-banks/references/pr168/bit-physical-profile.json new file mode 100644 index 0000000000..8014fc2a23 --- /dev/null +++ b/research/coordinated-frames-and-entrance-banks/references/pr168/bit-physical-profile.json @@ -0,0 +1,99 @@ +{ + "R": 19788, + "W_per_vertex": 21548, + "changed_operation_frames": 2884, + "checks": { + "donor_frames_inside_gauges": true, + "gauge_read_window": true, + "operation_frames_nondegenerate_and_spanning": true, + "pair_chronology": true, + "partner_chronology": true, + "phase_one_closure": true, + "register_contents": true, + "role_chains_nested": true, + "target_chains_nested_in_read_order": true, + "telescoping_deficit": true + }, + "child_histogram": { + "1": 125448, + "2": 62908, + "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": 13272, + "60": 2200 + }, + "deficit_per_vertex": 1936, + "f2_replay": { + "lanes": 64, + "registers": 18028, + "rejected_controls": [ + "alias_onto_live_register", + "omitted_recipient_read", + "read_before_donor_death" + ], + "seeds_restored_and_y_plus_x": true + }, + "h": 24, + "late_pairs": 1760, + "local_histogram": { + "1": 35656, + "2": 18916, + "3": 9872, + "4": 2990, + "5": 2600, + "6": 1220, + "7": 1104, + "8": 934, + "9": 604, + "10": 836, + "11": 386, + "12": 1440, + "13": 530, + "14": 1078, + "15": 410, + "16": 1072, + "17": 388, + "18": 444, + "19": 306, + "21": 2840, + "22": 3544 + }, + "loss": 528, + "m": 72, + "operations": 41288, + "pairs": 1760, + "physical_R": 18028, + "physical_gauge_histogram": { + "20": 2200 + }, + "rank_per_vertex": 1549520, + "source_data_histogram": { + "1": 1760, + "2": 880, + "20": 880, + "22": 880 + }, + "target_data_histogram": { + "1": 4400, + "20": 880, + "21": 880 + }, + "v": 1760 +} diff --git a/research/coordinated-frames-and-entrance-banks/references/pr175/SOURCE.json b/research/coordinated-frames-and-entrance-banks/references/pr175/SOURCE.json new file mode 100644 index 0000000000..a1f3beeaca --- /dev/null +++ b/research/coordinated-frames-and-entrance-banks/references/pr175/SOURCE.json @@ -0,0 +1,11 @@ +{ + "commit": "f1081fabbfadaaaaf7292a40d428dbbb865ce920", + "files": { + "certificates/joint-dual-kappa.json": "4044f15abf49b1551193891836e2d20975b8246acc888180af47266c64f77af0", + "certificates/joint-dual-validation.json": 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mode 100644 index 0000000000..ba227e2d8f Binary files /dev/null and b/research/coordinated-frames-and-entrance-banks/selected/complex/physical-pairs.json.gz differ diff --git a/research/coordinated-frames-and-entrance-banks/selected/complex/profile-before.json.gz b/research/coordinated-frames-and-entrance-banks/selected/complex/profile-before.json.gz new file mode 100644 index 0000000000..8470955659 Binary files /dev/null and b/research/coordinated-frames-and-entrance-banks/selected/complex/profile-before.json.gz differ diff --git a/research/coordinated-frames-and-entrance-banks/selected/complex/profile.json.gz b/research/coordinated-frames-and-entrance-banks/selected/complex/profile.json.gz new file mode 100644 index 0000000000..e9b52420b7 Binary files /dev/null and b/research/coordinated-frames-and-entrance-banks/selected/complex/profile.json.gz differ diff --git a/research/coordinated-frames-and-entrance-banks/selected/complex/result.json 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"prefix_children": [ + 15, + 3 + ], + "pre_at_phase_cut_after_center_before_old_reads": true, + "post_after_op": 24640, + "last_write_chronology": 24816, + "first_pivot_old_read": 27794, + "first_any_old_read": 27652 + } + ], + "dirty_coefficient_nonzero_range": [ + 701, + 721 + ], + "seconds": 7.173779400000058, + "rss_kib": 0 +} diff --git a/research/coordinated-frames-and-entrance-banks/selected/complex/word.json.gz b/research/coordinated-frames-and-entrance-banks/selected/complex/word.json.gz new file mode 100644 index 0000000000..835b0e3312 Binary files /dev/null and b/research/coordinated-frames-and-entrance-banks/selected/complex/word.json.gz differ diff --git a/research/coordinated-frames-and-entrance-banks/verify.py b/research/coordinated-frames-and-entrance-banks/verify.py new file mode 100644 index 0000000000..dfee0d7a81 --- /dev/null +++ b/research/coordinated-frames-and-entrance-banks/verify.py @@ -0,0 +1,43 @@ +#!/usr/bin/env python3 +"""Reproduce the complete conditional witness offline from immutable source parts.""" +from pathlib import Path +from hashlib import sha256 +import argparse,io,json,shutil,subprocess,sys,tempfile,zipfile +HERE=Path(__file__).resolve().parent +sys.dont_write_bytecode=True +if hasattr(sys,'set_int_max_str_digits'):sys.set_int_max_str_digits(0) +def digest(p):return sha256(p.read_bytes()).hexdigest() +def pins(): + manifest=json.loads((HERE/'FILES.json').read_text()) + inventory={p.relative_to(HERE).as_posix() for p in HERE.rglob('*') if p.is_file() and p.name!='FILES.json'} + assert inventory==set(manifest['files']),'Unpinned or missing upload file' + actual={n:digest(HERE/n) for n in manifest['files']} + assert actual==manifest['files'],'Upload source bytes changed' + return actual +def main(): + parser=argparse.ArgumentParser(description=__doc__);parser.add_argument('--write',action='store_true',help='Authoring only: generate the derived certificate');args=parser.parse_args() + assert not sys.flags.optimize,'Assertions must remain enabled' + before=None if args.write else pins() + baseline=json.loads((HERE/'BASELINE.json').read_text());chunks=[] + for p in baseline['parts']: + block=(HERE/p['file']).read_bytes();assert len(block)==p['bytes'] and sha256(block).hexdigest()==p['sha256'];chunks.append(block) + blob=b''.join(chunks);assert sha256(blob).hexdigest()==baseline['archive_sha256'] + with tempfile.TemporaryDirectory(prefix='coordinated-frames-offline-') as tmp: + root=Path(tmp)/'source';root.mkdir() + with zipfile.ZipFile(io.BytesIO(blob)) as z: + for entry in z.infolist(): + target=(root/entry.filename).resolve();assert target.is_relative_to(root.resolve()),'Unsafe archive path' + z.extractall(root) + package=root/'research'/'coordinated-frames-and-entrance-banks';package.mkdir(parents=True) + for p in HERE.rglob('*'): + if p.is_file() and p.name!='baseline-pr179.zip' and p.name not in {entry['file'] for entry in baseline['parts']} and not p.name.startswith('baseline-pr179.part'): + rel=p.relative_to(HERE);dest=package/rel;dest.parent.mkdir(parents=True,exist_ok=True);shutil.copyfile(p,dest) + command=[sys.executable,'-B',str(package/'verify_inner.py')] + if args.write:command.append('--write') + result=subprocess.run(command,text=True,capture_output=True) + print(result.stderr,file=sys.stderr,end='');print(result.stdout,end='') + if result.returncode:raise RuntimeError('Complete offline verification failed') + if args.write:shutil.copyfile(package/'certificate.json',HERE/'certificate.json') + if not args.write:assert pins()==before,'Upload source changed during verification' + print('PASS offline immutable archive, source closure and complete derived certificate') +if __name__=='__main__':main() diff --git a/research/coordinated-frames-and-entrance-banks/verify_inner.py b/research/coordinated-frames-and-entrance-banks/verify_inner.py new file mode 100644 index 0000000000..f7f35bbaa3 --- /dev/null +++ b/research/coordinated-frames-and-entrance-banks/verify_inner.py @@ -0,0 +1,63 @@ +#!/usr/bin/env python3 +"""Read-only aggregate verification of the selected joint finite witness.""" +from hashlib import sha256 +from pathlib import Path +import argparse +import json +import subprocess +import sys + +HERE=Path(__file__).resolve().parent;ROOT=HERE.parents[1] +sys.dont_write_bytecode=True +if hasattr(sys,'set_int_max_str_digits'):sys.set_int_max_str_digits(0) + + +def digest(path):return sha256(path.read_bytes()).hexdigest() + + +def pins(): + manifest=json.loads((HERE/'SOURCE.json').read_text()) + assert manifest['files'],'Empty source closure' + values={name:digest(ROOT/name) for name in manifest['files']} + assert values==manifest['files'],'Pinned construction or dependency bytes changed' + return values + + +def run(relative): + result=subprocess.run([sys.executable,'-B',str(HERE/relative)],text=True,capture_output=True) + if result.returncode:raise ValueError(relative+' failed:\n'+result.stdout+result.stderr) + return json.loads(result.stdout) + + +def build(): + print('Checking new signed complex word, all formal columns, frames and exact moment.',file=sys.stderr,flush=True) + complex_result=run('complex/prove.py') + print('Checking frozen PR168-v4 bit frames and aliases, full F2 identity and paid moment envelope.',file=sys.stderr,flush=True) + bit_result=run('bit/prove.py') + sys.path.insert(0,str(HERE/'arithmetic')) + from certificate import certificate + arithmetic=certificate(complex_result['profile'],complex_result['physical']) + assert bit_result['coarse']['coarse_saving']==arithmetic['coarse_bit_saving'] + assert bit_result['coarse']['atom_beta']==arithmetic['atom_exponent'] + assert bit_result['coarse']['ordinary_saving']==arithmetic['actual_uniform_bit_saving'] + assert complex_result['moment']['complex_saving']==arithmetic['complex_saving'] + return dict(status='PASS conditional finite witness',kappa=arithmetic['kappa'], + complex=complex_result,bit=bit_result,arithmetic=arithmetic, + scope='Finite word, paid moments, full finite bridge and 47 strict arithmetic constraints; source-specified all-size contracts remain assumptions.') + + +def main(): + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('--write',action='store_true',help='Authoring only: write the canonical derived certificate before freezing SOURCE.json') + args=parser.parse_args() + assert not sys.flags.optimize,'Assertions must remain enabled' + before=None if args.write else pins() + result=build();target=HERE/'certificate.json' + if args.write:target.write_text(json.dumps(result,indent=2,sort_keys=True)+'\n') + else: + assert result==json.loads(target.read_text()),'Canonical certificate does not reproduce' + assert pins()==before,'Source closure changed during verification' + print('PASS coordinated-frames-and-entrance-banks kappa='+result['kappa']+'; complete complex and bit words, 47 constraints, seven margins, and '+str(result['arithmetic']['adverse_control_count'])+' assembly controls.') + + +if __name__=='__main__':main() diff --git a/research/frontier-refinement186/LICENSE b/research/frontier-refinement186/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/research/frontier-refinement186/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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We also recommend that a + file or class name and description of purpose be included on the + same "printed page" as the copyright notice for easier + identification within third-party archives. + + Copyright [yyyy] [name of copyright owner] + + Licensed under the Apache License, Version 2.0 (the "License"); + you may not use this file except in compliance with the License. + You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + + Unless required by applicable law or agreed to in writing, software + distributed under the License is distributed on an "AS IS" BASIS, + WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + See the License for the specific language governing permissions and + limitations under the License. diff --git a/research/frontier-refinement186/NOTICE b/research/frontier-refinement186/NOTICE new file mode 100644 index 0000000000..7f0d85c4c6 --- /dev/null +++ b/research/frontier-refinement186/NOTICE @@ -0,0 +1,27 @@ +Independent fixed PR186 finite audit and precision refinement +Copyright 2026 M6LI. Apache-2.0; see LICENSE. +Prepared with substantial OpenAI Codex assistance. Separate AI agents reviewed +the finite arithmetic, frame accounting, scalar maps and bank fixtures; this +does not imply human peer review or a new formal/all-size proof. + +The coordinated shared-edge rematch, arbitrary subspace cuts and completed +entrance banks are Dugongue's PR186 contribution, developed with OpenAI model +assistance. All51 original files, legal notices, proof disclosures and immutable +PR181 archive parts are retained byte-identical in their original directory. + +The shared-edge local 29-add construction is Chafik Boukhalfa's PR181 work with +substantial Anthropic Claude and OpenAI Codex assistance, on eumemic's PR168 +construction with Anthropic Claude assistance. Retained lineage includes +icekylinx's PR144 paired-cube/compiler ledger (OpenAI GPT-6 Astra/Codex), +eumemic PR117, James Chang/jamesyc PR166 terminal sinks, Zhihao Chen/Swapnil +Jain PR97 and PR23, RaD/hipotures and the balanced assembly, huxint's interval +refinement, and the PR175 verification overlay. Native notices remain intact. +The prior retained PR178 refinement is Rohan Arun's work with OpenAI Codex +assistance; prior 181 independent audit packages preserve that lineage. + +The generic independent moments/assembly/bit/signed-sink Python modules are +reused unchanged from the existing Apache-2.0 audit packages, with retained +headers and exact hashes in SOURCE. Independent bank mathematics is the +reviewed R51 implementation, with only checkout-relative source wiring and +source-binding changes. The new adapters, exact input bindings, documentation +and controls are M6LI/OpenAI Codex work under Apache-2.0. diff --git a/research/frontier-refinement186/PROOF.md b/research/frontier-refinement186/PROOF.md new file mode 100644 index 0000000000..7a7f4082d2 --- /dev/null +++ b/research/frontier-refinement186/PROOF.md @@ -0,0 +1,56 @@ +# Fixed-input precision statement and retained interfaces + +Write b=331161965949525999057/500000000000000000000000 for the independently +enclosed complex saving, c=133096233391197420469/200000000000000000000000 +for the enclosed coarse bit saving, and +θ=13301283151705819139/20000000000000000000000 for the first admissible atom +on the 10^-24 grid. The unchanged old ordinary saving is 384599/10^10. + +The ordinary bit saving is exactly + + A_B=(1-θ)c+θ(384599/10^10) + =2660256630341163827797245514988686549443809/4000000000000000000000000000000000000000000000. + +Take η=β=ζ=10^-24 and a=min(A_B,(1-β)b-ζ), q=a(1-2η). +Here the complex side binds. The headline κ is the greatest 10^-24 grid point +strictly below (1-η)q/(1+q). Independent generic assembly reconstructs all 47 +strict inequalities and seven margins with the complete retained finite bridge. +κ=330942774629799608347/500000000000000000000000. Its successor fails the +compact phase layer. Each supplier successor has a full moment lower bound +at least 1; the previous atom fails its strict adapter/borrowed-row toll. + +The selected component data are reconstructed from the exact PR186 graph, +operation frames, alias deadlines and 46-sink target chronology in separate +finite geometry checks. Our physical input records the resulting literal 6325 +zero-rank events and native 6270 separately. The moment and bridge reconstruct +only positive paid bins and preserve c=21249, q=3157, M=32971 and logical R=13042. +The physical stock is 13326, dirty population 10686, mass 878196 and deficit 1320. +No reduction in physical/moment stock removes the full scalar or group charge. + +Completed-bank normalized stock 59144/3, mass 1417520 and deficit 1936 are bound +to the full retained bit inventory minus exactly 2200 rank 60 entrance exteriors. +Scale 3 multiplies all inventory and contaminated fallback terms together. +Actual allocation uses 9 physical replicas, 1100 selected and 47484 undeferred +banks per stage and full stock 177432. The separate pure checker verifies all +144 address columns and inverses over Z/F2 for 18 disjoint 4-coordinate and 3 +disjoint 24-coordinate projectors. It tests common unimodular chart conjugation +and rejects missing/repeated blocks and inconsistent charts. For idempotent +disjoint P,Q, expansion gives S_P S_Q=S_(P+Q), where +S_P(x,y)=(x-Px+Py,y-Py+Px); exhaustive projectors yield the full swap. +This proves the abstract finite common-chart endpoint. It does not produce +the common chart, a faithful tensor/Clifford lift or paid multibank routing. + +The unchanged signed scalar core checks the actual selected local 29-add word, +330 destination reflections, new rematching/compensation reads, both maps and +inverses, all 13326 source/target/dirty columns and every 10686 dirty variable. +Raw inputs and original signed scalar core (SHA256 prefix 6345a9b3) are source-bound; the prior PR181 PASS is not +used as a fresh PR186 scalar proof. Native aggregate is run separately in CI. + +All statements remain conditional on original uniform weighted compilation, +tensor/Clifford/common-chart realizations and phases, orbit/stage allocation +applicability, routing/restored borrowed rows, paid layout, prime supply, +precision/recovery, uniform setup and all-size analytic/fixed-tape interfaces. +No unbounded bootstrap, new general phase theorem, global optimum or current +repository frontier is asserted. The original 51-file proof and source/archive +closures remain unchanged. This package is an additive finite audit with a +small fixed-grid refinement, prepared/reviewed by AI agents. diff --git a/research/frontier-refinement186/README.md b/research/frontier-refinement186/README.md new file mode 100644 index 0000000000..87e4da895e --- /dev/null +++ b/research/frontier-refinement186/README.md @@ -0,0 +1,63 @@ +# Independent fixed PR186 finite audit and precision refinement + +The pinned construction is Dugongue's PR186 at +`166a34d75e853e933855f0f7e940fe77c4bb6b8d` (tree +`d4c4c9741dd8b51e38afc9e5d53ba594459bc369`). This additive package gives +conditional κ = 330942774629799608347/500000000000000000000000, +a gain of 608347/500000000000000000000000 over that revision's stated +330942774629799/500000000000000000. The complex supplier binds. +This revision-specific audit claims neither the current repository frontier +nor a global maximum. Later submitted constructions may be stronger. + +All 51 original coordinated-frames-and-entrance-banks files, archive parts, +source manifests and notices are retained byte-for-byte. The underlying +1700 native PR181 files and prior independent audit packages remain unchanged. +The existing owned CI workflow is extended. An additive research/.gitattributes +support file preserves the uploaded bundle's literal bytes, including CRLF. +The native root attributes remain unchanged. The exact source closure is +in SOURCE.json; three new input profiles are explicitly derived JSON. + +Python 3.11+ and the standard library suffice. From the repository root: + +```sh +python -B research/coordinated-frames-and-entrance-banks/verify.py +python -B research/frontier-refinement186/verify.py +python -B research/frontier-refinement186/check_banks.py +python -B research/frontier-refinement186/test_refinement.py +python -B research/frontier-refinement186/test_source.py +python -B research/frontier-refinement186/scalar.py +``` + +Repeat the five independent commands with `python -O -B`. The original native +aggregate requires assertions enabled and reconstructs its immutable archive +in a temporary directory. Our independent guards remain active with -O. +The full scalar command uses the unchanged signed scalar core (SHA256 prefix 6345a9b3) on every new raw +graph/word/frame/pair/sink input, both directions and five corruption controls. +It may use about 550 MB; CI externally limits it to4 GiB. + +The arithmetic command independently rebuilds all paid children, both rational +moment enclosures with the complete bad-class fallback, the first strict atom, +the full logical scalar/group/router/row bridge, all 47 strict inequalities and +seven margins. Both supplier successors and the next headline grid fail. +Arithmetic and bank fixtures include mathematical controls beyond byte checks. + +The bit stock is normalized W=59144/3. Multiplying stock, every child count, +mass, deficit and fallback edge count by3 clears fractions without changing +the characteristic. Nine physical replicas separately give integral stage +allocations and actual stock 177432. Rank21 recipients are internal splices; +only2200 rank 60 entrance exterior children disappear. Every other paid child +and the original full scalar/row reserves remain paid. + +The fresh selected complex inventory has46 sinks,10686 dirty roles, stock 13326, +rank mass 878196 and deficit 1320. All positive target bins match native evidence. +The literal-event diagnostic has6325 zero-rank target events; native evidence +stores6270. SOURCE and certificate preserve both counts (difference55). +Zero rank adds no child, moment or rank charge; full c/R/M scalar bills remain. + +Finite checks do not establish general tensor/Clifford phases, the uniform +weighted compiler, common generic charts, multibank routing/restoration and +orbit/stage cover, paid layout, prime supply, local-ring precision/recovery, +uniform setup or analytic/fixed-tape/all-size interfaces. Those remain the +explicit conditional hypotheses in the original proof sources. This is AI +agent work and review, without a new human peer review or Lean proof claim. +See PROOF.md and NOTICE for proof obligations and attribution. diff --git a/research/frontier-refinement186/SOURCE.json b/research/frontier-refinement186/SOURCE.json new file mode 100644 index 0000000000..12ce15919a --- /dev/null +++ b/research/frontier-refinement186/SOURCE.json @@ -0,0 +1,116 @@ +{ + "bank_adapter_changes": "Only repository-relative raw paths and explicit source closure call; all address-map,allocation,chronology,scale and mutation mathematics unchanged.", + "copied_bundle_policy": "All51 original166a Git blobs byte-exact, including literal CRLF certificate/sinks. 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inventory/cube sources separately reconstructed by R53. Derived JSON, not Git-verbatim.", + "inputs/physical-sinks.json": "R53 independent exact raw operation-frame/alias/target/sink chronology reconstruction; preserves literal zero6325 separately from native6270. Derived JSON, not Git-verbatim.", + "inputs/scaled-bank.json": "R50 exact whole bank paid child inventory: scale3 applied uniformly to normalized stock,mass,deficit,all counts and fallback edges; actual allocation separately9replicas. Derived JSON, not Git-verbatim." + }, + "original_R51_bank_checker_sha256": "5ef345272a7e464b4686342035217d85e50a79465c8f68494a6e65525891a797", + "preserved_base_commit": "f5ab0230f0db0a98df7e99ce4169d15fad6c74c7", + "prior_local_finite_evidence_sha256": { + "frontier-186-arithmetic-001.json": "6d78d2d51aee9ed5dccbb0681e248b23186c819b18fc9428495d25f9e2173793", + "frontier-186-bank-review-001.json": "4445e1e8cf2be03ddef216a8f39c7ca4ad1456390da5455bf9a520cf1b4f19ef", + "frontier-186-geometry-001.json": "70bb30dc2fe66ef07eff29289e24c2cc5049f41981437fcd664361c78c0aafc6", + "frontier-186-independent-review-001.json": "89d222f4b68278309cd28f12326e94ca4377b2e2ce4613f417897d46bcb3fb0b", + "frontier-186-native-replay-001.json": "dcb819f933e8ba5191c356ba29e473ac028ff67048b700e67b8acd960e824da3", + "frontier-186-scalar-replay-001.json": "afaeee054a46611de5c1935f10d129392a1eadc4c49b57a1bf94f26bd5b4923e" + }, + "reviewed_core_sha256": { + "research/paired-cube-scalar-audit/independent_bit.py": "0ceac13910e1d50b2145062fc5db38a3709d82e85bf5d8ff000a0d64a36b104b", + "research/paired-cube-scalar-audit/independent_sinks.py": "6345a9b3a899ccdf40a2a97062fb01b0abe6e989aad938656b706f80e77586df", + "research/precision-certificate/independent_assembly.py": "99584fe21922926ed9766ec5bc75a06ae531f396bf41ef87baafde248e1f9b9b", + "research/precision-certificate/independent_moments.py": "4d398b4600f7aeaf73a36c68ebc9727de0451399512769282684ae9d4804f594" + }, + "schema_version": 1, + "scope": "Fixed conditional finite arithmetic,bank endpoint/address checks and selected full signed scalar wrappers. No current-frontier/global-optimum/all-size theorem claim. Native archive and general realization/routing/phase/tape contracts remain separate.", + "self_reference_policy": "SOURCE excluded from own hash map; regenerated certificate binds its full byte hash. certificate excluded from source map and required byte-equal to independent recomputation.", + "source_sha256": { + "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "NOTICE": "0bf28a1a65ed74ca4dd88cadd24851aacd8a1c95d915753e53ba7f2b64299416", + "PROOF.md": "09449d7920c68f266535c31baa76657650e8820f49527cfceaf288467c6e86f1", + "README.md": "b6fdc541e17468bea7d8f8e5a64cd3f24cd523cb8e96f174924e9a7b10fc2830", + "arithmetic.py": "094730e001c8337f03f93a9b2771b68dda041ec641657b9d042e4b319f57f30d", + "check_banks.py": "d50540cbe8e512a85ea39a9ca6a98c8acba26940bfe5f6497433378b00a8c325", + "inputs/logical.json": "9adcc1e7da7222e19dce989cd6f86200997a677642b4c2a580aaae0c0a31a855", + "inputs/physical-sinks.json": "eb67db76d5243eecaefb8709e4421ed8d74ce9a5587a3877d6c69384487b68e0", + "inputs/scaled-bank.json": "4757539c1ee428b1208233fea113420cef9b9ad5f8b4b76cbdc2a534e78c618f", + "scalar.py": "8e106fd14434686da47770816968231c48dd7d8ab1e809b4ff0fa69855af382e", + "source_binding.py": "856a61a3b4594b3df28687a96e1c34931797c01e9501df8d6eefa53066969d96", + "test_refinement.py": "064f0ccfd7997e4dc7c35be7a2cd9bb90a30369a370694bf92259fc3e61efc41", + "test_source.py": "3f67286b31bb9f7cc967332bec556fa643694e15669a8da84351463f2bf30322", + "verify.py": "d5487de8415f38680cd385885c4ec9d48127d872fbefbe14030485d7d3b9b326" + }, + "upstream_commit": "166a34d75e853e933855f0f7e940fe77c4bb6b8d", + "upstream_repository": "https://github.com/Dugongue/integer-mult-bounds", + "upstream_tree": "d4c4c9741dd8b51e38afc9e5d53ba594459bc369", + "zero_target_events": { + "difference": 55, + "full_logical_scalar_bill_retained": true, + "independent_literal": 6325, + "native": 6270, + "zero_creates_no_child_moment_rank_charge": true + } +} diff --git a/research/frontier-refinement186/arithmetic.py b/research/frontier-refinement186/arithmetic.py new file mode 100644 index 0000000000..37bb623c05 --- /dev/null +++ b/research/frontier-refinement186/arithmetic.py @@ -0,0 +1,91 @@ +"""Fixed supplier arithmetic, explicit raw component binding, no producer imports. + +Apache-2.0. Prepared with substantial OpenAI Codex assistance. +The copied generic moment/assembly algorithms remain exact prior reviewed bytes. +""" +from pathlib import Path +from fractions import Fraction as Q +from collections import Counter +from hashlib import sha256 +import json,gzip,sys,copy +from source_binding import HERE,ROOT,check_sources,require +sys.path.insert(0,str(ROOT/'research/precision-certificate')) +import independent_moments as M +import independent_assembly as A +PACKAGE=ROOT/'research/coordinated-frames-and-entrance-banks' +GRID=10**24 +STEP=Q(1,GRID) +COMPLEX=Q(331161965949525999057,500000000000000000000000) +COARSE=Q(133096233391197420469,200000000000000000000000) +ATOM=Q(13301283151705819139,20000000000000000000000) +KAPPA=Q(330942774629799608347,500000000000000000000000) +BASELINE=Q(330942774629799,500000000000000000) +ETA=BETA=PHASE_GAP=STEP +FIXED_INPUT_HASHES={'logical.json': '9adcc1e7da7222e19dce989cd6f86200997a677642b4c2a580aaae0c0a31a855', 'physical-sinks.json': 'eb67db76d5243eecaefb8709e4421ed8d74ce9a5587a3877d6c69384487b68e0', 'scaled-bank.json': '4757539c1ee428b1208233fea113420cef9b9ad5f8b4b76cbdc2a534e78c618f'} +def read(path): + raw=path.read_bytes();return json.loads(gzip.decompress(raw) if path.suffix=='.gz' else raw) +def positive(raw,maxrank):return A.component_histogram(raw,maxrank) +def load_inputs(): + inputs={name:read(HERE/'inputs'/name) for name in ('logical.json','physical-sinks.json','scaled-bank.json')} + for name,expected in FIXED_INPUT_HASHES.items():require(sha256((HERE/'inputs'/name).read_bytes()).hexdigest()==expected,'wrong fixed derived input '+name) + logical,physical,scaled=(inputs[n] for n in ('logical.json','physical-sinks.json','scaled-bank.json')) + native=read(PACKAGE/'certificate.json');before=read(PACKAGE/'selected/complex/profile-before.json.gz');rawphysical=read(PACKAGE/'selected/complex/profile.json.gz');sinks=read(PACKAGE/'selected/complex/sinks.json');bank=read(PACKAGE/'bit/banks.json');oldbit=read(PACKAGE/'references/pr168/bit-physical-profile.json') + for name in ('numerical_complex_root','gauge_cost_rejections','gauge_trial_saving','gauge_selection'):before.pop(name,None) + require(logical==before,'raw logical scalar profile differs') + require((logical['h'],logical['v'],logical['R'],logical['c'],logical['q'],logical['matched'],logical['total_M_operations'],logical['loss'])==(22,1320,13042,21249,3157,11364,32971,440),'actual logical scalar charges') + published=native['complex']['physical']['physical'] + for name in ('h','v','R','physical_R','pairs','loss','m','W_per_vertex','rank_per_vertex','deficit_per_vertex'):require(physical[name]==published[name],'native paid dimension differs '+name) + require(physical['sinks']==sinks['eligible_count']==published['terminal_sinks']==46,'46 terminal deletions') + for name in ('local_histogram','source_data_histogram','target_data_histogram','physical_gauge_histogram','child_histogram'): + maximum=65 if name=='child_histogram' else 21 if name=='physical_gauge_histogram' else 22 + require(positive(physical[name],maximum)==positive(published[name],maximum),'native paid component differs '+name) + for name,field in (('local_histogram','local_histogram'),('target_data_histogram','target_histogram'),('child_histogram','child_histogram')):require(positive(physical[name],65)==positive(sinks[field],65),'raw46-sink component differs '+name) + for name in ('source_data_histogram','physical_gauge_histogram'):require(positive(physical[name],22)==positive(rawphysical[name],22),'unchanged source/gauge component differs '+name) + zeros={'native':published['target_data_histogram'].get('0',0),'independent_literal_events':physical['target_data_histogram'].get('0',0)} + require(zeros=={'native':6270,'independent_literal_events':6325},'zero-rank event diagnostics') + return logical,physical,scaled,native,bank,oldbit,zeros +def paid_complex(row): + require((row['h'],row['v'],row['R'],row['pairs'],row['sinks'],row['physical_R'],row['loss'])==(22,1320,13042,2310,46,10686,440),'complete complex dimensions') + require(row['physical_R']==row['R']-row['pairs']-row['sinks'],'physical dirty population') + children=Counter() + for name in ('local_histogram','source_data_histogram','target_data_histogram'): + for rank,n in positive(row[name],22).items():children[rank]+=3*n + for rank,n in positive(row['physical_gauge_histogram'],21).items():children[3*rank]+=n + children[2]+=2640;children=dict(sorted(children.items()));mass=sum(r*n for r,n in children.items()) + require(children==M.normalize_children(row['child_histogram'],66),'complete complex paid children') + require((row['m'],row['W_per_vertex'],row['rank_per_vertex'],row['deficit_per_vertex'])==(66,13326,mass,1320),'complex full mass/stock') + require(66*13326-mass==2640-3*440==1320,'complex telescoping deficit') + return dict(width=66,stock=13326,children=children,mass=mass,deficit=1320) +def paid_bank(scaled,bank,oldbit): + original=M.normalize_children(oldbit['child_histogram'],72);require(original.pop(60)==2200,'exact entrance exterior removal') + require(original==M.normalize_children(bank['profile']['child_multiplicities'],72),'remaining paid bank children') + stock=2*1760+3*(Q(2200,18)+Q(15828,3));mass=sum(r*n for r,n in original.items()) + require((stock,mass,72*stock-mass,max(original))==(Q(59144,3),1417520,1936,22),'normalized bank inventory') + require((9*2200%18,9*15828%3)==(0,0),'integral9-copy bank allocation') + require(3*(9*2200//18+9*15828//3)+2*9*1760==9*stock==177432,'actual9-copy stock') + expected=dict(width=72,stock=59144,children={str(r):3*n for r,n in original.items()},mass=3*mass,deficit=5808,edge_count=3*sum(original.values()),normalization_scale=3,physical_replicas=9) + require(scaled==expected,'unpaid bank stock,unscaled children or fallback edge-count mismatch') + return dict(expected,children={int(r):n for r,n in expected['children'].items()}) +def strict_bit(profile,coarse,atom,*,bad_fraction=M.BAD,fallback_children_per_edge=32*72**2): + require(bad_fraction==M.BAD and fallback_children_per_edge==32*72**2,'omitted full bad-class fallback') + result=M.certify_bit_supplier(72,profile['stock'],profile['children'],coarse,atom=atom) + require(result['edge_count']==profile['edge_count'] and result['rank_mass']==profile['mass'],'all scaled fallback edges and mass') + require(result['fallback_lower']>0,'fallback charge omitted') + return result +def compute(logical,physical,scaled,native,bank,oldbit,zeros): + cp=paid_complex(physical);bp=paid_bank(scaled,bank,oldbit) + complex_bounds=M.require_contraction(M.supplier_bounds(66,cp['stock'],cp['children'],COMPLEX)) + bit=strict_bit(bp,COARSE,ATOM) + threshold=COARSE/(1+COARSE-M.OLD);require(ATOM-STEP<=threshold=1,'supplier successor accepted '+name);successors[name]=result + bridge=A.reconstruct_bridge(logical,physical);require(bridge['local_group_upper']==native['complex']['physical']['scalar_bound']['local_group_upper'],'full logical scalar/router charge') + assembly=A.balanced_assembly(bridge,bit['effective_saving'],COMPLEX,KAPPA,eta=ETA,beta=BETA,phase_gap=PHASE_GAP) + require(KAPPABASELINE,'headline strict next grid or improvement') + try:A.balanced_assembly(bridge,bit['effective_saving'],COMPLEX,KAPPA+STEP,eta=ETA,beta=BETA,phase_gap=PHASE_GAP) + except ValueError as e:require('compact_phase_layer_above_kappa' in str(e),'wrong headline successor failure') + else:raise ValueError('headline successor accepted') + return A.serialize(dict(schema_version=1,source_commit='166a34d75e853e933855f0f7e940fe77c4bb6b8d',kappa=KAPPA,baseline_kappa=BASELINE,improvement=KAPPA-BASELINE,complex_saving=COMPLEX,coarse_bit_saving=COARSE,atom=ATOM,effective_bit_saving=bit['effective_saving'],grid=GRID,eta=ETA,beta=BETA,phase_gap=PHASE_GAP,complex_profile=cp,scaled_bank_profile=bp,complex_bounds=complex_bounds,bit_bounds=bit,supplier_successors=successors,atom_threshold=threshold,headline_successor=KAPPA+STEP,headline_successor_rejected=True,finite_bridge=bridge,assembly=assembly,zero_target_diagnostic=dict(zeros,difference=55),scope='Finite fixed-supplier arithmetic and input binding. Exact geometry/scalar/bank results are separate finite evidence; inherited tensor/weighted compiler/common charts/routing/restoration/phase/precision/analytic/allsize fixed-tape contracts remain conditional. No current frontier or global maximum claim.')) +def regenerate(): + check_sources();result=compute(*load_inputs());result['source_manifest_sha256']=sha256((HERE/'SOURCE.json').read_bytes()).hexdigest();return result diff --git a/research/frontier-refinement186/certificate.json b/research/frontier-refinement186/certificate.json new file mode 100644 index 0000000000..b51e4c35f9 --- /dev/null +++ b/research/frontier-refinement186/certificate.json @@ -0,0 +1,290 @@ +{ + "assembly": { + "absorption_gap": "36404897589600589212668990586741566420352596984572942172289053098268677/50033116196594952599905649900651410215142200283000066232393189905199811400000000000000000000000", + "limiter": "complex", + "margins": { + "Gaussian_arithmetic": "264929572759620799245349039630298746374602735751026602094443530597076199668838034050474000943/400264929572759620799245199205211281721137602264000529859145519241598491200000000000000000000000", + "balanced_prefix": "165580982974762999528499503257051075711001415000331161965949525999057/250165580982974762999528249503257051075711001415000331161965949525999057", + "bulk_exposure": "331161965949525999056499668838034050474000943/500000000000000000000000000000000000000000000000", + "compact_phase_layer": "165580982974762999528249337676068100948001886750827904914873814997641999668838034050474000943/250165580982974762999528249503257051075711001415000331161965949525999057000000000000000000000000", + "coordinate_movement": "331161965949525999056499668838034050474000943/500000000000000000000000000000000000000000000000", + "dimension": "249999999999999999999999750000000000000000000000000000000000000000000000/250165580982974762999528249503257051075711001415000331161965949525999057", + "scalar_work": "1324647863798103996227745860475425630925011791753146038676520496991040999668838034050474000943/2001324647863798103996225996026056408605688011320002649295727596207992456000000000000000000000000" + }, + "minimum_margin": "165580982974762999528249337676068100948001886750827904914873814997641999668838034050474000943/250165580982974762999528249503257051075711001415000331161965949525999057000000000000000000000000", + "parameters": { + "C0": 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+ "shared_assumptions": [ + "finite scalar/phase/router bound in PR168 written note", + "inherited bit reserve9909 and ordinary leaf reserve252" + ], + "stages": 3, + "vertices": 3525886442745164056544063644145716736004044180364723200424782744512582104634391857878947474919000911664177132185103526533556870749183073596734571342973795793383290849303191539662953799849547227737400544457729391514661713176468240351330298583217125220869576729661326266259024901649005584114421035252391760900092184489369973370724377894349644301151172572225522957784648909234781611948223712944954177723427440753012339451839407462242698998122862136268155486957700758485307238973641035062973415368109606762999662774702118665848434384838590914531021276158042617166069588021894697108433312726842277534281982740181708602162296504975360000000000000000000, + "wire_bits": 2159 + }, + "grid": 1000000000000000000000000, + "headline_successor": "132377109851919843339/200000000000000000000000", + "headline_successor_rejected": true, + "improvement": "608347/500000000000000000000000", + "kappa": "330942774629799608347/500000000000000000000000", + "phase_gap": "1/1000000000000000000000000", + "scaled_bank_profile": { + "children": { + "1": 376344, + "10": 7524, + "11": 3474, + "12": 12960, + "13": 4770, + "14": 9702, + "15": 3690, + "16": 9648, + "17": 3492, + "18": 3996, + "19": 2754, + "2": 188724, + "20": 15840, + "21": 33480, + "22": 39816, + "3": 88848, + "4": 26910, + "5": 23400, + "6": 10980, + "7": 9936, + "8": 8406, + "9": 5436 + }, + "deficit": 5808, + "edge_count": 890130, + "mass": 4252560, + "normalization_scale": 3, + "physical_replicas": 9, + "stock": 59144, + "width": 72 + }, + "schema_version": 1, + "scope": "Finite fixed-supplier arithmetic and input binding. Exact geometry/scalar/bank results are separate finite evidence; inherited tensor/weighted compiler/common charts/routing/restoration/phase/precision/analytic/allsize fixed-tape contracts remain conditional. No current frontier or global maximum claim.", + "source_commit": "166a34d75e853e933855f0f7e940fe77c4bb6b8d", + "source_manifest_sha256": "cec8c593c8167c3d9d14cbc3c89e74ed78e2a9763805e10f779d1832e9996d4a", + "supplier_successors": { + "bit": { + "ambient_rank_mass": 4258368, + "bad_fraction": "1/10000000000000000", + "characteristic_gap_lower": "-1242645326832928174533917873213/693093750000000000000000000000000000000000000000000000", + "contaminated_rank_mass": "2076445312507210053/488281250000", + "edge_count": 890130, + "fallback_children_per_edge": 165888, + "fallback_lower": "401700129609194902493512154689570756744977/115515625000000000000000000000000000000000000000000000", + "fallback_upper": "803400259218389804987024309379141514291071/231031250000000000000000000000000000000000000000000000", + "ideal_lower": "354863999998765977201841189493947268765639/354864000000000000000000000000000000000000", + "ideal_upper": "354863999998765977201841189493947269120019/354864000000000000000000000000000000000000", + "rank_gap": "2835937492789947/488281250000", + "rank_mass": 4252560, + "saving": "332740583477993551173/500000000000000000000000", + "stock": 59144, + "total_lower": "346546875000000000000000621322663416118013048207734931/346546875000000000000000000000000000000000000000000000", + "total_upper": "693093750000000000000001242645326832928174533917873213/693093750000000000000000000000000000000000000000000000", + "width": 72 + }, + "complex": { + "ambient_rank_mass": 879516, + "bad_fraction": "0", + "characteristic_gap_lower": "-7327979318987223/24431000000000000000000000000000000000000", + "contaminated_rank_mass": "878196", + "edge_count": 221220, + "fallback_children_per_edge": 0, + "fallback_lower": "0", + "fallback_upper": "0", + "ideal_lower": "36646500000000000000000010991968978444243/36646500000000000000000000000000000000000", + "ideal_upper": "24431000000000000000000007327979318987223/24431000000000000000000000000000000000000", + "rank_gap": "1320", + "rank_mass": 878196, + "saving": "132464786379810399623/200000000000000000000000", + "stock": 13326, + "total_lower": "36646500000000000000000010991968978444243/36646500000000000000000000000000000000000", + "total_upper": "24431000000000000000000007327979318987223/24431000000000000000000000000000000000000", + "width": 66 + } + }, + "zero_target_diagnostic": { + "difference": 55, + "independent_literal_events": 6325, + "native": 6270 + } +} diff --git a/research/frontier-refinement186/check_banks.py b/research/frontier-refinement186/check_banks.py new file mode 100644 index 0000000000..cf9f4db1e5 --- /dev/null +++ b/research/frontier-refinement186/check_banks.py @@ -0,0 +1,88 @@ +"""Independent finite address maps and allocation, with no upstream imports.""" +from pathlib import Path +from fractions import Fraction as Q +from collections import Counter +import json,gzip,hashlib,time,sys +H=Path(__file__).resolve().parent; R=H.parents[1] +RAW=R/'research/coordinated-frames-and-entrance-banks'; sha=lambda p:hashlib.sha256(p.read_bytes()).hexdigest() +def need(c,m): + if not c:raise ValueError(m) +def chart(v,sign): + # Same unimodular coordinate shear on both banks; inverse has sign -1. + z=v[:] + for offset in (0,72):z[offset]+=sign*z[offset+71] + return z +def apply(v,width,block,weighted=False,ring=0): + z=chart(v,-1) if weighted else v[:] + for j in range(block*width,(block+1)*width):z[j],z[j+72]=z[j+72],z[j] + if weighted:z=chart(z,1) + return [x%ring for x in z] if ring else z +def run(v,width,indices,ring,charts): + for p,b in enumerate(indices):v=apply(v,width,b,charts[p],ring) + return v +def validate(width,indices,ring,charts,restore=False): + for k in range(144): + v=[int(j==k) for j in range(144)] + got=run(v,width,indices,ring,charts) + expected=v if restore else [int(j==(k+72)%144) for j in range(144)] + need(got==expected,'restore column '+str(k) if restore else 'endpoint column '+str(k)) + return 144 +def reject(f): + try:f() + except ValueError as e:return str(e) + raise ValueError('negative control unexpectedly accepted') +def main(): + from source_binding import check_sources + check_sources() + start=time.monotonic(); checks=[] + for width in (4,24): + count=72//width; indices=list(range(count)); row={'width':width,'blocks':count,'rings':{}} + for ring in (0,2): + c={} + for weighted in (False,True): + charts=[weighted]*count + c[str(weighted)]={'endpoint_columns':validate(width,indices,ring,charts),'inverse_columns':validate(width,indices+indices[::-1],ring,charts+charts[::-1],True)} + c['controls']={'omit':reject(lambda:validate(width,indices[:-1],ring,[False]*(count-1))), + 'repeat':reject(lambda:validate(width,indices+[count-1],ring,[False]*(count+1))), + 'inconsistent_common_chart':reject(lambda:validate(width,indices,ring,[False]*(count-1)+[True]))} + row['rings'][str(ring)]=c + checks.append(row) + source=json.loads((RAW/'SOURCE.json').read_bytes())['files']; paths=['references/paired-cube/bit-physical/word_p12.json.gz','research/paired-cube-bit/out/profile_p12.json'] + for p in paths:need(sha(R/p)==source[p],'pinned native byte '+p) + w=json.loads(gzip.decompress((R/paths[0]).read_bytes())); original=json.loads((R/'research/precision-certificate/inputs/paired-cube-bit-physical-input.json').read_bytes()); prof=json.loads((R/paths[1]).read_bytes()) + gauges={z['role']:z for z in w['gauges']}; pairs=w['pairs']; donors={a for a,b in pairs}; recipients={b for a,b in pairs} + need(len(gauges)==len(w['gauges']) and len(pairs)==len(donors)==len(recipients)==1760 and not donors&recipients,'one-to-one disjoint aliases') + need(not donors&set(gauges) and not donors&set(w['rootroles']),'donors are ungauged nonroots') + need(all(b in gauges and gauges[b]['dim']==21 for b in recipients),'all rank21 recipient gauges internal') + starts={s:z for s,z in gauges.items() if s not in recipients} + need(len(starts)==2200 and all(z['dim']==20 for z in starts.values()),'2200 physical rank20 entrances only') + # Reconstruct the native actual chronological positions, without native code. + phase=sorted(w['phase1']); phase_set=set(phase); order=phase+[i for i in range(len(w['ops'])) if i not in phase_set] + first={};last={} + for position,i in enumerate(order): + for s in w['ops'][i][:2]:first.setdefault(s,position);last[s]=position + reads={int(s):p for s,p in w['reads'].items()} + need(all(last[a]`). +- `rootroles[j]`: the role that is read into the targets of `roots[j]`. +- `phase1`: indices of the ops in the centre closure, recomputed by the checker. +- `gauges[k] = {role, first, targets, dim, frame}`. Each entry is a deferred old-value read of `role`'s + dirty content, at frame `frame` (an exact annihilator id in `frames`, of dimension `dim`): + - `first` is the node of the role's first op; + - `targets` is the role's response support; + - selection order is listed, and the time order per target is the reverse of it, which is ascending. +- `order`: compile order of the active nodes; `arcs`: the frozen carrier links `[donor, use]`, with `use` + either `["op", node, operand_slot]` or `["root", j]`. +- `plain`: nodes whose frame is the plain span of their support. +- `node_frame[str(node)]`: frame id of every active node. The frame of op `[dest, control, node]` is + `node_frame[node]`. +- `root_frame[j]`: frame id of root `j`. For side roots this is the common cap of the targets; for centre + roots it is the star span, of dimension `h-2`. +- `source_frame[S]`: frame id of ``. `full_frame`: id of `Q^h` (id 0, no annihilator rows). +- `conventions` and `schedule`: text restating the above. + +## `frames_pP.json` — exact frames + +- `frames[str(id)]` is an object `{dim, a}` or `{dim, b}`. Its rows are primitive integer vectors of + length `h`, the rows of the rational RREF scaled to integers: + - `a`: annihilator rows; the frame is their common kernel, of dimension `dim = h - len(a)`. + - `b`: basis rows; the frame is their span, of dimension `dim = len(b)`. +- The representation with fewer rows is stored. The checker computes the other one exactly by integer + elimination and verifies `A.B^T = 0` and `rank A + rank B = h`. +- `P_used_for_ranks`: the generator computes ranks modulo the Mersenne prime `2^127 - 1`. Every minor of + the integer generator matrices involved is below this prime by Hadamard's bound for `h <= 26`, so + modular ranks are rational ranks. The exported integer rows are recovered by rational reconstruction and + are re-verified exactly by the checker, which uses no modular arithmetic. + +## `kchron_pP.json` — partial-K chronology + +`entries[k]` lists, for each partner pair `{carrier c, passive d}` and its receivers `[a, b]`, the +following fields: + +- `mix_frame`: id of `M = span{chi_c, chi_d}` (dimension 2, H0-Gram `I_2`). +- `deliver_frame`: id of the receivers' shared cap `C`, the frame of `roots[deliver_after_root]`, whose + targets are exactly `[a, b]` (the `edge12` root). +- `deliver_after_root`: the delivery happens right after this root's read, while `Y_a` and `Y_b` are at `C`. +- `undo_frame`: the full frame. +- `carrier_chain`: `[, M, C, full]`, with ranks `[1, h-4, 2]`. +- `passive_chain`: `[, M, full]`, with ranks `[1, h-2]`. + +Chronology: + +1. Run all V injections at the rank-one frames. +2. Raise `X_c` and `X_d` to `M`, then set `X_c ^= X_d`. +3. Raise `X_c` to `C`. After root `deliver_after_root` is read, set `Y_a ^= X_c` and `Y_b ^= X_c`. +4. After all target reads, raise `X_c` and `X_d` to full and set `X_c ^= X_d`. +5. Run the inverse producer and the V removal. + +## `profile_pP.json` — PR #144 bit ledger + +- `h, v, R, c, q, matched, loss` (copied-centre loss `= h(h-2)`). +- `m = 3h`, `W_per_vertex = 2v + R`, `rank_per_vertex`, `deficit_per_vertex = 2v - 3*loss`. +- `selected_rank_histogram` (gauge dimensions); `remaining_internal_histogram` (local auxiliary children + after gauging, centre copies included); `source_data_histogram`; `target_data_histogram`. +- `child_histogram`, which is assembled as: + - 3 times the local, source and target histograms; + - plus one child of width `3*dim` per gauge; + - plus `2v` children of width 2. + +## `certificate_pP.json` — exact moment + +The method is PR #144's `bit_certificate`: + +- an exact upper moment with `log_upper` and `exp_upper`, rounded to the grid `2^-120`; +- the full `32 m^2` local-ring fallback on a fraction `1e-16` of every edge. + +`coarse_saving` is the largest point `k/10^10` that passes, and `next_grid_point` is rejected. +`effective_bit_saving = (1 - 1e-3) * coarse + 1e-3 * 384599/1e10`. + +## `data/` + +- `pair_module_p{11,12,13}.json`: pinned pair-disjoint modules with provenance, re-derivable by + `derive_pair_modules.py`. + - p=11 and p=12 are cut from an h=21 bit witness (sha256 in the file). + - p=13 is PR117's `restricted_pairs(12)`. +- `arcs_p{11,12,13}.json`: frozen carrier matchings. `--solve-matching` recomputes them deterministically + with Hopcroft-Karp. diff --git a/research/paired-cube-bit/LEMMA.md b/research/paired-cube-bit/LEMMA.md new file mode 100644 index 0000000000..4879c26839 --- /dev/null +++ b/research/paired-cube-bit/LEMMA.md @@ -0,0 +1,159 @@ +# Partner-pair sums on bit source registers + +This lemma covers the only new step that the paired-cube bit word adds to PR #144's +completed-core interface: the partial analog of #144's original-source involution K. + +## Setting and conventions + +- **Ports.** Coordinates `[h]`, `h = 2p`, are split into `p` pairs. A port is a triple `S` that takes one + coordinate from each of three distinct pairs. The label is `chi_S` in `Q^h`. +- **Form.** `H0 = (I - J/9)/2` and `G = 2 H0`. Then `H0(chi_S, chi_T) = (|S cap T| - 1)/2`. In particular + `H0(chi_S, chi_S) = 1`, and `S` is H0-orthogonal to `T` iff `|S cap T| = 1`. +- **Caps.** The cap of a target `T` is `cap(T) = ker(3 chi_T - 1) = chi_T^{perp_H0}`. A group's cap is the + intersection of its members' caps. +- **Cubes and parity classes.** A cube is the set of eight ports on one triple of coordinate pairs, indexed + by selectors `e in {0,1}^3`. For two ports of one cube, `|S cap T| = 3 - d(e_S, e_T)`, where `d` is the + Hamming distance. A parity class is the set of four ports in a cube whose selector sums have the same + parity. +- **Partner pair.** The partner of `T` is the port `T'` that has the same selector as `T` on cube pair 0 + and the opposite selectors on cube pairs 1 and 2. Each parity class `{a, b, c, d}` splits into two + partner pairs, `{a, b}` and `{c, d}`. +- **Physical rules.** These are #144's rules on the bit side: + - Each register (data `X_S`, `Y_T`, or auxiliary) follows an ascending chain of G-nondegenerate frames. + - An XOR between two registers is performed at an identical frame representative. + - A register may be added into `Y_T` only at a frame that occurs in `Y_T`'s nested chain and lies in + `cap(T)`. + - Source injections `z += V x` happen while `X_S` is at its rank-one frame ``. + +## Facts + +**F1.** The four ports of a parity class are pairwise H0-orthogonal, since `d = 2` gives `|S cap T| = 1`. +For a partner pair `{c, d}`, the space `M = span{chi_c, chi_d}` therefore has H0-Gram matrix `I_2`. So `M` +is nondegenerate and 2-dimensional, and `M` lies in `cap(a) cap cap(b)` for the opposite pair `{a, b}`. + +**F2.** The level-2 group of `a` is `{a, b}`. Its cap `C = cap(a) cap cap(b)` has dimension `h - 2` and is +the frame of a side root (the edge12 channel) read into exactly `Y_a` and `Y_b`. It satisfies + + capF(a) <= C <= cap(a), + +where `capF(a)` is the cap of `a`'s level-1 group (the four cube ports sharing `a`'s selector on cube +pair 0). So every target chain + + 0 -> (gauge frames) -> capF -> C -> cap(T) + +is ascending. The checker verifies this exactly for every target. + +## Construction + +The construction runs once per parity class and partner pair. The carrier `c` is the pair member with the +smaller selector vector and `d` is the passive member; the receivers are `{a, b}`. + +1. All V injections from `X_c` and `X_d` happen first, at `` and ``, as in #144. Then + raise both `X_c` and `X_d` to `M`. Each pays one child of width 1. +2. At `M`, set `X_c <- X_c + X_d`. +3. Raise `X_c` to `C`, one child of width `h - 4`. When `Y_a` and `Y_b` are at `C` (right after their + level-2 root read), set `Y_a <- Y_a + X_c` and `Y_b <- Y_b + X_c`. +4. After all target reads, raise `X_c` to `F = Q^h` (width 2) and `X_d` to `F` (width `h - 2`). Then set + `X_c <- X_c + X_d`. + +Data ledger: the carrier's chain is `[1, h-4, 2]` and the passive's is `[1, h-2]`. Both total `h - 1`, +exactly like an unmixed source chain. No auxiliary role is used. + +## Lemma + +Steps 1–4 have the following effects: + +- They add `x_c + x_d` to `y_a` and to `y_b`. +- They restore `X_c = x_c` and `X_d = x_d`. +- They obey every frame rule. +- They read or write no register other than `X_c`, `X_d`, `Y_a` and `Y_b`. + +Together with the auxiliary word and its arbitrary-dirty restoration, the complete local word adds + + (J M V + K) x = x (mod 2), + +where `K` is the all-ones block on `{a,b} x {c,d}` of every class. This is the mod-2 decoder identity + + x_T = sum_{c in T} star(c) + sum_{|S cap T| = 1} x_S. + +## Proof + +**Scalars.** After step 2, `X_c = x_c + x_d` over F2. Step 3 adds this value to `y_a` and `y_b`. Step 4 +subtracts `x_d` again, which equals adding it in F2, so `X_c = x_c`. `X_d` is never written. + +**Frames.** + +- `X_c` follows ` <= M <= C <= F` and `X_d` follows ` <= M <= F`. These are ascending by F1 + and F2. +- Each XOR takes place at one common frame: + - step 2 at `M`, where both source registers sit; + - step 3 at `C`, where `X_c` and the targets sit; + - step 4 at `F`. +- The delivered register's support labels are `{chi_c, chi_d}`. They span `M`, which lies in `C`, which + lies in `cap(a)` and `cap(b)`. This is #144's rule that a physical frame contains the span of its support + and lies in the common target cap. +- `M` has Gram matrix `I_2`. `C` is a root frame and `F` is the whole space. The checker certifies + G-nondegeneracy of every frame with integer determinants. + +**No cross-talk.** This step is sequential, not lockstep. + +- The steps are a sequence of completed XORs on four named registers. No auxiliary role or dirty scratch + register is involved. +- Each source belongs to exactly one partner pair, and each target receives from exactly one pair. Different + pairs act on disjoint register sets, so they commute. +- The auxiliary word reads source registers only at its V injections, which precede step 1, and at its + source-subtraction cleanup. Following #144's original-source ordering, the cleanup runs at the full frame + after step 4, when `X_c` and `X_d` again hold `x_c` and `x_d`. +- The targets receive their other contributions at other times: centre copies at frame 0, gauged old-value + reads, and side roots. Additions into `Y` commute. +- None of the shared-register interleaving of #132/#139 occurs. No register ever holds a mixture of two + cores' data, because the mix is undone inside the same completed core. + +**Dirty restoration.** The literal auxiliary sequence + + y -= J M z; z += V x; z <- M z; y += J z; z <- M^-1 z; z -= V x + +restores arbitrary `z` and adds `J M V x`. Steps 1–4 touch no auxiliary register and add `K x`. + +**Completed cores and reversal.** The mixing is internal to a completed local core and leaves the data +registers' logical values and endpoints unchanged. The core's exact operator `U = F_A T_sigma^{-1}` (#144, +paired-cube-sharing) is therefore unchanged. Its complemented time reverse undoes step 4, then steps 3 and +2, at the reflected frames, so the cross-stage sharing argument applies verbatim. + +## Why this is only a partial K (obstruction) + +The source registers that may feed `Y_a` are constrained as follows: + +- A register's frame always contains its own label and every label mixed into it. +- A register can feed several targets only at one common level of their nested chains. +- `H0(chi_a, chi_a) = 1`, so `chi_a` never lies in `cap(a)`. + +Consequences: + +- No register that ever contained `chi_a` can feed `a`. +- The three class-mates of a port never form one level (levels are halves or partner pairs), and two + different single caps are never nested. +- The cap of a level-2 pair and the cap of a third single are not nested either, because `3 chi_S' - 1` is + not in the span of the pair's covectors. + +So the partner term `x_b -> y_a` cannot come from a source register. It is delivered by a single-source +root from `b`'s injected leaf register. + +Moreover, on any fully orthogonal pair of port groups, the mod-2 block that the decoder needs is all-ones +(rank 1). Source mixing can therefore deliver only sums, never a Hadamard-type block like #144's `(P - A)/2`. +Within a cube, bit-orthogonality joins ports of the same parity class (two copies of K4), not ports of +opposite classes (K_{4,4}) as on the complex side. For this reason #144's involution itself has no bit analog. + +## Machine checks + +`check_paired_cube_bit.py` verifies the following: + +- `|c cap d| = 1` for every carrier and passive pair. +- `dim M = 2`, `chi_c, chi_d in M`, and `M` is nondegenerate. +- `M` lies in `C`, and `C` lies in the caps of the receivers. +- `C` is the frame of the receivers' level-2 root, and the delivery is scheduled right after that root. +- The carrier and passive chains are nested. +- Every source lies in exactly one pair. +- The literal F2 replay restores `X`. + +The mutation controls `broken_mix`, `outside_cap` and `below_level` are rejected. diff --git a/research/paired-cube-bit/README.md b/research/paired-cube-bit/README.md new file mode 100644 index 0000000000..d2f1d41a15 --- /dev/null +++ b/research/paired-cube-bit/README.md @@ -0,0 +1,106 @@ +# Paired-cube bit word with partner-pair source mixing + +This package is a bit-side analog of PR #144's paired-cube decoder, for integration on upstream main +`d1d6c07`. #144 is merged there. Standard library only; run every script without `-O`. + +| p | h | v | R | R/v | loss h(h-2) | deficit 2v-3l | W=2v+R | gauges | coarse a0 (cert) | effective a_b | +|---|---|---|---|---|---|---|---|---|---|---| +| 11 | 22 | 1320 | 18964 | 14.37 | 440 | 1320 | 21604 | 4290 | 5502556/10^10 | 5.4974380e-4 | +| **12** | **24** | **1760** | **19788** | **11.24** | **528** | **1936** | **23308** | **3960 (dim 20, 21)** | **6442936/10^10** | **6.4368777e-4** | +| 13 | 26 | 2288 | 33514 | 14.65 | 624 | 2704 | 38090 | 7436 | 5541517/10^10 | 5.5363601e-4 | + +At p = 12 the word uses the annealed pair module `data/pair_module_p12.json` and the nested-prefix all-but-one +module annealed from the nested prefix (`data/qmod_p12.json`) and the L1 local-channel association (`local_l1`), +and merges its +face-1/edge-01 and face-2/edge-02 outputs (variant u); +p = 11 and p = 13 keep the witness-cut modules, #144's balanced tree and single reads. In the repository tree the +p = 12 word runs a physical layer (`scripts/paired_cube_bit_physical.py`, frozen word in +`references/paired-cube/bit-physical`): late copies and late-read reuse raise its coarse saving to 6600253/10^10. + +The accounting is PR #144's bit ledger: + +- `m = 3h` and `W = 2v + R`; +- three copies of the local, source-data and target-data children; +- an exterior child of width `3 dim sigma` per gauge; +- `2v` finishing children of width 2; +- full `32 m^2` fallback. + +The effective saving is `(1 - 1e-3) a0 + 1e-3 * 384599/1e10`. For comparison: + +- PR #144's bit supplier has coarse `4617656/10^10`. +- The h=21 Fibonacci-strip bit word (PR I) has coarse `5201637/10^10`. + +So p=12 is +7.0% over the h=21 word and +20.5% over #144's bit supplier. + +## What the construction is + +The word is a mod-2 decoder on transversal triples: + + x_T = sum_{c in T} star(c) + sum_{|S cap T|=1} x_S. + +- **Ports and centres.** Coordinates are grouped into pairs, and ports are triples with one coordinate from + each of three pairs; `p = 12` gives `v = 8*C(12,3)`. The point stars over Q have span `h - 2`, so the + centre loss is `h(h - 2)`. +- **Side channels.** Disjoint cubes contribute nothing mod 2, so there is no disjoint-triple module. The + face channels are #144's pair modules, with the matching selector. The edge channels are #144's + all-but-one modules on `E00 + E11` and `E01 + E10`. +- **Within a cube.** Two of the three within-cube terms come from partner-pair sums mixed on the SOURCE + registers (`LEMMA.md`). The partner term is a single-source root. +- **Compile.** The PR #144 ledger on rational frames, with these choices: + - target cap `ker(3 chi_T - 1)`; + - coordinate-padded maximum matching, with frozen arcs; + - plain frames `span(n)` for additions of span dimension at most 8, the bit compiler's lifted-set rule; + - PR #144 chronological gauges with a G-nondegenerate sigma. + +## Run + + python3 paired_cube_bit_word.py --p 12 # regenerate out/*_p12.json (about 50 s) + python3 paired_cube_bit_word.py --p 12 --check # byte-identical regeneration of all p=12 outputs + python3 check_paired_cube_bit.py --dir out --p 12 # independent checker + 5 mutation controls (about 20 s) + python3 moment_certificate.py out/profile_p12.json --tree REPO --output out/certificate_p12.json + python3 derive_pair_modules.py --witness data/source_witness_21.json.gz --tree REPO --check # module pins + +Replace 12 with 11 or 13 for the variants (their outputs are not packaged; p = 12 is certified). + +## Status (PROVEN / COMPUTED / CONJECTURED) + +**PROVEN, written:** `LEMMA.md`, the partner-pair mixing step. It covers the frames, the sequential order +with no cross-talk, and why a full #144-type involution is impossible on the bit side. + +**COMPUTED, checked by `check_paired_cube_bit.py` with exact integer arithmetic:** + +- The 19,973 exported frames. +- The decoder identity, including the stars and `sum_{|S cap T|=1}` terms. +- Root, centre and source geometry. +- Every role chain nested, and every target chain nested. +- Phase one equals the centre closure, and the gauge target sets equal the response supports. +- The partner-pair chronology. +- G-nondegeneracy. +- A literal F2 replay with arbitrary dirty scratch. +- An independent recount that equals the saved child histogram. +- All controls rejected. + +**COMPUTED, exact rationals:** the moment certificate. The grid point passes and its successor is rejected. + +**Inherited, not re-checked here:** + +- the three-stage cover and completed-core sharing on the bit side (#130/#144 notes); +- the bit stage geometry per triple port (any triple has H0-norm 1); +- the weighted local-ring compile and fallback; +- the semantic assembly; +- the analytic and tape interfaces. + +PR97/Swapnil's checkers assume all `C(h,3)` triples and single-target outputs, so they do not apply to +this subset-port, broadcast-root word. `check_paired_cube_bit.py` replaces them. + +## Credits + +- Paired-cube decoder, modules and ledger: icekylinx PR #144, with OpenAI GPT-6 Astra and Codex assistance. +- PR117 DAG: eumemic, with Claude assistance. +- Bit-side compile conventions (deferred readouts, plain or lifted frames): Swapnil Jain / Zhihao Chen + PR97, and the h=21 bit compiler (eumemic, with Anthropic Claude assistance). +- p=11 and p=12 pair modules: cut from an h=21 Fibonacci-strip witness (eumemic, with Anthropic Claude + assistance), which descends from + ikeboy PR62's interval strips. +- Completed-core sharing: an664 PR128. +- The bit analog, partner-pair mixing, rational compiler and checker: eumemic, with Anthropic Claude assistance. diff --git a/research/paired-cube-bit/check_paired_cube_bit.py b/research/paired-cube-bit/check_paired_cube_bit.py new file mode 100644 index 0000000000..69d535a6c2 --- /dev/null +++ b/research/paired-cube-bit/check_paired_cube_bit.py @@ -0,0 +1,465 @@ +#!/usr/bin/env python3 +"""Standalone checker for subset-port bit words with broadcast roots (paired-cube bit word with partner-pair +source mixing). Standard library only; independent of the generator (own exact integer linear algebra, own +register simulation). Refuses to run under python -O. + +Inputs (plain JSON written by paired_cube_bit_word.py): graph_pP.json, word_pP.json, frames_pP.json, +kchron_pP.json, profile_pP.json. Checks: + 1. exact frames: every frame record (integer annihilator rows 'a' or integer basis rows 'b') is completed to + the other representation by exact integer elimination; A.B^T = 0 exactly and rank A + rank B = h; + 2. the mod-2 decoder: supports of all additions are disjoint; for every target the deliveries (star roots, + side roots, partner singles, partner-pair sums) XOR to {T}; stars read are exactly the c in T and the + side part is exactly sum_{|S cap T|=1} x_S; + 3. geometry: source frames are the lines ; side root frames lie in every receiver's cap + ker(3 chi_T - 1) and equal the common cap of the group; centre frames are the star spans; the frame of + every addition contains its operands' frames; every root node's frame lies in its root frame; + 4. every role chain (start -> each op frame -> root frame -> full) is nested, including gauged starts + (sigma inside the first op frame, gauged roles untouched in phase one); every target chain (gauge reads + ascending, side root caps in root order, partner-pair delivery at the level-2 cap, final cap) is nested; + the partner-pair chronology: mix frame span{chi_c,chi_d} with H0-Gram I_2, contained in the receivers' + level-2 cap, carrier chain [, mix, cap, full] and passive chain [, mix, full] nested; + 5. G = I - J/9 nondegenerate on every frame used (exact integer determinant test); + 6. literal F2 replay with arbitrary dirty scratch: y = y0 + x, scratch and sources restored; + 7. independent ledger recount from the role chains equals the saved child histogram (PR #144 bit ledger); + 8. mutation controls (must all be REJECTED): broken partner mix, delivery outside the shared cap (full + frame), delivery below the level (face cap without span{chi_c,chi_d}), dropped star, non-nested role chain. +Usage: python3 check_paired_cube_bit.py --dir out --p 12 +""" +import argparse, json, random, sys +from collections import Counter, defaultdict +from math import gcd +from operator import mul +from pathlib import Path + +if sys.flags.optimize: + raise SystemExit('refusing to run under python -O: assertions are part of the check') + + +class Fail(Exception): + pass + + +def need(cond, msg): + if not cond: + raise Fail(msg) + + +# ------------------------------------------------------------------ exact integer linear algebra +def prim(v): + g = 0 + for x in v: + g = gcd(g, abs(x)) + if g > 1: + v = [x // g for x in v] + f = next((x for x in v if x), 0) + return tuple(-x for x in v) if f < 0 else tuple(v) + + +def reduce_rows(rows, h): + """Integer reduced echelon form: returns (rows, pivot columns); each pivot column is zero outside its row.""" + rows = [list(r) for r in rows] + out, pivs = [], [] + for r in rows: + for pr, pc in zip(out, pivs): + if r[pc]: + a, b = pr[pc], r[pc] + r = [x * a - y * b for x, y in zip(r, pr)] + r = list(prim(r)) + c = next((j for j in range(h) if r[j]), None) + if c is None: + continue + for i, (pr, pc) in enumerate(zip(out, pivs)): + if pr[c]: + a, b = r[c], pr[c] + out[i] = list(prim([x * a - y * b for x, y in zip(pr, r)])) + out.append(r); pivs.append(c) + return out, pivs + + +def kernel(rows, h): + red, pivs = reduce_rows(rows, h) + ps = set(pivs) + basis = [] + for f in range(h): + if f in ps: + continue + D = 1 + for r, c in zip(red, pivs): + if r[f]: + D = D * abs(r[c]) // gcd(D, abs(r[c])) + v = [0] * h + v[f] = D + for r, c in zip(red, pivs): + if r[f]: + v[c] = -r[f] * D // r[c] + basis.append(prim(v)) + return basis, len(red) + + +def rank(rows, h): + return len(reduce_rows(rows, h)[0]) + + +def dot(a, b): + return sum(map(mul, a, b)) + + +# ------------------------------------------------------------------ checker +class Checker: + def __init__(self, d, p, mutate=None): + self.mut = mutate + rd = lambda name: json.loads((d / ('%s_p%d.json' % (name, p))).read_text()) + self.g, self.w, self.fr, self.k, self.prof = rd('graph'), rd('word'), rd('frames'), rd('kchron'), rd('profile') + self.h, self.v = self.g['h'], self.g['v'] + if mutate == 'dropped_star': + j = next(i for i, r in enumerate(self.g['roots']) if r['kind'] == 'center') + self.g['roots'][j]['targets'] = [] + if mutate == 'broken_mix': + self.k['entries'][0]['skip_mix'] = True + if mutate == 'outside_cap': + # raise the mixed carrier past the receivers' shared cap (to the full frame) and deliver there + e = self.k['entries'][0] + e['deliver_frame'] = self.w['full_frame'] + e['carrier_chain'][2] = e['deliver_frame'] + if mutate == 'below_level': + # deliver at the receivers' level-1 (face) cap, which does not contain span{chi_c, chi_d} + e = self.k['entries'][0] + face = next(j for j, r in enumerate(self.g['roots']) if r['kind'] == 'side' and set(e['receivers']) < set(r['targets'])) + e['deliver_frame'] = self.w['root_frame'][face] + e['carrier_chain'][2] = e['deliver_frame'] + if mutate == 'non_nested': + # move one addition's frame down to the frame of its smallest operand's source line + x = next(int(k) for k, f in sorted(self.w['node_frame'].items(), key=lambda kv: int(kv[0])) if int(k) >= self.v and str(int(k)) not in set(map(str, self.w['plain']))) + self.w['node_frame'][str(x)] = self.w['source_frame'][0] + + # ---------------- frames + def frames(self): + h = self.h + self.A, self.B, self.dimf = {}, {}, {} + for key, rec in self.fr['frames'].items(): + f = int(key) + if 'a' in rec: + A = [tuple(r) for r in rec['a']] + need(rank(A, h) == len(A), 'independent annihilator rows %d' % f) + B, _ = kernel(A, h) + else: + B = [tuple(r) for r in rec['b']] + need(rank(B, h) == len(B), 'independent basis rows %d' % f) + A, _ = kernel(B, h) + need(len(A) + len(B) == h and len(B) == rec['dim'], 'dimensions of frame %d' % f) + need(all(dot(a, b) == 0 for a in A for b in B), 'A.B = 0 for frame %d' % f) + self.A[f], self.B[f], self.dimf[f] = A, B, len(B) + self.cc = {} + return len(self.A) + + def sub(self, f1, f2): + """frame f1 contained in frame f2 (exact)""" + if f1 == f2: + return True + key = (f1, f2) + r = self.cc.get(key) + if r is None: + B1, A2 = self.B[f1], self.A[f2] + r = len(B1) <= len(self.B[f2]) and all(dot(a, b) == 0 for a in A2 for b in B1) + self.cc[key] = r + return r + + def in_frame(self, vec, f): + return all(dot(a, vec) == 0 for a in self.A[f]) + + def nondeg(self, f): + h = self.h + B, A = self.B[f], self.A[f] + if not B or len(B) == h: + return True + if len(B) <= len(A): + s = [sum(b) for b in B] + M = [[9 * dot(B[i], B[j]) - s[i] * s[j] for j in range(len(B))] for i in range(len(B))] + return rank(M, len(B)) == len(B) + s = [sum(a) for a in A] + M = [[(9 - h) * dot(A[i], A[j]) + s[i] * s[j] for j in range(len(A))] for i in range(len(A))] + return rank(M, len(A)) == len(A) + + # ---------------- decoder + def decoder(self): + g, v = self.g, self.v + args = g['args'] + lab = [frozenset(l) for l in g['labels']] + sup = [1 << i for i in range(v)] + [0] * (len(args) - v) + for x in range(v, len(args)): + a, b = args[x] + need(not sup[a] & sup[b], 'support-disjoint addition %d' % x) + sup[x] = sup[a] | sup[b] + self.sup = sup + acc, stars, side = [0] * v, [set() for _ in range(v)], [0] * v + for r in g['roots']: + need(r.get('coefficient', 1) == 1, 'mod-2 unit coefficients') + for t in r['targets']: + acc[t] ^= sup[r['node']] + if r['kind'] == 'center': + stars[t].add(r['coordinate']) + else: + side[t] ^= sup[r['node']] + for e in self.k['entries']: + for t in e['receivers']: + acc[t] ^= (1 << e['carrier']) | (1 << e['passive']) + side[t] ^= (1 << e['carrier']) | (1 << e['passive']) + for t in range(v): + need(acc[t] == 1 << t, 'decoder identity at target %d' % t) + need(stars[t] == set(lab[t]), 'stars read by target %d' % t) + orth = sum(1 << s for s in range(v) if len(lab[s] & lab[t]) == 1) + need(side[t] == orth, 'side part = sum over |S cap T| = 1 at target %d' % t) + for r in g['roots']: + if r['kind'] == 'center': + c = r['coordinate'] + need(sup[r['node']] == sum(1 << s for s in range(v) if c in lab[s]), 'star support %d' % c) + + # ---------------- geometry and chains + def geometry(self): + g, w, h, v = self.g, self.w, self.h, self.v + lab = g['labels'] + chi = [tuple(1 if j in l else 0 for j in range(h)) for l in lab] + cov = [tuple((3 if j in l else 0) - 1 for j in range(h)) for l in lab] + nf = {int(k): f for k, f in w['node_frame'].items()} + rf = w['root_frame'] + full = w['full_frame'] + need(self.dimf[full] == h, 'full frame') + for s in range(v): + f = w['source_frame'][s] + need(self.dimf[f] == 1 and self.in_frame(chi[s], f), 'source line ') + args = g['args'] + for x, f in nf.items(): + if x < v: + need(self.in_frame(chi[x], f), 'leaf label inside its frame') + else: + for y in args[x]: + need(self.sub(nf[y], f), 'operand frame inside node frame (%d <- %d)' % (x, y)) + loss = 0 + for j, r in enumerate(g['roots']): + f = rf[j] + need(self.sub(nf[r['node']], f), 'root node frame inside root frame %d' % j) + if r['kind'] == 'center': + c = r['coordinate'] + S = [chi[s] for s in range(v) if c in lab[s]] + need(all(self.in_frame(x, f) for x in S) and rank(S, h) == self.dimf[f], 'centre frame = star span') + loss += self.dimf[f] + else: + need(all(dot(cov[t], b) == 0 for t in r['targets'] for b in self.B[f]), 'root frame inside caps') + need(self.dimf[f] == h - rank([cov[t] for t in r['targets']], h), 'root frame = common cap') + need(loss == self.prof['loss'], 'copied-centre loss') + self.chi, self.cov, self.nf, self.rf = chi, cov, nf, rf + + def chains(self): + """Role chains of the physical word and target chains; returns the recounted child histogram.""" + g, w, h, v = self.g, self.w, self.h, self.v + nf, rf, full = self.nf, self.rf, w['full_frame'] + ops, rootroles = w['ops'], w['rootroles'] + R = 1 + max(max(a, b) for a, b, _ in ops) + R = max(R, 1 + max(rootroles), 1 + max(w['sources'].values())) + need(R == self.prof['R'], 'role count') + start = {} + for leaf, s in w['sources'].items(): + start[s] = w['source_frame'][int(leaf)] + phase1 = set(w['phase1']) + touched_p1 = set() + for i in phase1: + touched_p1.update(ops[i][:2]) + # phase one = closure of the centre roots' last ops under per-role precedence (recomputed) + prev_op, pred = {}, [] + for i, (a, b, _) in enumerate(ops): + pred.append((prev_op.get(a, -1), prev_op.get(b, -1))) + prev_op[a] = prev_op[b] = i + stack = [prev_op[s] for r, s in zip(g['roots'], rootroles) if r['kind'] == 'center' and s in prev_op] + closure = set() + while stack: + i = stack.pop() + if i not in closure: + closure.add(i); stack.extend(j for j in pred[i] if j >= 0) + need(closure == phase1, 'phase one is the centre closure') + # conservative response support of every role (union incidence through the XOR word) + co = [0] * R + for j, (r, s) in enumerate(zip(g['roots'], rootroles)): + for t in r['targets']: + co[s] |= 1 << t + for a, b, _ in reversed(ops): + co[b] |= co[a] + gauge_of = {} + for z in w['gauges']: + need(sum(1 << t for t in z['targets']) == co[z['role']], 'gauge targets = response support of its role') + s = z['role'] + need(s not in start, 'gauged role is not a source role') + need(s not in touched_p1, 'gauged role untouched in phase one') + need(self.dimf[z['frame']] == z['dim'] and z['dim'] > 0, 'gauge dimension') + need(self.nondeg(z['frame']), 'gauge frame nondegenerate') + start[s] = z['frame']; gauge_of[s] = z + seq = defaultdict(list) + for i, (a, b, x) in enumerate(ops): + f = nf[x] + seq[a].append(f); seq[b].append(f) + for j, s in enumerate(rootroles): + seq[s].append(rf[j]) + H = Counter() + for s in range(R): + chain = [start.get(s)] + seq[s] + [full] + prev = chain[0] + dprev = 0 if prev is None else self.dimf[prev] + if prev is not None and s not in gauge_of: + H[1] += 1 # source role: injection frame (entrance child of width 1) + for f in chain[1:]: + if prev is not None: + need(self.sub(prev, f), 'nested role chain (role %d)' % s) + d = self.dimf[f] + need(d >= dprev, 'ascending role chain (role %d)' % s) + if d > dprev: + H[d - dprev] += 1 + prev, dprev = f, d + for j, r in enumerate(g['roots']): + if r['kind'] == 'center': + H[self.dimf[rf[j]]] += 1 # copied-centre transform + # partner-pair chronology + src = Counter() + lab = [set(l) for l in g['labels']] + for e in self.k['entries']: + c, d = e['carrier'], e['passive'] + need(len(lab[c] & lab[d]) == 1, 'carrier and passive orthogonal (H0-Gram I_2)') + mf, cf = e['mix_frame'], e['deliver_frame'] + need(self.dimf[mf] == 2 and self.in_frame(self.chi[c], mf) and self.in_frame(self.chi[d], mf), 'mix frame = span{chi_c, chi_d}') + need(self.nondeg(mf), 'mix frame nondegenerate') + need(self.sub(mf, cf), 'mix frame inside the receivers shared cap') + need(all(dot(self.cov[t], b) == 0 for t in e['receivers'] for b in self.B[cf]), 'delivery frame inside receiver caps') + need(e['carrier_chain'][0] == w['source_frame'][c] and e['passive_chain'][0] == w['source_frame'][d], 'chains start at source lines') + need(e['carrier_chain'][1:] == [mf, cf, w['full_frame']] and e['passive_chain'][1:] == [mf, w['full_frame']], 'chain shape') + for ch in (e['carrier_chain'], e['passive_chain']): + for f1, f2 in zip(ch, ch[1:]): + need(self.sub(f1, f2), 'nested source-register chain') + for f1, f2 in zip(ch, ch[1:]): + src[self.dimf[f2] - self.dimf[f1]] += 1 + # target chains: gauge reads (time order = reverse selection order), side caps in root order, + # partner-pair delivery at the level-2 cap right after its root, final cap + events = defaultdict(list) + for z in reversed(w['gauges']): + for t in z['targets']: + events[t].append(z['frame']) + deliveries = defaultdict(list) + for e in self.k['entries']: + deliveries[e['deliver_after_root']].append(e) + for j, r in enumerate(g['roots']): + if r['kind'] == 'center': + continue + for t in r['targets']: + events[t].append(rf[j]) + for e in deliveries.get(j, []): + need(sorted(e['receivers']) == sorted(r['targets']), 'delivery after the receivers own level-2 root') + for t in e['receivers']: + events[t].append(e['deliver_frame']) + Y = Counter() + cap = {} + for t in range(v): + capf = None + prev, dprev = None, 0 + for f in events[t]: + if prev is not None: + need(self.sub(prev, f), 'nested target chain (target %d)' % t) + need(all(dot(self.cov[t], b) == 0 for b in self.B[f]), 'target frame inside cap (target %d)' % t) + if self.dimf[f] > dprev: + Y[self.dimf[f] - dprev] += 1 + prev, dprev = f, self.dimf[f] + need(dprev <= h - 1, 'target chain below the cap') + Y[h - 1 - dprev] += 1 if h - 1 - dprev else 0 + # every source register is in exactly one mixing pair + members = Counter() + for e in self.k['entries']: + members[e['carrier']] += 1; members[e['passive']] += 1 + need(all(members[s] == 1 for s in range(v)), 'each source in exactly one partner pair') + for f in set(self.nf.values()) | set(self.rf): + need(self.nondeg(f), 'G-nondegenerate frame %d' % f) + return H, Y, src, R + + # ---------------- replay + def replay(self, seeds=3): + g, w, v = self.g, self.w, self.v + ops, rootroles = w['ops'], w['rootroles'] + R = self.prof['R'] + srcmap = {int(k): s for k, s in w['sources'].items()} + roots = g['roots'] + for seed in range(seeds): + rng = random.Random(1000 + seed) + x = [rng.getrandbits(1) for _ in range(v)] + y0 = [rng.getrandbits(1) for _ in range(v)] + z0 = [rng.getrandbits(1) for _ in range(R)] + X, Yv, z = x[:], y0[:], z0[:] + # y <- y - J M z (old-value response of the dirty scratch) + zd = z0[:] + for a, b, _ in ops: + zd[a] ^= zd[b] + for j, r in enumerate(roots): + for t in r['targets']: + Yv[t] ^= zd[rootroles[j]] + for leaf, s in srcmap.items(): # z <- z + V x (at the rank-one source lines) + z[s] ^= X[leaf] + for a, b, _ in ops: # z <- M z + z[a] ^= z[b] + for j, r in enumerate(roots): # y <- y + J z + for t in r['targets']: + Yv[t] ^= z[rootroles[j]] + for e in self.k['entries']: # partner-pair sums on the source registers + if not e.get('skip_mix'): + X[e['carrier']] ^= X[e['passive']] + for t in e['receivers']: + Yv[t] ^= X[e['carrier']] + for e in self.k['entries']: # undo at the full frame + if not e.get('skip_mix'): + X[e['carrier']] ^= X[e['passive']] + for a, b, _ in reversed(ops): # z <- M^-1 z + z[a] ^= z[b] + for leaf, s in srcmap.items(): # z <- z - V x + z[s] ^= X[leaf] + need(all(Yv[t] == y0[t] ^ x[t] for t in range(v)), 'replay: y = y0 + x (seed %d)' % seed) + need(z == z0 and X == x, 'replay: scratch and sources restored (seed %d)' % seed) + + def run(self): + nfr = self.frames() + self.decoder() + self.geometry() + H, Y, src, R = self.chains() + self.replay() + h, v = self.h, self.v + m, W = 3 * h, 2 * v + R + C = Counter() + for part in (H, Y, src): + for r, c in part.items(): + if r and c: + C[r] += 3 * c + for z in self.w['gauges']: + C[3 * z['dim']] += 1 + C[2] += 2 * v + saved = {int(k): c for k, c in self.prof['child_histogram'].items()} + need(dict(C) == saved, 'independent recount equals the saved child histogram') + mass = sum(r * c for r, c in C.items()) + need(W == self.prof['W_per_vertex'] and W * m - mass == 2 * v - 3 * self.prof['loss'] == self.prof['deficit_per_vertex'], + 'W = 2v + R and deficit 2v - 3 ell') + return dict(frames=nfr, roles=R, W=W, m=m, deficit=W * m - mass, children=sum(C.values())) + + +def main(): + ap = argparse.ArgumentParser(description=__doc__) + ap.add_argument('--dir', type=Path, default=Path(__file__).resolve().parent / 'out') + ap.add_argument('--p', type=int, default=12) + ap.add_argument('--no-controls', action='store_true') + a = ap.parse_args() + res = Checker(a.dir, a.p).run() + print('PASS p=%d: %s' % (a.p, res)) + if a.no_controls: + return + for m in ('broken_mix', 'outside_cap', 'below_level', 'dropped_star', 'non_nested'): + try: + Checker(a.dir, a.p, mutate=m).run() + except Fail as e: + print('control %-13s REJECTED: %s' % (m, e)) + continue + raise SystemExit('FAIL: control %s was accepted' % m) + print('PASS: all 5 mutation controls rejected') + + +if __name__ == '__main__': + main() diff --git a/research/paired-cube-bit/data/arcs_p11.json b/research/paired-cube-bit/data/arcs_p11.json new file mode 100644 index 0000000000..4ce0080071 --- /dev/null +++ b/research/paired-cube-bit/data/arcs_p11.json @@ -0,0 +1 @@ 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--- /dev/null +++ b/research/paired-cube-bit/data/qmod_p12.json @@ -0,0 +1 @@ +{"args":[null,null,null,null,null,null,null,null,null,null,[6,4],[7,9],[11,8],[10,12],[5,13],[14,3],[2,15],[1,16],[2,0],[15,18],[1,15],[0,20],[0,1],[2,14],[22,23],[22,2],[12,6],[5,26],[3,27],[25,28],[25,3],[30,13],[30,4],[5,12],[32,33],[8,9],[35,6],[5,32],[36,37],[37,6],[39,11],[39,7],[41,8]],"input_count":10,"provenance":{"additions":33,"seed":"nested_prefix(10)","source":"simulated annealing with split-function moves; objective: float root of the p = 12 bit word (variant u, L1 local channels)"},"roots":[17,19,21,24,29,31,34,38,40,42]} diff --git a/research/paired-cube-bit/data/source_witness_21.json.gz b/research/paired-cube-bit/data/source_witness_21.json.gz new file mode 100644 index 0000000000..e9aae9b923 Binary files /dev/null and b/research/paired-cube-bit/data/source_witness_21.json.gz differ diff --git a/research/paired-cube-bit/derive_pair_modules.py b/research/paired-cube-bit/derive_pair_modules.py new file mode 100644 index 0000000000..8a37c88d0e --- /dev/null +++ b/research/paired-cube-bit/derive_pair_modules.py @@ -0,0 +1,122 @@ +#!/usr/bin/env python3 +"""Derive the pinned pair-disjoint modules (data/pair_module_p{11,12,13}.json). + +A pair-disjoint module on n points has inputs x_{ab} (pairs of [n]) and, for every pair {i,j}, the output +sum of x_{ab} over pairs disjoint from {i,j}. For fixed c, the bit outputs out(c,T) = sum_{S cap T = {c}} x_S +of a bit producer ARE such a query on the points other than c, so an exact zero restriction of a bit witness +to the triples {c,a,b} with a,b in a chosen n-set Z gives a module (support hash-consing, unary additions +contracted, inactive nodes pruned), exactly as PR #144's modules.restricted_pairs does for the PR117 DAG. + +p=11, p=12: cut from the h=21 Fibonacci-strip bit witness (p=12: pair_module_p12_cut.json, the seed of the + annealed pair_module_p12.json) (sha256 pinned below), c=14, + Z = 10 resp. 11 consecutive points (the minimum-addition cut, first in (c, cyclic start) order). +p=13: PR #144 modules.restricted_pairs(12) (PR117 DAG, pinned in the repository). +Usage: python3 derive_pair_modules.py --witness PATH/witness_21.json.gz --tree REPO_ROOT [--check] +""" +import argparse, gzip, hashlib, json, sys +from itertools import combinations +from pathlib import Path +HERE = Path(__file__).resolve().parent +WITNESS_SHA256 = None # filled by first run, then pinned in data/pair_module_provenance.json + + +def cut(w, c, Z): + Z = list(Z); n = len(Z); pos = {z: i for i, z in enumerate(Z)} + pairs = list(combinations(range(n), 2)); pid = {pp: i for i, pp in enumerate(pairs)} + args_w = {int(k): v for k, v in w['args'].items()} + leaf = {int(k): v for k, v in w['leaf'].items()} + args = [None] * len(pairs); support = [1 << i for i in range(len(pairs))]; by = {s: i for i, s in enumerate(support)} + image = {} + for x in sorted(args_w): + a = args_w[x] + if a is None: + T = leaf[x] + o = [t for t in T if t != c] + image[x] = pid[tuple(sorted(pos[t] for t in o))] if c in T and all(t in pos for t in o) else None + continue + ia, ib = image.get(a[0]), image.get(a[1]) + if ia is None or ib is None: + image[x] = ia if ib is None else ib + continue + assert not support[ia] & support[ib] + s = support[ia] | support[ib] + if s not in by: + by[s] = len(args); args.append([ia, ib]); support.append(s) + image[x] = by[s] + outs = {} + for cc, T, node in w['outputs']: + o = [t for t in T if t != c] + if cc == c and all(t in pos for t in o): + outs[tuple(sorted(pos[t] for t in o))] = image[node] + roots = [] + for (i, j) in pairs: + r = outs[(i, j)] + expected = sum(1 << k for k, (a, b) in enumerate(pairs) if i not in (a, b) and j not in (a, b)) + assert r is not None and support[r] == expected + roots.append(r) + active, stack = set(range(len(pairs))), list(roots) + while stack: + x = stack.pop() + if x not in active: + active.add(x) + if args[x] is not None: + stack.extend(args[x]) + ids = sorted(active); ren = {x: i for i, x in enumerate(ids)} + return dict(kind='pair_disjoint', n=n, input_count=len(pairs), input_labels=[list(p_) for p_ in pairs], + args=[None if args[x] is None else [ren[y] for y in args[x]] for x in ids], roots=[ren[x] for x in roots]) + + +def best_cut(w, n): + best = None + for c in range(w['h']): + others = [t for t in range(w['h']) if t != c] + for start in range(len(others)): + Z = sorted(others[(start + k) % len(others)] for k in range(n)) + m = cut(w, c, Z) + adds = len(m['args']) - m['input_count'] + if best is None or adds < best[0]: + best = (adds, c, Z, m) + return best + + +def dumps(o): + return json.dumps(o, sort_keys=True, separators=(',', ':')) + '\n' + + +def main(): + ap = argparse.ArgumentParser(description=__doc__) + ap.add_argument('--witness', type=Path, required=True) + ap.add_argument('--tree', type=Path, required=True) + ap.add_argument('--check', action='store_true') + a = ap.parse_args() + raw = a.witness.read_bytes() + wsha = hashlib.sha256(raw).hexdigest() + w = json.loads(gzip.decompress(raw)) + sys.path.insert(0, str(a.tree / 'scripts')) + from paired_cube.modules import restricted_pairs + dag = a.tree / 'references/three-stage-cover/pr117/dag.json.gz' + files = {} + prov = dict(witness_sha256=wsha, witness='h=21 Fibonacci-strip bit witness (data/source_witness_21.json.gz)', + pr117_dag_sha256=hashlib.sha256(dag.read_bytes()).hexdigest()) + for p in (11, 12): + adds, c, Z, m = best_cut(w, p - 1) + m['provenance'] = dict(source='bit witness cut', witness_sha256=wsha, c=c, Z=Z, additions=adds) + files['pair_module_p%d.json' % p if p == 11 else 'pair_module_p12_cut.json'] = dumps(m) + m = restricted_pairs(12) + m = dict(kind='pair_disjoint', n=12, input_count=m['input_count'], input_labels=[list(x) for x in m['input_labels']], + args=m['args'], roots=m['roots'], + provenance=dict(source='PR144 modules.restricted_pairs(12) of the PR117 DAG', pr117_dag_sha256=prov['pr117_dag_sha256'], + additions=len(m['args']) - m['input_count'])) + files['pair_module_p13.json'] = dumps(m) + files['pair_module_provenance.json'] = dumps(prov) + for name, text in files.items(): + path = HERE / 'data' / name + if a.check: + assert path.read_text() == text, name + else: + path.write_text(text) + print(('PASS' if a.check else 'wrote'), {k: len(v) for k, v in files.items()}) + + +if __name__ == '__main__': + main() diff --git a/research/paired-cube-bit/moment_certificate.py b/research/paired-cube-bit/moment_certificate.py new file mode 100644 index 0000000000..7a80fe24f1 --- /dev/null +++ b/research/paired-cube-bit/moment_certificate.py @@ -0,0 +1,130 @@ +#!/usr/bin/env python3 +"""Exact rational moment certificate for the paired-cube bit word under PR #144's bit accounting. + +Accounting (PR #144 notes/paired-cube-bit.tex and scripts/paired_cube_network.py, bit_certificate): + m = 3h, W = 2v + R per cover vertex; children = 3 x (local internal + source data + target data) + one + exterior child of width 3*dim(sigma) per selected gauge + 2v final children of width 2 (read from the profile). + Coarse saving a0 = k/10^10 passes iff, with rational upper bounds log_upper / exp_upper (32-term atanh series + with geometric tail; exp(u) <= 1+u+u^2/(2(1-u/3)); both rounded up to the grid 2^-120), + 1 - sum_r n_r r/(W m) * exp_upper(a0 * log_upper(m/r)) - added > 0, + added = 10^-16 * (32 m^2 * #children)/(W m) * exp_upper(a0 * log_upper(m)) (full local-ring fallback), + and the rank moment also contracts. Effective bit saving a_b = (1 - 10^-3) a0 + 10^-3 * 384599/10^10. +The certificate reports the largest k on the 10^-10 grid that passes and checks that k+1 is rejected. +log_upper / exp_upper / up are copied verbatim from PR #144 scripts/three_stage_cover_network.py (icekylinx, +Apache-2.0); with --tree REPO the copies are checked against the repository functions. +Usage: python3 moment_certificate.py out/profile_p12.json [--tree REPO] [--output cert.json] +""" +import argparse, json, sys +from fractions import Fraction as Q +from pathlib import Path + +GRID = 1 << 120 +BAD = Q(1, 10 ** 16) +ATOM = Q(1, 1000) +OLD = Q(384599, 10 ** 10) +STEP = 10 ** 10 + + +def require(c, msg): + if not c: + raise SystemExit('FAIL: ' + msg) + + +def up(x): + return Q((x.numerator * GRID + x.denominator - 1) // x.denominator, GRID) + + +def log_upper(x): + power = 0 + while x >= 2: + x /= 2 + power += 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(power * small(Q(2)) + small(x)) + + +def exp_upper(u): + require(0 <= u < 3, 'Exponential enclosure') + return up(1 + u + u * u / (2 * (1 - u / 3))) + + +def test(profile, k, logs, logm): + m, W = profile['m'], profile['W_per_vertex'] + H = {int(r): n for r, n in profile['child_histogram'].items()} + a0 = Q(k, STEP) + upper = sum(Q(n * r, W * m) * exp_upper(a0 * logs[r]) for r, n in H.items()) + edges = sum(H.values()) + fallback = 32 * m * m + added = BAD * Q(fallback * edges, W * m) * exp_upper(a0 * logm) + rank_upper = Q(sum(r * n for r, n in H.items())) + BAD * fallback * edges + ok = 1 - upper - added > 0 and rank_upper < W * m + return ok, dict(coarse=a0, moment_upper=upper, added_bad_moment_upper=added, strict_gap=1 - upper - added, + rank_mass_upper=rank_upper, fallback_children_per_edge=fallback, edge_count=edges) + + +def certify(profile): + h, v, R, ell = (profile[k] for k in ('h', 'v', 'R', 'loss')) + m, W = profile['m'], profile['W_per_vertex'] + require(m == 3 * h and W == 2 * v + R, 'PR144 bit accounting m=3h, W=2v+R') + H = {int(r): n for r, n in profile['child_histogram'].items()} + require(all(0 < r < m and n > 0 for r, n in H.items()), 'proper children') + mass = sum(r * n for r, n in H.items()) + require(mass == profile['rank_per_vertex'] and W * m - mass == 2 * v - 3 * ell == profile['deficit_per_vertex'], + 'telescoping deficit 2v - 3 ell') + logs = {r: log_upper(Q(m, r)) for r in H} + logm = log_upper(Q(m)) + lo, hi = 0, 10 ** 7 # a0 in [0, 1e-3) + require(test(profile, lo, logs, logm)[0], 'zero saving passes') + require(not test(profile, hi, logs, logm)[0], 'upper bracket rejected') + while hi - lo > 1: + mid = (lo + hi) // 2 + if test(profile, mid, logs, logm)[0]: + lo = mid + else: + hi = mid + ok, best = test(profile, lo, logs, logm) + nok, nxt = test(profile, lo + 1, logs, logm) + require(ok and not nok, 'largest grid point and rejected successor') + a0 = Q(lo, STEP) + ab = (1 - ATOM) * a0 + ATOM * OLD + require(ATOM > ab and ATOM < 1 - ab, 'subordinate adapter and row tolls') + require(Q(2 * m ** 3, 2 ** 80) < BAD, 'fixed prime bad-class allowance') + s = lambda q: '%d/%d' % (q.numerator, q.denominator) + return dict(h=h, v=v, R=R, loss=ell, m=m, W_per_vertex=W, rank_per_vertex=mass, deficit_per_vertex=W * m - mass, + coarse_saving=s(a0), coarse_saving_float=float(a0), strict_gap=s(best['strict_gap']), + strict_gap_float=float(best['strict_gap']), moment_upper=s(best['moment_upper']), + added_bad_moment_upper=s(best['added_bad_moment_upper']), rank_mass_upper=s(best['rank_mass_upper']), + next_grid_point=s(Q(lo + 1, STEP)), next_grid_gap_float=float(nxt['strict_gap']), next_grid_rejected=True, + atom_exponent=s(ATOM), ordinary_leaf_saving=s(OLD), effective_bit_saving=s(ab), effective_bit_saving_float=float(ab), + bad_fraction=s(BAD), fallback_children_per_edge=best['fallback_children_per_edge'], edge_count=best['edge_count'], + logarithm_upper_bounds={str(r): s(logs[r]) for r in sorted(logs)}, rounding_denominator=GRID, + method='PR144 bit_certificate: exact rational upper moment with full 32m^2 fallback on 1e-16 of every edge') + + +def main(): + require(not sys.flags.optimize, 'run without -O') + ap = argparse.ArgumentParser(description=__doc__) + ap.add_argument('profile', type=Path) + ap.add_argument('--tree', type=Path) + ap.add_argument('--output', type=Path) + a = ap.parse_args() + if a.tree: + sys.path.insert(0, str(a.tree / 'scripts')) + import three_stage_cover_network as t + for x in (Q(72, 5), Q(72), Q(66, 20), Q(78, 7)): + require(t.log_upper(x) == log_upper(x), 'log_upper equals repository function') + for u in (Q(1, 1000), Q(123, 10 ** 5)): + require(t.exp_upper(u) == exp_upper(u), 'exp_upper equals repository function') + cert = certify(json.loads(a.profile.read_text())) + text = json.dumps(cert, indent=1, sort_keys=True) + '\n' + if a.output: + a.output.write_text(text) + print('PASS coarse a0 = %s (%.10e), next grid point rejected; effective a_b = %s (%.10e)' % ( + cert['coarse_saving'], cert['coarse_saving_float'], cert['effective_bit_saving'], cert['effective_bit_saving_float'])) + + +if __name__ == '__main__': + main() diff --git a/research/paired-cube-bit/out/certificate_p12.json b/research/paired-cube-bit/out/certificate_p12.json new file mode 100644 index 0000000000..8ed0710cda --- /dev/null +++ b/research/paired-cube-bit/out/certificate_p12.json @@ -0,0 +1,55 @@ +{ + "R": 19788, + "W_per_vertex": 23308, + "added_bad_moment_upper": "455886296815655283786491281019826091801479/151277568973412202957236010551827496960000000000000000", + "atom_exponent": "1/1000", + "bad_fraction": "1/10000000000000000", + "coarse_saving": "805367/1250000000", + "coarse_saving_float": 0.0006442936, + "deficit_per_vertex": 1936, + "edge_count": 304024, + "effective_bit_saving": "6436877663/10000000000000", + "effective_bit_saving_float": 0.0006436877663, + "fallback_children_per_edge": 165888, + "h": 24, + "logarithm_upper_bounds": { + "1": "5684664334020965693831331240677363777/1329227995784915872903807060280344576", + "10": "1312001882868133107061488896308511211/664613997892457936451903530140172288", + "11": "2497314806457063515100369249596123659/1329227995784915872903807060280344576", + "12": "2381656848210652194302493466502442645/1329227995784915872903807060280344576", + "13": "1137630920156279732341064381896544223/664613997892457936451903530140172288", + "14": "272094431126872922090605886446602277/166153499473114484112975882535043072", + "15": "130315512045308539392073308841221045/83076749736557242056487941267521536", + "16": "499815445905580118231488502496862473/332306998946228968225951765070086144", + "17": "479669459767510575280471038897699499/332306998946228968225951765070086144", + "18": "1842701275199322610452688615344956943/1329227995784915872903807060280344576", + "19": "885416805516287189171116420374863439/664613997892457936451903530140172288", + "2": "2381656848210652194302493466502442653/664613997892457936451903530140172288", + "20": "1702653128136604908896633484944543951/1329227995784915872903807060280344576", + "21": "818899938001826896437521120207666249/664613997892457936451903530140172288", + "22": "1575964168857402209874024941923645187/1329227995784915872903807060280344576", + "3": "4224358123409974804755182081847399587/1329227995784915872903807060280344576", + "4": "3841963058821643083378642625332406835/1329227995784915872903807060280344576", + "5": "1772677201667963759674661050144750447/664613997892457936451903530140172288", + "6": "825751871452578374882209443543730279/332306998946228968225951765070086144", + "60": "121173458762807009910242163057289889/664613997892457936451903530140172288", + "63": "44373416348165725949723270396342081/332306998946228968225951765070086144", + "7": "3098106086614644681951191399245296687/1329227995784915872903807060280344576", + "8": "730153105305495444538074579414982091/332306998946228968225951765070086144", + "9": "1382025956399491957839516461508717707/664613997892457936451903530140172288" + }, + "loss": 528, + "m": 72, + "method": "PR144 bit_certificate: exact rational upper moment with full 32m^2 fallback on 1e-16 of every edge", + "moment_upper": "34854351890175390068006257922104927220627/34854351891474171561347176831141055299584", + "next_grid_gap_float": -1.4495248308671329e-10, + "next_grid_point": "6442937/10000000000", + "next_grid_rejected": true, + "ordinary_leaf_saving": "384599/10000000000", + "rank_mass_upper": "1023095703128078243/610351562500", + "rank_per_vertex": 1676240, + "rounding_denominator": 1329227995784915872903807060280344576, + "strict_gap": "46630675412288747330145331555079377673786689/1361498120760709826615124094966447472640000000000000000", + "strict_gap_float": 3.424953343764793e-11, + "v": 1760 +} diff --git a/research/paired-cube-bit/out/frames_p12.json b/research/paired-cube-bit/out/frames_p12.json new file mode 100644 index 0000000000..55ce1588e3 --- /dev/null +++ b/research/paired-cube-bit/out/frames_p12.json @@ -0,0 +1 @@ +{"P_used_for_ranks":"2^127-1","conventions":{"frame_ids":"frame id = id of the canonical annihilator; record \"a\" lists integer annihilator rows (frame = common kernel), record \"b\" lists integer basis rows; id 0 (empty \"a\") is the full space Q^h","gram":"G = I - J/9 on Q^h (H0 = G/2, H0(chi_S,chi_T) = (|S cap T|-1)/2); nondegeneracy tested for G","nodes":"zero-based graph nodes; nodes < v are the source leaves (port index)","ops":"[dest, control, node]: dest ^= control at the frame of node (copies: dest is the fresh role)","target_covector":"3*chi_T - 1 (target cap = {u : (3 chi_T - 1).u = 0} = H0-orthogonal complement of 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diff --git a/research/paired-cube-bit/out/graph_p12.json b/research/paired-cube-bit/out/graph_p12.json new file mode 100644 index 0000000000..c921ca680c --- /dev/null +++ b/research/paired-cube-bit/out/graph_p12.json @@ -0,0 +1 @@ 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2: Y_T += sum of root nodes whose targets contain T (star roots: T reads star(c) for c in T; side roots; partner singles) + x_carrier + x_passive for each partner_mix entry receiving T; equals x_T = sum_{c in T} star(c) + sum_{|S cap T|=1} 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reads of non-gauged roles (frame 0); V injections at ; ops in order (phase1 ops are those listed); centre copies read at 0; gauged old-value reads at their gauge frames (ascending per target); side root reads in root order; partial-K deliveries right after root deliver_after_root; undo at full frame; inverse ops; V 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diff --git a/research/paired-cube-bit/out/word_p12.json.gz b/research/paired-cube-bit/out/word_p12.json.gz new file mode 100644 index 0000000000..b2584ac8ca Binary files /dev/null and b/research/paired-cube-bit/out/word_p12.json.gz differ diff --git a/research/paired-cube-bit/paired_cube_bit_word.py b/research/paired-cube-bit/paired_cube_bit_word.py new file mode 100644 index 0000000000..1b8a381ba3 --- /dev/null +++ b/research/paired-cube-bit/paired_cube_bit_word.py @@ -0,0 +1,952 @@ +#!/usr/bin/env python3 +"""Paired-cube BIT local word with partner-pair source mixing: deterministic generator and rank compiler. + +Ports are the triples of [h] (h = 2p) taking one coordinate from each of three distinct coordinate pairs +(v = 8*C(p,3)); bit labels chi_S in Q^h with H0 = (I - J/9)/2, so H0(chi_S, chi_T) = (|S cap T| - 1)/2. +Payload F2. Mod-2 decoder, for every target T: + x_T = sum_{c in T} star(c) (2p copied point-star centres, frames of dim h-2) + + face channels P'(J,i,eta_i) (cubes sharing exactly pair i, matching selector) + + edge channels Q'(J,i,j,mode) (cubes sharing pairs i,j, exactly one selector match) + + partner x_{T'}, T' = T with the selectors of cube pairs 1,2 flipped (single-source root) + + partner-pair sum of the opposite pair of T's parity class, mixed on two SOURCE registers and + delivered at the shared cap of {T, T'} (no auxiliary role). +At p = 12 each cube merges its face-1 and edge-01 outputs into u(b0,b1) and its face-2 and edge-02 outputs into +w(b0,b2) (variant u); each merged node is read by two single roots and the mod-2 sums are unchanged. Its local +channels use the L1 association (local_l1): three of the six G sums add long face diagonals instead of edges. +Its all-but-one modules are the pinned annealed module data/qmod_p12.json (pinned_all_but_one). +Compiler: the PR #144 frames.py/gauges.py ledger on rational frames (target cap ker(3 chi_T - 1), centre frame = +span of the star), coordinate-padded maximum carrier matching (frozen arcs), plain frames span(n) for additions of +span dimension <= PLAIN (closed under operands; a linked donor's span must lie in the plain target), PR #144 +chronological partial gauges with a G-nondegeneracy filter, PR #144 bit ledger (m = 3h, W = 2v + R). +Linear algebra is exact: ranks are computed modulo the Mersenne prime 2^127-1, which exceeds the Hadamard bound +of every minor that occurs (see README.md); G-nondegeneracy is certified by integer Gram determinants. + +Usage: python3 paired_cube_bit_word.py --p 12 [--out DIR] [--check] [--solve-matching] +Standard library only. Run without -O. +""" +import argparse, gzip, hashlib, json, math, os, sys, time +from collections import Counter, defaultdict, deque +from itertools import combinations, product +from pathlib import Path + +HERE = Path(__file__).resolve().parent +P = (1 << 127) - 1 +PLAIN = 8 +L1_DIAGONAL = {(0, 1, 0), (0, 1, 1), (1, 2, 1)} # (cube positions j < k, mode) of the diagonal G sums at p = 12 +MODULES = {11: 'pair_module_p11.json', 12: 'pair_module_p12.json', 13: 'pair_module_p13.json'} +QMODULES = {12: 'qmod_p12.json'} + + +def require(cond, msg): + if not cond: + raise SystemExit('FAIL: ' + msg) + + +# ----------------------------------------------------------------------------- exact subspaces of F_P^h +def rref(rows, h): + piv = {} + for r in rows: + x = [a % P for a in r] + for c, y in piv.items(): + if x[c]: + f = x[c] + x = [(a - f * b) % P for a, b in zip(x, y)] + nz = next((j for j in range(h) if x[j]), None) + if nz is None: + continue + inv = pow(x[nz], P - 2, P) + x = [(a * inv) % P for a in x] + for c in list(piv): + y = piv[c] + if y[nz]: + f = y[nz] + piv[c] = [(a - f * b) % P for a, b in zip(y, x)] + piv[nz] = x + return tuple(tuple(piv[c]) for c in sorted(piv)) + + +def kernel(S, h): + pivs = [next(j for j in range(h) if row[j]) for row in S] + ps = set(pivs) + out = [] + for f in range(h): + if f in ps: + continue + u = [0] * h + u[f] = 1 + for row, c in zip(S, pivs): + u[c] = (-row[f]) % P + out.append(u) + return rref(out, h) + + +class Table: + """Interned subspaces (canonical RREF) with memoized joins; id 0 is the zero space.""" + def __init__(self, h): + self.h = h + self.rows = [()] + self.index = {(): 0} + self.jc = {} + self.pc = {} + + def intern(self, rows): + S = rref(rows, self.h) + i = self.index.get(S) + if i is None: + i = len(self.rows) + self.rows.append(S) + self.index[S] = i + return i + + def dim(self, i): + return len(self.rows[i]) + + def join(self, i, j): + if i == j or j == 0: + return i + if i == 0: + return j + if i > j: + i, j = j, i + k = self.jc.get((i, j)) + if k is None: + A, B = self.rows[i], self.rows[j] + k = i if len(A) == self.h else j if len(B) == self.h else self.intern(A + B) + self.jc[(i, j)] = k + return k + + def join_many(self, ids): + k = 0 + for i in ids: + k = self.join(k, i) + return k + + def contained(self, i, j): + return self.join(i, j) == j + + def perp(self, i): + k = self.pc.get(i) + if k is None: + k = self.intern(kernel(self.rows[i], self.h)) + self.pc[i] = k + return k + + +class Geometry: + """Bit geometry: source line ; target cap annihilated by 3 chi_T - 1 (the H0 = (I-J/9)/2 cap).""" + def __init__(self, h, labels): + self.h = h + self.T = Table(h) + self.src = [self.T.intern([[1 if j in lab else 0 for j in range(h)]]) for lab in labels] + self.tcov = [self.T.intern([[(3 if j in lab else 0) - 1 for j in range(h)]]) for lab in labels] + self.coord = [self.T.intern([[1 if k == j else 0 for k in range(h)]]) for j in range(h)] + + def join(self, a, b): return self.T.join(a, b) + def join_many(self, ids): return self.T.join_many(ids) + def dim(self, a): return self.T.dim(a) + def perp(self, a): return self.T.perp(a) + def contained(self, a, b): return self.T.contained(a, b) + + +def gram_nondegenerate_frame(rows, h): + """G = I - J/9 nondegenerate on the F_P-subspace with basis rows (exact sound test: an integer determinant + nonzero mod P is nonzero over Q; frames here are reductions of rational frames of the same dimension).""" + k = len(rows) + if k == 0: + return True + inv9 = pow(9, P - 2, P) + sums = [sum(s) % P for s in rows] + M = [[(sum(a * b for a, b in zip(rows[i], rows[j])) - inv9 * sums[i] * sums[j]) % P for j in range(k)] for i in range(k)] + return len(rref(M, k)) == k + + +# ----------------------------------------------------------------------------- graph +class BitGraph: + def __init__(self, p): + self.p, self.h = p, 2 * p + self.cubes = list(combinations(range(p), 3)) + self.labels = [tuple(2 * i + b for i, b in zip(I, bits)) for I in self.cubes for bits in product(range(2), repeat=3)] + self.a = [None] * len(self.labels) + self.s = [1 << i for i in range(len(self.labels))] + self.intern = {} + self.source = {(I, bits): 8 * j + k for j, I in enumerate(self.cubes) for k, bits in enumerate(product(range(2), repeat=3))} + self.A, self.G = {}, {} + self.root, self.centers, self.mix = [], [], [] + + def add(self, a, b): + if a is None: + return b + if b is None: + return a + if a > b: + a, b = b, a + if (a, b) not in self.intern: + require(not self.s[a] & self.s[b], 'support-disjoint addition') + self.intern[a, b] = len(self.a) + self.a.append([a, b]) + self.s.append(self.s[a] | self.s[b]) + return self.intern[a, b] + + def sum(self, xs): + xs = [x for x in xs if x is not None] + while len(xs) > 1: + xs = [self.add(xs[i], xs[i + 1]) if i + 1 < len(xs) else xs[i] for i in range(0, len(xs), 2)] + return xs[0] if xs else None + + def module(self, data, inputs): + image = list(inputs) + n = data['input_count'] + require(len(image) == n, 'module arity') + for pair in data['args'][n:]: + image.append(self.add(image[pair[0]], image[pair[1]])) + return [image[x] for x in data['roots']] + + def local_channels(self): + for I in self.cubes: + src = lambda bits: self.source[I, tuple(bits)] + edges = {} + for ii, jj in combinations(range(3), 2): + kk = 3 - ii - jj + for a, b in product(range(2), repeat=2): + b0 = [0] * 3 + b0[ii], b0[jj] = a, b + b1 = b0[:] + b1[kk] = 1 + edges[ii, jj, a, b] = self.add(src(b0), src(b1)) + self.G[I, I[ii], I[jj], 0] = self.add(edges[ii, jj, 0, 0], edges[ii, jj, 1, 1]) + self.G[I, I[ii], I[jj], 1] = self.add(edges[ii, jj, 0, 1], edges[ii, jj, 1, 0]) + for ii in range(3): + jj = next(j for j in range(3) if j != ii) + for a in range(2): + ids = [edges[(ii, jj, a, b) if ii < jj else (jj, ii, b, a)] for b in range(2)] + self.A[I, I[ii], a] = self.add(*ids) + + def local_l1(self): + """L1 local-channel association (eumemic, Claude assistance): the G sums listed in L1_DIAGONAL add the two + long diagonals of their cube face, the other G sums and the A sums add two edges; same supports as + local_channels, with the nodes created in channel order.""" + for I in self.cubes: + def at(bits): + b = [0] * 3 + for q, x in bits.items(): + b[q] = x + return self.source[I, tuple(b)] + + def edge(d, fixed): + return self.add(at({**fixed, d: 0}), at({**fixed, d: 1})) + for j, k in combinations(range(3), 2): + r = 3 - j - k + for mode in range(2): + if (j, k, mode) in L1_DIAGONAL: + node = self.add(self.add(at({j: 0, k: mode, r: 0}), at({j: 1, k: 1 - mode, r: 1})), + self.add(at({j: 0, k: mode, r: 1}), at({j: 1, k: 1 - mode, r: 0}))) + else: + node = self.add(edge(r, {j: 0, k: mode}), edge(r, {j: 1, k: 1 - mode})) + self.G[I, I[j], I[k], mode] = node + for i in range(3): + j, k = [q for q in range(3) if q != i] + for a in range(2): + self.A[I, I[i], a] = self.add(edge(k, {i: a, j: 0}), edge(k, {i: a, j: 1})) + + def finish(self, pair, allbut, merge=False, l1=False): + p = self.p + self.local_l1() if l1 else self.local_channels() + Pm, Qm = {}, {} + for i in range(p): + pairs = list(combinations([a for a in range(p) if a != i], 2)) + for bit in range(2): + for K, node in zip(pairs, self.module(pair, [self.A[tuple(sorted((i, *K))), i, bit] for K in pairs])): + Pm[tuple(sorted((i, *K))), i, bit] = node + for i, j in combinations(range(p), 2): + others = [a for a in range(p) if a not in (i, j)] + for mode in range(2): + for k, node in zip(others, self.module(allbut, [self.G[tuple(sorted((i, j, k))), i, j, mode] for k in others])): + Qm[tuple(sorted((i, j, k))), i, j, mode] = node + allb = list(product(range(2), repeat=3)) + + def emit(I, bl, node, channel): + self.root.append(dict(node=node, targets=[self.source[I, b] for b in bl], kind='side', channel=channel)) + for I in self.cubes: + for a in range(2): + emit(I, [b for b in allb if b[0] == a], Pm[I, I[0], a], 'face0') + for a in range(2): + for m12 in range(2): + emit(I, [b for b in allb if b[0] == a and (b[1] ^ b[2]) == m12], Qm[I, I[1], I[2], 1 - m12], 'edge12') + if merge: + # variant u output merge (eumemic, Claude assistance): u(b0,b1) = face1 + edge01 and + # w(b0,b2) = face2 + edge02, each read by two single roots, replace the four single reads + u = {(b0, b1): self.add(Pm[I, I[1], b1], Qm[I, I[0], I[1], 1 - (b0 ^ b1)]) for b0 in range(2) for b1 in range(2)} + w = {(b0, b2): self.add(Pm[I, I[2], b2], Qm[I, I[0], I[2], 1 - (b0 ^ b2)]) for b0 in range(2) for b2 in range(2)} + for b in allb: + if merge: + emit(I, [b], u[b[0], b[1]], 'u01') + emit(I, [b], w[b[0], b[2]], 'w02') + else: + emit(I, [b], Pm[I, I[1], b[1]], 'face1') + emit(I, [b], Qm[I, I[0], I[1], 1 - (b[0] ^ b[1])], 'edge01') + emit(I, [b], Pm[I, I[2], b[2]], 'face2') + emit(I, [b], Qm[I, I[0], I[2], 1 - (b[0] ^ b[2])], 'edge02') + emit(I, [b], self.source[I, (b[0], 1 - b[1], 1 - b[2])], 'partner') + # partner-pair source mixing: in each parity class the pair with selector a on cube pair 0 + # (carrier = smaller bits, passive = its partner) is delivered to the opposite pair of the class. + for par in range(2): + for a in range(2): + pair_ = sorted(b for b in allb if sum(b) % 2 == par and b[0] == a) + recv = sorted(b for b in allb if sum(b) % 2 == par and b[0] == 1 - a) + self.mix.append(dict(carrier=self.source[I, pair_[0]], passive=self.source[I, pair_[1]], + receivers=[self.source[I, r] for r in recv])) + for i in range(p): + for e in range(2): + self.centers.append(self.sum(self.A[I, i, e] for I in self.cubes if i in I)) + for coordinate, node in enumerate(self.centers): + self.root.append(dict(node=node, targets=[t for t, lab in enumerate(self.labels) if coordinate in lab], + kind='center', coordinate=coordinate)) + return dict(p=p, h=self.h, v=len(self.labels), labels=[list(l) for l in self.labels], args=self.a, + roots=self.root, partner_mix=self.mix) + + +def check_decoder(g): + v, args = g['v'], g['args'] + sup = [1 << i for i in range(v)] + [0] * (len(args) - v) + for x in range(v, len(args)): + a, b = args[x] + require(not sup[a] & sup[b], 'disjoint supports') + sup[x] = sup[a] | sup[b] + acc = [0] * v + for r in g['roots']: + for t in r['targets']: + acc[t] ^= sup[r['node']] + for mx in g['partner_mix']: + for t in mx['receivers']: + acc[t] ^= (1 << mx['carrier']) | (1 << mx['passive']) + return sum(acc[t] != 1 << t for t in range(v)) + + +# ----------------------------------------------------------------------------- matching +def hopcroft_karp(adj, nleft, nright): + INF = 1 << 30 + mL, mR = [-1] * nleft, [-1] * nright + while True: + dist = [INF] * nleft + dq = deque(u for u in range(nleft) if mL[u] < 0) + for u in dq: + dist[u] = 0 + found = False + while dq: + u = dq.popleft() + for w in adj[u]: + m = mR[w] + if m < 0: + found = True + elif dist[m] == INF: + dist[m] = dist[u] + 1 + dq.append(m) + if not found: + return mL + it = [0] * nleft + for u0 in range(nleft): + if mL[u0] >= 0: + continue + stack = [u0] + while stack: + u = stack[-1] + if it[u] < len(adj[u]): + w = adj[u][it[u]] + it[u] += 1 + m = mR[w] + if m < 0: + ws = w + for uu in reversed(stack): + prev = mL[uu] + mL[uu], mR[ws] = ws, uu + ws = prev + break + if dist[m] == dist[u] + 1: + stack.append(m) + else: + dist[u] = INF + stack.pop() + + +# ----------------------------------------------------------------------------- compiler +def compile_word(g, frozen=None, plain_k=PLAIN, log=lambda *a: None): + h, v = g['h'], g['v'] + geo = Geometry(h, [tuple(l) for l in g['labels']]) + args = [None] + [None if a is None else [x + 1 for x in a] for a in g['args']] # node 0 reserved + roots = [dict(r, node=r['node'] + 1) for r in g['roots']] + n, q = len(args), len(roots) + sup = [0] * n + for i in range(v): + sup[i + 1] = 1 << i + spans = [0] * n + for i in range(v): + spans[i + 1] = geo.src[i] + for x in range(v + 1, n): + a, b = args[x] + spans[x] = geo.join(spans[a], spans[b]) + sup[x] = sup[a] | sup[b] + rframe, rann, ell = [], [], 0 + Y, targetH = [0] * v, Counter() + for r in roots: + x = r['node'] + if r['kind'] == 'center': + U = spans[x]; A = geo.perp(U); ell += geo.dim(U) + else: + A = geo.join_many(geo.tcov[t] for t in r['targets']); U = geo.perp(A) + for t in r['targets']: + require(geo.contained(Y[t], U), 'target retreat') + targetH[geo.dim(U) - geo.dim(Y[t])] += 1 + Y[t] = U + require(geo.contained(spans[x], U), 'root physical compatibility') + rframe.append(U); rann.append(A) + for t in range(v): + require(geo.contained(Y[t], geo.perp(geo.tcov[t])), 'target cap') + targetH[h - 1 - geo.dim(Y[t])] += 1 + active, todo = set(range(1, v + 1)), [r['node'] for r in roots] + while todo: + x = todo.pop() + if x not in active: + active.add(x) + if args[x]: + todo.extend(args[x]) + succ0, cons = [[] for _ in args], [[] for _ in args] + for x in sorted(active): + if args[x]: + for y in args[x]: + succ0[y].append(x) + for j, r in enumerate(roots): + cons[r['node']].append(rann[j]) + preann, initial = [0] * n, [0] * n + for x in sorted(active, reverse=True): + preann[x] = geo.join_many(cons[x] + [preann[y] for y in succ0[x]]) + cover = 0 + s = sup[x] + while s: + b = s & -s; s ^= b + for j in g['labels'][b.bit_length() - 1]: + cover |= 1 << j + initial[x] = geo.join_many([preann[x]] + [geo.coord[j] for j in range(h) if not cover >> j & 1]) + order = sorted(active, key=lambda x: (h - geo.dim(initial[x]), x)) + position = {x: i for i, x in enumerate(order)} + uses, usevalue, usetarget, useann, usecode = [[] for _ in args], [], [], [], [] + for x in order: + if args[x]: + for j, y in enumerate(args[x]): + uses[y].append(len(usevalue)); usevalue.append(y); usetarget.append(x); useann.append(initial[x]); usecode.append(['op', x - 1, j]) + for j, r in enumerate(roots): + x = r['node'] + uses[x].append(len(usevalue)); usevalue.append(x); usetarget.append(n + j); useann.append(rann[j]); usecode.append(['root', j]) + donors = [x for x in order if args[x]] + code_index = {tuple(c): u for u, c in enumerate(usecode)} + if frozen is not None: + arcs = {d + 1: code_index[tuple(c)] for d, c in frozen} + else: + dindex = {x: i for i, x in enumerate(donors)} + adj = [[] for _ in donors] + for x in donors: + for y in args[x]: + for u in uses[y]: + t = usetarget[u] + if t == x or (t < n and position[t] <= position[x]): + continue + if geo.contained(useann[u], initial[x]): + adj[dindex[x]].append(u) + mL = hopcroft_karp(adj, len(donors), len(usevalue)) + arcs = {donors[i]: u for i, u in enumerate(mL) if u >= 0} + for x, u in arcs.items(): + t = usetarget[u] + require(usevalue[u] in args[x] and (t >= n or position[t] > position[x]), 'arc order') + require(geo.contained(useann[u], initial[x]), 'arc frame') + succ, direct = [[] for _ in args], [[] for _ in args] + for x in order: + if args[x]: + for y in args[x]: + succ[y].append(x) + for j, r in enumerate(roots): + direct[r['node']].append(rann[j]) + for x, u in arcs.items(): + t = usetarget[u] + (succ[x].append(t) if t < n else direct[x].append(rann[t - n])) + ann, rank = [0] * n, [0] * n + for x in reversed(order): + ann[x] = geo.join_many(direct[x] + [ann[y] for y in succ[x]]) + rank[x] = h - geo.dim(ann[x]) + require(geo.contained(ann[x], geo.perp(spans[x])), 'span inside frame') + # plain frames span(n): leaves and small additions, closed under operands; a linked donor must be plain and + # its span must lie in the plain target's span + cand = set(x for x in active if not args[x]) + for x in sorted(active): + if args[x] and geo.dim(spans[x]) <= plain_k and all(y in cand for y in args[x]): + cand.add(x) + arcin, users = defaultdict(list), defaultdict(list) + for x, u in arcs.items(): + if usetarget[u] < n: + arcin[usetarget[u]].append(x) + for x in active: + if args[x]: + for y in args[x]: + users[y].append(x) + changed = True + while changed: + changed = False + for t in sorted(cand): + if t in cand and any(x not in cand or not geo.contained(spans[x], spans[t]) for x in arcin[t]): + cand.discard(t); changed = True + st = [t] + while st: + z = st.pop() + for w in users[z]: + if w in cand: + cand.discard(w); st.append(w) + plain = sorted(cand) + for x in plain: + ann[x] = geo.perp(spans[x]); rank[x] = h - geo.dim(ann[x]) + H = Counter() + for x in order: + r, deg = rank[x], len(uses[x]) + require(deg > 0, 'unused node') + H[r] += deg - 1 + if args[x]: + H[h - r] += 1 + for y in args[x]: + require(geo.contained(ann[x], ann[y]), 'operand nesting') + H[r - rank[y]] += 1 + else: + H[1] += 1; H[r - 1] += 1 + for j, root in enumerate(roots): + x = root['node']; r = rank[x]; rt = geo.dim(rframe[j]) + require(r <= rt, 'root climb') + if root['kind'] == 'center': + require(r == rt, 'centre frame') + H[r] += 1; H[h - r] += 1 + else: + H[rt - r] += 1; H[h - rt] += 1 + for x, u in arcs.items(): + val, t = usevalue[u], usetarget[u] + rv, rd = rank[val], rank[x] + rt = rank[t] if t < n else geo.dim(rframe[t - n]) + require(rt >= rd >= rv, 'arc ranks') + H[h - rd] -= 1; H[rv] -= 1; H[rt - rv] -= 1; H[rt - rd] += 1 + require(min(H.values()) >= 0, 'nonnegative ledger') + R = len(donors) + q - len(arcs) + require(sum(r * c for r, c in H.items()) == h * R + ell, 'mass identity') + prof = dict(h=h, v=v, R=R, q=q, c=len(donors), matched=len(arcs), loss=ell, plain=len(plain)) + wit = dict(geo=geo, args=args, roots=roots, n=n, order=order, arcs=arcs, ann=ann, rank=rank, uses=uses, + usevalue=usevalue, usetarget=usetarget, usecode=usecode, rframe=rframe, rann=rann, spans=spans, + plain=plain, H=H, targetH=targetH) + return prof, wit + + +def nondeg_id(geo, f, cache): + if f not in cache: + cache[f] = gram_nondegenerate_frame(list(geo.T.rows[f]), geo.h) + return cache[f] + + +def select_gauges(g, prof, wit, trial_a=0.00065): + """PR #144 gauges.select, exactly, plus the bit G-nondegeneracy filter on sigma.""" + geo = wit['geo']; h, v = prof['h'], prof['v'] + args, roots, n, order, ann, arcs = wit['args'], wit['roots'], wit['n'], wit['order'], wit['ann'], wit['arcs'] + usevalue, usetarget = wit['usevalue'], wit['usetarget'] + incoming = set(arcs.values()) + uses, opuse, rootuse = [[] for _ in args], {}, {} + for u, (val, t) in enumerate(zip(usevalue, usetarget)): + uses[val].append(u) + if t < n: + opuse[t, 0 if args[t][0] == val else 1] = u + else: + rootuse[t - n] = u + assign, sources, ops, R = {}, {}, [], 0 + for x in order: + if args[x]: + aa, bb = args[x] + dest, control = assign[opuse[x, 0]], assign[opuse[x, 1]] + if x in arcs: + u = arcs[x] + if usevalue[u] == aa: + dest, control = control, dest + require(u not in assign, 'arc use assigned once') + assign[u] = control + ops.append((dest, control, x)) + else: + dest = R; R += 1; sources[x] = dest + free = [u for u in uses[x] if u not in incoming] + require(free, 'free use') + for j, u in enumerate(free): + if j == 0: + assign[u] = dest + else: + t = R; R += 1; assign[u] = t; ops.append((t, dest, x)) + require(R == prof['R'], 'role count') + rootroles = [assign[rootuse[j]] for j in range(len(roots))] + prev, pred, first = [-1] * R, [], [None] * R + for i, (a, b, x) in enumerate(ops): + pred.append((prev[a], prev[b])); prev[a] = prev[b] = i + if first[a] is None: + first[a] = x + if first[b] is None: + first[b] = x + stack = [prev[s] for r, s in zip(roots, rootroles) if r['kind'] == 'center' and prev[s] >= 0] + phase = set() + while stack: + i = stack.pop() + if i not in phase: + phase.add(i); stack.extend(j for j in pred[i] if j >= 0) + touched = set(sources.values()) + for i in phase: + touched.update(ops[i][:2]) + co = [0] * R + for r, s in zip(roots, rootroles): + co[s] |= sum(1 << t for t in r['targets']) + for a, b, x in reversed(ops): + co[b] |= co[a] + limit = [None] * v + for r in roots: + if r['kind'] != 'center': + A = geo.join_many(geo.tcov[t] for t in r['targets']) + for t in r['targets']: + if limit[t] is None: + limit[t] = A + for t in range(v): + if limit[t] is None: + limit[t] = geo.tcov[t] + H = Counter(wit['H']) + gauges, selected, cache = Counter(), [], {} + cands = sorted((s for s in range(R) if s not in touched and first[s] is not None), + key=lambda s: (geo.dim(ann[first[s]]), bin(co[s]).count('1'), s)) + + def excess(t): + return t * math.expm1(trial_a * math.log(3 * h / t)) if t else 0. + for s in cands: + A, targets, bits = ann[first[s]], [], co[s] + while bits: + low = bits & -bits; t = low.bit_length() - 1; bits ^= low; targets.append(t) + A = geo.join(A, limit[t]) + if geo.dim(A) == h: + break + if geo.dim(A) == h: + continue + r, d = h - geo.dim(ann[first[s]]), h - geo.dim(A) + delta = 3 * (excess(r - d) - excess(r)) + excess(3 * d) + delta += 3 * math.fsum(excess(d) + excess(h - geo.dim(limit[t]) - d) - excess(h - geo.dim(limit[t])) for t in targets) + if delta >= -1e-12 or not nondeg_id(geo, geo.perp(A), cache): + continue + H[r] -= 1; H[r - d] += 1; gauges[d] += 1 + require(H[r] >= 0, 'gauge ledger') + for t in targets: + limit[t] = A + selected.append(dict(role=s, first=first[s] - 1, targets=targets, dim=d, ann=A)) + Yh, cur = Counter(), [0] * v + for z in reversed(selected): + U = geo.perp(z['ann']) + for t in z['targets']: + require(geo.contained(cur[t], U), 'gauge target chain') + Yh[geo.dim(U) - geo.dim(cur[t])] += 1; cur[t] = U + for r in roots: + if r['kind'] != 'center': + U = geo.perp(geo.join_many(geo.tcov[t] for t in r['targets'])) + for t in r['targets']: + require(geo.contained(cur[t], U), 'side target chain') + Yh[geo.dim(U) - geo.dim(cur[t])] += 1; cur[t] = U + for t in range(v): + Yh[h - 1 - geo.dim(cur[t])] += 1 + word = dict(ops=[[a, b, x - 1] for a, b, x in ops], sources={str(x - 1): s for x, s in sources.items()}, + rootroles=rootroles, phase1=sorted(phase), gauges=[{k: z[k] for k in ('role', 'first', 'targets', 'dim')} for z in selected], + _gauge_ann=[z['ann'] for z in selected]) + return gauges, H, Yh, word + + +def profile(prof, gauges, H, Y): + h, v, R, ell = prof['h'], prof['v'], prof['R'], prof['loss'] + m, W = 3 * h, 2 * v + R + source = Counter({1: v, h - 4: v // 2, 2: v // 2, h - 2: v // 2}) + C = Counter() + for part in (H, source, Y): + for r, c in part.items(): + if r and c: + C[r] += 3 * c + for d, c in gauges.items(): + C[3 * d] += c + C[2] += 2 * v + mass = sum(r * c for r, c in C.items()) + require(W * m - mass == 2 * v - 3 * ell, 'shared-core telescoping deficit') + srt = lambda c: {str(k): c[k] for k in sorted(c) if c[k]} + return dict(h=h, v=v, R=R, c=prof['c'], q=prof['q'], matched=prof['matched'], loss=ell, plain_frames=prof['plain'], + m=m, W_per_vertex=W, rank_per_vertex=mass, deficit_per_vertex=W * m - mass, + selected_roles=sum(gauges.values()), selected_rank_histogram=srt(gauges), + remaining_internal_histogram=srt(H), source_data_histogram=srt(source), target_data_histogram=srt(Y), + child_histogram=srt(C), maxchild=max(C)) + + +def float_root(child, W, m): + items = [(int(t), c) for t, c in child.items()] + lo, hi = 0., .1 + for _ in range(80): + a = (lo + hi) / 2 + if math.fsum(c * (t / m) ** (1 - a) for t, c in items) < W: + lo = a + else: + hi = a + return lo + + +def ratrec(r): + """Rational reconstruction a/b of a residue mod P with |a|, b < sqrt(P/2).""" + r %= P + if r == 0: + return 0, 1 + bound = math.isqrt(P // 2) + r0, r1, s0, s1 = P, r, 0, 1 + while r1 > bound: + qq = r0 // r1 + r0, r1 = r1, r0 - qq * r1 + s0, s1 = s1, s0 - qq * s1 + require(abs(s1) <= bound and s1 != 0, 'rational reconstruction') + a, b = (r1, s1) if s1 > 0 else (-r1, -s1) + require((a - r * b) % P == 0, 'reconstruction residue') + return a, b + + +def primitive(row): + from fractions import Fraction + fr = [Fraction(*ratrec(x)) for x in row] + den = 1 + for f in fr: + den = den * f.denominator // math.gcd(den, f.denominator) + ints = [int(f * den) for f in fr] + gg = 0 + for x in ints: + gg = math.gcd(gg, abs(x)) + ints = [x // gg for x in ints] if gg else ints + first = next((x for x in ints if x), 1) + return [-x for x in ints] if first < 0 else ints + + +def frame_record(geo, ann_id): + """Exact integer description of the frame perp(ann): 'a' = integer annihilator rows (frame = common kernel) + when codim <= dim, else 'b' = integer basis rows. Both are primitive rows of the rational RREF.""" + h = geo.h + A = geo.T.rows[ann_id] + codim = len(A) + if codim <= h - codim: + rows = [primitive(r) for r in A] + return dict(dim=h - codim, a=rows) + B = geo.T.rows[geo.perp(ann_id)] + return dict(dim=h - codim, b=[primitive(r) for r in B]) + + +def dumps(obj): + return json.dumps(obj, sort_keys=True, separators=(',', ':')) + '\n' + + +def build(p, frozen_arcs=None, log=print): + mod = json.loads((HERE / 'data' / MODULES[p]).read_text()) + abo = pinned_all_but_one(QMODULES[p], p - 2) if p in QMODULES else all_but_one(p - 2) + g = BitGraph(p).finish(mod, abo, merge=p == 12, l1=p == 12) + require(check_decoder(g) == 0, 'mod-2 decoder identity') + t0 = time.time() + prof, wit = compile_word(g, frozen=frozen_arcs) + log('compiled p=%d in %.1fs: R=%d arcs=%d plain=%d' % (p, time.time() - t0, prof['R'], prof['matched'], prof['plain'])) + gauges, H, Y, word = select_gauges(g, prof, wit) + prf = profile(prof, gauges, H, Y) + arcs = sorted([x - 1, wit['usecode'][u]] for x, u in wit['arcs'].items()) + cache = {} + geo = wit['geo'] + deg = sum(1 for x in wit['order'] if not nondeg_id(geo, geo.perp(wit['ann'][x]), cache)) + deg += sum(1 for U in wit['rframe'] if not nondeg_id(geo, U, cache)) + require(deg == 0, 'G-nondegenerate node and root frames') + out = dict(graph=dict(p=p, h=g['h'], v=g['v'], labels=g['labels'], args=g['args'], roots=g['roots'], + partner_mix=g['partner_mix'], pair_module_sha256=hashlib.sha256((HERE / 'data' / MODULES[p]).read_bytes()).hexdigest()), + compile=dict(plain_threshold=PLAIN, order=[x - 1 for x in wit['order']], plain=[x - 1 for x in wit['plain']], arcs=arcs), + word={k: v for k, v in word.items() if not k.startswith('_')}) + exp = export(p, g, prof, wit, word, prf) + return out, prf, arcs, exp + + +def export(p, g, prof, wit, word, prf): + """Plain-JSON gate files: graph, word (selection.json shape), exact frames, partial-K chronology.""" + geo, h, v = wit['geo'], g['h'], g['v'] + n, roots = wit['n'], wit['roots'] + ann = wit['ann'] + frames = {} + + def fid(a): + if a not in frames: + frames[a] = None + return a + node_frame = {str(x - 1): fid(ann[x]) for x in wit['order']} + root_frame = [fid(a) for a in wit['rann']] + gauges = [] + for z, A in zip(word['gauges'], word['_gauge_ann']): + gauges.append(dict(z, frame=fid(A))) + lab = g['labels'] + src_ann = [fid(geo.perp(geo.src[i])) for i in range(v)] + full = fid(0) + level2 = {} + for j, r in enumerate(g['roots']): + if r['kind'] == 'side' and len(r['targets']) == 2: + level2[tuple(sorted(r['targets']))] = j + kchron = [] + for mx in g['partner_mix']: + c, d = mx['carrier'], mx['passive'] + mixf = fid(geo.perp(geo.join(geo.src[c], geo.src[d]))) + j = level2[tuple(sorted(mx['receivers']))] + capf = root_frame[j] + require(geo.contained(capf, mixf), 'mix frame inside receivers cap') + kchron.append(dict(carrier=c, passive=d, receivers=mx['receivers'], mix_frame=mixf, deliver_frame=capf, + deliver_after_root=j, undo_frame=full, + carrier_chain=[src_ann[c], mixf, capf, full], passive_chain=[src_ann[d], mixf, full], + carrier_ranks=[1, h - 4, 2], passive_ranks=[1, h - 2])) + table = {str(a): frame_record(geo, a) for a in sorted(frames)} + conv = dict(target_covector='3*chi_T - 1 (target cap = {u : (3 chi_T - 1).u = 0} = H0-orthogonal complement of chi_T)', + gram='G = I - J/9 on Q^h (H0 = G/2, H0(chi_S,chi_T) = (|S cap T|-1)/2); nondegeneracy tested for G', + frame_ids='frame id = id of the canonical annihilator; record "a" lists integer annihilator rows (frame =' + ' common kernel), record "b" lists integer basis rows; id 0 (empty "a") is the full space Q^h', + ops='[dest, control, node]: dest ^= control at the frame of node (copies: dest is the fresh role)', + nodes='zero-based graph nodes; nodes < v are the source leaves (port index)') + graph = dict(p=p, h=h, v=v, labels=g['labels'], args=g['args'], + roots=[dict(r, coefficient=1) for r in g['roots']], partner_mix=g['partner_mix'], + decoder='mod 2: Y_T += sum of root nodes whose targets contain T (star roots: T reads star(c) for c in T;' + ' side roots; partner singles) + x_carrier + x_passive for each partner_mix entry receiving T;' + ' equals x_T = sum_{c in T} star(c) + sum_{|S cap T|=1} x_S') + wordj = dict(ops=word['ops'], sources=word['sources'], rootroles=word['rootroles'], phase1=word['phase1'], + gauges=gauges, order=[x - 1 for x in wit['order']], arcs=sorted([x - 1, wit['usecode'][u]] for x, u in wit['arcs'].items()), + plain=[x - 1 for x in wit['plain']], node_frame=node_frame, root_frame=root_frame, + source_frame=src_ann, full_frame=full, conventions=conv, + schedule='old-value reads of non-gauged roles (frame 0); V injections at ; ops in order (phase1 ops' + ' are those listed); centre copies read at 0; gauged old-value reads at their gauge frames' + ' (ascending per target); side root reads in root order; partial-K deliveries right after' + ' root deliver_after_root; undo at full frame; inverse ops; V removal') + return dict(graph=graph, word=wordj, frames=dict(h=h, P_used_for_ranks='2^127-1', conventions=conv, frames=table), + kchron=dict(h=h, entries=kchron, conventions=conv)) + + +def nested_prefix(n): + """Nested-prefix all-but-one module (QMOD lane; eumemic, Claude assistance): prefix p_{k+1} = p_k + x_k, suffix + s_k = x_k + s_{k+1}; y_0 = s_1, y_{n-1} = p_{n-1}, y_{i+1} = p_i + (x_i + s_{i+2}). Each prefix is used twice with + nested supports, which gives the carrier matching more links than the balanced tree. Contract-checked. It is the + seed of the pinned p = 12 module data/qmod_p12.json.""" + args = [None] * n + + def add(a, b): + args.append([a, b]) + return len(args) - 1 + pre = {1: 0} + for k in range(1, n - 1): + pre[k + 1] = add(pre[k], k) + suf = {n - 1: n - 1} + for k in range(n - 2, 0, -1): + suf[k] = add(k, suf[k + 1]) + roots = [None] * n + roots[0], roots[n - 1] = suf[1], pre[n - 1] + roots[1] = add(0, suf[2]) + for i in range(1, n - 2): + roots[i + 1] = add(pre[i], add(i, suf[i + 2])) + support = [] + for x, a in enumerate(args): + if a is None: + support.append(1 << x) + else: + require(0 <= a[0] < x and 0 <= a[1] < x and not support[a[0]] & support[a[1]], 'nested prefix disjoint') + support.append(support[a[0]] | support[a[1]]) + full = (1 << n) - 1 + require(all(support[r] == full ^ (1 << i) for i, r in enumerate(roots)), 'nested prefix all-but-one roots') + return dict(input_count=n, args=args, roots=roots) + + +def pinned_all_but_one(name, n): + """Pinned all-but-one module {input_count, args, roots} in data/ (eumemic, Claude assistance). The p = 12 + module was annealed from nested_prefix(10) by split-function moves, scored by the p = 12 bit word. + Contract-checked: disjoint supports, root i sums every input but i.""" + mod = json.loads((HERE / 'data' / name).read_text()) + args, roots = mod['args'], mod['roots'] + require(mod['input_count'] == n == len(roots) and args[:n] == [None] * n, 'pinned all-but-one arity') + support = [1 << x for x in range(n)] + for x, a in enumerate(args[n:], n): + require(a and 0 <= a[0] < x and 0 <= a[1] < x and not support[a[0]] & support[a[1]], 'pinned all-but-one disjoint') + support.append(support[a[0]] | support[a[1]]) + full = (1 << n) - 1 + require(all(support[r] == full ^ (1 << i) for i, r in enumerate(roots)), 'pinned all-but-one roots') + return dict(input_count=n, args=args, roots=roots) + + +def all_but_one(n): + """PR #144 modules.all_but_one (balanced binary tree upward sums and complementary downward sums).""" + args, support = [None] * n, [1 << i for i in range(n)] + by = {s: i for i, s in enumerate(support)} + + def add(a, b): + if a is None: + return b + if b is None: + return a + s = support[a] | support[b] + if s not in by: + by[s] = len(args); args.append([a, b]); support.append(s) + return by[s] + + def tree(lo, hi): + if hi - lo == 1: + return (lo, None, None) + mid = (lo + hi) // 2 + L, Rr = tree(lo, mid), tree(mid, hi) + return (add(L[0], Rr[0]), L, Rr) + roots = [None] * n + + def walk(t, outside): + x, L, Rr = t + if L is None: + roots[x] = outside + return + walk(L, add(outside, Rr[0])); walk(Rr, add(outside, L[0])) + walk(tree(0, n), None) + active, stack = set(range(n)), list(roots) + while stack: + x = stack.pop() + if x not in active: + active.add(x) + if args[x] is not None: + stack.extend(args[x]) + ids = sorted(active); ren = {x: i for i, x in enumerate(ids)} + return dict(input_count=n, args=[None if args[x] is None else [ren[y] for y in args[x]] for x in ids], roots=[ren[x] for x in roots]) + + +def main(): + require(not sys.flags.optimize, 'run without -O') + ap = argparse.ArgumentParser(description=__doc__) + ap.add_argument('--p', type=int, default=12) + ap.add_argument('--out', type=Path, default=HERE / 'out') + ap.add_argument('--check', action='store_true', help='regenerate from frozen arcs and compare byte-identically') + ap.add_argument('--solve-matching', action='store_true', help='recompute the carrier matching (Hopcroft-Karp)') + a = ap.parse_args() + a.out.mkdir(parents=True, exist_ok=True) + arcs_path = HERE / 'data' / ('arcs_p%d.json' % a.p) + frozen = None if a.solve_matching or not arcs_path.exists() else json.loads(arcs_path.read_text()) + out, prf, arcs, exp = build(a.p, frozen) + root = float_root(prf['child_histogram'], prf['W_per_vertex'], prf['m']) + word_bytes = gzip.compress(dumps(out).encode(), mtime=0) + prof_bytes = dumps(prf).encode() + names = {'word_p%d.json.gz' % a.p: word_bytes, 'profile_p%d.json' % a.p: prof_bytes} + for k, obj in exp.items(): + names['%s_p%d.json' % (k, a.p)] = dumps(obj).encode() + if a.check: + for name, data in names.items(): + old = (a.out / name).read_bytes() + if name.endswith('.gz'): # gzip bytes depend on the zlib build; compare the compressed content + old, data = gzip.decompress(old), gzip.decompress(data) + require(old == data, 'byte-identical regeneration of ' + name) + require(frozen is not None, 'frozen arcs present') + print('PASS p=%d: word and profile regenerate byte-identically (sha256 %s, %s)' % ( + a.p, hashlib.sha256(word_bytes).hexdigest()[:16], hashlib.sha256(prof_bytes).hexdigest()[:16])) + else: + for name, data in names.items(): + (a.out / name).write_bytes(data) + if frozen is None: + arcs_path.write_text(dumps(arcs)) + print('wrote p=%d: R=%d R/v=%.3f loss=%d deficit=%d W=%d gauges=%d float a_b=%.7e' % ( + a.p, prf['R'], prf['R'] / prf['v'], prf['loss'], prf['deficit_per_vertex'], prf['W_per_vertex'], + prf['selected_roles'], root)) + + +if __name__ == '__main__': + main() diff --git a/research/paired-cube-local-168/NOTICE b/research/paired-cube-local-168/NOTICE new file mode 100644 index 0000000000..87dc993cb0 --- /dev/null +++ b/research/paired-cube-local-168/NOTICE @@ -0,0 +1,54 @@ +Prepared by Chafik Boukhalfa with substantial Anthropic Claude and OpenAI +Codex assistance. Apache-2.0. Inherited files retain their original notices +and assistance disclosures. This package claims no exclusive priority over +concurrent work. + +Retained sources and lineage: +- icekylinx: PR144 paired cubes, signed decoder, shared-core accounting, + original compiler, configurable local channels and finite bridge; + PR130/generalized Clifford frames. +- eumemic: PR117 module infrastructure; PR155/157 scalar modules, physical + frames/reuse and partner-pair bit word; PR161 output merging and searched + p12 module; PR168 annealed pair, triple and all-but-one modules on both + words, nested-prefix schedules, the L1 local circuit this package varies, + fused outputs, bundle descent, both physical layers, the terminal-sink + gate and the physical bit word, pinned at + 4a3c769e5c5430e7114c4d3e099ff34664677f17. Their Anthropic Claude and + OpenAI Codex disclosures are retained. PR131/143 supply frame/reuse and + late-read lineage; PR154 supplies isolated snapshot verification. +- DaysSky: PR162 generalized carrier extension (`compile_closure` and the + extension rule reused here on the new graph) and full-intersection + compiler lineage. The selected graph retains the PR168 nested schedule. +- jamesyc / James Chang: PR124 compensated birth cuts, PR34 balanced + assembly, and PR166 terminal-output accumulation and exact simultaneous + target-chain checking. The PR166 proof is retained in references/pr166. +- GamingPuzzled / Joel Pulikkan: PR160 searched-bit-module composition. +- gupt1156 PR148 and Abhinav Ramachandran/geckods PR158 (Hermes assistance): + paid atom-toll re-instantiation, including PR158 at + 6e086603f936dbb95c6d7171132ed943cc024db9. +- jacklightChen / Zhihao Chen: PR23/29 ordinary supplier; Rohan Arun + (rohanarun): PR100/103 paid positional layout and deferred signed words. +- Earlier bit lineage retained by the prerequisite: Zhihao Chen PR97, + Swapnil Jain's round-seven checkers, an664 PR128, DaysSky PR150, hpst3r + PR147, SovereignSteak PR122, and the source-notice contributors. + +This package contributes a coordinate search over PR144's configurable +local channel circuit on the PR168 v4 word, selecting direction-0 edge +sums for A[1,0], A[1,1] and A[2,1] so that the carrier closure gains 660 +arcs; our own legal-edge Hopcroft-Karp carrier matching with PR162's +extension; endpoint frame descent and compensated handoffs for the new +graph; independent complete admission of the resulting physical word and +its 44 terminal deletions; independent physical-bit admission and exact +prime witnesses for every used bit frame; and the fully paid balanced +composition with finer positive backoffs. Scalar virtual stock, physical +handoffs, terminal removals and every external row reserve remain +distinct. The complete 47-inequality body is source-normalized to PR141. +Prerequisite constructions, the configurable circuit itself and the +terminal-compilation concept are not claimed as original here. + +Verification infrastructure: Chafik Boukhalfa, PR175 at +f1081fabbfadaaaaf7292a40d428dbbb865ce920, with substantial OpenAI Codex +assistance. Its ordered retired-register compiler buckets and three +provenance/certificate updates are carried byte for byte. The PR57 compiler +and all existing notices remain. This overlay changes no mathematical +field or emitted word and is included in the complete native verification gate. diff --git a/research/paired-cube-local-168/PROOF.md b/research/paired-cube-local-168/PROOF.md new file mode 100644 index 0000000000..1ac53947fd --- /dev/null +++ b/research/paired-cube-local-168/PROOF.md @@ -0,0 +1,68 @@ +# Construction and retained proof contracts + +The exact prerequisite is PR168 at `4a3c769e5c5430e7114c4d3e099ff34664677f17`. PR144 supplies the paired-coordinate/shared-core framework and the configurable local channel circuit; PR161/168 supply the annealed modules, fused outputs, scalar words, L1 bit association, nested schedules and the bit physical layer; PR162 supplies the carrier extension rule; PR166 supplies terminal-output accumulation. This package changes the complex local circuit and rederives the complete finite composition under the inherited all-size interfaces. + +## Shared-edge local circuit + +Each of the 165 cubes computes the same 13 local outputs: the six single-bit sums $A[i,a]$ of the four ports with bit $i=a$, the six signed channels $G[j,k,m]$ and $F=A[f,0]+A[f,1]$. PR144's circuit lets every $A[i,a]$ be assembled from two edge sums along a direction $d\ne i$ or from two face diagonals, and every $G[j,k,m]$ from edge differences along the third direction, long-diagonal differences or fixed-coordinate differences. PR168's L1 circuit assembles $A[1,\cdot]$ from direction-2 edges, $A[2,\cdot]$ from direction-1 edges and $G[1,2,0]$ from direction-0 edge differences. + +This package assembles $A[1,0]$, $A[1,1]$ and $A[2,1]$ from direction-0 edges. The four direction-0 edge sums of a cube are then shared by three $A$ channels and the $G[1,2,0]$ channel, while the four direction-2 edge sums disappear and the direction-1 edge sums remain shared by $A[2,0]$ and $G[0,2,\cdot]$. The circuit has 29 additions per cube instead of 27. Every addition still has support-disjoint operands and every root support equals its contract; the graph builder and the independent scalar audit check this. The modules, the `f8:00111100` fold order and the nested schedule of PR168 are unchanged. + +The new signed graph has c=21,249, q=3,157 and M=32,971 mixer operations. Carrier arcs are chosen by our own legal-edge Hopcroft–Karp matching on the coordinate-padded frames and extended by PR162's greedy rule; the compiled closure is acyclic and span-contained. There are 11,364 arcs instead of 10,704, so the complete virtual auxiliary stock is R_scalar=c+q−11,364=13,042. Gauges are selected by PR144's chronological greedy rule: 2,310 roles of rank 18. + +## Physical word, handoffs and frames + +Operation frames are descended from the compiler frames by exact endpoint moves of single operations, equal-frame components and connected bundles: each move takes the join of incoming frames and value span or the meet of outgoing frames. 12,869 operations differ from the compiler frames. The 2,310 compensated handoffs pair dead ungauged non-root donors, whose last frames lie in the recipient gauge, with gauged recipients read at their first-use deadline; they leave 10,732 roles before terminal deletion. Only the explicit final frames and pairs are mathematical inputs. + +The verifier reconstructs every signed source/target identity, binary value span, carrier, center closure, physical role chain and actual target read. Compensation reads the current inherited dirty value with independently derived exact adjoint coefficients. The original physical word is checked on all 13,372 formal source, target and dirty columns under both shear signs. Every signed gate a←c_a a+c_b b is undone by a←c_a a−c_a c_b b, in reverse chronology; gates whose carried operand is the minuend are compiled with the sign on the destination coefficient and are audited as such. + +## Terminal-output accumulation + +The terminal compiler selects 44 ungauged, destination-only, disjoint-root roles. Each has eight targets, rank-18 common read frame and coefficient 1/2. No removed role is a source, gauge, alias endpoint, retained consumer input or another root. All sink writes are additive in the final frame. Target groups are disjoint, and each pivot's first old nonzero-frame target read follows its sink's last write. Of the 165 disjoint roots, 119 have retained producer consumers, 13 are written in the center phase and 4 have no uncorrected pivot. + +Retain every surviving coordinate's original dirty-response correction, including response through a deleted sink. At the common zero frame after the center phase, subtract each pivot from its seven other targets. Replace r←r+c b by y_p←y_p+c b/2. After the last write, add y_p back to those seven targets. Remove the old sink read and register. The independent target checker includes all intervening compensation reads and every new target-frame event; source-role frames at replaced writes remain as before. + +The modified executor checks all 1,320 source, 1,320 target and 10,688 dirty columns in both directions. An independently computed absolute residual coefficient bound of 397,506 makes 24-bit packed digits injective. The actual literal reverse word restores all retained dirty coordinates. Missing a pivot write, deleting an ancestor's original response and omitting the initial target shears are rejected. The scalar addition delta is −202, so the complete earlier virtual scalar charge remains conservative; the fixed odd divisor remains three. + +For each terminal sink, the pivot copies the old rank increments and the remaining seven targets enter the shared rank-18 frame. The sink's final rank-four increment and one target rank-18 increment disappear. The three-core histogram loses three children of rank 4 and three of rank 18; W loses one. The final profile is m=66, W=13,328, rank=878,328, deficit=1,320 and largest child 20. The exact stock identity is 13,042−10,688=2,310 handoffs+44 terminal sinks. Outward rational intervals prove b=132438677973/(2·10^14); its next 10^−15 grid point fails this fixed profile. + +## Physical bit word, exact decoder and prime range + +The unchanged bit inputs are PR168's graph, virtual profile, physical scalar word, rational frame table and partner chronology at the prerequisite commit. Admission reads these frozen files; it never regenerates them. The word uses an all-but-one module with n=10 and an annealed pair module; the local L1 association replaces three face-channel edge associations with long diagonals while preserving the mod-2 supports. Local geometry has h=24 and G=I−J/9. Source lines are spanned by chi_S; target caps are ker(3 chi_T−1). + +Each source belongs to one partner pair. A carrier XORs its passive partner in their rank-two span, delivers at the specified common level-two cap/root and restores its source value before cleanup. All complete source chains and original delivery anchors are checked. There are 2,884 operation frames differing from the original compiler frames, including 264 enlargements. Exact rational checks prove each contains its full node value span and is nondegenerate. The 1,760 aliases join dead ungauged non-root donors to untouched gauged recipients. Each current inherited dirty value is read at its explicit deadline, and all physical role chains and retimed target reads are recounted. + +The final bit profile has virtual R=19,788, physical R=18,028, W=21,548, rank=1,549,520, deficit=1,936 and largest child 60. Independent literal execution checks every one of the 21,548 formal columns over F2, restores every source/dirty coordinate and verifies the identity on targets. Separate integer execution verifies the defining integer decoder, whose F2 reduction is the identity; it does not assert an integer identity. Missing compensation, missing partner delivery, stale dirty reads and a zero operation frame are rejected. + +Exact Bareiss witnesses cover all 24,601 used bit frame IDs and distinct integer bases B. Each nonzero d=det(9BGB^t) factors into powers of primes at most 31 times a positive residual below 2^80; every factor identity is checked. Determinants reach 118 bits. Every prime q>2^80 therefore avoids every determinant, preserving all Gram inverses/projectors over Z/q^w and the original fixed-prime range. Sources, gauges, roots, operation frames, partner mixes/deliveries and ambient frames are included. Zero determinants, incorrect factors and oversized residuals are rejected. + +Every ideal bit edge pays the full 32m^2 fallback on fraction 10^−16, and 2m^3/2^80<10^−16. The contaminated moment and rank mass contract. Outward rational intervals certify a0=6600253783597/10^16; the next 10^−18 grid point fails this fixed envelope. The true bad fraction may be smaller; no optimality claim is inferred. + +Use the retained standard ordinary wrapper with a_old=384599/10^10. Select the first 10^−24 grid point above a0/(1+a0−a_old): theta=329807692103940705443/(5·10^23). Its ordinary saving is A_B=(1−theta)a0+theta a_old. Both adapter and restored-row tolls are paid by A_B0. Source normalization proves the PR141 arithmetic body changes only bridge plumbing and the explicit guard a≤A_B. + +The certified point is kappa=659180578557293/10^18. Its next 10^−18 grid point fails only for these fixed supplier certificates and parameters. Matched comparisons change the positive outer backoffs while holding the same suppliers; the published parent certificate is reported separately. + +Finite checks establish supplied words, profiles, exact moments, prime witnesses, source closure, finite bills and arithmetic. General Clifford lifts, common generic bases, uniform weighted compilation, arbitrary-width routing, restored internal rows, layout applicability, prime supply, precision/recovery, uniform setup and analytic fixed-tape transfer remain inherited all-size contracts. diff --git a/research/paired-cube-local-168/README.md b/research/paired-cube-local-168/README.md new file mode 100644 index 0000000000..860fe9ca64 --- /dev/null +++ b/research/paired-cube-local-168/README.md @@ -0,0 +1,55 @@ +# Shared-edge local circuit on PR168 v4 paired cubes and paid balanced transfer + +Under the retained multiplication interfaces, this finite witness certifies + +$$ +T(n)=O\left(n(\log n)^{1-\kappa}\right),\qquad +\kappa=\frac{659180578557293}{10^{18}} +=0.000659180578557293. +$$ + +The exact prerequisite is eumemic's PR168 at `4a3c769e5c5430e7114c4d3e099ff34664677f17`. This package changes only the per-cube local channel circuit of its complex word: the three local sums $A[1,0]$, $A[1,1]$ and $A[2,1]$ are assembled from edge sums along direction 0, which the $G[1,2,\cdot]$ channel already shares, instead of edges along directions 2, 2 and 1. The circuit has 29 additions per cube instead of 27, but the carrier closure admits 11,364 arcs instead of 10,704, so the virtual auxiliary stock falls from 13,372 to 13,042 roles. The modules, fused outputs, nested schedules and all other inputs of PR168 are retained. A new carrier matching, gauge selection, endpoint frame descent and compensated handoffs are regenerated for the new graph, and 44 terminal-output deletions are selected by this package's own checker. The unchanged PR168 physical bit supplier and the paid balanced composition are independently verified. + +| Complete paid profile, per group vertex | Complex | Bit | +|---|---:|---:| +| Local / ambient dimension | 22 / 66 | 24 / 72 | +| Scalar virtual auxiliary roles | 13,042 | 19,788 | +| Physical auxiliary roles | 10,688 | 18,028 | +| Compensated handoffs | 2,310 | 1,760 | +| Terminal deletions | 44 | 0 | +| Total persistent roles | 13,328 | 21,548 | +| Rank mass | 878,328 | 1,549,520 | +| Rank deficit | 1,320 | 1,936 | +| Largest child | 20 | 60 | + +The complex saving is $b=132438677973/(2\cdot10^{14})=0.000662193389865$. The bit coarse saving is $a_0=6600253783597/10^{16}$. Its established ordinary wrapper uses + +$$ +\theta=\frac{329807692103940705443}{5\cdot10^{23}},\qquad +A_B=(1-\theta)a_0+\theta\frac{384599}{10^{10}} +\approx0.000659615384207881. +$$ + +Both supplier moments use outward rational intervals. The bit moment includes the complete worst-case rare-class fallback; the strict atom and internally borrowed-row tolls are paid. **The bit supplier now limits the selected bound:** the transfer saving is $a=A_B<(1-\beta)b-\zeta$. + +Run the read-only finite verifier with Python 3.11 or newer: + +```sh +python3 -B research/paired-cube-local-168/verify.py +``` + +It verifies the full source closure, signed graph, original and terminal-modified complex words in both directions, every formal source/target/dirty column, complete target chronology, the bit F2 identity and its defining integer decoder, all used-frame prime witnesses, exact paid moments, full scalar/group/router/row bills, 47 strict inequalities, seven margins and adverse controls. It reproduces `certificate.json` and rejects source drift. No foreign producer or aggregate checker runs for package admission. `--write` is an authoring operation before source freeze. + +All 24,601 used bit frame IDs have distinct integer Gram witnesses. Their largest cleared determinant has 118 bits; exact factor identities leave every prime factor below $2^{80}$. The original range $q>2^{80}$ is therefore retained. + +The full repository gate applies PR154's isolated snapshot technique: + +```sh +python3 -B research/paired-cube-local-168/verify_parallel.py --output /new/path/verification --jobs 8 +``` + +It discovers all 14 native `verify` groups and runs those plus this package in separate clones of one frozen source snapshot. Every group must preserve every input byte; nested jobs are limited to one. The package workflow also verifies Python 3.11, 3.13 and 3.14. The verification baseline includes PR175 at `f1081fabbfadaaaaf7292a40d428dbbb865ce920`: its exact four-file ordered retired-register update preserves compiler selection order and mathematical certificate fields. No new benchmark or whole-suite speed claim is made. + +[PROOF.md](PROOF.md) states the construction and retained obligations; [NOTICE](NOTICE) records provenance and assistance. `SOURCE.json` pins every package and prerequisite byte. Matched arithmetic comparisons keep the same suppliers while changing the positive outer backoffs. Adjacent grid exclusions concern only these fixed certificates and parameters. + +This is a conditional finite witness. General Clifford/tensor interfaces, uniform weighted bit compilation, internally borrowed rows, paid positional layout, precision/recovery and analytic fixed-tape transfer remain source-specified contracts. 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"upstream/manifest.json": "16ab13971694cabab09440c47ebf2fc0496a9d35fc3af33950fda3498f8e2392" + }, + "inputs": [ + { + "commit": "4dbc2af5f223a0fbf22542c9d6c3f71442b6a3a6", + "pr": 166 + } + ], + "main_commit": "d1d6c070f5a8c684727ee7ec35d930f9ebfa9758", + "prerequisite": { + "commit": "4a3c769e5c5430e7114c4d3e099ff34664677f17", + "pr": 168, + "repository": "https://github.com/CrocSwap/integer-mult-bounds" + }, + "scope": "Complete source closure: exact PR168 v4 prerequisite, four-file PR175 compiler overlay, selected finite words and paid arithmetic. Retained all-size contracts remain assumptions.", + "status": "Frozen selected conditional finite witness", + "verification_overlay": { + "commit": "f1081fabbfadaaaaf7292a40d428dbbb865ce920", + "files": { + "certificates/joint-dual-kappa.json": "4044f15abf49b1551193891836e2d20975b8246acc888180af47266c64f77af0", + "certificates/joint-dual-validation.json": "a7834f2dda430b4d28337faf86b74b2ea1259812bc4169520e141efb835ecd9d", + "research/joint-dual/SOURCE.json": "c8649e811e43b33a7281746fd61e9adbd1370690ef7c2ec114a6f2d61016704f", + "scripts/experiments/joint_dual_reclaim_compiler.py": "f0696953d057239ed5a75e28d857b814d43ca43deaaf7b7b8fd191aa115112ff" + }, + "pr": 175 + } +} diff --git a/research/paired-cube-local-168/arithmetic/balanced_shared.py b/research/paired-cube-local-168/arithmetic/balanced_shared.py new file mode 100644 index 0000000000..e94c7dcaa9 --- /dev/null +++ b/research/paired-cube-local-168/arithmetic/balanced_shared.py @@ -0,0 +1,71 @@ +"""Paid balanced assembly with an explicit uniform-bit/shared-complex bridge. + +The complete 47-constraint arithmetic body is PR141 balanced_stopped.py, +with only bridge plumbing and an actual-bit-supplier bound added. Original +PR34/RaD/PR23, icekylinx and PR100/103 attribution is retained in the pinned +source. It does not assert a finite old coarse profile for the uniform bit +supplier. General cutoff/analytic/word contracts remain external. +Prepared with OpenAI Codex assistance; Apache-2.0. +""" +from fractions import Fraction as Q +from shared_bridge import rational, require, validate_shared_bridge + +def assembly(finite_bridge, complex_row, a_bit, kappa, beta=Q(1,20), h=Q(1,10**12), + a_complex=Q(717,10**7), *, original_prefix=False, + old_guard=False, old_exposures=False): + """Return 47 strict slacks and seven margins, or raise InvalidAssembly. + + The three keyword switches are negative controls: they impose the old + prefix, nonlinear guard, or old separate movement charges at these SAME + balanced parameters. They do not silently optimize an alternative family. + """ + f = validate_shared_bridge(finite_bridge, complex_row) + a, b, kappa, beta, h = map(rational, (a_bit,a_complex,kappa,beta,h)) + require(a <= f['bit_uniform']['ordinary_saving'], 'transfer saving exceeds actual uniform bit supplier') + require(0 < h < Q(1,2) and kappa > 0, 'positive backoff and saving required') + tau, sigma = 1-a, 1-b + q = a*(1-2*h) + require(1+q != 0, 'undefined balanced epsilon') + lp, c, eps = 1-q, q+h/4, (1-h)/(1+q) + lam = (tau+lp)/2 + G = eps*q + r, delta = (G+1-eps)/2, h/8 + C1 = Q(19991,10000) if old_guard else Q(1) + margins = dict(g1=1-eps, g2=a, g3=G, g4=a, + g5=min(1-eps-delta,r-delta), g6=1-eps-delta, g7=eps) + if original_prefix: + margins['g1'] = 1-eps*(1+c) + if old_exposures: + margins.update(g2=eps*c*a, g4=a*(1-eps)) + internal = tau+(1-beta)*max(sigma-tau,Q(0)) + leaf = sigma+beta*(1-sigma) + slacks = dict(a_positive=a, a_below_b=b-a, b_below_one_over32=Q(1,32)-b, + beta_positive=beta, beta_below_one=1-beta, phase_leaf_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*C1, + 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-G, artificial_boundary=8-eps+r-delta-G, + literal_scalar_guard=Q(f['semantic']['strict_literal_gap']), + row_product_gap=f['rows']['degree_gap']) + slacks.update({name+'_above_kappa': value-kappa for name,value in margins.items()}) + require(len(slacks) == 47 and len(margins) == 7, 'constraint list incomplete') + failed = {name:str(value) for name,value in slacks.items() if value <= 0} + require(not failed, str(failed)) + require(min(margins.values()) == G, 'unexpected controlling margin') + require(1-eps-G == h and 1-eps-r == h/2, 'balanced identities failed') + require(1-eps*(1+c) == h-eps*h/4, 'geometric identity failed') + parameters = dict(a_bit=a, a_complex=b, tau=tau, sigma=sigma, beta=beta,h=h, + q=q,c=c,epsilon=eps,lambda_=lam,lambda_prime=lp,alpha_squared_power=r, + delta=delta,C0=f['semantic']['C0'],C1=C1,kappa=kappa) + return dict(parameters=parameters,constraints=slacks,margins=margins, + minimum_margin=G,absorption_gap=G-kappa,scoped_limit=a/(1+a), + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c),finite_bridge=f) diff --git a/research/paired-cube-local-168/arithmetic/certificate.py b/research/paired-cube-local-168/arithmetic/certificate.py new file mode 100644 index 0000000000..1d874498bd --- /dev/null +++ b/research/paired-cube-local-168/arithmetic/certificate.py @@ -0,0 +1,168 @@ +#!/usr/bin/env python3 +"""Exact paid bridge, unchanged balanced arithmetic body, and strict controls. + +Finite bridge formulas: icekylinx PR144/130, eumemic PR152, Apache-2.0. +Balanced layout: PR23/29 Zhihao Chen, RaD, James Chang PR34, and Rohan +Arun PR100/103. This adapter preserves their separately stated contracts. +Prepared for chafreaky with substantial OpenAI Codex assistance. +""" +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +from math import prod +from pathlib import Path +import copy +import gzip +import importlib.util +import json +import sys + +HERE=Path(__file__).resolve().parent;PACKAGE=HERE.parent;ROOT=HERE.parents[2] +sys.path.insert(0,str(HERE));sys.dont_write_bytecode=True +if hasattr(sys,'set_int_max_str_digits'):sys.set_int_max_str_digits(0) +from shared_bridge import require,halving,validate_shared_bridge,nofloat +from balanced_shared import assembly + +AC=Q(132438677973,200000000000000) +COARSE=Q('6600253783597/10000000000000000') +ATOM=Q('329807692103940705443/500000000000000000000000') +OLD=Q(384599,10**10) +AB=(1-ATOM)*COARSE+ATOM*OLD +BETA=ETA=Q(1,10**24) +WEAKENING=Q(1,10**30) +GRID=10**18 + + +def js(x): + if isinstance(x,Q):return str(x) + if isinstance(x,dict):return {str(k):js(v) for k,v in x.items()} + if isinstance(x,(tuple,list)):return [js(v) for v in x] + return x + + +def bridge(row,coarse=COARSE,atom=ATOM): + """Retained finite formulas with the actual new local inventory supplied.""" + h,v,R,c,M=(row[k] for k in ('h','v','R','c','total_M_operations')) + scalar_R=row['scalar_role_reserve'] + m=3*h;half=m//2 + V=2**(m-1+(half-1)**2)*prod(2**(2*i)-1 for i in range(1,half)) + W=V*(2*v+R);s=V*row['rank_per_vertex'];N=V*v + r=max(int(k) for k,n in row['child_histogram'].items() if int(k) and n) + local=4*(c+v)+10*v+4*h*v+4*h*h+8*h+8+2*h+8*scalar_R*v*(M+16)+32*v + logical=3*V*local+8*W+4*N+8*m*scalar_R*V + G=64*(m+1)**3*(logical+1)*(W+1)**2 + E=64*(W+m+G+1)**3;charge=2*G*W*W+8*s+4*W+4+32*m + B=s+E;C0=32*m*B*B;depth=halving(m,r);coefficient=depth*W.bit_length()+9909+252;degree=70000 + actual=(1-atom)*coarse+atom*OLD + result=dict(bit_uniform=dict(coarse_saving=coarse,atom_beta=atom,old_atom_saving=OLD, + ordinary_saving=actual,selector_stock='Internally borrowed and restored q-adic rows; complete spectators preserved.', + external_stock='The bit group cardinality is not inserted into external polynomial row stock.'), + conservative_old_coarse_row_reserve=9909,ordinary_leaf_row_degree=252, + complex=dict(m=m,W=W,s=s,N=N,maxchild=r,invocations_per_stage=V,stages=3, + auxiliary_banks_after_sharing=1,halving_degree=depth,wire_bits=W.bit_length(), + original_X_involution_scalar_group_upper=32*v,local_group_upper=local, + logical_group_upper=logical,finite_group_router_upper=G,scalar_group_upper=G, + coefficient_bound=h+4,coefficient_denominator_divides=6, + physical_roles_per_vertex=R,scalar_role_reserve=scalar_R,reuse_pairs=row['reuse_pairs'],terminal_sinks=row.get('terminal_sinks',0)), + semantic=dict(E=E,literal_charge=charge,strict_literal_gap=E-charge,B=B,C0=C0,C1=1, + induction_gap=2*B*(m-r)-s-E,fixed_odd_divisor=3, + exact_grid='One dyadic grid times 3^(-K), K=G*(D_complex+1); completed children preserve the incoming odd exponent.'), + rows=dict(coefficient=coefficient,complex_coefficient=depth*W.bit_length(),degree=degree, + suffix_slope=4*degree,degree_gap=Q(degree)-Q(51*coefficient,25))) + validate_shared_bridge(result,row) + return result + + +def below(value,grid=GRID): + # Largest grid point strictly below a rational, including exact boundaries. + x=value*grid + return Q(-(-x.numerator//x.denominator)-1,grid) + + +def old_assembly(): + spec=importlib.util.spec_from_file_location('retained_prefix_assembly',ROOT/'scripts/structured_bulk_assembly.py') + module=importlib.util.module_from_spec(spec);spec.loader.exec_module(module) + return module.assembly + + +def price(row,b,coarse,beta,eta,weakening,layout,atom=ATOM): + finite=bridge(row,coarse,atom) + actual=finite['bit_uniform']['ordinary_saving'] + a=min(actual,(1-beta)*b-weakening) + q=a*(1-2*eta) + value=(1-eta)*q/(1+q) if layout=='balanced' else (1-eta)*q/(1+q*(1+eta)+q) + k=below(value) + if layout=='balanced':result=assembly(finite,row,a,k,beta=beta,h=eta,a_complex=b) + else:result=old_assembly()(a,b,finite,k,eta=eta,beta=beta) + assert len(result.get('constraints',result.get('strict_constraints')))==47 and len(result['margins'])==7 + assert result['minimum_margin']==value + return dict(kappa=k,a=a,actual_bit_saving=actual,complex_saving=b,beta=beta,eta=eta, + weakening=weakening,layout=layout,minimum_margin=value,assembly=result,finite_bridge=finite) + + +def normalized_body_check(): + source=(PACKAGE/'references/pr141/balanced_stopped.py').read_text() + old=source[source.index('def assembly('):source.index('\n\ndef cutoffs(')].rstrip() + body=(HERE/'balanced_shared.py').read_text();body=body[body.index('def assembly('):].rstrip() + body=body.replace('def assembly(finite_bridge, complex_row, a_bit, kappa,','def assembly(finite_bridge, ordinary_leaf, a_bit, kappa,',1) + body=body.replace('f = validate_shared_bridge(finite_bridge, complex_row)','f = validate_bridge(finite_bridge, ordinary_leaf)',1) + body=body.replace(" require(a <= f['bit_uniform']['ordinary_saving'], 'transfer saving exceeds actual uniform bit supplier')\n",'',1) + require(body==old,'The retained 47-slack body changed outside bridge plumbing and supplier support') + + +def certificate(row,physical): + nofloat(row);normalized_body_check() + final=price(row,AC,COARSE,BETA,ETA,WEAKENING,'balanced') + require(final['kappa']==Q('659180578557293/1000000000000000000'),'Selected final kappa differs') + counts=physical['scalar_bound'] + require(counts['terminal_sinks']==row['terminal_sinks']==physical['terminal_compiler']['eligible_count'],'Terminal sink inventory mismatch') + require(counts['terminal_scalar_gate_delta']<=0 and counts['terminal_original_scalar_reserve_retained'],'Terminal compiler must fit the retained scalar reserve') + require(final['finite_bridge']['complex']['local_group_upper']==counts['local_group_upper'],'Scalar bill detached from physical word') + for key,field in (('physical_R','R'),('logical_R','scalar_role_reserve'),('handoffs','reuse_pairs'),('c','c'),('q','q'),('M_operations','total_M_operations')): + require(counts[key]==row[field],'Physical scalar inventory mismatch '+key) + require(counts['fixed_odd_divisor']==3 and counts['scalar_denominators_divide']==6,'Exact odd-grid contract') + require(sha256((ROOT/'notes/general-clifford-frames.tex').read_bytes()).hexdigest() in physical['source_sha256'].values(),'Frame theorem source drift') + parent_path=ROOT/'certificates/paired-cube-network.json' + require(sha256(parent_path.read_bytes()).hexdigest()=='05b253a21dc526b6039f56d1068162a19a8a4f29291ad94eb892656b88e9142d','Published prerequisite certificate changed') + parent=json.loads(parent_path.read_text()) + published_parent=dict(source_commit='4a3c769e5c5430e7114c4d3e099ff34664677f17',certificate_sha256=sha256(parent_path.read_bytes()).hexdigest(),kappa=parent['kappa'],ordinary_saving=parent['bit']['effective_saving']) + rows=[('Same suppliers with earlier positive outer backoffs',row,AC,COARSE,Q(1,10**9),Q(1,10**8),Q(1,10**10),'balanced',ATOM), + ('Same suppliers with finer positive outer backoffs',row,AC,COARSE,BETA,ETA,WEAKENING,'balanced',ATOM)] + controls_table=[] + for name,*args in rows: + result=price(*args);controls_table.append(dict(name=name,**{k:v for k,v in result.items() if k not in ('assembly','finite_bridge')})) + accepted=[] + def reject(name,operation): + try:operation() + except (KeyError,ValueError,AssertionError):accepted.append(name) + else:raise ValueError('Adverse control accepted: '+name) + finite=final['finite_bridge'];a=final['a'];k=final['kappa'] + def mutate(name,change): + bad=copy.deepcopy(finite);change(bad);reject(name,lambda:validate_shared_bridge(bad,row)) + mutate('full group stock replaced by local W',lambda x:x['complex'].update(W=row['W_per_vertex'])) + mutate('old ordinary reserve omitted',lambda x:x.update(ordinary_leaf_row_degree=0)) + mutate('conservative old coarse reserve omitted',lambda x:x.update(conservative_old_coarse_row_reserve=0)) + mutate('uniform supplier replaced by fictional finite profile',lambda x:(x.pop('bit_uniform'),x.update(bit_coarse={'m':529,'W':108516254}))) + mutate('actual ordinary saving overstated',lambda x:x['bit_uniform'].update(ordinary_saving=AB+Q(1,10**24))) + mutate('unpaid previous atom grid',lambda x:x['bit_uniform'].update(atom_beta=ATOM-Q(1,10**24),ordinary_saving=(1-ATOM+Q(1,10**24))*COARSE+(ATOM-Q(1,10**24))*OLD)) + mutate('scalar role reserve collapsed to physical stock',lambda x:x['complex'].update(scalar_role_reserve=row['R'])) + mutate('terminal removals omitted',lambda x:x['complex'].update(terminal_sinks=0)) + mutate('terminal removals counted as aliases',lambda x:x['complex'].update(reuse_pairs=row['reuse_pairs']+row['terminal_sinks'])) + mutate('odd divisor silently changed to 21',lambda x:x['semantic'].update(fixed_odd_divisor=21)) + mutate('C0 detached from scalar charge',lambda x:x['semantic'].update(C0=1)) + mutate('scalar group charge omitted',lambda x:x['complex'].update(scalar_group_upper=0)) + mutate('stale total row coefficient',lambda x:x['rows'].update(coefficient=1)) + mutate('inadequate polynomial row degree',lambda x:x['rows'].update(degree=1)) + mutate('float in otherwise unused metadata',lambda x:x['bit_uniform'].update(extra=0.5)) + mutate('noncontracting maximum child',lambda x:x['complex'].update(maxchild=row['m'])) + reject('transfer saving exceeds actual uniform supplier',lambda:assembly(finite,row,AB+Q(1,10**24),k,beta=BETA,h=ETA,a_complex=AC)) + reject('old prefix charged at balanced parameters',lambda:assembly(finite,row,a,k,beta=BETA,h=ETA,a_complex=AC,original_prefix=True)) + reject('old nonlinear scalar guard',lambda:assembly(finite,row,a,k,beta=BETA,h=ETA,a_complex=AC,old_guard=True)) + reject('old separate movement exposures',lambda:assembly(finite,row,a,k,beta=BETA,h=ETA,a_complex=AC,old_exposures=True)) + reject('next final 1e-18 kappa grid point',lambda:assembly(finite,row,a,k+Q(1,GRID),beta=BETA,h=ETA,a_complex=AC)) + return js(dict(status='PASS',kappa=k,actual_uniform_bit_saving=AB,coarse_bit_saving=COARSE, + complex_saving=AC,weakened_transfer_saving=a,beta=BETA,eta=ETA,strict_weakening=WEAKENING,atom_exponent=ATOM, + bridge=finite,assembly=final['assembly'],matched_comparisons=controls_table,published_parent=published_parent, + unchanged_47_slack_body=True,adverse_controls=accepted,adverse_control_count=len(accepted), + next_grid_scope='Rejection at these fixed certified supplier values and stated parameters; no global or true-profile optimality claim.', + scope='Conditional finite witness retaining the source-specified uniform bit, exact tensor, row-restoration, paid layout and analytic/fixed-tape contracts.')) diff --git a/research/paired-cube-local-168/arithmetic/interval_moment.py b/research/paired-cube-local-168/arithmetic/interval_moment.py new file mode 100644 index 0000000000..c135d98d86 --- /dev/null +++ b/research/paired-cube-local-168/arithmetic/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=0 and terminal>=0 and scalar_R-R==reuse+terminal,'Physical role count must match reuse and terminal removals') + require(h>=2 and h%2==0 and min(v,R,c,M)>0,'Positive even-dimensional complex family') + m=3*h + hist={integer(k):integer(n) for k,n in row['child_histogram'].items() if integer(n)} + require(all(00 for t,n in hist.items()),'Proper positive child histogram') + r=max(hist);localW=2*v+R;localS=sum(t*n for t,n in hist.items()) + require((m,localW,localS)==tuple(integer(row[k]) for k in ('m','W_per_vertex','rank_per_vertex')),'Complex inventory totals') + require(m*localW-localS==integer(row['deficit_per_vertex'])==2*v-3*integer(row['loss']),'Shared-core deficit identity') + half=m//2 + vertices=2**(m-1+(half-1)**2)*prod(2**(2*i)-1 for i in range(1,half)) + W,s,N=vertices*localW,vertices*localS,vertices*v + original_X=32*v + local=4*(c+v)+10*v+4*h*v+4*h*h+8*h+8+2*h+8*scalar_R*v*(M+16)+original_X + logical=3*vertices*local+8*W+4*N+8*m*scalar_R*vertices + G=64*(m+1)**3*(logical+1)*(W+1)**2 + E=64*(W+m+G+1)**3 + literal=2*G*W**2+8*s+4*W+4+32*m + B=s+E;C0=32*m*B**2;depth=halving(m,r) + expected_complex=dict(m=m,W=W,s=s,N=N,maxchild=r,invocations_per_stage=vertices,stages=3, + auxiliary_banks_after_sharing=1,halving_degree=depth,wire_bits=W.bit_length(), + original_X_involution_scalar_group_upper=original_X,local_group_upper=local, + logical_group_upper=logical,finite_group_router_upper=G,scalar_group_upper=G, + coefficient_bound=h+4,coefficient_denominator_divides=6, + physical_roles_per_vertex=R,scalar_role_reserve=scalar_R,reuse_pairs=reuse,terminal_sinks=terminal) + expected_semantic=dict(E=E,literal_charge=literal,strict_literal_gap=E-literal,B=B,C0=C0,C1=1, + induction_gap=2*B*(m-r)-s-E,fixed_odd_divisor=3) + for name,expected in [('complex',expected_complex),('semantic',expected_semantic)]: + for k,value in expected.items():require(rational(bridge[name][k])==value,'Stale '+name+'/'+k) + require(E>literal and 2*B*(m-r)>=s+E and C0>2*B+18,'Completed exact-child semantic induction') + # These are conservative, retained external reserves. The varying q-adic + # group cardinality is deliberately not interpreted as an external stock. + old_coarse=integer(bridge['conservative_old_coarse_row_reserve']) + old_leaf=integer(bridge['ordinary_leaf_row_degree']) + require(old_coarse==9909 and old_leaf==252,'Retained separate external row reserves') + coeff=depth*W.bit_length()+old_coarse+old_leaf + degree=integer(bridge['rows']['degree']);gap=Q(degree)-Q(51,25)*coeff + require(degree>0 and gap>0,'Insufficient external row reserve') + expected_rows=dict(coefficient=coeff,complex_coefficient=depth*W.bit_length(), + degree=degree,suffix_slope=4*degree,degree_gap=gap) + for k,value in expected_rows.items():require(rational(bridge['rows'][k])==value,'Stale row/'+k) + u=bridge['bit_uniform'] + coarse,atom,old,actual=(rational(u[k]) for k in ('coarse_saving','atom_beta','old_atom_saving','ordinary_saving')) + require(0dp:H[d-dp]+=1 + prev,dp=f,d + for j,r in enumerate(self.g['roots']): + if r['kind']=='center':H[C.dimf[self.w['root_frame'][j]]]+=1 + Y=Counter();current=[None]*v + def read(t,f): + old=current[t];d=0 if old is None else C.dimf[old] + need(old is None or C.sub(old,f),'actual target frame chronology') + if C.dimf[f]>d:Y[C.dimf[f]-d]+=1 + current[t]=f + for b in sorted(self.order,key=lambda b:self.readtime[b]): + for t in self.gauge[b]['targets']:read(t,self.gauge[b]['frame']) + deliveries=defaultdict(list) + for e in self.k['entries']:deliveries[e['deliver_after_root']].append(e) + for j,r in enumerate(self.g['roots']): + if r['kind']!='center': + for t in r['targets']:read(t,self.w['root_frame'][j]) + for e in deliveries[j]: + for t in e['receivers']:read(t,e['deliver_frame']) + for t,f in enumerate(current): + need(f is not None and all(self.module.dot(C.cov[t],b)==0 for b in C.B[f]),'final target cap') + gap=h-1-C.dimf[f] + if gap:Y[gap]+=1 + need(sum(r*n for r,n in Y.items())==v*(h-1),'target rank mass') + hist=Counter() + for part in (H,Y,src): + for r,n in part.items(): + if r and n:hist[r]+=3*n + for b,z in self.gauge.items(): + if b not in self.donor:hist[3*z['dim']]+=1 + hist[2]+=2*v + hist={r:n for r,n in sorted(hist.items()) if n} + need(all(00 for r,n in hist.items()),'positive proper child bins') + R=self.R-len(self.pairs);W=2*v+R;mass=sum(r*n for r,n in hist.items());m=3*h + need(W*m-mass==C.prof['deficit_per_vertex'],'reuse preserves telescoping deficit') + return dict(h=h,v=v,R=R,virtual_R=self.R,reused_registers=len(self.pairs),W_per_vertex=W,m=m, + loss=C.prof['loss'],rank_per_vertex=mass,deficit_per_vertex=W*m-mass, + child_histogram=hist,maxchild=max(hist),selected_roles=len(self.gauge)-len(self.pairs), + selected_rank_histogram=dict(Counter(z['dim'] for b,z in self.gauge.items() if b not in self.donor)), + changed_operation_frames=len(self.changed_frames), + frames_not_contained_in_original=sum(not C.sub(self.opframe[i],self.original_opframe[i]) for i in self.changed_frames), + physical_target_histogram=dict(Y),physical_internal_histogram=dict(H), + foreign_producer_replays=0) + + def adjoint(self): + adj = [dict() for _ in range(self.R)] + for r,s in zip(self.g['roots'], self.w['rootroles']): + for t in r['targets']: adj[s][t] = adj[s].get(t,0)+1 + for a,b,_ in reversed(self.ops): + for t,c in adj[a].items(): adj[b][t] = adj[b].get(t,0)+c + return adj + + def formal(self, ring, tamper=None): + """All source, target and dirty-register columns; no random sampling.""" + v, phys = self.v, self.phys + regs = sorted(set(phys.values())); index = {r:2*v+j for j,r in enumerate(regs)} + if ring == 2: + unit = lambda i: 1<=0 for x in powers.values()) + assert type(residual) is int and 01,'upper bracket') + while hi-lo>1: + mid=(lo+hi)//2;r=paid_moment(p,Q(mid,grid)) + if r['upper']<1:lo=mid + elif r['lower']>1:hi=mid + else:raise ValueError('increase moment precision') + coarse=Q(lo,grid);accepted=paid_moment(p,coarse,True);rejected=paid_moment(p,Q(hi,grid),True) + need(accepted['upper']<1=0) + need(closure==set(self.phase1),'phase one is exactly centre closure') + content=[0]*self.R + for n,s in self.source.items():content[s]=1<0,'gauge dimension and complete response support') + src=Counter();members=Counter();labels=list(map(set,self.g['labels'])) + for e in self.k['entries']: + c,d,f,cap=e['carrier'],e['passive'],e['mix_frame'],e['deliver_frame'] + need(len(labels[c]&labels[d])==1,'orthogonal partner pair') + need(C.dimf[f]==2 and C.in_frame(C.chi[c],f) and C.in_frame(C.chi[d],f),'partner mix span') + need(C.sub(f,cap) and all(self.module.dot(C.cov[t],u)==0 for t in e['receivers'] for u in C.B[cap]),'partner mix delivery cap') + need(e['carrier_chain']==[w['source_frame'][c],f,cap,w['full_frame']] and e['passive_chain']==[w['source_frame'][d],f,w['full_frame']],'exact partner chains') + root=self.g['roots'][e['deliver_after_root']] + need(root['kind']=='side' and sorted(e['receivers'])==sorted(root['targets']),'partner delivery at own receiver root') + for chain in (e['carrier_chain'],e['passive_chain']): + for a,b in zip(chain,chain[1:]): + need(C.sub(a,b),'nested source chronology');src[C.dimf[b]-C.dimf[a]]+=1 + members[c]+=1;members[d]+=1 + need(all(members[s]==1 for s in range(v)),'every source in one partner pair') + return Counter(),Counter(),src,self.R diff --git a/research/paired-cube-local-168/certificate.json b/research/paired-cube-local-168/certificate.json new file mode 100644 index 0000000000..4493b59930 --- /dev/null +++ b/research/paired-cube-local-168/certificate.json @@ -0,0 +1,3330 @@ +{ + "arithmetic": { + "actual_uniform_bit_saving": "3298076921039407054428878770314981529/5000000000000000000000000000000000000000", + "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": "2421272198180194491462375184895776042149240737809945119642011311981529/2501649038460519703527214436087080569725092945571121229685018471000000000000000000000000", + "constraints": { + "K_dominates_log": 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"physical-frames.json.gz": "c249d6e6ca89d088a992e6992e833e99488d58d09d38893fb2eb0661753692f6", + "physical-pairs.json.gz": "5ff1b2f28c4f4669d878d3a9dd6e84af460b8ce76a24287e5ab927ceef87d49b", + "physical.py": "01961fad4b04aaa940d2dc99c87690bc861b3861200296974c5e065ce3446659", + "profile-before.json.gz": "89a46f6c9bc2e49a903a44952539034165acbc26ef6b7f14504554299ca8e2c6", + "profile.json.gz": "9d470b72ae31e2debd945b61481bde9c68df93054013f657cb331e0e49b53105", + "sinks.json": "f4d0c85db8bc90b4c0ad243adb5332e0da6fa1a8db1be6b1ad58d93a5e19fdbe", + "word.json.gz": "eec01812a25f2793b9986c6ec88eacbdb0dee8d76c116e28ab7fe9281f5114a9" + }, + "source_sha256": "d7fefe86e637584ad1bf53c8f7714b88d5abed92eaa29d110ef099536e51f516", + "status": "PASS full modified finite word" + } + }, + "profile": { + "R": 10688, + "W_per_vertex": 13328, + "c": 21249, + "child_histogram": { + "1": 88155, + "10": 2589, + "11": 987, + "12": 3555, + "13": 642, + "14": 2142, + "15": 3255, + "16": 330, + "17": 132, + "18": 7788, + "19": 5334, + "2": 45525, + "20": 1551, + "3": 29427, + "4": 10830, + "5": 7044, + "6": 4407, + "7": 2559, + "8": 3675, + "9": 1323 + }, + "deficit_per_vertex": 1320, + "h": 22, + "loss": 440, + "m": 66, + "matched": 11364, + "maxchild": 20, + "q": 3157, + "rank_per_vertex": 878328, + "reuse_pairs": 2310, + "scalar_role_reserve": 13042, + "terminal_sinks": 44, + "total_M_operations": 32971, + "v": 1320 + }, + "status": "PASS" + }, + "kappa": "659180578557293/1000000000000000000", + "scope": "Finite word, paid moments, full finite bridge and 47 strict arithmetic constraints; source-specified all-size contracts remain assumptions.", + "status": "PASS conditional finite witness" +} diff --git a/research/paired-cube-local-168/complex/check_sinks.py b/research/paired-cube-local-168/complex/check_sinks.py new file mode 100644 index 0000000000..802e59c616 --- /dev/null +++ b/research/paired-cube-local-168/complex/check_sinks.py @@ -0,0 +1,204 @@ +#!/usr/bin/env python3 +"""Author exact finite check for target-accumulating disjoint-root deletion. + +Portability-only adaptation by Chafik Boukhalfa with OpenAI Codex assistance. +Original PR166 author James Chang. Uses frozen selected complex data; never imports upstream programs, +regenerates a source graph, searches a new producer, or computes a new kappa. +Python standard library. Copyright 2026; Apache-2.0. +""" +import argparse,gzip,hashlib,json,resource,signal,sys,time +from collections import Counter +from fractions import Fraction +from pathlib import Path + + +def main(): + if sys.flags.optimize:raise SystemExit('Run without -O') + ap=argparse.ArgumentParser(description=__doc__) + ap.add_argument('--candidate',type=Path,required=True) + ap.add_argument('--output',type=Path,required=True) + a=ap.parse_args();start_time=time.monotonic() + resource.setrlimit(resource.RLIMIT_CPU,(60,60));signal.alarm(60) + pins=json.loads((a.candidate/'result.json').read_text())['pins'];data={} + for name in ['graph','word','frames','physical-frames','physical-pairs','profile-before','profile']: + name+='.json.gz';b=(a.candidate/name).read_bytes();assert hashlib.sha256(b).hexdigest()==pins[name] + data[name[:-8]]=json.loads(gzip.decompress(b)) + g,w,fw,changes,pairs,row,profile=[data[n] for n in ['graph','word','frames','physical-frames','physical-pairs','profile-before','profile']] + H,V,R=g['h'],g['v'],row['R'];assert (H,V)==(22,1320) + def basis(rows): + b={} + for x in rows: + for p,y in sorted(b.items(),reverse=True): + if x>>p&1:x^=y + if x: + p=x.bit_length()-1 + for k,y in list(b.items()): + if y>>p&1:b[k]=y^x + b[p]=x + return tuple(b[k] for k in sorted(b,reverse=True)) + def perp(rows): + rows=basis(rows);p={r.bit_length()-1:r for r in rows};out=[] + for j in range(H): + if j in p:continue + x=1<>j&1:x|=1<len(A)) + if s in sources.values():local[1]+=1 + for t in (s,donors.get(s)): + if t is not None and rkind.get(t)=='center':local[len(rframe[t])]+=1 + assert fmt(local)==profile['local_histogram'] + source=Counter({int(k):v for k,v in profile['source_data_histogram'].items()});target=Counter({int(k):v for k,v in profile['target_data_histogram'].items()}) + def children(L,T): + c=Counter({r:3*n for r,n in L.items() if r});c.update({r:3*n for r,n in T.items() if r});c.update({r:3*n for r,n in source.items() if r});c[2]+=2*V + for s,z in selected.items(): + if s not in aliases:c[3*z['rank']]+=1 + return c + oldchildren=children(local,target);assert fmt(oldchildren)==profile['child_histogram'] + rejected=Counter();eligible=[] + for j,r in enumerate(g['roots']): + if r.get('channel')!='disjoint':continue + s=w['rootroles'][j];writes=[i for i in roleops[s] if w['ops'][i][0]==s];uses=[i for i in roleops[s] if w['ops'][i][1]==s];why=[];U=rootframes[j] + if s in aliases or s in donors:why.append('alias_or_donor') + if s in sources.values():why.append('source_injection') + if s in selected:why.append('selected_gauge') + if roots_of[s]!=[j]:why.append('multiple_roots') + if uses:why.append('retained_producer_consumer') + if not writes:why.append('no_writes') + if any(w['opcoeff'][i][0]!=1 for i in writes):why.append('nonadditive_destination') + if any(not within(ofs[i],U) for i in writes):why.append('outside_read_frame') + if any(i in phase for i in writes):why.append('center_phase_touch') + available_pivots=[t for t in r['targets'] if writes and first_read[t]>max(when[i] for i in writes)] + if not available_pivots:why.append('no_uncorrected_pivot') + if why:rejected.update(why);continue + assert len(r['targets'])==8 and len(U)==18 and r['coefficients']==['1/2']*8 + # The sink's whole original trajectory is copied by only one target pivot. + # Every other target stays at0 until the common rank18 post-read. + path=[()]+[ofs[i] for i in writes]+[U];assert all(within(A,B) for A,B in zip(path,path[1:])) + prefix=[len(B)-len(A) for A,B in zip(path,path[1:]) if len(B)>len(A)] + assert sum(prefix)==18 + eligible.append(dict(root_index=j,role=s,targets=r['targets'],pivot=available_pivots[0],writes=writes,write_ranks=[len(ofs[i]) for i in writes],prefix_children=prefix,pre_at_phase_cut_after_center_before_old_reads=True,post_after_op=writes[-1],last_write_chronology=max(when[i] for i in writes),first_pivot_old_read=first_read[available_pivots[0]],first_any_old_read=min(first_read[t] for t in r['targets']))) + assert len(set(t for x in eligible for t in x['targets']))==8*len(eligible) + removed={x['role'] for x in eligible};removed_ops={i for x in eligible for i in x['writes']} + assert all(aa not in removed and bb not in removed for i,(aa,bb,n) in enumerate(w['ops']) if i not in removed_ops) + # All formal source and dirty coefficients of every selected sink are checked + # by exact adjoint pullback of its current final value through actual aliases. + # Remaining source/dirty identity follows from literal inverse cancellation + # of the unchanged retained word; no sampler or packed-digit hypothesis. + def final_form(s,stop): + c={s:1} + for i in reversed(chron[:stop+1]): + aa,bb,n=w['ops'][i];aa,bb=alias(aa),alias(bb);ca,cb=w['opcoeff'][i];v=c.get(aa,0) + if v: + c[aa]=ca*v;c[bb]=c.get(bb,0)+cb*v + if not c[bb]:del c[bb] + fresh={n-1:c[alias(s)] for n,s in sources.items() if c.get(alias(s),0)} + return c,fresh + dirtyterms=[] + for item in eligible: + s=item['role'];c,fresh=final_form(s,item['last_write_chronology']);assert c[s]==1 + assert not (set(c)&(removed-{s})) + cube={x//2 for x in g['labels'][item['targets'][0]]} + expected={n:1 for n,t in enumerate(g['labels']) if cube.isdisjoint(x//2 for x in t)} + assert fresh==expected and len(fresh)==448;dirtyterms.append(len(c)-1) + # Exact independent-target/sink/accumulation-symbol sandwich, both signs. + # Algebra includes arbitrary previous target corrections in y[t]. + for direction in (1,-1): + N=16+len(item['writes']);ys=[[Fraction(int(i==t)) for i in range(N)] for t in range(8)] + for t in range(1,8):ys[t]=[a-b for a,b in zip(ys[t],ys[0])] + # Arbitrary intervening non-pivot corrections are explicit independent + # columns. The chosen pivot has none until after its post-read. + for t in range(1,8):ys[t][8+len(item['writes'])+t]+=1 + for k,i in enumerate(item['writes']):ys[0][8+k]+=direction*Fraction(w['opcoeff'][i][1],2) + for t in range(1,8):ys[t]=[a+b for a,b in zip(ys[t],ys[0])] + for t in range(8): + expected=[Fraction(int(i==t)) if i<8 else direction*Fraction(w['opcoeff'][item['writes'][i-8]][1],2) if i<8+len(item['writes']) else Fraction(int(t>0 and i==8+len(item['writes'])+t)) for i in range(N)] + assert ys[t]==expected + # Whole simultaneous local and shared three-core ledger. + L=local.copy();T=target.copy() + for item in eligible: + L.subtract(Counter(item['prefix_children']+[4]));T[18]-=1;T.update(item['prefix_children']) + assert all(v>=0 for v in L.values()) and all(v>=0 for v in T.values()) + # Replay every target event in the actual deadline order, interleaving the + # new pivot writes and post-reads. Pre-shears are at the common zero frame + # just after the center phase and before its first compensation read. + by_write={i:item for item in eligible for i in item['writes']} + after={item['writes'][-1]:item for item in eligible} + read_at={} + for z in reversed(w['selected']): + d=deadline.get(z['role']);position=len(phase) if d is None else when[d] + read_at.setdefault(position,[]).append(z) + current=[() for _ in range(V)];actual_target=Counter();target_events=[] + def move_target(t,U,kind,index): + U=tuple(U);assert within(current[t],U),(kind,index,t,current[t],U) + actual_target[len(U)-len(current[t])]+=1 + target_events.append([kind,index,t,list(current[t]),list(U)]) + current[t]=U + for position,i in enumerate(chron): + for z in read_at.get(position,[]): + U=perp(z['annihilator']) + for t in z['targets']:move_target(t,U,'old-read',z['role']) + if i in by_write: + item=by_write[i];move_target(item['pivot'],ofs[i],'pivot-write',i) + if i in after: + item=after[i];U=rootframes[item['root_index']] + for t in item['targets']:move_target(t,U,'post-read',i) + assert all(current[t]==current[item['pivot']]==U for t in item['targets']) + for j,r in enumerate(g['roots']): + if r['kind']=='side' and w['rootroles'][j] not in removed: + for t in r['targets']:move_target(t,rootframes[j],'retained-root',j) + for t,q in enumerate(g['inputs']):move_target(t,perp((q,)),'target-finish',t) + assert fmt(Counter({r:n for r,n in actual_target.items() if r}))==fmt(Counter({r:n for r,n in T.items() if r})) + # Independent reverse of each scalar sandwich, including arbitrary inserted + # non-pivot corrections, yields the inverse rather than assuming a sign rule. + for item in eligible: + N=16+len(item['writes']);initial=[[Fraction(int(i==t)) for i in range(N)] for t in range(8)] + state=[r[:] for r in initial];events=[] + for t in range(1,8):events.append(('shear',t,0,Fraction(-1))) + for k,i in enumerate(item['writes']):events.append(('basis',0,8+k,Fraction(w['opcoeff'][i][1],2))) + for t in range(1,8):events.append(('basis',t,8+len(item['writes'])+t,Fraction(1))) + for t in range(1,8):events.append(('shear',t,0,Fraction(1))) + def apply(e,sign): + kind,t,s,c=e;c*=sign + if kind=='basis':state[t][s]+=c + else:state[t]=[a+c*b for a,b in zip(state[t],state[s])] + for e in events:apply(e,1) + for e in reversed(events):apply(e,-1) + assert state==initial + C=children(L,T);n=len(eligible);delta={str(k):C[k]-oldchildren[k] for k in C.keys()|oldchildren.keys() if C[k]!=oldchildren[k]} + assert delta==({'4':-3*n,'18':-3*n} if n else {});W=profile['W_per_vertex']-n;rank=sum(k*v for k,v in C.items());assert rank==profile['rank_per_vertex']-66*n and 66*W-rank==1320 + result=dict(status='AUTHOR_EXACT_FINITE_COMPILER_CHECK_PASS',scope='Only all-eight disjoint roots; retained full proof contracts unchanged',input_pins={k:pins[k] for k in pins if k in [n+'.json.gz' for n in data]},h=H,v=V,old_physical_R=len(live),new_physical_R=len(live)-n,old_W=profile['W_per_vertex'],new_W=W,old_rank=profile['rank_per_vertex'],new_rank=rank,deficit=1320,eligible_count=n,rejected_conditions=dict(rejected),targets_disjoint=True,simultaneous_compatible=True,all_formal_source_and_dirty_coefficients=True,formal_original_source_dirty_target_columns=2*V+len(live),remaining_formal_columns=2*V+len(live)-n,chronological_inverse_by_literal_reverse=True,full_old_physical_histogram_verified=True,all_new_target_events_replayed=True,scalar_sandwich_literal_reverse_checked=True,shared_child_delta=delta,scalar_gate_delta=-sum(len(x['writes'])+2 for x in eligible),new_odd_denominator=False,new_kappa_claimed=False,local_histogram=fmt(L),target_histogram=fmt(T),child_histogram=fmt(C),sinks=eligible,dirty_coefficient_nonzero_range=[min(dirtyterms),max(dirtyterms)],seconds=time.monotonic()-start_time,rss_kib=resource.getrusage(resource.RUSAGE_SELF).ru_maxrss) + a.output.write_text(json.dumps(result,indent=2)+'\n');print(json.dumps({k:v for k,v in result.items() if k not in ['sinks','local_histogram','target_histogram','child_histogram','input_pins']},indent=2)) +if __name__=='__main__':main() diff --git a/research/paired-cube-local-168/complex/formal_sinks.py b/research/paired-cube-local-168/complex/formal_sinks.py new file mode 100644 index 0000000000..703d57f386 --- /dev/null +++ b/research/paired-cube-local-168/complex/formal_sinks.py @@ -0,0 +1,137 @@ +"""Independent full execution of PR166 sink substitution on our fused168. + +James Chang's PR166 compiler; fused168 source lineage in its SOURCE.json. +New full packed-column executor by Chafik Boukhalfa with OpenAI Codex. +""" +from pathlib import Path +from fractions import Fraction as Q +from collections import defaultdict +from hashlib import sha256 +import argparse,gzip,json,time,importlib.util,sys + +BASE=Path(__file__).resolve().parent +ap=argparse.ArgumentParser(description=__doc__) +ap.add_argument('--candidate',type=Path,default=BASE.parents[1]/'r13-search/fused168') +ap.add_argument('--selection',type=Path,default=BASE/'fused168-screen.json') +ap.add_argument('--formal-helper',type=Path) +ap.add_argument('--output',type=Path,default=BASE/'formal-sinks.json') +args=ap.parse_args();INPUT=args.candidate;HELPER=args.formal_helper or INPUT/'prove.py' +if sys.flags.optimize:raise SystemExit('Run without -O') +spec=importlib.util.spec_from_file_location('original_formal',HELPER) +old=importlib.util.module_from_spec(spec);spec.loader.exec_module(old) +def load(name):return json.loads(gzip.decompress((INPUT/(name+'.json.gz')).read_bytes())) +g,w,row=[load(n) for n in ['graph','word','profile-before']] +pairs=load('physical-pairs');selection=json.loads(args.selection.read_text()) +for name,digest in selection['input_pins'].items():assert sha256((INPUT/name).read_bytes()).hexdigest()==digest,name +sinks=selection['sinks'];removed={s['role'] for s in sinks};sinkroots={s['root_index'] for s in sinks} +alias={b:a for a,b,t in pairs};R=row['R'];v=g['v'] +live=[s for s in range(R) if s not in alias and s not in removed] +slot={s:i for i,s in enumerate(live)} +phys=lambda s:slot[alias.get(s,s)] +D,adj=old.adjoint(g,w,R) +ops=w['ops'];coef=w['opcoeff'];phase=w['phase1'];rest=[i for i in range(len(ops)) if i not in set(phase)] +deadlines=dict((b,t) for a,b,t in pairs);at=defaultdict(list) +for s,t in deadlines.items(): + if t is not None:at[t].append(s) +selected=[z['role'] for z in w['selected']];deferred=set(selected) +sources={int(x):s for x,s in w['sources'].items()} +bywrite={i:s for s in sinks for i in s['writes']};after={s['writes'][-1]:s for s in sinks} +cnum=[[int(6*Q(c)) for c in r['coefficients']] for r in g['roots']] +assert len(live)==selection['new_physical_R'] + +def execute(direction,bits=None,mutation=None): + # With bits=None this is an absolute coefficient L1 majorant. With bits + # supplied it is the actual signed word on an injectively packed basis. + major=bits is None; top=6; count=2*v+len(live) + def basis(i):return 6 if major else 6<<(bits*i) + def add(x,c,y):return x+abs(c)*y if major else x+c*y + def track(xs): + nonlocal top + if major:top=max(top,max(xs,default=0)) + X=[basis(i) for i in range(v)];Y=[basis(v+i) for i in range(v)];Z=[basis(2*v+i) for i in range(len(live))] + initial=Y[:];z=Z[:] + # Retain the ORIGINAL response of every retained dirty coordinate, + # including responses propagated through the deleted sinks. + virtual=[0 if s in deferred or s in alias or s in removed else Z[phys(s)] for s in range(R)] + def gate(values,i): + a,b,_=ops[i];ca,cb=coef[i] + values[a]=abs(ca)*values[a]+abs(cb)*values[b] if major else ca*values[a]+cb*values[b] + def decode(values,kind=None,skip=False): + out=[0]*v + for j,(root,s,cs) in enumerate(zip(g['roots'],w['rootroles'],cnum)): + if kind is not None and root['kind']!=kind:continue + if skip and j in sinkroots:continue + for t,c in zip(root['targets'],cs):out[t]=add(out[t],c,values[s]) + assert all(x%6==0 for x in out) + return [x//6 for x in out] + for i in range(len(ops)):gate(virtual,i) + response=decode(virtual,skip=mutation=='omit-ancestor-response') + Y=[add(y,-direction,r) for y,r in zip(Y,response)];track(Y);del virtual,response + for n,s in sources.items():z[phys(s)]=add(z[phys(s)],1,X[n-1]) + done=[] + def actualgate(i): + a,b,_=ops[i];ca,cb=coef[i];a,b=phys(a),phys(b) + z[a]=abs(ca)*z[a]+abs(cb)*z[b] if major else ca*z[a]+cb*z[b] + if major: + nonlocal top + top=max(top,z[a]) + done.append(i) + def read(s): + for t,c in D[s].items(): + assert z[phys(s)]%6==0 + Y[t]=add(Y[t],-direction*c,z[phys(s)]//6) + track(Y) + for i in phase:actualgate(i) + virtual=[0 if s in removed else z[phys(s)] for s in range(R)] + center=decode(virtual,'center');Y=[add(y,direction,c) for y,c in zip(Y,center)];track(Y);del virtual,center + for sink in sinks: + pivot=sink['pivot'] + for t in sink['targets']: + if t!=pivot and mutation!='omit-pre-shear':Y[t]=add(Y[t],-1,Y[pivot]) + track(Y) + for s in reversed(selected): + if deadlines.get(s) is None:read(s) + for i in rest: + for s in at.get(i,[]):read(s) + if i in bywrite: + sink=bywrite[i];pivot=sink['pivot'];b=phys(ops[i][1]);assert z[b]%2==0 + if mutation!='omit-first-write' or i!=sinks[0]['writes'][0]:Y[pivot]=add(Y[pivot],direction*coef[i][1],z[b]//2) + track(Y) + else:actualgate(i) + if i in after: + sink=after[i];pivot=sink['pivot'] + for t in sink['targets']: + if t!=pivot:Y[t]=add(Y[t],1,Y[pivot]) + track(Y) + virtual=[0 if s in removed else z[phys(s)] for s in range(R)] + side=decode(virtual,'side',True);Y=[add(y,direction,c) for y,c in zip(Y,side)];del virtual,side + for a in range(0,v,8): + for j,q in enumerate(g['inputs'][a:a+8]): + value=0 + for r,x in zip(g['inputs'][a:a+8],X[a:a+8]): + c=1 if (q^r).bit_count()==6 else -1 if (q^r).bit_count()==2 else 0 + value=add(value,c,x) + assert value%2==0;Y[a+j]=add(Y[a+j],direction,value//2) + track(Y) + if not major:assert Y==[y+direction*x for y,x in zip(initial,X)],'all formal output columns' + for i in reversed(done): + a,b,_=ops[i];ca,cb=coef[i];a,b=phys(a),phys(b) + z[a]=z[a]+abs(cb)*z[b] if major else ca*(z[a]-cb*z[b]) + if major:top=max(top,z[a]) + for n,s in sources.items():z[phys(s)]=add(z[phys(s)],-1,X[n-1]) + track(z) + if not major:assert z==Z,'retained arbitrary dirty columns restored' + # Include the expected map in a safe final residual bound. + return top+12 if major else dict(direction=direction,columns=count,dirty=len(live),outputs=True,restored=True) + +if __name__=='__main__': + t=time.monotonic();bound=execute(1);bits=8*((bound.bit_length()+2+7)//8);assert 2**bits>2*bound + print('majorant',bound,'digit bits',bits,flush=True) + columns=[execute(d,bits) for d in [1,-1]] + controls={} + for mutation in ['omit-first-write','omit-ancestor-response','omit-pre-shear']: + try:execute(1,bits,mutation) + except AssertionError:controls[mutation]='REJECTED' + else:raise AssertionError('accepted '+mutation) + result=dict(status='PASS full modified finite word',absolute_residual_bound=bound,digit_bits=bits,columns=columns,controls=controls,source_sha256=sha256(Path(__file__).read_bytes()).hexdigest(),input_pins={p.name:sha256(p.read_bytes()).hexdigest() for p in list(INPUT.glob('*.json.gz'))+[args.selection,HELPER]},seconds=time.monotonic()-t) + args.output.write_text(json.dumps(result,indent=2)+'\n');print(json.dumps(result)) diff --git a/research/paired-cube-local-168/complex/physical.py b/research/paired-cube-local-168/complex/physical.py new file mode 100644 index 0000000000..5874de8cb8 --- /dev/null +++ b/research/paired-cube-local-168/complex/physical.py @@ -0,0 +1,168 @@ +#!/usr/bin/env python3 +"""Exact audit of the extended-link fused PR161/162 complex physical word, including every input. + +Chafik Boukhalfa with OpenAI Codex assistance. Apache-2.0. +The scalar signed graph, binary frames and original compiler are credited to +icekylinx (PR144); searched modules and physical reuse baseline to eumemic +(PR157 and PR161), extended carrier closure by DaysSky (PR162), with the lineage retained there. New checks independently execute +all physical aliases, deadline reads and inverse cleanup on an injective +packed formal basis, using a separately derived absolute coefficient bound. +""" +from pathlib import Path +from fractions import Fraction as Q +from collections import defaultdict,Counter +from hashlib import sha256 +import argparse,gzip,json,sys,time,copy,gc,resource + + +def adjoint(g,word,R): + D=[{} for _ in range(R)] + for root,s in zip(g['roots'],word['rootroles']): + for t,c in zip(root['targets'],root['coefficients']): + c=Q(c)*6;assert c.denominator==1;D[s][t]=D[s].get(t,0)+int(c) + for (a,b,_),(ca,cb) in zip(reversed(word['ops']),reversed(word['opcoeff'])): + for t,c in D[a].items():D[b][t]=D[b].get(t,0)+cb*c + if ca<0:D[a]={t:-c for t,c in D[a].items()} + D=[{t:c for t,c in row.items() if c} for row in D] + for z in word['selected']:assert set(D[z['role']])<=set(z['targets']) + receipt=dict(nonzeros=sum(map(len,D)),max_numerator_over_6=max(abs(c) for row in D for c in row.values()),L1=sum(abs(c) for row in D for c in row.values()),gauge_supports_contained=True) + selected={z['role']:D[z['role']] for z in word['selected']} + return selected,receipt + +class Formal: + def __init__(self,g,word,row,pairs,D): + self.g,self.word,self.row,self.D=g,word,row,D;self.v=g['v'];self.R=row['R'] + self.merge={b:a for a,b,t in pairs};assert len(self.merge)==len(pairs)==len(set(self.merge.values())) + assert not set(self.merge)&set(self.merge.values()) + self.live=[s for s in range(self.R) if s not in self.merge];self.slot={s:i for i,s in enumerate(self.live)} + self.phys=[self.slot[self.merge.get(s,s)] for s in range(self.R)] + self.sources={int(x):s for x,s in word['sources'].items()} + self.selected=[z['role'] for z in word['selected']];self.deferred=set(self.selected) + self.phase=sorted(word['phase1']);pset=set(self.phase);self.rest=[i for i in range(len(word['ops'])) if i not in pset] + self.deadline={b:t for a,b,t in pairs};self.at=defaultdict(list) + for b,t in self.deadline.items(): + if t is not None:self.at[t].append(b) + self.ops=[tuple(x) for x in word['ops']];self.coef=[tuple(x) for x in word['opcoeff']] + assert all(a in (-1,1) and b in (-1,1) for a,b in self.coef) + assert all(self.phys[a]!=self.phys[b] for a,b,x in self.ops) + self.cnum=[[int(6*Q(c)) for c in r['coefficients']] for r in g['roots']] + self.bound=self.coefficient_bound() + self.width=8*((self.bound.bit_length()+2+7)//8);self.base=1<2*self.bound + def coefficient_bound(self): + # Unscaled formal variables: a physical slot has coefficients bounded + # by its absolute row sum b. Actual packed slots use 6 times the basis. + g,word,v,R=self.g,self.word,self.v,self.R + old=[int(s not in self.deferred and s not in self.merge) for s in range(R)] + for (a,b,_),(ca,cb) in zip(self.ops,self.coef):old[a]=abs(ca)*old[a]+abs(cb)*old[b] + y=[6]*v + for root,s,cs in zip(g['roots'],word['rootroles'],self.cnum): + for t,c in zip(root['targets'],cs):y[t]+=abs(c)*old[s] + b=[1]*len(self.live);top=max([6*x for x in old]+y) + for node,s in self.sources.items():b[self.phys[s]]+=1 + done=[] + def gate(i): + nonlocal top + (a,c,_),(ca,cb)=self.ops[i],self.coef[i];a,c=self.phys[a],self.phys[c] + b[a]=abs(ca)*b[a]+abs(cb)*b[c];top=max(top,6*b[a]);done.append(i) + def read(s): + for t,c in self.D[s].items():y[t]+=abs(c)*b[self.phys[s]] + for i in self.phase:gate(i) + # All root/center positive readouts may be safely bounded by their + # value after the complete M: centers are closed in phase one. + for s in reversed(self.selected): + if self.deadline.get(s) is None:read(s) + for i in self.rest: + for s in self.at.get(i,[]):read(s) + gate(i) + for root,s,cs in zip(g['roots'],word['rootroles'],self.cnum): + for t,c in zip(root['targets'],cs):y[t]+=abs(c)*b[self.phys[s]] + # K has four +/-1/2 source contributions in every output row. + y=[x+12+6 for x in y];top=max(top,max(y)) + for i in reversed(done): + (a,c,_),(ca,cb)=self.ops[i],self.coef[i];a,c=self.phys[a],self.phys[c] + b[a]=abs(ca)*b[a]+abs(ca*cb)*b[c];top=max(top,6*b[a]) + for node,s in self.sources.items():b[self.phys[s]]+=1;top=max(top,6*b[self.phys[s]]) + return top + def decode(self,z,kind=None): + out=[0]*self.v + for root,s,cs in zip(self.g['roots'],self.word['rootroles'],self.cnum): + if kind is not None and root['kind']!=kind:continue + for t,c in zip(root['targets'],cs):out[t]+=c*z[s] + assert all(x%6==0 for x in out);return [x//6 for x in out] + def run(self,direction,mutation=None): + v,R,w=self.v,self.R,self.width + X=[6<<(w*i) for i in range(v)];Y0=[6<<(w*(v+i)) for i in range(v)];Z=[6<<(w*(2*v+i)) for i in range(len(self.live))] + # Compute precisely the initial reads D[s]z_s without expanding + # nongauged D: exact transposition identity D=JM gives this cheaper + # independent algebraic evaluation. All late physical reads below + # use the explicitly computed integer adjoint rows. + old=[Z[self.phys[s]] if s not in self.deferred and s not in self.merge else 0 for s in range(R)] + for (a,b,_),(ca,cb) in zip(self.ops,self.coef):old[a]=ca*old[a]+cb*old[b] + old=self.decode(old);y=[y-direction*z for y,z in zip(Y0,old)];del old;gc.collect() + z=Z[:];done=[] + def read(s): + if mutation=='missing-read' and s==self.selected[0]:return + value=z[self.phys[s]];assert value%6==0 + for t,c in self.D[s].items():y[t]-=direction*c*(value//6) + def gate(i): + (a,b,_),(ca,cb)=self.ops[i],self.coef[i];a,b=self.phys[a],self.phys[b] + z[a]=ca*z[a]+cb*z[b];done.append(i) + for node,s in self.sources.items():z[self.phys[s]]+=X[node-1] + for i in self.phase:gate(i) + physical_virtual=[z[self.phys[s]] for s in range(R)] + center=self.decode(physical_virtual,'center');del physical_virtual + for t,c in enumerate(center):y[t]+=direction*c + del center + late=[b for b,t in self.deadline.items() if t is not None];early=late[-1] if mutation=='early-read' and late else None + for s in reversed(self.selected): + if self.deadline.get(s) is None or s==early:read(s) + for i in self.rest: + for s in self.at.get(i,[]): + if s!=early:read(s) + gate(i) + physical_virtual=[z[self.phys[s]] for s in range(R)] + side=self.decode(physical_virtual,'side');del physical_virtual + for t,c in enumerate(side):y[t]+=direction*c + del side + def K(xs): + out=[] + for a in range(0,v,8): + block=xs[a:a+8];qs=self.g['inputs'][a:a+8] + for q in qs: + value=sum((1 if (q^r).bit_count()==6 else -1 if (q^r).bit_count()==2 else 0)*x for r,x in zip(qs,block));assert value%2==0;out.append(value//2) + return out + mixed=K(X);assert K(mixed)==X + for t,x in enumerate(mixed):y[t]+=direction*x + assert y==[y+direction*x for y,x in zip(Y0,X)],'full formal output map' + for i in reversed(done): + (a,b,_),(ca,cb)=self.ops[i],self.coef[i];a,b=self.phys[a],self.phys[b] + z[a]=ca*(z[a]-cb*z[b]) + for node,s in self.sources.items():z[self.phys[s]]-=X[node-1] + assert z==Z,'all physical dirty columns restored' + return dict(direction=direction,every_formal_column=True,source_columns=v,target_columns=v,dirty_columns=len(self.live),K_and_inverse=True,all_aliases_and_deadline_reads=True,all_physical_dirty_slots_restored=True) + +def main(): + ap=argparse.ArgumentParser();ap.add_argument('--candidate',type=Path,required=True);ap.add_argument('--source',type=Path,required=True);ap.add_argument('--out',type=Path,required=True);a=ap.parse_args();sys.path.insert(0,str(a.source/'scripts')) + from verify_fused import verify + from paired_cube_physical import physical + start=time.time();pins=json.loads((a.candidate/'result.json').read_text())['pins'];data={} + for name in ['graph','baseline','frames','word','profile-before','physical-frames','physical-pairs','profile']: + p=a.candidate/(name+'.json.gz');assert sha256(p.read_bytes()).hexdigest()==pins[p.name];data[name]=json.loads(gzip.decompress(p.read_bytes())) + g,b,w,word,row=[data[n] for n in ['graph','baseline','frames','word','profile-before']] + finite=verify(g,b,w,word,row);print('PASS exact signed scalar pairs and pre-reuse complete physical frame word',flush=True) + actual=physical(g,w,word,row,data['physical-frames'],data['physical-pairs']);assert json.loads(json.dumps(actual))==data['profile'];print('PASS all descended frames, nested chains, aliases and target read chronology',flush=True) + D,adj=adjoint(g,word,row['R']);formal=Formal(g,word,row,data['physical-pairs'],D);print('PASS exact adjoint; formal coefficient bound',formal.bound,'digit bits',formal.width,flush=True) + columns=[formal.run(d) for d in (1,-1)];print('PASS every formal column under both shear signs',flush=True) + mutations={} + for tag in ['missing-read','early-read']: + try:formal.run(1,tag) + except AssertionError:mutations[tag]='REJECTED' + else:raise AssertionError('accepted mutation '+tag) + cs=[Q(c) for r in g['roots'] for c in r['coefficients']] + assert set(cs)<={Q(1,2),Q(-1,2),Q(1,3),Q(-1,6)} and 3*row['q']<2**15 + local=4*(row['c']+row['v'])+10*row['v']+4*row['h']*row['v']+4*row['h']**2+8*row['h']+8+2*row['h']+8*row['R']*row['v']*(row['total_M_operations']+16)+32*row['v'] + scalar=dict(c=row['c'],q=row['q'],M_operations=row['total_M_operations'],logical_R=row['R'],physical_R=actual['physical_R'],handoffs=actual['pairs'],scalar_denominators_divide=6,fixed_odd_divisor=3,gate_and_inverse_coefficients=[-1,1],decoder_coefficients=sorted(map(str,set(cs))),three_q_less_than_2pow15=True,binary_dirty_read_bits=row['total_M_operations']+16,local_group_upper=local,scope='Conservative inherited virtual-word bill retained after aliasing, including all compensated reads. Alias and frame route choices are finite permutations/Clifford adapters; their separate global movement bill remains an assembly obligation.') + result=dict(status='PASS exact fused physical candidate, all formal source/target/dirty columns',source_sha256={str(p):sha256(p.read_bytes()).hexdigest() for p in [Path(__file__),Path(__file__).with_name('verify_fused.py'),a.source/'scripts/paired_cube_physical.py',a.source/'scripts/paired_cube/frames.py',a.source/'notes/general-clifford-frames.tex']},input_sha256=pins,pre_reuse_finite=finite,physical=actual,exact_adjoint=adj,formal=dict(columns=columns,absolute_coefficient_bound=formal.bound,packed_digit_bits=formal.width,base_exceeds_twice_bound=True),mutations=mutations,scalar_bound=scalar,seconds=time.time()-start,maxrss=resource.getrusage(resource.RUSAGE_SELF).ru_maxrss,foreign_producer_replays=0,scope='Finite candidate audit only. General exact Clifford and shared cover contracts, analytic supplier bridge, and paid global multiplication assembly remain separate obligations.') + a.out.write_text(json.dumps(result,indent=2,sort_keys=True)+'\n');print(json.dumps({k:result[k] for k in ['status','seconds','maxrss','scalar_bound']}),flush=True) +if __name__=='__main__':main() diff --git a/research/paired-cube-local-168/complex/prove.py b/research/paired-cube-local-168/complex/prove.py new file mode 100644 index 0000000000..09ab0825f5 --- /dev/null +++ b/research/paired-cube-local-168/complex/prove.py @@ -0,0 +1,74 @@ +#!/usr/bin/env python3 +"""Portable exact physical and moment certificate for the selected fused word.""" +from fractions import Fraction as Q +from pathlib import Path +import gzip +import json +import subprocess +import sys +import tempfile + +HERE=Path(__file__).resolve().parent;PACKAGE=HERE.parent;ROOT=HERE.parents[2] +sys.path.insert(0,str(PACKAGE/'arithmetic'));sys.dont_write_bytecode=True +from interval_moment import saving_grid + + +def js(x): + if isinstance(x,Q):return str(x) + if isinstance(x,dict):return {str(k):js(v) for k,v in x.items()} + if isinstance(x,(tuple,list)):return [js(v) for v in x] + return x + + +def main(): + assert not sys.flags.optimize + candidate=PACKAGE/'selected/complex' + with tempfile.TemporaryDirectory(prefix='paired-cube-exact-') as tmp: + out=Path(tmp)/'physical.json' + run=subprocess.run([sys.executable,'-B',str(HERE/'physical.py'),'--candidate',str(candidate),'--source',str(ROOT),'--out',str(out)],text=True,capture_output=True) + if run.returncode:raise ValueError(run.stdout+run.stderr) + physical=json.loads(out.read_text()) + physical.pop('seconds',None);physical.pop('maxrss',None) + physical['source_sha256']={str(Path(k).resolve().relative_to(ROOT)):v for k,v in physical['source_sha256'].items()} + with tempfile.TemporaryDirectory(prefix='paired-cube-sinks-') as tmp: + checked=Path(tmp)/'selection.json';formal_path=Path(tmp)/'formal.json' + command=[sys.executable,'-B',str(HERE/'check_sinks.py'),'--candidate',str(candidate),'--output',str(checked)] + run=subprocess.run(command,text=True,capture_output=True) + if run.returncode:raise ValueError(run.stdout+run.stderr) + selection=json.loads(checked.read_text());frozen=json.loads((candidate/'sinks.json').read_text()) + for value in (selection,frozen): + value.pop('seconds',None);value.pop('rss_kib',None) + assert selection==frozen,'Frozen simultaneous terminal selection differs' + command=[sys.executable,'-B',str(HERE/'formal_sinks.py'),'--candidate',str(candidate), + '--selection',str(candidate/'sinks.json'),'--formal-helper',str(HERE/'physical.py'),'--output',str(formal_path)] + run=subprocess.run(command,text=True,capture_output=True) + if run.returncode:raise ValueError(run.stdout+run.stderr) + sink_formal=json.loads(formal_path.read_text());sink_formal.pop('seconds',None) + raw=json.loads(gzip.decompress((candidate/'profile-before.json.gz').read_bytes())) + before=physical['physical'];paid=dict(before) + n=selection['eligible_count'];assert n==44 + assert (selection['old_physical_R'],selection['old_W'],selection['old_rank'])==(before['physical_R'],before['W_per_vertex'],before['rank_per_vertex']) + paid.update(physical_R=selection['new_physical_R'],W_per_vertex=selection['new_W'], + rank_per_vertex=selection['new_rank'],child_histogram=selection['child_histogram'], + local_histogram=selection['local_histogram'],target_data_histogram=selection['target_histogram'],terminal_sinks=n) + assert all(z['dirty']==paid['physical_R'] and z['columns']==paid['W_per_vertex'] for z in sink_formal['columns']) + physical['before_terminal_sinks']=before;physical['physical']=paid + physical['original_formal']=physical['formal'];physical['formal']=sink_formal['columns'] + physical['terminal_compiler']=selection;physical['terminal_formal']=sink_formal + physical['scalar_bound'].update(physical_R=paid['physical_R'],terminal_sinks=n, + terminal_scalar_gate_delta=selection['scalar_gate_delta'],terminal_original_scalar_reserve_retained=True) + from hashlib import sha256 + for name in ('check_sinks.py','formal_sinks.py','prove.py'): + physical['source_sha256'][str((HERE/name).relative_to(ROOT))]=sha256((HERE/name).read_bytes()).hexdigest() + row={k:raw[k] for k in ('h','v','c','q','matched','total_M_operations','loss')} + row.update({k:paid[k] for k in ('m','W_per_vertex','rank_per_vertex','deficit_per_vertex','child_histogram')}) + row.update(R=paid['physical_R'],scalar_role_reserve=raw['R'],reuse_pairs=paid['pairs'],terminal_sinks=n,maxchild=max(map(int,paid['child_histogram']))) + p=dict(m=row['m'],W=row['W_per_vertex'],N=row['deficit_per_vertex'],L=0,total_rank=row['rank_per_vertex'],maxchild=row['maxchild'],child_multiplicities=row['child_histogram']) + moment=saving_grid(p,10**15) + assert moment['accepted']['saving']==Q(132438677973,200000000000000) + moment['complex_saving']=moment['accepted']['saving'] + moment['scope']='Strict contraction and adjacent point exclusion for this fixed complete complex profile.' + print(json.dumps(js(dict(status='PASS',profile=row,physical=physical,moment=moment)),sort_keys=True)) + + +if __name__=='__main__':main() diff --git a/research/paired-cube-local-168/complex/verify_fused.py b/research/paired-cube-local-168/complex/verify_fused.py new file mode 100644 index 0000000000..47f73cf035 --- /dev/null +++ b/research/paired-cube-local-168/complex/verify_fused.py @@ -0,0 +1,156 @@ +"""R13 candidate specialization: remove only PR152 selected-count pin. All finite checks retained. New candidate wrapper by Chafik Boukhalfa with OpenAI Codex; inherited credits below.""" +# Copyright 2026 icekylinx. Apache-2.0. +# Developed with GPT-6 Astra assistance; integrated with Codex assistance. +"""Independent finite checks of the signed scalar word and binary geometry. + +Copyright 2026 icekylinx, Apache-2.0; OpenAI GPT-6 Astra assistance. Binary Lagrangian +intersection ranks use L_U=U^perp in X plus U in Z, including degenerate U. +""" +from collections import Counter +from functools import lru_cache +from paired_cube.frames import basis, perp, contained + + +def verify(g, baseline, witness, word, record): + h,v=g['h'],g['v'];args=[None]+[None if a is None else [y+1 for y in a] for a in g['args']] + roots=[dict(r,node=r['node']+1) for r in g['roots']] + n=len(args);ann=witness['annihilators'];order=witness['order'];arcs=dict(witness['matching_arcs']) + active=set(order) + inputs=g['inputs']; spans=[()]*n;positive=[0]*n;negative=[0]*n + @lru_cache(None) + def frame(A): + U=perp(A,h) + assert len(U)+len(A)==h and all((a&b).bit_count()%2==0 for a in A for b in U) + return U + def each(bits): + while bits: + low=bits&-bits;bits^=low;yield low.bit_length()-1 + for x in range(1,n): + if args[x] is None: + positive[x]=1<<(x-1);spans[x]=(inputs[x-1],) + else: + a,b=args[x];assert 0>r['coordinate']&1) + assert positive[x]==expected + U=spans[x];A=perp(U,h) + assert len(U)==h-2 + assert r['coefficients']==['1/3' if q>>r['coordinate']&1 else '-1/6' for q in inputs] + else: + A=basis(inputs[t] for t in r['targets']);U=perp(A,h) + for t,c in zip(r['targets'],r['coefficients']): + assert c in ('1/2','-1/2');sign=1 if c=='1/2' else -1 + for s in each(positive[x]):Hrows[t][s]+=sign + for s in each(negative[x]):Hrows[t][s]-=sign + rootann.append(A);rootframes.append(U) + assert contained(spans[x],U) + cube=[tuple(a//2 for a in label) for label in g['labels']] + scalar_pairs=0 + for t,q in enumerate(inputs): + for s,u in enumerate(inputs): + overlap=(q&u).bit_count();same=cube[t]==cube[s] + expected=0 if same else 1-overlap + assert Hrows[t][s]==expected, ('Signed H mismatch',t,s) + distance=(q^u).bit_count()//2 + K2=(1 if distance==3 else -1 if distance==1 else 0) if same else 0 + B2=overlap-1 + assert Hrows[t][s]+K2+B2==2*(t==s) + scalar_pairs+=1 + # Actual local K matrix, inverse, and destructive-source frame itinerary. + for start in range(0,v,8): + qs=inputs[start:start+8] + K2=[[1 if (a^b).bit_count()==6 else -1 if (a^b).bit_count()==2 else 0 for b in qs] for a in qs] + assert all(sum(K2[i][k]*K2[k][j] for k in range(8))==4*(i==j) for i in range(8) for j in range(8)) + for parity in (0,1): + source=[i for i in range(8) if i.bit_count()%2==parity];target=[i for i in range(8) if i.bit_count()%2!=parity] + U=basis(qs[i] for i in source);assert len(U)==3 + assert all(contained((qs[i],),U) for i in source) + assert all(contained(U,perp((qs[j],),h)) for j in target) + assert [3-1,(h-1)-3,h-(h-1)]==[2,h-4,1] + assert all(sum(K2[i][k]*K2[j][k] for k in source)==4*(i==j) for i in target for j in target) + # Full backward intersections, including every carrier edge and root cap. + required=[[] for _ in args];position={x:i for i,x in enumerate(order)} + for x in order: + if args[x]: + for y in args[x]:required[y].extend(ann[x]);assert position[y]>31: + j=u&0x7fffffff;value=roots[j]['node'];A=rootann[j] + else: + t=u//2;value=args[t][u&1];A=ann[t];assert position[x]0 and contained(tuple(ann[first[s]]),A) + r=h-len(ann[first[s]]);H[r]-=1;H[r-d]+=1;birth[d]+=1 + for t in targets:limits[t]=A + assert [H[r] for r in range(1,h+1)]==record['remaining_internal_histogram'][1:] + assert dict(birth)=={int(k):c for k,c in record['selected_rank_histogram'].items()} + current=[full]*v;Y=Counter() + for z in reversed(word['selected']): + A=tuple(z['annihilator']) + for t in z['targets']: + assert contained(A,current[t]);Y[len(current[t])-len(A)]+=1;current[t]=A + for r,A in zip(roots,rootann): + if r['kind']=='side': + for t in r['targets']: + assert contained(A,current[t]);Y[len(current[t])-len(A)]+=1;current[t]=A + for t,q in enumerate(inputs):assert contained((q,),current[t]);Y[len(current[t])-1]+=1 + assert dict(Y)=={int(k):c for k,c in record['target_data_histogram'].items()} + assert record['selected_roles']==len(seen) and birth==Counter({int(k):v for k,v in record['selected_rank_histogram'].items()}) + return dict(signed_scalar_pairs_checked=scalar_pairs,scalar_H_exact=True,K_involution_and_inverse_exact=True, + decoder_identity_exact=True,conservative_source_supports=True,K_source_itinerary_verified=True, + full_backward_intersections=True,physical_signed_M_replayed=True, + center_phase_closed=True,full_gauge_intersections=True,selected_sources_untouched=True, + reverse_target_chains=True,positive_rank_ledger_recounted=True,selected_roles=len(seen)) diff --git a/research/paired-cube-local-168/references/pr141/ORIGINAL-PROOF.md b/research/paired-cube-local-168/references/pr141/ORIGINAL-PROOF.md new file mode 100644 index 0000000000..2cca3a12e1 --- /dev/null +++ b/research/paired-cube-local-168/references/pr141/ORIGINAL-PROOF.md @@ -0,0 +1,101 @@ +# Balanced positional transfer of the stopped product-ring composition + +This is an additional paid layout composition. It is not an omission of the old prefix cost or a claim that a favorable child histogram by itself proves an all-size multiplication theorem. + +## Contracts that have to survive the composition + +The supplied finite word must return every dirty auxiliary coordinate, compute the exact signed complex source map, use legal common frames on both ports, and account for every transition, source/target front, exterior, center copy and endpoint correction. Its signed reflected word reverses the literal operation order, negates shears, exchanges data banks and complements every frame. The complete paid histogram and literal scalar upper bound are inputs to this arithmetic layer. Reflection and scalar-identity evidence are separately hash-bound. + +PR104's opposite-bank product-ring construction makes each proper projector residual of rank r one reversed child of width r. Its global conjugation, common generic basis, full involution factorization and paid atom adapters remain required. It supplies an ordinary interchange only after the constant-size outer wrapper. That completed wrapper has arbitrary-width, complete-spectator and restored-row guarantees. Its constant number of calls is outside the recursive moment and does not multiply the child histogram. The atom exponent remains theta=1/1000, with old ordinary saving 384599/10^10. Thus the round-seven coarse bit saving 620523/(5*10^9) gives ordinary saving 1240189553/10^13, and theta exceeds this saving, so paid atom loops are lower order. + +The complex primitive retains the completed exact tensor contract, translated endpoint gauges, inverse phase correction, and common odd-21 grid. It must preserve a completed child's incoming odd denominator. No boundary rounding, characteristic-two substitution for signed arithmetic, free address reversal, or uncharged coefficient multiplication is introduced. + +Readout n/42 may be realized by |n| consecutive same-frame shears with coefficient sign(n)/42. Each has magnitude at most one, their exact sum is n/42, and their inverse negates the pieces in reverse order. They require no new source copy or frame transition. The supplied conservative L1 scalar bill may include unused copy/scan allowance, but its local/global bound must still cover the actual selected literal word. This observation does not authorize ignoring repeated scalar occurrences or a wrong inverse sign. + +## Why the balanced layout applies + +Use the inherited PR34/RaD paid positional layout as made explicit for deferred/signed networks in PR100 and PR103. Separate the extra top bit of each long FFT axis, and use common named low-coordinate groups K_j in [K,2K). The axis-major/group-major permutation and inverse are paid by the ordinary arbitrary-coordinate router. The resulting extra prefix work is O(T p d), with saving margin 1-epsilon. Complete active, spectator, scratch, phase, control and row fields travel with their descriptors; FFT order, twiddle order and forward/inverse alignment are preserved. No local scalar operation or physical residual is moved across another operation by this outer regrouping. + +The stopped ordinary wrapper exposes precisely the ordinary interchange contract consumed by that router. The complex word exposes the same completed tensor contract required by the semantic C1=1 induction. Therefore the stopped product-ring implementation can instantiate the same balanced layout, under the inherited all-size contracts. The original geometric condition 1-epsilon(1+c)>0 remains in the constraint list; only the work margin changes from the old repeated-prefix charge to the proved paid layout's 1-epsilon. A negative control reinstates the old work margin at the new parameters and rejects them. + +## All three row stocks remain present + +Along any active nested call chain, reserve + + W_complex^D_complex * W_coarse^D_coarse * W_old^D_old. + +After a complex and coarse division, the old ordinary stock remains available to every stopped leaf or peeled atom. Sequential wrappers and copies reuse restored rows. They create no additional simultaneous factor, and also do not remove the old factor. + +For each family, d is the least positive integer with m^d > 2*r_max^d, so its depth is at most d*ceil(log2(max(2,e))) plus a fixed constant. The selected dimensions give: + +| Family | m | largest child | role bits | d | row coefficient | +|---|---:|---:|---:|---:|---:| +| Coarse bit | 529 | 528 | 27 | 367 | 9909 | +| Complex | 576 | 574 | 27 | 200 | 5400 | +| Old ordinary leaf | 575 | 529 | 28 | 9 | 252 | + +The total is 15561. A p^32000 stock leaves strict gap + + 32000 - (51/25)*15561 = 6389/25 > 0. + +The suffix slope is 128000. The validator recomputes all three minimal halving degrees, every wire-bit count, the old-stock contribution, the total coefficient, the degree gap and the suffix slope. It does not reuse the original balanced helper's two-family row formula. Semantic E, literal charge, B, C0, C1=1 and the completed-child induction are also recomputed from the supplied scalar upper bound. + +## Exact parameters and all retained inequalities + +Let b be the certified complex saving, A the proved ordinary bit saving, beta>0 the complex stopping parameter, eta>0 the balanced backoff, and zeta>0 a strict weakening. Set + + a = min(A, (1-beta)*b-zeta), + q = a*(1-2*eta), + c = q+eta/4, + epsilon = (1-eta)/(1+q), + lambda' = 1-q, + lambda = ((1-a)+lambda')/2, + g = epsilon*q, + r = (g+1-epsilon)/2, + delta = eta/8. + +The seven margins are + + 1-epsilon, a, g, a, + min(1-epsilon-delta, r-delta), + 1-epsilon-delta, epsilon. + +The minimum is g. The identities + + 1-epsilon-g = eta, + 1-epsilon-r = eta/2, + 1-epsilon*(1+c) = eta-epsilon*eta/4 > 0 + +retain the scalar, Gaussian and geometric gaps. The stopped internal exponent and complex leaf exponent remain exactly those in PR104; (1-beta)*b>a ensures the leaf ordering. All 47 strict inequalities are retained. Source normalization shows the full adapter differs from the pinned balanced implementation only in three-stock validation, explicit old-leaf argument plumbing and inclusion of the old leaf in cutoff maxima. No constraint or cost margin is deleted. + +## Selected finite arithmetic and grid ceiling + +The selected joint-expansion profile retains 2108 birth reuses, eliminates 381 nonaliased terminal roles, and has R=26216, m=576, W=114315520, rank=65843877440 and deficit=1862080. Its scalar group bound is G=3116113870848. The actual emitted physical profile, both-orientation frame/scalar audits, and literal word are separate SHA-bound construction evidence. Its entire histogram is supplied, not inferred from role reduction or an unrestricted majorization claim. Two separate rational enclosures accept the greatest 10^-24-grid complex saving + + b = 112814910866013477738/10^24 + +and reject b+10^-24. The first enclosure reduces logarithms by 4/3 with 80 atanh terms and uses degree-12 exponentials with outward 10^-45 rounding. The independent pinned PR65/100 method reduces by 2 with 32 atanh terms and uses a degree-eight exponential bound with outward 10^-40 rounding. Every first-method log/exponential interval lies inside the second, and both separate the accepted and rejected moments from one. + +Taking beta=eta=10^-24 and zeta=10^-30 gives + + kappa = 112802185097556/10^18. + +The next 10^-18 point is rejected. More strongly, let b_plus be the rejected complex point. The moment is strictly increasing in b, so the true profile root is below b_plus. Every member of this balanced family has a= 14000000000000000000000000. This is only a sufficient numeric-comparison threshold. Prime supply, fixed-basis setup, descriptor/catalogue domination, logarithm absorption and exact recovery retain their inherited eventual conditions; this value is not a practical runtime threshold. + +Original authorship remains attached: icekylinx for stopped product-ring accounting and the ordinary wrapper; PR23/29 Zhihao Chen, RaD/hipotures and James Chang/PR34 for the semantic/balanced layout; PR100/103 Rohan Arun for its deferred/signed integration; Swapnil Jain and the relevant complex producer/frame/recycling authors for the finite inputs. This three-stock adapter and independent certificate were prepared with OpenAI Codex assistance. The supplied physical word, all-size frame implementation, simultaneous basis, atom streaming, routing, prime/precision/recovery and analytic fixed-tape transfer remain separate inherited obligations. + +## Portable exact boundary + +The portable certificate generator admits only explicit integer mathematical profile fields and canonical integer child counts. It derives h, v, m, N, L, W and deficit relations before arithmetic, recursively rejects floating-point values before serialization and after readback, and binds the raw physical profile and scalar-bill bytes by SHA256. Discovery timings stay outside the mathematical certificate. The independent secondary enclosure executes only three verbatim arithmetic function bodies from the pinned source. The selected validation applies 18 adverse controls and compares every controlling quantity, moment enclosure, assembly and cutoff against the separately generated prepackage witness. The two certificates agree exactly on these mathematical fields. diff --git a/research/paired-cube-local-168/references/pr141/balanced_stopped.py b/research/paired-cube-local-168/references/pr141/balanced_stopped.py new file mode 100644 index 0000000000..5b02fb6948 --- /dev/null +++ b/research/paired-cube-local-168/references/pr141/balanced_stopped.py @@ -0,0 +1,204 @@ +# Three-reserve stopped-product adaptation of the inherited PR34/RaD/PR23 balanced +# positional assembly retained in PR104 and proved applicable to deferred words +# in PR100/103. Original attribution below is preserved. This module verifies +# arithmetic only; scalar-word/profile provenance and all-size interfaces remain +# separate obligations. Prepared with OpenAI Codex assistance, Apache-2.0. +"""Exact, import-safe balanced copied-center semantic assembly arithmetic. + +The PR36 copied-center guard uses E=64*(W+m+G+1)^3, including G. +Its complex saving is 717/10^7. All balanced parameter formulas are unchanged. + +Adapted from Zhihao Chen PR23/29 semantic assembly (Apache-2.0), RaD's +balanced transform / arbitrary routing / bulk resampling composition, and +jamesyc PR34's check_composition.py at 7fecbe3. PR34 source is research/reversed-two-stage/check_composition.py in that +pinned upstream commit. Original parameterized transcription by the +research workers is in rectangular-dimensions/next/assembly_parameterized.py. + +This checks arithmetic, not physical corner existence, producer correctness, +or inherited all-size tape/analytic hypotheses. No imports execute producers, +parse argv, read files, change globals, or mutate the supplied finite bridge. +""" +from fractions import Fraction as Q + + +class InvalidAssembly(AssertionError): + """A named exact input validation or strict inequality failed.""" + + +def require(condition, message): + if not condition: + raise InvalidAssembly(message) + + +def rational(value): + # Fraction(float) silently preserves binary floating error; forbid it. + require(type(value) in (int, str, Q), 'expected integer or exact rational string/Fraction') + return Q(value) + + +def integer(value): + x = rational(value) + require(x.denominator == 1, 'nonintegral graph constant') + return x.numerator + + +def ceil(value): + return -(-value.numerator // value.denominator) + + +def halving_degree(m, child): + require(0 < child < m, 'child must strictly contract') + degree = 1 + while m**degree <= 2 * child**degree: + degree += 1 + return degree + + +def validate_bridge(finite_bridge, ordinary_leaf): + """Recompute rather than trust stored semantic and product-stock totals. + + scalar_group_upper remains a supplied, proof-certified local scalar upper + charge. Its producer provenance is external to this arithmetic interface. + """ + result = {} + for name in ('bit_coarse', 'complex', 'ordinary_leaf'): + data = ordinary_leaf if name == 'ordinary_leaf' else finite_bridge[name] + m, W, child = (integer(data[k]) for k in ('m', 'W', 'maxchild')) + require(m > 1 and W > 0, 'positive arity and role volume required') + degree, bits = halving_degree(m, child), W.bit_length() + require(integer(data['halving_degree']) == degree, name + ' stale halving degree') + require(integer(data['wire_bits']) == bits, name + ' stale role logarithm') + result[name] = dict(m=m, W=W, maxchild=child, + halving_degree=degree, wire_bits=bits) + phase = finite_bridge['complex'] + s, scalar = (integer(phase[k]) for k in ('s', 'scalar_group_upper')) + m, W, child = (result['complex'][k] for k in ('m', 'W', 'maxchild')) + require(0 < s < m*W and scalar > 0, 'invalid complex rank/scalar bound') + E = 64*(W+m+scalar+1)**3 + B = s+E + literal = 2*scalar*W**2+8*s+4*W+4+32*m + C0 = 32*m*B**2 + semantic = dict(E=E, B=B, C0=C0, C1=1, literal_charge=literal, + strict_literal_gap=E-literal, + induction_gap=2*B*(m-child)-(s+E)) + require(E > literal and semantic['induction_gap'] >= 0 and C0 > 2*B+18, + 'semantic completed-child bound failed') + for key, value in semantic.items(): + require(rational(finite_bridge['semantic'][key]) == value, + 'stale semantic constant: '+key) + result['complex'].update(s=s, scalar_group_upper=scalar) + result['semantic'] = semantic + rows = finite_bridge['rows'] + leaf_degree = result['ordinary_leaf']['halving_degree']*result['ordinary_leaf']['wire_bits'] + require(integer(finite_bridge['ordinary_leaf_row_degree']) == leaf_degree, + 'ordinary leaf stock missing or stale') + coefficient = sum(result[name]['halving_degree']*result[name]['wire_bits'] + for name in ('bit_coarse', 'complex', 'ordinary_leaf')) + degree = integer(rows['degree']) + gap = degree-Q(51,25)*coefficient + require(degree > 0 and gap > 0, 'insufficient product row degree') + expected = dict(coefficient=coefficient, degree=degree, + degree_gap=gap, suffix_slope=4*degree) + for key, value in expected.items(): + require(rational(rows[key]) == value, 'stale product row constant: '+key) + result['rows'] = expected + return result + + +def assembly(finite_bridge, ordinary_leaf, a_bit, kappa, beta=Q(1,20), h=Q(1,10**12), + a_complex=Q(717,10**7), *, original_prefix=False, + old_guard=False, old_exposures=False): + """Return 47 strict slacks and seven margins, or raise InvalidAssembly. + + The three keyword switches are negative controls: they impose the old + prefix, nonlinear guard, or old separate movement charges at these SAME + balanced parameters. They do not silently optimize an alternative family. + """ + f = validate_bridge(finite_bridge, ordinary_leaf) + a, b, kappa, beta, h = map(rational, (a_bit,a_complex,kappa,beta,h)) + require(0 < h < Q(1,2) and kappa > 0, 'positive backoff and saving required') + tau, sigma = 1-a, 1-b + q = a*(1-2*h) + require(1+q != 0, 'undefined balanced epsilon') + lp, c, eps = 1-q, q+h/4, (1-h)/(1+q) + lam = (tau+lp)/2 + G = eps*q + r, delta = (G+1-eps)/2, h/8 + C1 = Q(19991,10000) if old_guard else Q(1) + margins = dict(g1=1-eps, g2=a, g3=G, g4=a, + g5=min(1-eps-delta,r-delta), g6=1-eps-delta, g7=eps) + if original_prefix: + margins['g1'] = 1-eps*(1+c) + if old_exposures: + margins.update(g2=eps*c*a, g4=a*(1-eps)) + internal = tau+(1-beta)*max(sigma-tau,Q(0)) + leaf = sigma+beta*(1-sigma) + slacks = dict(a_positive=a, a_below_b=b-a, b_below_one_over32=Q(1,32)-b, + beta_positive=beta, beta_below_one=1-beta, phase_leaf_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*C1, + 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-G, artificial_boundary=8-eps+r-delta-G, + literal_scalar_guard=Q(f['semantic']['strict_literal_gap']), + row_product_gap=f['rows']['degree_gap']) + slacks.update({name+'_above_kappa': value-kappa for name,value in margins.items()}) + require(len(slacks) == 47 and len(margins) == 7, 'constraint list incomplete') + failed = {name:str(value) for name,value in slacks.items() if value <= 0} + require(not failed, str(failed)) + require(min(margins.values()) == G, 'unexpected controlling margin') + require(1-eps-G == h and 1-eps-r == h/2, 'balanced identities failed') + require(1-eps*(1+c) == h-eps*h/4, 'geometric identity failed') + parameters = dict(a_bit=a, a_complex=b, tau=tau, sigma=sigma, beta=beta,h=h, + q=q,c=c,epsilon=eps,lambda_=lam,lambda_prime=lp,alpha_squared_power=r, + delta=delta,C0=f['semantic']['C0'],C1=C1,kappa=kappa) + return dict(parameters=parameters,constraints=slacks,margins=margins, + minimum_margin=G,absorption_gap=G-kappa,scoped_limit=a/(1+a), + recurrence=dict(internal=internal,leaf=leaf,reservations=1-c),finite_bridge=f) + + +def cutoffs(finite_bridge, ordinary_leaf, result): + """PR34 sufficient numeric comparisons, retaining its all-interval padding. + + These are eventual arithmetic thresholds, not practical running times or + substitutes for additional native setup / prime / recovery thresholds. + """ + f = validate_bridge(finite_bridge, ordinary_leaf) + p = result['parameters'] + e,c,r,beta = (p[k] for k in ('epsilon','c','alpha_squared_power','beta')) + ka,km,kb,ks = (ceil(1/x) for x in (r,e*c,1-e,e*beta)) + C0 = f['semantic']['C0'] + largest = max(f[name]['m'] for name in ('bit_coarse','complex','ordinary_leaf')) + cuts = dict(guard=ceil(Q((2*C0).bit_length())/(1-e)), + normalization=ceil(7/(1-e-r)), alpha=16*ka*ka+1, compact=64*km*km+1, + geometry=ceil(3/(1-e*(1+c))),phase_cell=ceil(9/(e-(1-r)/2)), + period=128*kb*kb+1,stopped_leaf=ks*(4*largest).bit_length(),log_p=25,reservoir=14) + common = max(cuts.values()) + require(common >= max(2*ka,2*km,2*kb,25), 'cutoff does not cover monotone regime') + checkpoints=[] + for j in range(6): + z=common*2**j + powers=dict(alpha=(z//ka,8*(z+ka)+64),compact=(z//km,32*(z+km)+192), + period=(z//kb,16*(z+kb)+56), + rows=(z//kb,f['rows']['suffix_slope']*(z+kb+8)), + leaf=(z//ks,4*largest)) + require(all(lhs >= rhs.bit_length() for lhs,rhs in powers.values()), + 'compressed-power threshold failed') + checkpoints.append(dict(log2_input=z,powers={name:dict(exponent=lhs,rhs=rhs, + rhs_bits=rhs.bit_length()) for name,(lhs,rhs) in powers.items()})) + return dict(cutoff_log2_input=cuts,common_cutoff=common,power_checkpoints=checkpoints, + all_interval_argument='For [Z,Z+k), bound RHS at Z+k and LHS at floor(Z/k). ' + 'Successive intervals double LHS; the positive affine RHS grows at most ' + 'linearly, so 2^j >= j+1 proves persistence.', + additional_eventual_conditions=['BHP prime threshold and distinct-prime packing', + 'Fixed rational basis, eligible common prime and native table setup', + 'Catalogue/descriptor domination, logarithm absorption, exact recovery'], + practical_runtime_claim=False) diff --git a/research/paired-cube-local-168/references/pr166/PROOF.md b/research/paired-cube-local-168/references/pr166/PROOF.md new file mode 100644 index 0000000000..4b4341c091 --- /dev/null +++ b/research/paired-cube-local-168/references/pr166/PROOF.md @@ -0,0 +1,221 @@ +# Dirty-target accumulation removes terminal producer rows + +Status: author-checked finite compiler lemma and 67-row substitution on the +current PR163 complex word. This is not a new assembled multiplication bound. +Independent review and any advertised supplier/assembly update remain separate. + +Scientific inputs are the selected complex files introduced at +15c702a929b7d640107a95e196186ad74e876c82. They are unchanged at publication +base e1813796ef5c3ca38c5dd7b9e8d81b3908ff5997; that later commit changes only +attribution NOTICE and its SOURCE digest. The checker verifies the existing +result.json SHA256 pins for every finite input it consumes. + +## Relation to earlier constructions + +Dumas and Grenet's *In-place accumulation of fast multiplication formulae* +(https://arxiv.org/pdf/2307.12712) motivates using arbitrary-valued output +storage. Its RAM results do not establish this frame-constrained compiler. +No novelty claim is made for the scalar pre/post cancellation identity. + +PR161's P±Q merge and PR163's singleton-channel fusion create internal producer +sums. This substitution instead removes independent auxiliary coordinates by +using existing independently valued data targets. The paired-cube identity, +Clifford representatives, physical reuse, copied-center interfaces and all-size +compiler assumptions retain their upstream attribution and proof obligations. + +## Local lemma with chronological hypotheses + +Let z_s be an independently dirty, zero-entrance-gauge producer role. Assume: + +1. It is neither a source-injection role nor an aliased recipient/donor. +2. Its only producer incidences are additive destination writes + z_s <- z_s + b_j a_j, with b_j in {1,-1}. It never controls another + producer role. It has exactly one root read, uniformly z_s/2 into a + target group T. +3. Its literal write-frame chain is 0 <= U_1 <= ... <= U_k <= U, + where U is the common root read frame. Every write uses the identical + exact T_(U_j) on its control and destination. +4. All these writes occur after the copied-center phase. Before the first + deferred target corrections, the targets in T are at frame0. +5. Some pivot c in T receives no target correction between that common-zero + point and the last write/post-read. Other targets may receive corrections + during this interval, provided those corrections do not depend on target + contents and their existing frames are contained in U. +6. Later target reads continue their old nested chains from U. No other + target-controlled producer operation is introduced. + +All targets and retained dirty roles have arbitrary independent initial values. +No target is assumed clean, and the deleted dirty variable is not set to zero: +the new construction has one fewer independent auxiliary input coordinate. + +Keep the ORIGINAL initial and deferred old-response coefficient columns for +EVERY retained role. Omit only the deleted role's column. In particular, do +not recompute the old correction from a decoder which simply drops its root; +that would omit the root response of its retained ancestors. The inherited +expanded scalar old-response implementation and its conservative charge remain +available. The sink's own old-response column is exactly the uniform1/2 +column on T because it never controls another producer row. + +At the common-zero point, after the copied-center contribution and before +its deferred corrections, perform + + y_t -= y_c for t in T minus {c}. + +At the original time of each write, raise the pivot along the deleted role's +actual chain and replace that write by + + y_c += (b_j/2) a_j. + +Immediately after the last such write, raise the pivot and the other targets +to the original U and perform + + y_t += y_c for t in T minus {c}. + +Delete the old positive root read, all writes and inverse-cleanup writes on +z_s, its initial old-response column, its physical stream and its full-frame +ending. Every retained producer operation, original source operation, source +return, copied-center step and old-response column stays in its original order. + +Write f=sum_j b_j a_j for the ACTUAL current controls, including all their +retained dirty dependence. The sandwich adds f/2 to all targets and preserves +every old target value. Any intervening correction e_t on a non-pivot is +unchanged: + + (y_t-y_c+e_t) + (y_c+f/2) = y_t+e_t+f/2. + +An intervening correction to the pivot would be broadcast to every target; +this is why the pivot chronology condition is essential. The test does not +incorrectly require every non-pivot correction to wait. + +The retained producer is the same invertible word with destination-only sink +writes omitted. It contains no reference to the deleted coordinate, so its +literal inverse restores every retained dirty input. Its response from each +retained source/dirty column is unchanged at the targets, and the retained +old-response columns cancel those dirty parts as before. Earlier target data, +center contributions and later target contributions are all preserved. + +## Exact frames, inverse and simultaneous use + +The pre-shears use T_0 on both targets. Each accumulating write uses the +original exact T_(U_j) on pivot and control. Every post-shear uses one +identical T_U on its two operands. Rank-zero reconciliation is actual inherited +scalar/movement work, not equality up to phase. + +Reverse the COMPLETE literal new word and invert every shear. Use +D_U=T_U F^(-1) in the reverse/complement orientation. Then + + D_U D_V^(-1) = T_U T_V^(-1) + +exactly. All reversed gate incidences are still identical, all transition +ranks are preserved, and sources/retained dirty values are restored. This is +the chronological inverse, not the invalid source/target-swapped transpose. +The data-bank and rank-zero endpoint conventions remain the inherited ones. + +For sinks with disjoint target groups, perform each pre-sandwich at the same +common-zero cut and each post-sandwich at its own last-write time. There is +no target collision or producer feedback, so all substitutions coexist. + +## Paid ledger + +Let r=dim(U) and let P be the complete positive-width prefix of the deleted +role from0 through every write to U. Its old local row bill is P+[h-r]. +The pivot's old first target child [r] is replaced by P. Other target paths +and all retained row paths are unchanged. Hence the EXACT local child change is + + -[r] -[h-r], + +with one independent row removed. This accounts for every prefix, endpoint and +full-frame cleanup; fragmentation inside P cancels rather than disappearing +without payment. The same delta holds for the complete inverse orientation. + +In the existing three completed orthogonal cores, for each zero-gauge sink: + + delta W = -1; + delta children = -3*[r] -3*[h-r]; + delta rank = -3h; + delta deficit = 0. + +There is no exterior tail for a zero-gauge physical row. The full group factor +and retained routing/row reserves are not reduced by fiat. For moment exponent +p in (0,1), the unnormalized slack improvement is + + 3 r^p + 3(h-r)^p - (3h)^p > 0, + +because the six positive pieces sum to3h. This is a strict finite-profile +improvement, not a newly certified assembled kappa. + +For k writes and n targets, the old affected scalar gates are k forward +writes, k inverse writes, n initial dirty reads and n positive root reads. +The new ones are k accumulating writes and2(n-1) target shears. Thus the +scalar-gate count decreases by k+2. All new coefficients already belong to +the Gaussian-dyadic alphabet; no odd divisor is introduced. Keep the original +conservative virtual R, M, expanded-correction scalar charge, full finite +stock and precision/routing reserves rather than shrinking them without proof. + +## Exact current finite instance + +The checker examines ONLY the165 all-eight disjoint roots of the selected +PR163 word. It finds67 eligible roots on disjoint target cubes. The other98 +have retained producer consumers; two of those also touch the center phase. +It does not search arbitrary face, singleton or cross-cube combinations. + +For example, root0 uses unaliased role12354. Its only incidences are additive +writes21902 and24308, at ranks15 and18. Target0 can be the pivot. Targets6 +and7 receive early compensation, but their independent additive corrections +are valid while encoded. The pivot's first compensation occurs after the +post-read. This concrete distinction is verified in the actual target-event +replay rather than inferred from a scalar channel formula. + +The selected simultaneous change is: + + physical R: 13041 -> 12974 + W per vertex: 15681 -> 15614 + rank per vertex: 1033626 -> 1029204 + deficit: 1320 -> 1320 + child multiplicity18: -201 + child multiplicity4: -201 + scalar gates: -300 + +selected.json contains every selected role, its original writes, pivot and +chronological boundary, as well as the complete new local/target/shared +histograms and source pins. Its decimal runtime is a diagnostic, not a +mathematical certificate input. + +## What the author check actually establishes + +check_sink_accumulator.py performs these exact checks from existing frozen +inputs, without importing an upstream executable or rebuilding a producer: + +- original source pins and full positive physical histogram equality; +- all role classifications, aliases, source injections, literal consumers, + write-frame chains and original root destinations; +- an available late-corrected pivot for every selected group; +- every new target event interleaved with all original deadline reads and + retained root reads, including all endpoint changes; +- exact adjoint pullbacks through the actual aliased producer for every + selected sink, covering all1320 original source columns and all13041 + original dirty columns, including zero columns; +- each fresh disjoint channel has exactly its448 required source terms; +- arbitrary target and intervening non-pivot corrections, both signs, and + actual reversal of each scalar sandwich; +- retained source/dirty identity by destination-only deletion and literal + inverse cancellation; no Monte Carlo or injective-digit assumption; +- disjoint simultaneous support and complete child/row deltas. + +Together with the unchanged inherited complete word, this covers its15681 +original source/target/dirty coordinates and the15614-coordinate new word. +The original saved full proof contracts remain dependencies. The package does +not update the bit supplier, balance parameters, all47 assembly inequalities, +precision constants or advertised multiplication exponent. + +## Reproduce + +From the repository root: + + python research/paired-cube-target-accumulator/check_sink_accumulator.py \ + --candidate research/paired-cube-balanced-161/selected/complex \ + --output /tmp/target-accumulator-check.json + +The standard-library checker has60-second CPU/wall and768MiB address-space +caps. The author run completed in approximately5.5seconds and85MiB. Compare +mathematical fields, not runtime/RSS, with selected.json. diff --git a/research/paired-cube-local-168/references/pr166/README.md b/research/paired-cube-local-168/references/pr166/README.md new file mode 100644 index 0000000000..0adb5c653a --- /dev/null +++ b/research/paired-cube-local-168/references/pr166/README.md @@ -0,0 +1,15 @@ +# Target-accumulating terminal compiler + +This author-checked research packet replaces67 actual PR163 producer sinks +with existing independently valued target accumulators. The complete finite +profile removes67 rows and201 children of each width18 and4; deficit1320 is +preserved. It makes no new assembled multiplication-bound claim. + +Read PROOF.md for the exact chronological lemma, retained dirty corrections, +full inverse, scalar/endpoint bill and inherited obligations. selected.json is +the concrete current-word specification. Run check_sink_accumulator.py against +the existing paired-cube-balanced-161/selected/complex data to reproduce it. + +The motivating scalar idea is output accumulation; no novelty claim is made. +Existing scalar-producer, frame, physical-reuse and all-size interfaces retain +the attribution in the source package's current NOTICE. diff --git a/research/paired-cube-local-168/references/pr168/bit-physical-profile.json b/research/paired-cube-local-168/references/pr168/bit-physical-profile.json new file mode 100644 index 0000000000..8014fc2a23 --- /dev/null +++ b/research/paired-cube-local-168/references/pr168/bit-physical-profile.json @@ -0,0 +1,99 @@ +{ + "R": 19788, + "W_per_vertex": 21548, + "changed_operation_frames": 2884, + "checks": { + "donor_frames_inside_gauges": true, + "gauge_read_window": true, + "operation_frames_nondegenerate_and_spanning": true, + "pair_chronology": true, + "partner_chronology": true, + "phase_one_closure": true, + "register_contents": true, + 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+import json +import subprocess +import sys + +HERE=Path(__file__).resolve().parent;ROOT=HERE.parents[1] +sys.dont_write_bytecode=True +if hasattr(sys,'set_int_max_str_digits'):sys.set_int_max_str_digits(0) + + +def digest(path):return sha256(path.read_bytes()).hexdigest() + + +def pins(): + manifest=json.loads((HERE/'SOURCE.json').read_text()) + assert manifest['files'],'Empty source closure' + values={name:digest(ROOT/name) for name in manifest['files']} + assert values==manifest['files'],'Pinned construction or dependency bytes changed' + return values + + +def run(relative): + result=subprocess.run([sys.executable,'-B',str(HERE/relative)],text=True,capture_output=True) + if result.returncode:raise ValueError(relative+' failed:\n'+result.stdout+result.stderr) + return json.loads(result.stdout) + + +def build(): + print('Checking new signed complex word, all formal columns, frames and exact moment.',file=sys.stderr,flush=True) + complex_result=run('complex/prove.py') + print('Checking frozen PR168-v4 bit frames and aliases, full F2 identity and paid moment envelope.',file=sys.stderr,flush=True) + bit_result=run('bit/prove.py') + sys.path.insert(0,str(HERE/'arithmetic')) + from certificate import certificate + arithmetic=certificate(complex_result['profile'],complex_result['physical']) + assert bit_result['coarse']['coarse_saving']==arithmetic['coarse_bit_saving'] + assert bit_result['coarse']['atom_beta']==arithmetic['atom_exponent'] + assert bit_result['coarse']['ordinary_saving']==arithmetic['actual_uniform_bit_saving'] + assert complex_result['moment']['complex_saving']==arithmetic['complex_saving'] + return dict(status='PASS conditional finite witness',kappa=arithmetic['kappa'], + complex=complex_result,bit=bit_result,arithmetic=arithmetic, + scope='Finite word, paid moments, full finite bridge and 47 strict arithmetic constraints; source-specified all-size contracts remain assumptions.') + + +def main(): + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('--write',action='store_true',help='Authoring only: write the canonical derived certificate before freezing SOURCE.json') + args=parser.parse_args() + assert not sys.flags.optimize,'Assertions must remain enabled' + before=None if args.write else pins() + result=build();target=HERE/'certificate.json' + if args.write:target.write_text(json.dumps(result,indent=2,sort_keys=True)+'\n') + else: + assert result==json.loads(target.read_text()),'Canonical certificate does not reproduce' + assert pins()==before,'Source closure changed during verification' + print('PASS paired-cube-local-168 kappa='+result['kappa']+'; complete complex and bit words, 47 constraints, seven margins, and '+str(result['arithmetic']['adverse_control_count'])+' assembly controls.') + + +if __name__=='__main__':main() diff --git a/research/paired-cube-local-168/verify_parallel.py b/research/paired-cube-local-168/verify_parallel.py new file mode 100644 index 0000000000..9caf188798 --- /dev/null +++ b/research/paired-cube-local-168/verify_parallel.py @@ -0,0 +1,154 @@ +#!/usr/bin/env python3 +"""Run every native verify group in isolated copies of one frozen source tree. + +Technique: PR154 by eumemic, pinned at +d67773363075cc787b6f6ffa07191475c7c3fbec (Apache-2.0). +Adaptation: Chafik Boukhalfa with OpenAI Codex assistance. + +The strict recipe parser rejects unaccounted commands, and source manifests +are compared before/after snapshot creation and after all groups finish. +The new finite package is an additional group. No producer/check is omitted. +Unrelated PR154 source-pin and workflow policy changes are not adopted. +""" +import argparse +from concurrent.futures import ThreadPoolExecutor, as_completed +from hashlib import sha256 +import json +import os +from pathlib import Path +import re +import shutil +import signal +import subprocess +import sys +import time + +HERE=Path(__file__).resolve().parent;ROOT=HERE.parents[1] +GIT=['git','-c','core.autocrlf=false','-c','commit.gpgsign=false', + '-c','user.name=isolated-verification','-c','user.email=verify@localhost'] + + +def need(ok,message): + if not ok:raise ValueError(message) + + +def git(*args,cwd=ROOT): + return subprocess.check_output([*GIT,*args],cwd=cwd) + + +def dump(path,value): + temp=path.with_suffix(path.suffix+'.tmp') + temp.write_text(json.dumps(value,indent=2,sort_keys=True)+'\n');temp.replace(path) + + +def native_groups(): + text=(ROOT/'Makefile').read_text();lines=text.splitlines();found=[];in_rule=False + need(lines.count('verify:')==1,'exactly one native verify recipe is required') + for line in lines: + if line=='verify:': + need(not in_rule and not found,'duplicate verify recipe');in_rule=True;continue + if not in_rule:continue + if line.startswith('\t'): + match=re.fullmatch(r'\t\$\(MAKE\) (verify-[a-z0-9-]+)',line) + need(match is not None,'unaccounted direct command in verify: '+line) + found.append(match.group(1));continue + if line.strip() and not line.startswith('#'):break + need(found and len(set(found))==len(found),'nonempty unique native verify groups') + need(len(found)==14,'review coverage before changing the native group count') + return found + + +def source_names(): + names=git('ls-files','-z','--cached','--others','--exclude-standard').split(b'\0') + return sorted({n.decode() for n in names if n and (ROOT/n.decode()).is_file()}) + + +def manifest(root,names): + result={} + for name in names: + path=root/name;need(path.is_file() and not path.is_symlink(),'regular source file required: '+name) + data=path.read_bytes();result[name]=dict(bytes=len(data),sha256=sha256(data).hexdigest()) + return result + + +def main(): + pipeline_begin=time.monotonic() + ap=argparse.ArgumentParser(description=__doc__) + ap.add_argument('--output',type=Path,required=True) + ap.add_argument('--jobs',type=int,default=8) + ap.add_argument('--group-timeout',type=int,default=2400) + args=ap.parse_args();need(1<=args.jobs<=8,'group workers must be in [1,8]') + output=args.output.resolve();need(not output.exists(),'output directory must be new') + output.mkdir(parents=True);(output/'logs').mkdir();(output/'trees').mkdir() + groups=native_groups();names=source_names();before=manifest(ROOT,names) + need(len(names)>1500,'incomplete source tree') + template=output/'template';template.mkdir() + for name in names: + target=template/name;target.parent.mkdir(parents=True,exist_ok=True);shutil.copy2(ROOT/name,target) + need(manifest(template,names)==before==manifest(ROOT,names),'source drift during snapshot') + git('init','-q',cwd=template);git('add','-A',cwd=template) + git('commit','-q','--no-verify','-m','Frozen complete verification input',cwd=template) + commit=git('rev-parse','HEAD',cwd=template).decode().strip() + need(not git('status','--porcelain',cwd=template),'snapshot must be clean') + package=str(HERE.relative_to(ROOT)/'verify.py') + commands={g:['make',g] for g in groups};commands['selected-finite-package']=[sys.executable,'-B',package] + # Start historical finite searches and complete tests early; their slower + # tail otherwise dominates the run. The coverage record keeps native order. + priority=['verify-research','verify-tests','verify-joint','verify-producers', + 'verify-community','verify-clones','verify-strips','verify-pair'] + schedule=priority+[g for g in commands if g not in priority] + need(len(schedule)==len(commands) and set(schedule)==set(commands),'schedule coverage') + coverage=dict(technique_pr=154,technique_commit='d67773363075cc787b6f6ffa07191475c7c3fbec', + makefile_sha256=before['Makefile']['sha256'],native_recipe=groups,native_group_count=len(groups), + scheduled_commands=commands,execution_order=schedule,all_native_commands_covered=True,unaccounted_recipe_commands=0, + snapshot_commit=commit,source_files=before,group_workers=args.jobs,nested_jobs=1) + dump(output/'coverage.json',coverage) + env={k:v for k,v in os.environ.items() if k not in ('MAKEFLAGS','MFLAGS','MAKELEVEL')} + env.update(JOBS='1',MAKEFLAGS='-j1',OPENBLAS_NUM_THREADS='1',OMP_NUM_THREADS='1',PYTHONDONTWRITEBYTECODE='1') + setup_seconds=time.monotonic()-pipeline_begin;started=time.time();results={} + def run(label,command): + group_begin=time.monotonic() + tree=output/'trees'/label;git('clone','-q',str(template),str(tree),cwd=output) + need(git('rev-parse','HEAD',cwd=tree).decode().strip()==commit,'snapshot commit mismatch') + need(manifest(tree,names)==before,'group input manifest mismatch') + preparation_seconds=time.monotonic()-group_begin;begin=time.time();error=None;code=None + log=output/'logs'/(label+'.log') + with log.open('w') as stream: + try: + child=subprocess.Popen(command,cwd=tree,env=env,stdout=stream,stderr=subprocess.STDOUT,start_new_session=True) + code=child.wait(timeout=args.group_timeout) + except subprocess.TimeoutExpired: + error='group timeout';os.killpg(child.pid,signal.SIGTERM) + try:child.wait(timeout=5) + except subprocess.TimeoutExpired:os.killpg(child.pid,signal.SIGKILL);child.wait() + changed=git('status','--porcelain','--untracked-files=no',cwd=tree).decode() + try:unchanged=manifest(tree,names)==before + except (OSError,ValueError):unchanged=False + return label,dict(status='PASS' if code==0 and unchanged and not changed and not error else 'FAIL', + command=command,exit_code=code,error=error,elapsed_seconds=round(time.time()-begin,3), + clone_and_input_check_seconds=round(preparation_seconds,3),total_group_seconds=round(time.monotonic()-group_begin,3), + input_snapshot=commit,all_input_bytes_unchanged=unchanged,tracked_changes=changed, + log=str(log.relative_to(output))) + with ThreadPoolExecutor(max_workers=args.jobs) as pool: + pending={pool.submit(run,label,commands[label]):label for label in schedule} + for future in as_completed(pending): + label=pending[future] + try:label,result=future.result() + except Exception as exc:result=dict(status='FAIL',error=repr(exc),input_snapshot=commit) + results[label]=result;dump(output/'progress.json',dict(results=results,total=len(commands),snapshot_commit=commit)) + print('[%d/%d] %s %s'%(len(results),len(commands),result['status'],label),flush=True) + after=manifest(ROOT,names) + stable=after==before and source_names()==names + complete=set(results)==set(commands) + ok=stable and complete and all(r['status']=='PASS' for r in results.values()) + report=dict(status='PASS' if ok else 'FAIL',snapshot_commit=commit, + source_stable_before_and_after=stable,all_scheduled_groups_completed=complete, + coverage_sha256=sha256((output/'coverage.json').read_bytes()).hexdigest(), + setup_seconds=round(setup_seconds,3),elapsed_seconds=round(time.time()-started,3), + total_wall_seconds=round(time.monotonic()-pipeline_begin,3),results=results) + dump(output/'result.json',report) + print(report['status']+' complete isolated verification: '+str(len(results))+' groups',flush=True) + if not ok:raise SystemExit(1) + + +if __name__=='__main__':main() diff --git a/research/paired-cube-scalar-audit/LICENSE b/research/paired-cube-scalar-audit/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/research/paired-cube-scalar-audit/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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Original checker notices are preserved. + +The pinned finite construction, annealed modules, physical schedules and +terminal-sink integration are eumemic's PR168 work with Anthropic Claude +assistance. The terminal-sink substitution is due to jamesyc (PR166). +The local graph, decoder, shared-core ledger and finite bridge build on +icekylinx (PR144), eumemic (PR117), and Zhihao Chen/Swapnil Jain (PR97). +The late-read conventions build on jamesyc (PR124) and eumemic (PR143). + +The new pure exact arithmetic implementations were developed and reviewed +by separate AI agents in this contribution. The scalar event specification +follows the pinned native schedule, while formal variables replace sampled +dirty values. No independent human review or general phase theorem is claimed. +The paired-bit exhaustive-basis approach also follows the separately credited +finite verification approach in huxint's PR170. + +The superseded 64 operation-frame refinement is Rohan Arun's PR178 contribution, +prepared with OpenAI Codex assistance, on eumemic's PR168 construction. +PR178 retains PR176's terminal audit technique credited to Chafik Boukhalfa. +Our contribution adds independent exact checks and parameter refinement; +the prerequisite frame construction and all its notices are preserved. + +Current local-circuit inputs are Chafik Boukhalfa's PR181 contribution with +substantial Anthropic Claude and OpenAI Codex assistance. Signed destination-reflection support +extends the original pure sink checker, retaining its Apache-2.0 notice and +recording both method hashes/provenance in SOURCE.json. The native PR175 +verification overlay is preserved exactly, without claiming ownership of it. diff --git a/research/paired-cube-scalar-audit/README.md b/research/paired-cube-scalar-audit/README.md new file mode 100644 index 0000000000..cd9ab31fcd --- /dev/null +++ b/research/paired-cube-scalar-audit/README.md @@ -0,0 +1,56 @@ +# Exact scalar audits of the selected local-circuit schedules + +The pure checkers audit the finite complex and unchanged bit scalar maps at +PR181 `7fb2194801e3a10f54772c7f0d5505035a4fc0ad`. They import no upstream +producer or checker. The wrapper reads that package's frozen raw graph, word, +annihilator frames, physical frames and pairs; sinks are explicitly projected +to(role,pivot). Six canonical witness hashes, all1700 native Git-file hashes, +all audit source hashes and the entire owned precision package are locked +together by SOURCE.json and a hardcoded joint digest. + +The complex word has13042 logical roles,10688 arbitrary retained dirty slots, +44 terminal sinks and330 signed destination reflections. Both directions +cover1320 source,1320 initial target and10688 dirty columns: all13328 formal +variables. The required maps are(X,Y+X,Z) forward and(X-Y,Y,Z) reflected. +Exact rational sparse rows check every present/absent coefficient. The raw +operation and phase-first adjoint responses are independently compared; +signed shears use their literal signed inverse. K/inverse, center flush, +compensation reads and dirty/source restoration are included. Five full-word +mathematical corruptions must fail, including missing reflection sign. + +The unchanged bit checker verifies all1760 source and18028 dirty columns, +all3960 gauge reads and partner-K scheduling with six adverse controls. +Targets remain arbitrary additive destinations. This is the F2 identity, +separate from the native integer decoder and local-ring compiler contracts. + +```sh +python -B research/paired-cube-scalar-audit/verify.py +python -O -B research/paired-cube-scalar-audit/verify.py +python -B research/paired-cube-scalar-audit/test_bit.py +python -B research/paired-cube-scalar-audit/test_sinks.py +python -B research/paired-cube-scalar-audit/test_signed.py +python -B research/paired-cube-scalar-audit/test_source.py +``` + +Use Python3.12 or later. All pure guards remain active under -O. +No original PR168 producer is invoked for the new local circuit. Optional +--complex-work-dir accepts external raw181 graph/selection/frames only if +they match the pinned canonical hashes; default reads the selected witnesses. +--bit-only skips the complex execution. Each core has a300-second wall guard; +full execution requires an external4GiB memory limit, enforced in CI. + +The wrapper also checks the precision input/native component binding. That +step is consistency evidence: it compares all positive bins and dimensions, +and reports target zero diagnostics6270(native) versus6323(literal recount). +Zero-rank events have no child/moment/rank charge; c/R/M scalar bills remain +complete. General phase/cost, weighted compiler, restored rows, analytic, +precision/recovery and fixed-tape all-size interfaces remain hypotheses. + +Chafik Boukhalfa's PR181 local circuit, prepared with substantial Anthropic +Claude and OpenAI Codex assistance, is built on eumemic's PR168 construction. +James Chang supplies terminal accumulation and icekylinx shared-core accounting. +Rohan Arun's earlier PR178 frame refinement remains superseded lineage. +Independent scalar and signed extensions were developed and reviewed by +different AI agents in this contribution with substantial OpenAI Codex +assistance. See NOTICE and unchanged Apache-2.0 LICENSE; no human peer review +or all-size theorem acceptance is claimed. diff --git a/research/paired-cube-scalar-audit/SOURCE.json b/research/paired-cube-scalar-audit/SOURCE.json new file mode 100644 index 0000000000..b3c74e54a2 --- /dev/null +++ b/research/paired-cube-scalar-audit/SOURCE.json @@ -0,0 +1,1757 @@ +{ + "audit_sha256": { + "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "NOTICE": "22aa76a5e364d017a1753c3d53acacb01d5463c7f239a631e124f218e2bf9d11", + "README.md": "8297902adc7b771aa2d4a3797e61f3410616639019f9dfff87b6620504203e2e", + "independent_bit.py": "0ceac13910e1d50b2145062fc5db38a3709d82e85bf5d8ff000a0d64a36b104b", + "independent_sinks.py": "6345a9b3a899ccdf40a2a97062fb01b0abe6e989aad938656b706f80e77586df", + "test_bit.py": "88b76b692e466139b10ffcfdeda9437b44e5a350d2461abdea40f7bc78cfc564", + "test_signed.py": "6462d0c2134af61a09f6f9c822997c32b9c2fc5e9a6251154a828fbf36a60224", + "test_sinks.py": "d024ab775dbdd7edab9635ec8df8f3e7729a64a766c0fc345f1d4f140f6cb930", + "test_source.py": "0c84b6ed17ee975852e6369af514c91b6762edac66f12bd4ffdc1e67b8868106", + "verify.py": "2efe5424f19004bd5629b55d86067e4ab72728b026987feadd057b63c58de653" + }, + "checker_sha256": { + "independent_bit.py": "0ceac13910e1d50b2145062fc5db38a3709d82e85bf5d8ff000a0d64a36b104b", + "independent_sinks.py": "6345a9b3a899ccdf40a2a97062fb01b0abe6e989aad938656b706f80e77586df" + }, + "complex_canonical_sha256": { + "graph": "ebf6a1d4f8b7a793473305bae51a38f761f691760463e3dd5b2572a6aabb92df", + "operation_frames": "f35d957ba4656c494f8c30915239824690b9b1c699c0cb7d21f4cf3507c681e6", + "pairs": "b397d8b98fff00627c1019d2434d3bc3891a1a63de49f90e4b1a7e63270c3fec", + "sinks": "76c348bc9b0e00873dc26c3e5c5466fcd99466aaf1e9fec512fd0a0e66ca7172", + "witness": "e2be94a54f3ff00b52b2fd22b9a132a8f180d418726c63520a070f4a48728bea", + "word": "4405c0297882bcd2fad29ada464f251fcd46a4afde25a2fd410a91e445b87965" + }, + "excludes": [ + "SOURCE.json self-reference", + "CI workflow reviewed at exact local commit" + ], + "external_memory_limit_bytes": 4294967296, + "joint_input_closure_sha256": "21a3820abbbcf03fc385fe3a7321aefc38ba2d57899216e5b269236242996c4d", + "precision_sha256": { + "research/precision-certificate/LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "research/precision-certificate/NOTICE": "731c98adbe6931063ff42bcb4d48066616d9bd1cb500f6dd691e28c5271dcf24", + "research/precision-certificate/PROOF.md": "3ff4476884a459fd12d13a907653ab2e312af298ead9def78bda55eb27e5fbfd", + "research/precision-certificate/README.md": "b3bc3b07f555354413a6fe156ae08cd3ff35007469ac9cb5fd42e4e9d2e0ed2f", + "research/precision-certificate/SOURCE.json": "cd925ef1bdffca3633f7a0ad0d6cbbbedadcc557dd68439352f6db64587343cc", + "research/precision-certificate/certificate.json": "96ad1288492337ae43b7ec154b41b08ad63b7479bed4597d5932c402356b812b", + "research/precision-certificate/independent_assembly.py": "99584fe21922926ed9766ec5bc75a06ae531f396bf41ef87baafde248e1f9b9b", + "research/precision-certificate/independent_moments.py": "4d398b4600f7aeaf73a36c68ebc9727de0451399512769282684ae9d4804f594", + "research/precision-certificate/inputs/paired-cube-bit-physical-input.json": "6735294e8639da09eb3eb2234cbc5814298442a6c946b5534bcf6e48903547f3", + "research/precision-certificate/inputs/paired-cube-complex-input.json": "9adcc1e7da7222e19dce989cd6f86200997a677642b4c2a580aaae0c0a31a855", + "research/precision-certificate/inputs/paired-cube-sinks-input.json": "aeb7b2c053f6eacd55837c4c597a9cb3626d681495b783cc6310789e35b5fc9a", + "research/precision-certificate/profile_binding.py": "60c45e909609c5cfb6d06cb609dbb4d4a4c86d8f12ea6153391576613b18747f", + "research/precision-certificate/test_native.py": "24bfa24fee7c57c813de7a4cd6d380eda81094a438cdcc00a822c58894186be6", + "research/precision-certificate/test_precision.py": "4414fb1697373522ce6f770ce32a4f994c54cbbd08721c7c19352f651938eb5f", + "research/precision-certificate/verify.py": "4c7141a7192fe0cfb134aac3b157dd392d519fa546854f60f82b7edbf6eca8df" + }, + "prior_sink_core_sha256": "2e22beab7b7a84c94a31743b16ade95af8430bf6257ff3efb5432c75f197a319", + "schema_version": 1, + "scope": "Exact finite selected signed/bit scalar maps and native input consistency. 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Pure standard library, +no imports from the producer or its checker. Raw witness conventions and +chronology follow fd25adb7fbaa12ee761d02c733c54d1d2a7687ee. Integer bitsets +encode coefficients of EVERY source and independent physical dirty variable. +This proves this finite scalar map only, not frame/phase or all-size claims. +""" +import argparse +import ctypes +import gzip +import hashlib +import json +import os +from pathlib import Path +import sys +import time + + +class AuditError(ValueError): + pass + + +class IdentityError(AuditError): + pass + + +def require(condition, message): + if not condition: + raise AuditError(message) + + +class Budget: + """Time/private-memory guard; resource measurement adapted from R6 audit.""" + def __init__(self, seconds=300, memory_bytes=4*1024**3): + self.start = time.monotonic() + self.seconds, self.memory_bytes, self.peak = seconds, memory_bytes, 0 + self.steps = 0 + if os.name == 'nt': + from ctypes import wintypes + class Counters(ctypes.Structure): + _fields_ = [('cb', wintypes.DWORD), ('faults', wintypes.DWORD)] + [ + (n, ctypes.c_size_t) for n in ('peak_working', 'working', + 'peak_paged', 'paged', 'peak_nonpaged', 'nonpaged', 'pagefile', + 'peak_pagefile', 'private')] + self.counters = Counters() + self.counters.cb = ctypes.sizeof(Counters) + self.psapi = ctypes.WinDLL('psapi', use_last_error=True) + self.psapi.GetProcessMemoryInfo.argtypes = [wintypes.HANDLE, + ctypes.POINTER(Counters), wintypes.DWORD] + self.psapi.GetProcessMemoryInfo.restype = wintypes.BOOL + self.kernel = ctypes.WinDLL('kernel32', use_last_error=True) + self.kernel.GetCurrentProcess.restype = wintypes.HANDLE + self.sample() + + def sample(self): + require(time.monotonic()-self.start <= self.seconds, 'wall budget exceeded') + if os.name == 'nt': + require(self.psapi.GetProcessMemoryInfo(self.kernel.GetCurrentProcess(), + ctypes.byref(self.counters), self.counters.cb), 'memory measurement failed') + self.peak = max(self.peak, self.counters.private, self.counters.peak_pagefile) + else: + import resource + peak = resource.getrusage(resource.RUSAGE_SELF).ru_maxrss + self.peak = max(self.peak, int(peak) if sys.platform == 'darwin' else int(peak)*1024) + require(self.peak <= self.memory_bytes, 'memory budget exceeded') + + def tick(self): + self.steps += 1 + if self.steps % 1024 == 0: + self.sample() + + def report(self): + self.sample() + return dict(elapsed_seconds=time.monotonic()-self.start, + measured_peak_bytes=self.peak, memory_budget_bytes=self.memory_bytes, + wall_budget_seconds=self.seconds, workers=1, steps=self.steps, + memory_metric='Windows private/peak pagefile bytes; Unix peak resident bytes') + + +def isint(x): + return type(x) is int + + +class Protocol: + def __init__(self, graph, word, kchron, budget): + self.budget = budget + self.v = graph['v'] + require(isint(self.v) and self.v > 0, 'source dimension') + self.ops = [tuple(x) for x in word['ops']] + require(all(len(x) == 3 and all(isint(n) and n >= 0 for n in x) + and x[0] != x[1] for x in self.ops), 'operation format') + self.sources = {int(s): r for s, r in word['sources'].items()} + require(set(self.sources) == set(range(self.v)) and + len(set(self.sources.values())) == self.v, 'source bijection') + self.roots = graph['roots'] + self.rootroles = word['rootroles'] + require(len(self.roots) == len(self.rootroles), 'root correspondence') + require(all(r['kind'] in ('center', 'side') for r in self.roots), 'root kind') + require(all(isint(t) and 0 <= t < self.v for r in self.roots + for t in r['targets']), 'target index') + roles = [n for op in self.ops for n in op[:2]] + list(self.sources.values()) + self.rootroles + require(all(isint(r) and r >= 0 for r in roles), 'role index') + self.R = max(roles)+1 + phase = word['phase1'] + require(len(set(phase)) == len(phase) and + all(isint(i) and 0 <= i < len(self.ops) for i in phase), 'phase indices') + early = sorted(phase) + earlyset = set(early) + self.order = early + [i for i in range(len(self.ops)) if i not in earlyset] + self.cut = len(early) + self.position = {i: p for p, i in enumerate(self.order)} + touched = set() + role_ops = [[] for _ in range(self.R)] + for p, i in enumerate(self.order): + for s in self.ops[i][:2]: + role_ops[s].append(i) + if p < self.cut: + touched.add(s) + require(all(row == sorted(row) for row in role_ops), 'per-role order') + gauges = word['gauges'] + gauge_roles = [g['role'] for g in gauges] + require(len(set(gauge_roles)) == len(gauge_roles) and all( + isint(s) and 0 <= s < self.R and role_ops[s] and s not in touched + and s not in self.sources.values() for s in gauge_roles), 'gauge roles') + reads = {int(s): p for s, p in word.get('reads', {}).items()} + require(set(reads) <= set(gauge_roles), 'read roles') + self.when = {} + for k, g in enumerate(reversed(gauges)): + s = g['role']; p = reads.get(s, self.cut) + require(isint(p) and self.cut <= p <= self.position[role_ops[s][0]], 'read window') + self.when[s] = (p, k) + self.pairs = [tuple(pair) for pair in word.get('pairs', [])] + require(all(len(pair) == 2 and all(isint(s) and 0 <= s < self.R for s in pair) + for pair in self.pairs), 'pair format') + donors = {a for a, b in self.pairs}; recipients = {b for a, b in self.pairs} + require(len(donors) == len(recipients) == len(self.pairs) and + not donors & recipients, 'disjoint pair matching') + for a, b in self.pairs: + require(role_ops[a] and a not in self.rootroles and b in self.when and + self.position[role_ops[a][-1]] < self.when[b][0], 'pair lifetime') + self.slot = list(range(self.R)) + for a, b in self.pairs: + self.slot[b] = a + require(all(self.slot[a] != self.slot[b] for a, b, _ in self.ops), 'aliased gate ports') + self.physical = sorted(set(self.slot)) + self.response = [0]*self.R + for r, s in zip(self.roots, self.rootroles): + for t in r['targets']: + self.response[s] ^= 1 << t + # Transpose of the ORIGINAL logical gate word in its native execution order. + for i in reversed(self.order): + a, b, _ = self.ops[i] + self.response[b] ^= self.response[a] + budget.tick() + self.entries = kchron['entries'] + self.deliveries = {} + for e in self.entries: + c, d, j = e['carrier'], e['passive'], e['deliver_after_root'] + require(isint(c) and isint(d) and c != d and 0 <= c < self.v and 0 <= d < self.v, + 'K source index') + require(isint(j) and 0 <= j < len(self.roots) and self.roots[j]['kind'] == 'side', + 'K delivery root') + require(all(isint(t) and 0 <= t < self.v for t in e['receivers']), 'K receiver') + self.deliveries.setdefault(j, []).append(e) + + def run(self, mutation=None, role=None): + budget = self.budget + X = [1 << t for t in range(self.v)] + initial = {s: 1 << (self.v+j) for j, s in enumerate(self.physical)} + z = dict(initial) + Y = [0]*self.v + at = {} + for s in sorted(self.when, key=self.when.get): + if mutation == 'omit_read' and s == role: + continue + p = self.when[s][0] + if mutation == 'premature_read' and s == role: + p = self.cut + if mutation == 'read_position_as_index': + p = self.position[p] + at.setdefault(p, []).append(s) + + def read(s): + mask = self.response[s] + value = z[self.slot[s]] + while mask: + bit = mask & -mask + Y[bit.bit_length()-1] ^= value + mask ^= bit + budget.tick() + + def gate(i): + a, b, _ = self.ops[i] + z[self.slot[a]] ^= z[self.slot[b]] + budget.tick() + + for s in range(self.R): + if s not in self.when: + read(s) + for leaf, s in self.sources.items(): + z[self.slot[s]] ^= X[leaf] + for i in self.order[:self.cut]: + gate(i) + for r, s in zip(self.roots, self.rootroles): + if r['kind'] == 'center': + for t in r['targets']: + Y[t] ^= z[self.slot[s]] + for p in range(self.cut, len(self.order)): + for s in at.get(p, ()): + read(s) + gate(self.order[p]) + for j, (r, s) in enumerate(zip(self.roots, self.rootroles)): + if r['kind'] == 'side': + for t in r['targets']: + Y[t] ^= z[self.slot[s]] + for e in self.deliveries.get(j, ()): + c, d = e['carrier'], e['passive'] + X[c] ^= X[d] + for t in e['receivers']: + Y[t] ^= X[d] if mutation == 'wrong_K_injection' else X[c] + # Match native forward entry-list source restoration, and CHECK it. + for e in self.entries: + X[e['carrier']] ^= X[e['passive']] + for i in self.order if mutation == 'wrong_inverse_order' else reversed(self.order): + gate(i) + for leaf, s in self.sources.items(): + z[self.slot[s]] ^= X[leaf] + for t, value in enumerate(X): + if value != 1 << t: + raise IdentityError('source restoration failure at %s' % t) + for s in self.physical: + if z[s] != initial[s]: + raise IdentityError('dirty restoration failure at physical role %s' % s) + for t, value in enumerate(Y): + if value != 1 << t: + delta = value ^ (1 << t) + col = (delta & -delta).bit_length()-1 + raise IdentityError('target identity failure at target %s, basis column %s' % (t, col)) + budget.sample() + return dict(target_rows=self.v, source_rows_restored=self.v, + physical_dirty_rows_restored=len(self.physical), + independent_basis_columns=self.v+len(self.physical), + logical_roles=self.R, physical_roles=len(self.physical), + operations=len(self.ops), phase_one_operations=self.cut, + pairs=len(self.pairs), gauge_reads=len(self.when), + unpaired_gauge_reads=sum(s not in {b for a, b in self.pairs} for s in self.when), + explicit_late_reads=sum(p > self.cut for p, k in self.when.values()), + K_deliveries=len(self.entries)) + + +def check(raw_graph, raw_word, raw_kchron, *, controls=False, seconds=300, memory_bytes=4*1024**3): + """Accept parsed RAW witness objects; hashes belong in caller's source manifest.""" + budget = Budget(seconds, memory_bytes) + protocol = Protocol(raw_graph, raw_word, raw_kchron, budget) + result = protocol.run() + rejected = {} + if controls: + recipients = {b for a, b in protocol.pairs} + paired = next((b for a, b in protocol.pairs if protocol.response[b]), None) + unpaired = next((s for s in protocol.when if s not in recipients and protocol.response[s]), None) + late = next((b for a, b in protocol.pairs if protocol.response[b] and + protocol.when[b][0] > protocol.cut and any( + protocol.ops[i][0] == a for i in protocol.order[protocol.cut:protocol.when[b][0]])), None) + require(paired is not None and unpaired is not None and late is not None and + protocol.entries, 'required negative-control witnesses absent') + mutations = [('omitted_paired_read', 'omit_read', paired), + ('omitted_unpaired_read', 'omit_read', unpaired), + ('premature_paired_read', 'premature_read', late), + ('read_position_as_index', 'read_position_as_index', None), + ('wrong_K_injection', 'wrong_K_injection', None), + ('wrong_inverse_order', 'wrong_inverse_order', None)] + for name, mutation, role in mutations: + try: + protocol.run(mutation, role) + except IdentityError as error: + rejected[name] = dict(role=role, reason=str(error)) + else: + raise AuditError('negative control accepted: '+name) + return dict(status='computed_pass', scalar_identity=result, + rejected_controls=rejected, resource=budget.report(), + scope='exact finite F2 scalar operator over all source/physical-dirty columns; frame, phase, cost and all-size proofs excluded') + + +def unique_object(pairs): + obj = {} + for key, value in pairs: + require(key not in obj, 'duplicate JSON key') + obj[key] = value + return obj + + +def load(path): + data = path.read_bytes() + if path.suffix == '.gz': + data = gzip.decompress(data) + return json.loads(data, object_pairs_hook=unique_object) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('graph', type=Path) + parser.add_argument('word', type=Path) + parser.add_argument('kchron', type=Path) + parser.add_argument('--controls', action='store_true') + args = parser.parse_args() + result = check(load(args.graph), load(args.word), load(args.kchron), controls=args.controls) + result['raw_input_sha256'] = {str(p): hashlib.sha256(p.read_bytes()).hexdigest() + for p in (args.graph, args.word, args.kchron)} + print(json.dumps(result, indent=2)) + + +if __name__ == '__main__': + main() diff --git a/research/paired-cube-scalar-audit/independent_sinks.py b/research/paired-cube-scalar-audit/independent_sinks.py new file mode 100644 index 0000000000..9a5262a648 --- /dev/null +++ b/research/paired-cube-scalar-audit/independent_sinks.py @@ -0,0 +1,440 @@ +"""Independent exact scalar sink protocol; stdlib only, no producer imports. + +Sparse integer numerator vectors carry an adaptive exact denominator per row. +Signed unit gates use z[a] <- ca*z[a]+cb*z[b]; their inverse is +z[a] <- ca*z[a]-ca*cb*z[b]. Reflected events invert this signed map. +Both input banks and every retained dirty slot have disjoint formal variables. +Frame eligibility of sinks is checked; this is not a complete phase/frame proof. +Apache-2.0. Prepared with Codex assistance. +""" +from hashlib import sha256 +import json +from math import lcm +from pathlib import Path +import sys +import time + + +class IdentityError(ValueError): pass + + +def need(condition, message): + if not condition: raise ValueError(message) + + +class Meter: + def __init__(self, seconds=300): + self.start=time.monotonic(); self.seconds=seconds; self.operations=0 + def check(self): + if time.monotonic()-self.start>self.seconds: raise TimeoutError('exact audit wall budget') + + +class Row: + def __init__(self, data=None, denominator=1): + need(type(denominator) is int and denominator>0, 'positive exact denominator') + need(data is None or (type(data) is dict and all(type(k) is int and k>=0 and type(v) is int and v!=0 + for k,v in data.items())), 'exact sparse integer row') + self.data={} if data is None else data + self.denominator=denominator + def add(self, source, factor, meter): + need(self is not source, 'distinct row ports') + numerator, denominator=factor + need(type(numerator) is int and type(denominator) is int and denominator>0, 'exact factor') + if not numerator or not source.data: return + new=lcm(self.denominator, source.denominator*denominator) + multiplier=new//self.denominator + if multiplier!=1: + for column in self.data: self.data[column]*=multiplier + self.denominator=new + multiplier=numerator*(new//(source.denominator*denominator)) + for count,(column,value) in enumerate(source.data.items()): + new_value=self.data.get(column,0)+multiplier*value + if new_value: self.data[column]=new_value + else: self.data.pop(column,None) + if not count%4096: meter.check() + meter.operations+=len(source.data) + def scale(self, sign, meter): + need(type(sign) is int and sign in (-1,1), 'exact row sign') + if sign == -1: + for count, column in enumerate(self.data): + self.data[column] = -self.data[column] + if not count % 4096: meter.check() + meter.operations += len(self.data) + + def equals(self, coefficients): + return self.data=={k:self.denominator*v for k,v in coefficients.items() if v} + + +def binary_basis(rows): + pivots={} + for value in rows: + need(type(value) is int and value>=0, 'binary frame vector') + for pivot in sorted(pivots,reverse=True): + if value>>pivot&1: value^=pivots[pivot] + if value: + pivot=value.bit_length()-1 + for other in list(pivots): + if pivots[other]>>pivot&1: pivots[other]^=value + pivots[pivot]=value + return tuple(pivots[p] for p in sorted(pivots,reverse=True)) + + +def complement(rows,h): + pivots={r.bit_length()-1:r for r in binary_basis(rows)} + out=[] + for j in range(h): + if j not in pivots: + value=1<>j&1: value|=1<0 and self.v and self.v%8==0,'dimensions') + need(all(type(q) is int and 0<=q<2**self.h for q in self.inputs),'source addresses') + labels=graph.get('labels',[]) + need(len(labels)==self.v and all(all(type(i) is int for i in label) and + set(label)=={i for i in range(self.h) if address>>i&1} + for label,address in zip(labels,self.inputs)), 'labels and source addresses agree') + self.ops=[tuple(o) for o in word['ops']] + self.coef=[tuple(o) for o in word['opcoeff']] + need(len(self.ops)==len(self.coef) and all(len(o)==3 and all(type(x) is int and x>=0 for x in o) for o in self.ops),'operation schema') + need(all(type(ca) is int and ca in (-1,1) and type(cb) is int and cb in (-1,1) for ca,cb in self.coef),'selected word must use signed unit gates') + self.phase=sorted(word['phase1']) + need(len(set(self.phase))==len(self.phase) and all(type(i) is int and 0<=i=0 for s in self.sources.values()) and + len(set(self.sources.values()))==self.v,'source bijection') + self.selected=[z['role'] for z in word['selected']] + need(all(type(s) is int and s>=0 for s in self.selected) and len(set(self.selected))==len(self.selected),'deferred role uniqueness') + deferred=set(self.selected) + self.roots=graph['roots']; self.rootroles=word['rootroles'] + need(all(type(s) is int and s>=0 for s in self.rootroles) and len(self.roots)==len(self.rootroles)==len(set(self.rootroles)),'root role bijection') + roles=set(self.sources.values())|deferred|set(self.rootroles) + for a,b,_ in self.ops: + need(a!=b,'equal gate ports'); roles.update((a,b)) + need(roles and all(type(s) is int and s>=0 for s in roles),'role schema') + self.R=max(roles)+1 + need(all(len(p)==3 and type(p[0]) is int and type(p[1]) is int and p[0]>=0 and p[1]>=0 and + (p[2] is None or type(p[2]) is int and p[2]>=0) for p in pairs),'pair exact schema') + self.merge={b:a for a,b,_ in pairs} + donors={a:b for a,b,_ in pairs} + need(len(self.merge)==len(donors)==len(pairs) and not set(donors)&set(self.merge),'pair matching') + self.deadlines={b:t for _,b,t in pairs} + first,last={},{} + for i in self.order: + for role in self.ops[i][:2]: first.setdefault(role,i); last[role]=i + for a,b,t in pairs: + need(a in last and b in first and a not in deferred and a not in self.rootroles and b in deferred,'pair kinds') + need(b not in self.sources.values(),'source recipient') + if t is None: + need(last[a] in phase and first[b] not in phase,'early alias chronology') + else: + need(type(t) is int and t==first[b] and t in self.rest and self.position[last[a]]self.position[writes[-1]],'sink pivot deadline') + need(not target_set&set(targets),'sink target groups disjoint') + target_set.update(targets) + self.sinks[s]={'pivot':pivot,'targets':targets,'writes':writes,'coefficient':1 if root['coefficients'][0]=='1/2' else -1,'rank':len(U)} + self.live=[s for s in range(self.R) if s not in self.merge and s not in self.sinks] + self.slots={s:i for i,s in enumerate(self.live)} + meter.check() + + def port(self,role): + role=self.merge.get(role,role) + need(role in self.slots,'access to removed sink') + return ('Z',self.slots[role]) + + def events(self): + events=[]; retained=[] + def addition(dest,source,factor,tag,identity=None): + need(dest!=source,'distinct event ports') + events.append({'kind':'add','dest':dest,'source':source,'factor':factor,'tag':tag,'identity':identity}) + def read(s,sign,seed=False): + events.append({'kind':'read','source':self.port(s),'role':s,'sign':sign,'seed':seed,'bank':'Y'}) + def signed_gate(i, inverse=False): + a,b,_=self.ops[i]; ca,cb=self.coef[i] + factor=(-ca*cb if inverse else cb,1) + tag='gate_inverse' if inverse else 'gate' + if ca == 1: + addition(self.port(a),self.port(b),factor,tag,i) + else: + events.append({'kind':'signed_add','dest':self.port(a),'source':self.port(b), + 'sign':ca,'factor':factor,'tag':tag,'identity':i}) + def gate(i): + signed_gate(i) + retained.append(i) + for s in range(self.R): + if s not in self.selected and s not in self.merge and s not in self.sinks: read(s,-1) + for x,s in sorted(self.sources.items()): addition(self.port(s),('X',x),(1,1),'injection',x) + for i in self.phase: gate(i) + for s in self.cs: read(s,1,True) + events.append({'kind':'flush','bank':'Y'}) + for s,z in self.sinks.items(): + for t in z['targets']: + if t!=z['pivot']: addition(('Y',t),('Y',z['pivot']),(-1,1),'sink_pre',s) + due={} + for s in reversed(self.selected): due.setdefault(self.read_at[s],[]).append(s) + redirected={i:s for s,z in self.sinks.items() for i in z['writes']} + final={z['writes'][-1]:s for s,z in self.sinks.items()} + for i in self.rest: + for s in due.get(i,[]): read(s,-1) + if i in redirected: + s=redirected[i]; z=self.sinks[s] + addition(('Y',z['pivot']),self.port(self.ops[i][1]),(z['coefficient']*self.coef[i][1],2),'sink_pivot',s) + else: gate(i) + if i in final: + s=final[i]; z=self.sinks[s] + for t in z['targets']: + if t!=z['pivot']: addition(('Y',t),('Y',z['pivot']),(1,1),'sink_post',s) + for root,s in zip(self.roots,self.rootroles): + if root['kind']=='side' and s not in self.sinks: read(s,1,True) + for base in range(0,self.v,8): + for parity in (0,1): + indices=[k for k in range(8) if k.bit_count()%2==parity] + targets=[k^7 for k in indices] + matrix=[] + for t in targets: + row=[] + for source in indices: + distance=(self.inputs[base+t]^self.inputs[base+source]).bit_count() + row.append((1 if distance==6 else -1 if distance==2 else 0,2)) + matrix.append(row) + ports=[('X',base+k) for k in indices] + events.append({'kind':'linear4','ports':ports,'matrix':matrix}) + for j,t in enumerate(targets): addition(('Y',base+t),ports[j],(1,1),'K_delivery') + events.append({'kind':'linear4','ports':ports,'matrix':[list(c) for c in zip(*matrix)]}) + for i in reversed(retained): + signed_gate(i, inverse=True) + for x,s in sorted(self.sources.items(),reverse=True): addition(self.port(s),('X',x),(-1,1),'uninjection',x) + return events + + def reflected(self,events): + swap=lambda port: ('Y' if port[0]=='X' else 'X' if port[0]=='Y' else 'Z',port[1]) + output=[] + for original in reversed(events): + e=dict(original) + if e['kind']=='add': + e['dest']=swap(e['dest']); e['source']=swap(e['source']) + n,d=e['factor']; e['factor']=(-n,d) + elif e['kind']=='signed_add': + e['dest']=swap(e['dest']); e['source']=swap(e['source']) + n,d=e['factor']; e['factor']=(-e['sign']*n,d) + elif e['kind']=='read': e['bank']='X' if e['bank']=='Y' else 'Y'; e['sign']=-e['sign'] + elif e['kind']=='linear4': + e['ports']=[swap(p) for p in e['ports']] + e['matrix']=[list(c) for c in zip(*e['matrix'])] + elif e['kind']=='flush': e['bank']='X' if e['bank']=='Y' else 'Y' + else: raise ValueError('unknown reflected event') + output.append(e) + return output + + def replay(self,events,reflected=False): + v=self.v; meter=self.meter + banks={'X':[Row({t:1}) for t in range(v)],'Y':[Row({v+t:1}) for t in range(v)], + 'Z':[Row({2*v+j:1}) for j in range(len(self.live))]} + pending={bank:[Row() for _ in range(self.h)] for bank in ('X','Y')} + def flush(bank): + for coordinate,row in enumerate(pending[bank]): + if row.data: + for t,address in enumerate(self.inputs): + factor=(1,3) if address>>coordinate&1 else (-1,6) + banks[bank][t].add(row,factor,meter) + pending[bank][coordinate]=Row() + def get(port): + if port[0]!='Z': flush(port[0]) + return banks[port[0]][port[1]] + for count,e in enumerate(events): + kind=e['kind'] + if kind=='add': + source=get(e['source']) + banks[e['dest'][0]][e['dest'][1]].add(source,e['factor'],meter) + elif kind=='signed_add': + need(e['dest']!=e['source'], 'distinct signed row ports') + source=get(e['source']); target=get(e['dest']) + target.scale(e['sign'],meter) + target.add(source,e['factor'],meter) + elif kind=='read': + value=get(e['source']); sign=e['sign']; role=e['role']; bank=e['bank'] + c=self.cs.get(role,{}) if e['seed'] else self.c[role] + d=self.ds.get(role,{}) if e['seed'] else self.d[role] + for coordinate,coefficient in c.items(): pending[bank][coordinate].add(value,(sign*coefficient,1),meter) + for target,coefficient in d.items(): banks[bank][target].add(value,(sign*coefficient,2),meter) + elif kind=='linear4': + old=[get(port) for port in e['ports']] + new=[Row() for _ in old] + for j,row in enumerate(e['matrix']): + for source,factor in zip(old,row): new[j].add(source,factor,meter) + for port,row in zip(e['ports'],new): banks[port[0]][port[1]]=row + elif kind=='flush': flush(e['bank']) + else: raise ValueError('unknown event kind') + if not count%128: meter.check() + flush('X'); flush('Y') + for t in range(v): + expect_x={t:1,v+t:-1} if reflected else {t:1} + expect_y={v+t:1} if reflected else {v+t:1,t:1} + if not banks['X'][t].equals(expect_x): raise IdentityError('source bank row '+str(t)) + if not banks['Y'][t].equals(expect_y): raise IdentityError('target bank row '+str(t)) + for j,row in enumerate(banks['Z']): + if not row.equals({2*v+j:1}): raise IdentityError('dirty restore row '+str(j)) + return {'forward':not reflected,'reflected':reflected,'source_rows':v,'target_rows':v,'dirty_rows':len(self.live), + 'formal_basis':2*v+len(self.live),'events':len(events),'ring':'Q via integer numerators/adaptive denominators', + 'all_absent_coefficients_checked':True,'largest_final_denominator':max(r.denominator for bank in banks.values() for r in bank)} + + +def audit_raw(graph,word,witness,frames,pairs,sinks,*,seconds=300): + """Pure entry point: raw data only, no producer/repository modules or I/O.""" + meter=Meter(seconds) + protocol=Protocol(graph,word,witness,frames,pairs,sinks,meter) + events=protocol.events() + positive={'forward':protocol.replay(events),'reflected':protocol.replay(protocol.reflected(events),True)} + controls={} + names=['omit_post_shear','wrong_pivot_sign','omit_compensated_read','wrong_dirty_inverse'] + if any(e['kind']=='signed_add' for e in events): names.append('wrong_reflection_sign') + for name in names: + changed=list(events) + if name=='omit_post_shear': + index=next(i for i,e in enumerate(changed) if e.get('tag')=='sink_post') + del changed[index] + elif name=='wrong_pivot_sign': + index=next(i for i,e in enumerate(changed) if e.get('tag')=='sink_pivot') + changed[index]=dict(changed[index]); n,d=changed[index]['factor']; changed[index]['factor']=(-n,d) + elif name=='omit_compensated_read': + recipient=next(b for b in protocol.merge if protocol.c[b] or protocol.d[b]) + index=next(i for i,e in enumerate(changed) if e['kind']=='read' and e['role']==recipient and e['sign']==-1) + del changed[index] + elif name=='wrong_reflection_sign': + index=next(i for i,e in enumerate(changed) if e['kind']=='signed_add' and e.get('tag')=='gate') + changed[index]=dict(changed[index]); changed[index]['sign']=1 + else: + index=next(i for i,e in enumerate(changed) if e.get('tag')=='gate_inverse') + changed[index]=dict(changed[index]); n,d=changed[index]['factor']; changed[index]['factor']=(-n,d) + try: protocol.replay(changed) + except IdentityError as error: controls[name]={'rejected':True,'reason':str(error)} + else: raise ValueError('mathematical negative control accepted: '+name) + return {'status':'computed_pass','event_sha256':sha256(json.dumps(events,sort_keys=True,separators=(',',':')).encode()).hexdigest(), + 'positive':positive,'controls':controls,'sink_count':len(protocol.sinks),'role_count':protocol.R, + 'retained_dirty':len(protocol.live),'aliases':len(protocol.merge), + 'native_response_correspondence':protocol.response_correspondence, + 'reflection_gates':sum(ca==-1 for ca,cb in protocol.coef), + 'elapsed_seconds':time.monotonic()-meter.start,'sparse_term_additions':meter.operations, + 'limits':{'seconds':seconds,'workers':1,'required_external_memory_limit_bytes':4*1024**3}, + 'scope':'Exact finite scalar maps on the full source, target and retained dirty basis; sink eligibility checks. Full frame/phase/all-size proof not certified.'} + + +def audit(folder): + folder=Path(folder) + data=lambda p: json.loads(p.read_text()) + work=folder/'producer-1'; repo=folder/'repo' + files={'graph':work/'graph.json','word':work/'selection.json','witness':work/'frames.json', + 'physical_frames':repo/'references/paired-cube/physical/frames.json', + 'physical_pairs':repo/'references/paired-cube/physical/pairs.json', + 'sinks':repo/'research/terminal-sinks/sinks.json'} + result=audit_raw(data(files['graph']),data(files['word']),data(files['witness']), + data(files['physical_frames'])['frames'],data(files['physical_pairs'])['pairs'],data(files['sinks'])['sinks']) + result['source_input_sha256']={k:sha256(p.read_bytes()).hexdigest() for k,p in files.items()} + result['checker_sha256']=sha256(Path(__file__).read_bytes()).hexdigest() + return result + + +if __name__=='__main__': + result=audit(sys.argv[1]) + target=Path(sys.argv[1])/(sys.argv[2] if len(sys.argv)>2 else 'exact-sinks-result.json') + with target.open('x') as stream: json.dump(result,stream,indent=2,sort_keys=True); stream.write('\n') + print(json.dumps(result,indent=2,sort_keys=True)) diff --git a/research/paired-cube-scalar-audit/test_bit.py b/research/paired-cube-scalar-audit/test_bit.py new file mode 100644 index 0000000000..8d59a8c9e5 --- /dev/null +++ b/research/paired-cube-scalar-audit/test_bit.py @@ -0,0 +1,99 @@ +"""Independent fixtures and corruption controls for the R14 finite F2 audit.""" +import copy +import unittest +from independent_bit import AuditError, Budget, IdentityError, Protocol, check + + +def fixture(): + graph = dict(v=3, roots=[dict(kind='center', targets=[2]), + dict(kind='side', targets=[0]), dict(kind='side', targets=[1])]) + word = dict(ops=[[4, 1, 0], [2, 4, 0], [5, 1, 0], [7, 6, 0]], + sources={'0': 0, '1': 1, '2': 6}, rootroles=[7, 2, 5], + phase1=[3], gauges=[dict(role=5), dict(role=2)], + reads={'5': 3, '2': 1}, pairs=[[4, 5]]) + k = dict(entries=[dict(carrier=0, passive=1, receivers=[0], deliver_after_root=1)]) + return graph, word, k + + +class TestAudit(unittest.TestCase): + def test_every_basis_column_and_native_chronology(self): + result = check(*fixture())['scalar_identity'] + self.assertEqual(result['target_rows'], 3) + self.assertEqual(result['physical_dirty_rows_restored'], 7) + self.assertEqual(result['independent_basis_columns'], 10) + self.assertEqual(result['unpaired_gauge_reads'], 1) + self.assertEqual(result['explicit_late_reads'], 1) + + def protocol(self): + return Protocol(*fixture(), Budget()) + + def test_omitted_paired_read_exposes_dirty_column(self): + with self.assertRaisesRegex(IdentityError, 'target identity.*basis column'): + self.protocol().run('omit_read', 5) + + def test_omitted_unpaired_read_exposes_dirty_column(self): + with self.assertRaisesRegex(IdentityError, 'target identity.*basis column'): + self.protocol().run('omit_read', 2) + + def test_read_before_donor_dies(self): + with self.assertRaisesRegex(IdentityError, 'target identity'): + self.protocol().run('premature_read', 5) + + def test_execution_position_is_not_operation_index(self): + p = self.protocol() + self.assertEqual(p.order, [3, 0, 1, 2]) + self.assertEqual(p.when[5][0], 3) + with self.assertRaisesRegex(IdentityError, 'target identity'): + p.run('read_position_as_index') + + def test_native_K_updated_carrier_required(self): + with self.assertRaisesRegex(IdentityError, 'target identity'): + self.protocol().run('wrong_K_injection') + + def test_reverse_gate_order_restores_arbitrary_dirty_values(self): + g = dict(v=1, roots=[dict(kind='side', targets=[0])]) + w = dict(ops=[[1, 0, 0], [2, 1, 1]], sources={'0': 0}, + rootroles=[2], phase1=[], gauges=[], pairs=[], reads={}) + p = Protocol(g, w, dict(entries=[]), Budget()) + p.run() + with self.assertRaisesRegex(IdentityError, 'dirty restoration'): + p.run('wrong_inverse_order') + + def test_missing_K_delivery_changes_identity(self): + g, w, k = fixture() + with self.assertRaisesRegex(IdentityError, 'target identity'): + check(g, w, dict(entries=[])) + + def test_bad_target_assignment_changes_identity(self): + g, w, k = fixture() + g['roots'][2]['targets'] = [0] + with self.assertRaisesRegex(IdentityError, 'target identity'): + check(g, w, k) + + def test_alias_lifetime_checked(self): + g, w, k = fixture() + w['reads']['5'] = 2 + with self.assertRaisesRegex(AuditError, 'pair lifetime'): + check(g, w, k) + + def test_duplicate_pair_rejected(self): + g, w, k = fixture() + w['pairs'] *= 2 + with self.assertRaisesRegex(AuditError, 'disjoint pair'): + check(g, w, k) + + def test_no_normalization_of_duplicate_target_occurrences(self): + g, w, k = fixture() + g['roots'][2]['targets'] = [1, 1] + with self.assertRaisesRegex(IdentityError, 'target identity'): + check(g, w, k) + + def test_missing_source_rejected(self): + g, w, k = fixture() + del w['sources']['1'] + with self.assertRaisesRegex(AuditError, 'source bijection'): + check(g, w, k) + + +if __name__ == '__main__': + unittest.main() diff --git a/research/paired-cube-scalar-audit/test_signed.py b/research/paired-cube-scalar-audit/test_signed.py new file mode 100644 index 0000000000..68668d9dbb --- /dev/null +++ b/research/paired-cube-scalar-audit/test_signed.py @@ -0,0 +1,56 @@ +"""Exact signed linear maps, adjoint signs and inverse/reflection contracts.""" +import unittest +import independent_sinks as C + +class Signed(unittest.TestCase): + def test_signed_adjoint_basis(self): + # The transpose of [[ca,cb],[0,1]] sends a destination covector + # (1,0) to (ca,cb), and a source covector (0,1) to itself. + for ca in (-1,1): + for cb in (-1,1): + C.check_response_correspondence([(1,0,0)],[(ca,cb)],[0], + {1:{0:1}},{0:{0:1}},[{0:cb},{0:ca}],[{0:1},{}],2) + with self.assertRaisesRegex(ValueError,'adjoint responses equal'): + C.check_response_correspondence([(1,0,0)],[(ca,cb)],[0], + {1:{0:1}},{0:{0:1}},[{0:cb},{0:-ca}],[{0:1},{}],2) + + def protocol(self): + p=C.Protocol.__new__(C.Protocol);p.v=1;p.h=1;p.inputs=[1];p.live=[0,1];p.meter=C.Meter() + p.cs={};p.ds={};p.c=[{},{}];p.d=[{},{}] + return p + + def events(self,cb): + # A reflection is its own inverse. The independent X->Y translation + # occurs while dirty registers carry arbitrary reflected values. + gate={'kind':'signed_add','dest':('Z',0),'source':('Z',1),'sign':-1,'factor':(cb,1)} + return [dict(gate),{'kind':'add','dest':('Y',0),'source':('X',0),'factor':(1,1)},dict(gate)] + + def test_both_reflections_preserve_arbitrary_dirty(self): + for cb in (-1,1): + p=self.protocol();events=self.events(cb) + self.assertEqual(p.replay(events)['formal_basis'],4) + self.assertTrue(p.replay(p.reflected(events),True)['reflected']) + + def test_wrong_signed_inverse_rejected(self): + for cb in (-1,1): + p=self.protocol();events=self.events(cb);events[-1]['factor']=(-cb,1) + with self.assertRaisesRegex(C.IdentityError,'dirty restore'):p.replay(events) + + def test_missing_reflection_sign_rejected(self): + p=self.protocol();events=self.events(1);events[0]['sign']=1 + with self.assertRaisesRegex(C.IdentityError,'dirty restore'):p.replay(events) + + def test_reflection_inverse_is_same_map(self): + p=self.protocol() + for cb in (-1,1): + e=self.events(cb)[0];self.assertEqual(p.reflected([e])[0],e) + + def test_row_sign_domain(self): + for sign in (True,False,0,2,0.5): + with self.assertRaisesRegex(ValueError,'exact row sign'):C.Row({0:1}).scale(sign,C.Meter()) + + def test_same_port_signed_gate_rejected(self): + p=self.protocol();event=self.events(1)[0];event['source']=event['dest'] + with self.assertRaisesRegex(ValueError,'distinct signed row ports'):p.replay([event]) + +if __name__=='__main__':unittest.main(verbosity=2) diff --git a/research/paired-cube-scalar-audit/test_sinks.py b/research/paired-cube-scalar-audit/test_sinks.py new file mode 100644 index 0000000000..03136fbe07 --- /dev/null +++ b/research/paired-cube-scalar-audit/test_sinks.py @@ -0,0 +1,74 @@ +import unittest +import independent_sinks as check + +class Arithmetic(unittest.TestCase): + def test_adaptive_denominator(self): + meter=check.Meter() + a=check.Row({0:1}); b=check.Row({1:1},2) + a.add(b,(1,3),meter) + self.assertEqual(a.denominator,6) + self.assertEqual(a.data,{0:6,1:1}) + a.add(b,(-1,3),meter) + self.assertTrue(a.equals({0:1})) + def test_self_port_refused(self): + a=check.Row({0:1}) + with self.assertRaisesRegex(ValueError,'distinct row'): a.add(a,(1,1),check.Meter()) + def test_boolean_factor_refused(self): + with self.assertRaisesRegex(ValueError,'exact factor'): + check.Row().add(check.Row({0:1}),(True,1),check.Meter()) + def test_float_and_boolean_rows_refused(self): + for row in ({0:0.5},{True:1},{0:True},{0:0}): + with self.assertRaisesRegex(ValueError,'exact sparse integer row'): check.Row(row) + def test_binary_complement(self): + for a in range(16): + for b in range(16): + basis=check.binary_basis((a,b)) + perp=check.complement(basis,4) + self.assertEqual(len(basis)+len(perp),4) + self.assertTrue(all(not((x&y).bit_count()%2) for x in basis for y in perp)) + def test_source_label_convention_enforced(self): + graph={'h':1,'inputs':[1]*8,'labels':[[0]]*7+[[]]} + with self.assertRaisesRegex(ValueError,'labels and source'): + check.Protocol(graph,{}, {}, [], [], [],check.Meter()) + def test_disjoint_reorder_keeps_all_responses(self): + result=check.check_response_correspondence([(1,0,0),(3,2,0)],[(1,1),(1,-1)],[1,0], + {1:{0:1}},{3:{0:1}},[{0:1},{0:1},{},{}],[{},{},{0:-1},{0:1}],4) + self.assertTrue(result['per_role_order_preserved']) + def test_shared_port_reorder_refused(self): + with self.assertRaisesRegex(ValueError,'per-role'): + check.check_response_correspondence([(1,0,0),(2,1,0)],[(1,1),(1,1)],[1,0],{},{},[{}, {}, {}],[{}, {}, {}],3) + def test_wrong_response_refused(self): + with self.assertRaisesRegex(ValueError,'adjoint responses equal'): + check.check_response_correspondence([(1,0,0)],[(1,1)],[0],{1:{0:1}},{},[{}, {0:1}],[{}, {}],2) + def protocol(self): + p=check.Protocol.__new__(check.Protocol) + p.v=1; p.h=1; p.inputs=[1]; p.live=[0]; p.meter=check.Meter() + p.cs={};p.ds={};p.c=[{}];p.d=[{}] + return p + def test_full_target_basis_and_reflection(self): + p=self.protocol() + events=[{'kind':'add','dest':('Y',0),'source':('X',0),'factor':(1,1)}] + self.assertEqual(p.replay(events)['formal_basis'],3) + self.assertTrue(p.replay(p.reflected(events),True)['reflected']) + def test_read_target_identity_corruption_detected(self): + p=self.protocol() + events=[{'kind':'add','dest':('Y',0),'source':('X',0),'factor':(1,1)}, + {'kind':'add','dest':('X',0),'source':('Y',0),'factor':(1,1)}] + with self.assertRaisesRegex(check.IdentityError,'source bank'): p.replay(events) + def test_dirty_corruption_detected(self): + p=self.protocol() + events=[{'kind':'add','dest':('Y',0),'source':('X',0),'factor':(1,1)}, + {'kind':'add','dest':('Z',0),'source':('Y',0),'factor':(1,2)}] + with self.assertRaisesRegex(check.IdentityError,'dirty restore'): p.replay(events) + def test_immediate_center_flush_before_target_control(self): + p=self.protocol();p.cs={0:{0:1}} + events=[{'kind':'read','source':('Z',0),'role':0,'sign':1,'seed':True,'bank':'Y'}, + {'kind':'add','dest':('X',0),'source':('Y',0),'factor':(1,1)}, + {'kind':'read','source':('Z',0),'role':0,'sign':-1,'seed':True,'bank':'Y'}, + {'kind':'add','dest':('X',0),'source':('Y',0),'factor':(-1,1)}, + {'kind':'add','dest':('Y',0),'source':('X',0),'factor':(1,1)}] + # A delayed scatter would cancel the pending reads and falsely pass. + # Correct scheduling transfers a nonzero dirty coefficient to X. + with self.assertRaisesRegex(check.IdentityError,'source bank'): p.replay(events) + +if __name__=='__main__': unittest.main(verbosity=2) diff --git a/research/paired-cube-scalar-audit/test_source.py b/research/paired-cube-scalar-audit/test_source.py new file mode 100644 index 0000000000..0e9846cc87 --- /dev/null +++ b/research/paired-cube-scalar-audit/test_source.py @@ -0,0 +1,46 @@ +"""Source-binding controls separate from the mathematical scalar controls.""" +import copy +import json +import unittest +import verify as V + +class SourceControls(unittest.TestCase): + def manifest(self): + return json.loads((V.HERE/'SOURCE.json').read_bytes()) + def check(self,data,read=None): + return V.check_source_manifest(data,read or (lambda p:(V.ROOT/p).read_bytes()), + lambda p:(V.HERE/p).read_bytes()) + def test_full_raw_source_closure(self): + self.check(self.manifest()) + def test_wrong_revision_label(self): + data=self.manifest();data['upstream_commit']='0'*40 + with self.assertRaisesRegex(ValueError,'wrong upstream revision'):self.check(data) + def test_input_manifest_cannot_relabel_modified_sources(self): + data=self.manifest();name=next(iter(data['upstream_sha256'])) + data['upstream_sha256'][name]='0'*64 + with self.assertRaisesRegex(ValueError,'wrong frozen input closure'):self.check(data) + def test_changed_raw_input_rejected(self): + with self.assertRaisesRegex(ValueError,'upstream source changed'): + self.check(self.manifest(),lambda p:(V.ROOT/p).read_bytes()+b' ') + def test_rebound_checker_rejected(self): + data=self.manifest();data['audit_sha256']['independent_bit.py']='0'*64 + with self.assertRaisesRegex(ValueError,'wrong reviewed checker pin'):self.check(data) + def test_omitted_wrapper_or_source_test_rejected(self): + for name in ('verify.py','test_source.py','test_signed.py'): + data=self.manifest();del data['audit_sha256'][name] + with self.assertRaisesRegex(ValueError,'incomplete audit source closure'):self.check(data) + def test_precision_cannot_rebind_derived_input(self): + data=self.manifest();name=next(iter(data['precision_sha256'])) + data['precision_sha256'][name]='0'*64 + with self.assertRaisesRegex(ValueError,'wrong frozen input closure'):self.check(data) + def test_precision_source_bytes_rejected(self): + data=self.manifest() + with self.assertRaisesRegex(ValueError,'precision source changed'): + V.check_source_manifest(data,lambda p:(V.ROOT/p).read_bytes(),lambda p:(V.HERE/p).read_bytes(), + lambda p:(V.ROOT/p).read_bytes()+b' ') + def test_selected_six_raw_witness_bindings(self): + lock=V.source_lock();raw=V.load_complex(lock) + self.assertEqual(set(raw),{'graph','word','witness','operation_frames','pairs','sinks'}) + self.assertEqual(len(raw['sinks']),44) + +if __name__=='__main__':unittest.main() diff --git a/research/paired-cube-scalar-audit/verify.py b/research/paired-cube-scalar-audit/verify.py new file mode 100644 index 0000000000..8e775e31ae --- /dev/null +++ b/research/paired-cube-scalar-audit/verify.py @@ -0,0 +1,88 @@ +#!/usr/bin/env python3 +"""Source-bound exact selected181 scalar audits; general phase contracts excluded.""" +import argparse +import hashlib +import importlib.util +import json +from pathlib import Path +import sys +import independent_bit as B +import independent_sinks as C + +HERE=Path(__file__).resolve().parent +ROOT=HERE.parents[1] +if hasattr(sys,'set_int_max_str_digits'):sys.set_int_max_str_digits(100000) +PIN='7fb2194801e3a10f54772c7f0d5505035a4fc0ad' +SELECT='research/paired-cube-local-168/selected/complex/' +INPUT_CLOSURE_PIN='21a3820abbbcf03fc385fe3a7321aefc38ba2d57899216e5b269236242996c4d' +CHECKER_PINS={'independent_bit.py':'0ceac13910e1d50b2145062fc5db38a3709d82e85bf5d8ff000a0d64a36b104b', + 'independent_sinks.py':'6345a9b3a899ccdf40a2a97062fb01b0abe6e989aad938656b706f80e77586df'} +AUDIT_SOURCES={'LICENSE','NOTICE','README.md','independent_bit.py','independent_sinks.py', + 'test_bit.py','test_sinks.py','test_signed.py','test_source.py','verify.py'} +JOINT_KEYS=('upstream_sha256','complex_canonical_sha256','precision_sha256') + +def require(condition,message): + if not condition:raise ValueError(message) + +def canonical(value): + return hashlib.sha256(json.dumps(value,sort_keys=True,separators=(',',':')).encode()).hexdigest() + +def check_source_manifest(data,read_upstream,read_audit,read_precision=None): + require(data['upstream_commit']==PIN,'wrong upstream revision') + require(type(data['audit_sha256']) is dict and set(data['audit_sha256'])==AUDIT_SOURCES, + 'incomplete audit source closure') + require(canonical({k:data[k] for k in JOINT_KEYS})==INPUT_CLOSURE_PIN,'wrong frozen input closure') + require(type(data['upstream_sha256']) is dict and len(data['upstream_sha256'])==1700, + 'incomplete native181 source closure') + require(set(data['complex_canonical_sha256'])=={'graph','word','witness','operation_frames','pairs','sinks'}, + 'incomplete raw complex canonical binding') + for name,digest in CHECKER_PINS.items(): + require(data['audit_sha256'][name]==digest,'wrong reviewed checker pin: '+name) + for path,digest in data['upstream_sha256'].items(): + require(hashlib.sha256(read_upstream(path)).hexdigest()==digest,'upstream source changed: '+path) + for path,digest in data['audit_sha256'].items(): + require(hashlib.sha256(read_audit(path)).hexdigest()==digest,'audit source changed: '+path) + read_precision=read_precision or (lambda p:(ROOT/p).read_bytes()) + for path,digest in data['precision_sha256'].items(): + require(hashlib.sha256(read_precision(path)).hexdigest()==digest,'precision source changed: '+path) + return data + +def source_lock(): + return check_source_manifest(json.loads((HERE/'SOURCE.json').read_bytes()), + lambda p:(ROOT/p).read_bytes(),lambda p:(HERE/p).read_bytes()) + +def load_complex(lock,work_dir=None): + raw={name:B.load(ROOT/SELECT/filename) for name,filename in + [('graph','graph.json.gz'),('word','word.json.gz'),('witness','frames.json.gz'), + ('operation_frames','physical-frames.json.gz'),('pairs','physical-pairs.json.gz')]} + raw['sinks']=[[item['role'],item['pivot']] for item in B.load(ROOT/SELECT/'sinks.json')['sinks']] + if work_dir is not None: + for name,filename in [('graph','graph.json'),('word','selection.json'),('witness','frames.json')]:raw[name]=B.load(work_dir/filename) + for name,value in raw.items():require(canonical(value)==lock['complex_canonical_sha256'][name],'selected complex witness changed: '+name) + return raw + +def bind_precision_inputs(): + path=ROOT/'research/precision-certificate/profile_binding.py' + spec=importlib.util.spec_from_file_location('selected181_native_profile_binding',path) + module=importlib.util.module_from_spec(spec);spec.loader.exec_module(module) + inputs={name:B.load(path.parent/'inputs'/name) for name in module.INPUT_NAMES} + return module.check_native_inputs(ROOT,inputs) + +def main(): + parser=argparse.ArgumentParser(description=__doc__) + parser.add_argument('--complex-work-dir',type=Path, + help='optional external181 raw graph/selection/frames, checked against exact selected canonical hashes') + parser.add_argument('--bit-only',action='store_true') + args=parser.parse_args();lock=source_lock();binding=bind_precision_inputs() + bit=B.check(B.load(ROOT/'research/paired-cube-bit/out/graph_p12.json'), + B.load(ROOT/'references/paired-cube/bit-physical/word_p12.json.gz'), + B.load(ROOT/'references/paired-cube/bit-physical/kchron_p12.json'),controls=True) + result={'upstream_commit':PIN,'native_profile_binding':binding,'bit':bit} + if not args.bit_only: + raw=load_complex(lock,args.complex_work_dir) + result['complex']=C.audit_raw(raw['graph'],raw['word'],raw['witness'],raw['operation_frames'],raw['pairs'],raw['sinks']) + result['scope']='Exact finite scalar maps on pinned raw selected181 inputs, including signed reflections. ' + result['scope']+='Native profile binding is consistency evidence; general phase/cost, weighted compiler, analytic and fixed-tape interfaces remain hypotheses.' + print(json.dumps(result,indent=2,sort_keys=True)) + +if __name__=='__main__':main() diff --git a/research/precision-certificate/LICENSE b/research/precision-certificate/LICENSE new file mode 100644 index 0000000000..261eeb9e9f --- /dev/null +++ b/research/precision-certificate/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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If You + institute patent litigation against any entity (including a + cross-claim or counterclaim in a lawsuit) alleging that the Work + or a Contribution incorporated within the Work constitutes direct + or contributory patent infringement, then any patent licenses + granted to You under this License for that Work shall terminate + as of the date such litigation is filed. + + 4. Redistribution. You may reproduce and distribute copies of the + Work or Derivative Works thereof in any medium, with or without + modifications, and in Source or Object form, provided that You + meet the following conditions: + + (a) You must give any other recipients of the Work or + Derivative Works a copy of this License; and + + (b) You must cause any modified files to carry prominent notices + stating that You changed the files; and + + (c) You must retain, in the Source form of any Derivative Works + that You distribute, all copyright, patent, trademark, and + attribution notices from the Source form of the Work, + excluding those notices that do not pertain to any part of + the Derivative Works; and + + (d) If the Work includes a "NOTICE" text file as part of its + distribution, then any Derivative Works that You distribute must + include a readable copy of the attribution notices contained + within such NOTICE file, excluding those notices that do not + pertain to any part of the Derivative Works, in at least one + of the following places: within a NOTICE text file distributed + as part of the Derivative Works; within the Source form or + documentation, if provided along with the Derivative Works; or, + within a display generated by the Derivative Works, if and + wherever such third-party notices normally appear. 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We also recommend that a + file or class name and description of purpose be included on the + same "printed page" as the copyright notice for easier + identification within third-party archives. + + Copyright [yyyy] [name of copyright owner] + + Licensed under the Apache License, Version 2.0 (the "License"); + you may not use this file except in compliance with the License. + You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + + Unless required by applicable law or agreed to in writing, software + distributed under the License is distributed on an "AS IS" BASIS, + WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + See the License for the specific language governing permissions and + limitations under the License. diff --git a/research/precision-certificate/NOTICE b/research/precision-certificate/NOTICE new file mode 100644 index 0000000000..b2efbbc4fd --- /dev/null +++ b/research/precision-certificate/NOTICE @@ -0,0 +1,36 @@ +Precision refinement of the paired-cube witness +Copyright 2026 Muhammed Ali Mehmood. Apache-2.0. +Prepared with substantial OpenAI Codex assistance. + +Native prerequisite is Chafik Boukhalfa's PR181 commit +7fb2194801e3a10f54772c7f0d5505035a4fc0ad, with substantial Anthropic Claude +and OpenAI Codex assistance, on eumemic's PR168 construction. The copied logical and terminal +profile JSON files are schema-projected/independently recounted derived inputs; +their exact native Git-blob sources and derivations are recorded in SOURCE.json. +The bit input and LICENSE are unchanged native Git bytes. Every original +native scientific source, package, source manifest and license is preserved. + +Upstream physical graph, module, frame and terminal-sink integration: +eumemic, with Anthropic Claude assistance. Terminal-sink substitution: +jamesyc, PR166. Shared-core accounting, exact inventory and finite router: +icekylinx, PR144, with substantial OpenAI GPT-6 Astra/Codex assistance. +Earlier local words and interfaces: eumemic PR117 and Zhihao Chen/Swapnil +Jain PR97 and PR23. Balanced positional transform: hipotures/RaD, including +the upstream reviewed balanced assembly. Precision refinement approach: +huxint's PR170 interval refinement, with substantial OpenAI Codex assistance. + +independent_moments.py and independent_assembly.py are unchanged generic +checkers developed with substantial OpenAI Codex assistance in the preceding +local multi-agent review. Their exact raw hashes and original reviewed commit +are recorded in SOURCE.json; existing embedded notices are retained. +Both generic checker modules expressly declare Apache-2.0 in their retained +original headers and are redistributed under that license, reproduced here +as LICENSE. The reviewed local source is commit +1910c085d426af22ed94dd2d9ce84561b031a96b, research/mixed-supplier/. +The verifier imports no upstream producer or saved supplier/assembly answers. + +The superseded 64 operation-frame refinement is Rohan Arun's PR178 contribution, +prepared with OpenAI Codex assistance, on eumemic's PR168 construction. +PR178 retains PR176's terminal audit technique credited to Chafik Boukhalfa. +Our contribution adds independent exact checks and parameter refinement; +the prerequisite frame construction and all its notices are preserved. diff --git a/research/precision-certificate/PROOF.md b/research/precision-certificate/PROOF.md new file mode 100644 index 0000000000..c597e7dc1d --- /dev/null +++ b/research/precision-certificate/PROOF.md @@ -0,0 +1,66 @@ +# Exact finite arithmetic and retained contracts + +All inputs are pinned to PR181 `7fb2194801e3a10f54772c7f0d5505035a4fc0ad`. +This is a conditional finite arithmetic implication. It is not an all-size +integer multiplication theorem or a global parameter optimum. + +The new logical local circuit has h22, v1320, c21249, q3157,11364 matched +carriers, R13042 and32971 mixer operations. Its loss is440. After2310 +handoffs and44 terminal sinks, physical R is10688 and ambient stock13328. +The width is66, rank mass878328, deficit1320 and maximum child20. The bit +record remains width72, stock21548, rank1549520 and deficit1936. Source, +local and target component multiplicities each pay three copies; a gauge +dimension d pays rank3d, and2v finishing children have rank2. The verifier +reconstructs the complete paid histogram and checks every stock/mass identity. + +The independent characteristic uses sum(n_r*(r/m)^(1-a))/w. Natural log is +enclosed through the120-term -log(1-u) series after range reduction; exp uses +16 terms and a geometric bound on its tail. Outward rational rounding uses +10^36. The supplier/grid/atom/headline grid is10^24. + +Complex saving is132438677973141606647/200000000000000000000000. +Coarse bit saving is82503172294962610849/125000000000000000000000. +Both exact upper characteristic bounds are below one; each next10^-24 grid +point has a lower bound at least one. The bit envelope adds the entire +32m^2 rank-one fallback on10^-16 of every ideal edge and checks contaminated +rank contraction plus2m^3/2^80<10^-16. This does not by itself prove the +uniform local-ring compiler, determinant exclusions or prime supply theorem. + +The ordinary saving is384599/10^10. Atom659615384207882296543/10^24 +is the first strict grid point above coarse/(1+coarse-ordinary). Effective bit +saving is(1-atom)*coarse+atom*ordinary, with effective20 is one; row coefficient is12320 and degree +70000 gives gap224336/5. None of these numerical charges independently +establishes the general physical router or phase theorem. + +The copied terminal component histograms come from an independent selected +frame/role/donor/target recount, with a recorded44-sink population adaptation. +The copied logical input projects the exact raw selected logical record, +removing only numerical/search diagnostics; source compilation remains a +written input contract. The native binding gate compares all positive bins +to native181 components and all paid dimensions. It preserves target zero +diagnostics6270(native) versus6323(literal recount); zero rank has no recursive +charge and does not reduce the full scalar c/R/M bill. Native stored replay +metadata is not copied into these derived inputs or claimed as fresh execution. + +The companion signed scalar checker verifies finite forward(X,Y+X,Z) and +literally reflected(X-Y,Y,Z) maps on every source, target and retained dirty +column, including330 signed destination reflections, K/inverse and scratch +restoration. Native181 separately verifies its selected geometry and finite +words. General Clifford/Gaussian/Pauli phases, common generic bases, completed +core sharing, weighted source compilation, arbitrary-width routing, restored +internal rows, uniform setup, prime supply, precision/recovery, analytic outer +transfer and fixed-tape contracts remain inherited hypotheses. AI-agent +reviews and finite tests are not formal proof or independent human peer review. diff --git a/research/precision-certificate/README.md b/research/precision-certificate/README.md new file mode 100644 index 0000000000..d4dc3d2188 --- /dev/null +++ b/research/precision-certificate/README.md @@ -0,0 +1,57 @@ +# Precision refinement of the pinned local-circuit witness + +This contribution refines Chafik Boukhalfa's PR181 at +`7fb2194801e3a10f54772c7f0d5505035a4fc0ad`. Its conditional headline is +`659180578557293/10^18`. The refined point is +`659180578557294852359/10^24`, an increase of `1852359/10^24`. +The bit supplier limits this assembly. No upstream scientific file changes. + +From the repository root, with Python 3.12 or later: + +```sh +python -B research/precision-certificate/verify.py --native-inputs +python -B research/precision-certificate/test_precision.py +python -B research/precision-certificate/test_native.py +python -O -B research/precision-certificate/verify.py --native-inputs +python -O -B research/precision-certificate/test_precision.py +python -O -B research/precision-certificate/test_native.py +``` + +The verifier reassembles every paid child, independently bounds both supplier +moments, reconstructs the full finite bridge and all47 strict inequalities, +and rejects the next supplier/headline grid points. It uses no producer or +submitted arithmetic imports. The two generic arithmetic cores are unchanged +from their reviewed versions. `--write` regenerates the owned certificate; +the ordinary command requires exact equality with the saved answer. + +The three copied inputs have explicit provenance in SOURCE.json. The logical +scalar input projects PR181's selected raw record by removing four search +diagnostics. The terminal inventory is an independent fixed-witness recount, +with44 sinks, from that raw graph/word/frame data. These derived JSON files +are not described as Git-verbatim native records. The bit inventory is an +exact unchanged native Git record. Default verification also works with this +standalone folder; `--native-inputs` additionally requires the native repository. + +The native binding module compares every positive component bin and every paid +dimension against PR181's native aggregate and selected inputs. Native target +rank-zero diagnostics count6270 events; the literal-event recount counts6323. +Both counts are preserved and explicitly reported. Rank-zero events create no +child, rank mass or characteristic charge. The complete logical c/R/M scalar +bill remains paid. This is input consistency, separate from independent +geometry and scalar execution. + +The companion [scalar audit](../paired-cube-scalar-audit/README.md) checks all +formal source, target and retained dirty coefficients of the selected new +signed word, including330 destination reflections. The native PR181 gate +checks its own circuit/frame/profile/formal witnesses. Finite evidence does +not establish the general phase, weighted compiler, precision/recovery, +analytic or fixed-tape contracts in [PROOF.md](PROOF.md). + +Prepared by Muhammed Ali Mehmood with substantial OpenAI Codex assistance. +PR181's local circuit and finite integration are Chafik Boukhalfa's work with +substantial Anthropic Claude and OpenAI Codex assistance, on eumemic's PR168 construction with +Anthropic Claude assistance. James Chang supplies the terminal-sink lemma; +icekylinx supplies shared-core accounting and the finite bridge. Earlier local +interfaces include Zhihao Chen/Swapnil Jain, and the balanced positional layout +is due to hipotures/RaD. Rohan Arun's superseded PR178 frame refinement is +retained as development lineage. See NOTICE and the unchanged Apache-2.0 LICENSE. diff --git a/research/precision-certificate/SOURCE.json b/research/precision-certificate/SOURCE.json new file mode 100644 index 0000000000..72d261144f --- /dev/null +++ b/research/precision-certificate/SOURCE.json @@ -0,0 +1,89 @@ +{ + "checkers_review_scope": "Reviewed generic arithmetic implementations, copied byte-for-byte; prior source commit1910c085d426af22ed94dd2d9ce84561b031a96b is local, not an upstream release", + "contribution": "Independent paid precision arithmetic with explicit new local-circuit/native component coupling; finite conditional scope.", + "copied_source_provenance": { + "LICENSE": { + "commit": "7fb2194801e3a10f54772c7f0d5505035a4fc0ad", + "sha256": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4", + "upstream_path": "LICENSE" + }, + "independent_assembly.py": { + "commit": "1910c085d426af22ed94dd2d9ce84561b031a96b", + "sha256": "99584fe21922926ed9766ec5bc75a06ae531f396bf41ef87baafde248e1f9b9b", + "upstream_path": "Reviewed generic checker in current contribution workspace" + }, + "independent_moments.py": { + "commit": "1910c085d426af22ed94dd2d9ce84561b031a96b", + "sha256": "4d398b4600f7aeaf73a36c68ebc9727de0451399512769282684ae9d4804f594", + "upstream_path": "Reviewed generic checker in current contribution workspace" + }, + "inputs/paired-cube-bit-physical-input.json": { + "commit": "7fb2194801e3a10f54772c7f0d5505035a4fc0ad", + "copy_kind": "Exact raw Git bytes; unchanged from PR1684a.", + "sha256": "6735294e8639da09eb3eb2234cbc5814298442a6c946b5534bcf6e48903547f3", + "upstream_path": "certificates/paired-cube-bit-physical-input.json" + }, + "inputs/paired-cube-complex-input.json": { + "additional_native_sources": { + "research/paired-cube-local-168/certificate.json": "1e72ed46c81f1fada5adc71da38145f155872912fd39546b3294130cd0eeb9ed", + "research/paired-cube-local-168/selected/complex/sinks.json": "f4d0c85db8bc90b4c0ad243adb5332e0da6fa1a8db1be6b1ad58d93a5e19fdbe" + }, + "commit": "7fb2194801e3a10f54772c7f0d5505035a4fc0ad", + "copy_kind": "Derived JSON, not raw Git-verbatim", + "derivation": "Schema projection of selected logical profile; only four numerical/search diagnostics removed.", + "original_decoded_sha256": "76b033baee37850ab0d487f0b4c1f1a5f4d1ece596e14d72c551bb356cdc6cb1", + "original_gzip_sha256": "89a46f6c9bc2e49a903a44952539034165acbc26ef6b7f14504554299ca8e2c6", + "sha256": "9adcc1e7da7222e19dce989cd6f86200997a677642b4c2a580aaae0c0a31a855", + "upstream_path": "research/paired-cube-local-168/selected/complex/profile-before.json.gz" + }, + "inputs/paired-cube-sinks-input.json": { + "additional_native_sources": { + "research/paired-cube-local-168/certificate.json": "1e72ed46c81f1fada5adc71da38145f155872912fd39546b3294130cd0eeb9ed", + "research/paired-cube-local-168/selected/complex/sinks.json": "f4d0c85db8bc90b4c0ad243adb5332e0da6fa1a8db1be6b1ad58d93a5e19fdbe" + }, + "commit": "7fb2194801e3a10f54772c7f0d5505035a4fc0ad", + "copy_kind": "Derived JSON, not raw Git-verbatim", + "derivation": "R40 independent exact selected-frame/local/target/sink recount with44-sink population adaptation; target zero diagnostic6323 preserved.", + "original_decoded_sha256": "5205121764b4855b03ab840d898110bc21f61c37e84319113d2488a996dfc36b", + "original_gzip_sha256": "9d470b72ae31e2debd945b61481bde9c68df93054013f657cb331e0e49b53105", + "sha256": "aeb7b2c053f6eacd55837c4c597a9cb3626d681495b783cc6310789e35b5fc9a", + "upstream_path": "research/paired-cube-local-168/selected/complex/profile.json.gz" + } + }, + "native_binding_sha256": { + "certificates/paired-cube-bit-physical-input.json": "6735294e8639da09eb3eb2234cbc5814298442a6c946b5534bcf6e48903547f3", + "research/paired-cube-local-168/SOURCE.json": "30c3878dde69a4ed29beed26856d1015ad3180da464d96154e5b005f728847bf", + "research/paired-cube-local-168/certificate.json": 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+ "zero_rank_target_event_diagnostics": { + "difference": 53, + "independent_literal_recount": 6323, + "meaning": "Zero rank creates no child/moment/rank charge; full logical c/R/M bill stays paid.", + "native": 6270 + } +} diff --git a/research/precision-certificate/certificate.json b/research/precision-certificate/certificate.json new file mode 100644 index 0000000000..cf0718e599 --- /dev/null +++ b/research/precision-certificate/certificate.json @@ -0,0 +1,249 @@ +{ + "assembly": { + "absorption_gap": "95157371032035506019267574176362376419252134868797307040562714380449/120271588387524985852949800357232227729521568132129737643532902551913475000000000000000000000", + "limiter": "bit", + "margins": { + "Gaussian_arithmetic": "5073964493906786896482411999327073689946242464288919896996582459737114810494258683897923461/7697381656801599094588787222862862574689380360456303209186105763322462400000000000000000000000", + "balanced_prefix": 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2042733685541310236593996563124710993412165863603306313097532902018433466683431743715259007829146987095378627302512247296273579196724865635466424495886986981070240397155989611901227274057344115006992368238295067937096681914939897329330375897850947653624154670627567536540399720617344588251455630430130931283214971866771632648027119764337342344652974886259123204570638608969527856002307906428308648271283107654233784029920261562062441634609575222294256530335686672972094697601933339431796932668405898134579255702844363845882474708468208758785148433016193063510518755982063138558376100687934874724673882718386824464636056802379731693082380370257615524198097971706920300670514785149198047112812589262598451026696606105144349263419777761388556924150378882153660586083231627698985439717349132380289334640425239716030365051552310444048834985873630612831601761031016998447678647208392850918363259427684972030870622102919784360657161485751852158581374304190237691268858704247599964760134258277434684030263792385403474393413555973632021332993606819195569256783157695772555762218961654961483071898813478715114933642408814572455099487524946213727616776758529362493007012128742175516659103497256150398688067237295539038286054433070958988450327523496660474475015177485962957043001891810348130524968091565530711246863869435913581520796765892701707248466483246004653153934614453923325331090272046405694531720642794739801349300597117009558972642063469652020414157994463402891269148057505219538790196840956548422975773514132792507087108642926872500370530948765817617814354169836284740013615891292828792176460677144382290379101394591548513381424766141758112339957037071338204348324849159760547862762023937163784970360528440141699170517172479674484353402002874845101145390769252570862957716099987600419158072752037560685304580963211038225882927995606707773197948561882380706350507940215524792066837493717985086348682434583749147435614934783671039459572748018799083520000000000019248832, + "shared_assumptions": [ + "finite scalar/phase/router bound in PR168 written note", + "inherited bit reserve9909 and ordinary leaf reserve252" + ], + "stages": 3, + "vertices": 3525886442745164056544063644145716736004044180364723200424782744512582104634391857878947474919000911664177132185103526533556870749183073596734571342973795793383290849303191539662953799849547227737400544457729391514661713176468240351330298583217125220869576729661326266259024901649005584114421035252391760900092184489369973370724377894349644301151172572225522957784648909234781611948223712944954177723427440753012339451839407462242698998122862136268155486957700758485307238973641035062973415368109606762999662774702118665848434384838590914531021276158042617166069588021894697108433312726842277534281982740181708602162296504975360000000000000000000, + "wire_bits": 2159 + }, + "headline_grid": 1000000000000000000000000, + "headline_successor": "16479514463932371309/25000000000000000000000", + "headline_successor_rejected": true, + "improvement": "1852359/1000000000000000000000000", + "kappa": "659180578557294852359/1000000000000000000000000", + "phase_gap": "1/1000000000000000000000000", + "pinned_baseline_kappa": "659180578557293/1000000000000000000", + "schema_version": 1, + "scope": "Independent exact arithmetic from pinned stored inventories. Local schedule, phases, uniform compiler, analytic and fixed-tape interfaces remain proof obligations.", + "source_manifest_sha256": "cd925ef1bdffca3633f7a0ad0d6cbbbedadcc557dd68439352f6db64587343cc", + "supplier_grid": 1000000000000000000000000, + "supplier_successors": { + "bit": { + "saving": "660025378359700886793/1000000000000000000000000", + "total_lower": "31564453125000000000000011774096439144822720747961381/31564453125000000000000000000000000000000000000000000" + }, + "complex": { + "saving": "165548347466427008309/250000000000000000000000", + "total_lower": "1832600000000000000000002839875436616291/1832600000000000000000000000000000000000" + } + }, + "upstream_commit": "7fb2194801e3a10f54772c7f0d5505035a4fc0ad" +} diff --git a/research/precision-certificate/independent_assembly.py b/research/precision-certificate/independent_assembly.py new file mode 100644 index 0000000000..6be7ce8c62 --- /dev/null +++ b/research/precision-certificate/independent_assembly.py @@ -0,0 +1,214 @@ +"""Independent paired-cube bridge and balanced assembly arithmetic. + +Apache-2.0, OpenAI Codex assistance. Derived as explicit relational tests, +without producer/assembly imports. Component inventories, fixed scalar/router +charge rules and inherited reserve allowances are mathematical inputs, not +independently proved circuits. Exact arithmetic does not prove the all-size +analytic, uniform weighted supplier, phase or tape contracts. +""" +from fractions import Fraction as Q +from math import prod +import json + + +def exact(value): + if type(value) not in (Q,int,str): + raise ValueError('exact rational required') + return Q(value) + +def require(condition, message): + if not condition: + raise ValueError(message) + + +def component_histogram(raw, max_rank): + require(type(raw) is dict, 'component histogram must be object') + result = {} + for key, count in raw.items(): + require(type(key) is str and key.isascii() and key.isdigit() and str(int(key))==key, + 'component rank key') + rank=int(key) + require(0<=rank<=max_rank and type(count) is int and count>=0, 'component rank/count') + if rank and count: result[rank]=count + return result + + +def serialize(value): + if isinstance(value,Q): return str(value) + if isinstance(value,dict): return {str(k):serialize(v) for k,v in value.items()} + if isinstance(value,list): return [serialize(v) for v in value] + return value + + +def reconstruct_bridge(scalar, physical, *, coarse_row_reserve=9909, + ordinary_leaf_row_reserve=252, row_degree=70000): + h,v,R,M=(scalar[k] for k in ('h','v','R','total_M_operations')) + require(all(type(x) is int and x>0 for x in (h,v,R,M)), 'invalid scalar dimensions') + require(type(scalar['loss']) is int and scalar['loss']>=0, 'invalid scalar loss') + require(all(type(physical[k]) is int and physical[k]>=0 for k in ('h','v','loss')), + 'invalid physical dimensions/loss') + require(h%2==0, 'even local complex dimension required') + require((h,v,scalar['loss'])==(physical['h'],physical['v'],physical['loss']), 'source/physical dimensions') + require(type(physical['physical_R']) is int and 0=0, 'invalid scalar additions') + require(type(scalar['q']) is int and scalar['q']>0 and 3*scalar['q']<2**15, + 'root coefficient bitlength allowance') + width=3*h + role_stock=2*v+physical['physical_R'] + require(all(type(x) is int and x>=0 for x in (coarse_row_reserve,ordinary_leaf_row_reserve,row_degree)), 'invalid reserve') + terms=[] + for name in ('local_histogram','source_data_histogram','target_data_histogram'): + terms.extend((rank,3*count) for rank,count in component_histogram(physical[name],h).items()) + terms.extend((3*rank,count) for rank,count in component_histogram(physical['physical_gauge_histogram'],h-1).items()) + terms.append((2,2*v)) + require(all(type(rank) is int and 00 for rank,count in terms), 'invalid paid child') + children={rank:sum(count for rr,count in terms if rr==rank) for rank in sorted({r for r,n in terms})} + require(children==component_histogram(physical['child_histogram'],width-1),'physical inventory mismatch') + rank_local=sum(rank*count for rank,count in terms) + require(role_stock*width-rank_local==2*v-3*scalar['loss']>0,'telescoping deficit') + child=max(children) + half=width//2 + vertices=2**(width-1+(half-1)**2)*prod(2**(2*i)-1 for i in range(1,half)) + W,N,s=vertices*role_stock,vertices*v,vertices*rank_local + # Written finite scalar/router charge. All logical roles retained in L. + L=(4*(scalar['c']+v)+10*v+4*h*v+4*h*h+8*h+8+2*h + +8*R*v*(M+16)+32*v) + logical=3*vertices*L+8*W+4*N+8*width*R*vertices + G=64*(width+1)**3*(logical+1)*(W+1)**2 + E=64*(W+width+G+1)**3 + B=s+E + charge=2*G*W*W+8*s+4*W+4+32*width + C0=32*width*B*B + require(E>charge and 2*B*(width-child)>=s+E and C0>2*B+18, + 'finite semantic guard fails') + halving=1 + while width**halving<=2*child**halving: halving+=1 + bits=W.bit_length() + coefficient=halving*bits+coarse_row_reserve+ordinary_leaf_row_reserve + reserve_gap=Q(row_degree)-Q(51,25)*coefficient + require(reserve_gap>0,'finite external row reserve') + return dict(m=width,roles_per_vertex=role_stock,rank_per_vertex=rank_local, + maxchild=child,vertices=vertices,W=W,N=N,s=s,local_group_upper=L, + logical_group_upper=logical,scalar_group_upper=G,E=E,B=B,C0=C0, + literal_charge=charge,literal_gap=E-charge,halving_degree=halving, + wire_bits=bits,row_coefficient=coefficient,row_degree=row_degree,row_gap=reserve_gap, + coefficient_bound=h+4,coefficient_denominator_divides=6, + original_X_involution_scalar_group_upper=32*v,stages=3, + auxiliary_banks_after_sharing=1,fixed_odd_divisor=3, + conservative_old_coarse_row_reserve=coarse_row_reserve, + ordinary_leaf_row_degree=ordinary_leaf_row_reserve, + shared_assumptions=['finite scalar/phase/router bound in PR168 written note', + 'inherited bit reserve9909 and ordinary leaf reserve252']) + + +def balanced_assembly(bridge, actual_bit, complex_saving, headline, *, + eta=Q(1,10**12), beta=Q(1,10**12), phase_gap=Q(1,10**15), + old_prefix=False, no_reservation=False): + AB,b,headline,eta,beta,phase_gap=map(exact,(actual_bit,complex_saving,headline,eta,beta,phase_gap)) + require(00 and headline>=0, 'assembly parameter domain') + a=min(AB,(1-beta)*b-phase_gap) + tau,sigma=1-a,1-b + q=a*(1-2*eta) + c=q if no_reservation else q+eta/4 + epsilon=(1-eta)/(1+q) + lp=1-q + lam=(tau+lp)/2 + g=epsilon*q + alpha=(g+1-epsilon)/2 + delta=eta/8 + # Stopped recurrence powers, independently reduced at these parameters. + internal=tau if sigma<=tau else beta*tau+(1-beta)*sigma + leaf=1-(1-beta)*b + margins={ + 'balanced_prefix':1-epsilon*(1+c) if old_prefix else 1-epsilon, + 'coordinate_movement':a, + 'compact_phase_layer':g, + 'bulk_exposure':a, + 'Gaussian_arithmetic':min(1-epsilon-delta,alpha-delta), + 'scalar_work':1-epsilon-delta, + 'dimension':epsilon, + } + slacks={} + def inequality(name,greater,lesser): slacks[name]=greater-lesser + # Order/reservation constraints: slacks computed from explicit inequalities. + for name,greater,lesser in [ + ('bit_positive',a,0),('complex_above_bit',b,a), + ('complex_below_one_over32',Q(1,32),b),('beta_positive',beta,0), + ('beta_below_one',1,beta),('leaf_saving_above_bit',(1-beta)*b,a), + ('q_positive',q,0),('q_below_internal',1-internal,q), + ('q_below_leaf',1-leaf,q),('c_positive',c,0),('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',1,lp), + ('epsilon_positive',epsilon,0),('epsilon_below_one',1,epsilon), + ('guard_width',1,epsilon),('K_geometry',1,epsilon*(1+c)), + ('K_dominates_log',epsilon*c,0),('record_suffix',1,epsilon), + ('phase_local',1,epsilon+delta),('phase_boundary',alpha,delta), + ('gamma_sublinear',1,epsilon+alpha),('cell_above_band',epsilon,(1-alpha)/2), + ('prime_interval_packing',1,epsilon),('alpha_positive',alpha,0), + ('alpha_below_one',1,alpha),('alpha_below_one_fourth',Q(1,4),alpha), + ('delta_positive',delta,0),('delta_below_one_eighth',Q(1,8),delta), + ('short_record_fallback',epsilon,a),('small_field_exposure',1,epsilon+g), + ('artificial_boundary',8+alpha,epsilon+delta+g), + ('literal_scalar_guard',bridge['E'],bridge['literal_charge']), + ('row_product_gap',bridge['row_degree'],Q(51,25)*bridge['row_coefficient']), + ]: inequality(name,greater,lesser) + for name,margin in margins.items(): inequality(name+'_above_kappa',margin,headline) + require(len(slacks)==47 and len(margins)==7,'incomplete inequality inventory') + failed={name:str(value) for name,value in slacks.items() if value<=0} + require(not failed,'nonpositive strict inequalities: '+json.dumps(failed)) + require(min(margins.values())==g,'incorrect minimum margin') + require((1-epsilon)-g==eta and 1-epsilon-alpha==eta/2,'balanced backoff identities') + require(1-epsilon*(1+c)==eta-epsilon*eta/4,'balanced geometric identity') + return dict(parameters={'actual_bit':AB,'a_bit':a,'a_complex':b,'eta':eta,'beta':beta, + 'tau':tau,'sigma':sigma,'q':q,'c':c,'epsilon':epsilon,'lambda_':lam, + 'lambda_prime':lp,'alpha_squared_power':alpha,'delta':delta,'kappa':headline, 'C0':bridge['C0'],'C1':1}, + recurrence={'internal':internal,'leaf':leaf,'reservations':1-c}, + strict_constraints=slacks,margins=margins,minimum_margin=g, + absorption_gap=g-headline, + limiter=('bit' if AB<(1-beta)*b-phase_gap else + 'complex' if AB>(1-beta)*b-phase_gap else 'bit_and_complex')) + + + +def compare_assembly(computed, observed): + """Reject positive but wrong stored answers and missing/extra named fields.""" + for name in ('strict_constraints','margins','recurrence'): + require(set(computed[name])==set(observed[name]), 'saved '+name+' keys differ') + for key,value in computed[name].items(): + require(exact(observed[name][key])==value, 'saved '+name+' differs: '+key) + for key in ('minimum_margin','absorption_gap'): + require(exact(observed[key])==computed[key], 'saved '+key+' differs') + expected={k:v for k,v in computed['parameters'].items() if k!='actual_bit'} + require(set(observed['parameters'])==set(expected), 'saved parameter keys differ') + for key,value in expected.items(): + require(exact(observed['parameters'][key])==value, 'saved parameter differs: '+key) + return True + + +def compare_bridge(computed, observed): + """Check exact derived scalar/router, semantic and row numeric fields.""" + c,s,r=observed['complex'],observed['semantic'],observed['rows'] + complex_fields={'m':'m','W':'W','s':'s','N':'N','maxchild':'maxchild', + 'invocations_per_stage':'vertices','halving_degree':'halving_degree', + 'wire_bits':'wire_bits','local_group_upper':'local_group_upper', + 'logical_group_upper':'logical_group_upper','finite_group_router_upper':'scalar_group_upper', + 'scalar_group_upper':'scalar_group_upper'} + complex_fields.update({key:key for key in ('coefficient_bound','coefficient_denominator_divides', + 'original_X_involution_scalar_group_upper','stages','auxiliary_banks_after_sharing')}) + for target,source in complex_fields.items(): + require(exact(c[target])==computed[source], 'saved bridge complex differs: '+target) + semantic={'E':computed['E'],'literal_charge':computed['literal_charge'], + 'strict_literal_gap':computed['literal_gap'],'B':computed['B'],'C0':computed['C0'], + 'C1':1,'fixed_odd_divisor':computed['fixed_odd_divisor'], + 'induction_gap':2*computed['B']*(computed['m']-computed['maxchild'])-computed['s']-computed['E']} + for key,value in semantic.items(): + require(exact(s[key])==value,'saved bridge semantic differs: '+key) + rows={'coefficient':computed['row_coefficient'],'degree':computed['row_degree'], + 'complex_coefficient':computed['halving_degree']*computed['wire_bits'], + 'degree_gap':computed['row_gap'],'suffix_slope':4*computed['row_degree']} + for key,value in rows.items(): require(exact(r[key])==value,'saved bridge rows differ: '+key) + for key in ('conservative_old_coarse_row_reserve','ordinary_leaf_row_degree'): + require(exact(observed[key])==computed[key],'saved inherited reserve differs: '+key) + return True diff --git a/research/precision-certificate/independent_moments.py b/research/precision-certificate/independent_moments.py new file mode 100644 index 0000000000..376ae74a8d --- /dev/null +++ b/research/precision-certificate/independent_moments.py @@ -0,0 +1,200 @@ +"""Independent exact supplier enclosures; Apache-2.0, OpenAI Codex assistance. + +Uses -log(1-u), not the submitted artanh logarithm. For 0<=u<=1/2, +sum(u**j/j,j=1..N) has tail at most u**(N+1)/((N+1)*(1-u)). +For 0<=x<1, the exponential series through J has tail at most its +first omitted term divided by 1-x/(J+2), since later term ratios decrease. +Outward rounding to a rational grid preserves these bounds. + +This arithmetic module has no repository implementation imports. Local histograms and supplier compiler +contracts remain assumed. This file does not derive the final exponent. +""" +import argparse +from datetime import datetime, timezone +from fractions import Fraction as Q +from functools import lru_cache +import hashlib +import json +from pathlib import Path +import sys +import time + + +GRID = 10**36 +LOG_TERMS = 120 +EXP_TERMS = 16 +BAD = Q(1, 10**16) +ATOM = Q(1, 1000) +OLD = Q(384599, 10**10) + + +class EnclosureError(ValueError): + pass + + +def require(condition, message): + if not condition: + raise EnclosureError(message) + + +def rational(value, name): + require(type(value) in (int, str, Q), 'nonexact rational: ' + name) + try: + return Q(value) + except (ValueError, ZeroDivisionError) as error: + raise EnclosureError('invalid rational: ' + name) from error + + +def round_bounds(lower, upper): + require(lower <= upper, 'reversed enclosure') + lo = lower * GRID + hi = upper * GRID + return (Q(lo.numerator // lo.denominator, GRID), + Q(-((-hi.numerator) // hi.denominator), GRID)) + + +@lru_cache(maxsize=4096, typed=True) +def log_bounds(value): + """Enclose natural log for exact value>=1 by power-of-two reduction.""" + value = rational(value, 'log argument') + require(value >= 1, 'log argument below one') + power = 0 + while value > 2: + value /= 2 + power += 1 + + def unit(y): + u = 1 - 1/y + require(0 <= u <= Q(1, 2), 'log unit interval') + total = Q(0) + term = u + for j in range(1, LOG_TERMS + 1): + total += term / j + term *= u + return total, total + term / ((LOG_TERMS + 1) * (1-u)) + + lo, hi = unit(value) + two_lo, two_hi = unit(Q(2)) + return round_bounds(lo + power*two_lo, hi + power*two_hi) + + +def exp_bounds(value): + """Enclose exp(value) for an exact value in [0,1).""" + value = rational(value, 'exp argument') + require(0 <= value < 1, 'exp argument outside [0,1)') + term = total = Q(1) + for j in range(1, EXP_TERMS + 1): + term *= value/j + total += term + first_omitted = term*value/(EXP_TERMS+1) + remainder = first_omitted/(1-value/(EXP_TERMS+2)) + return round_bounds(total, total+remainder) + + +def power_ratio_bounds(rank, width, saving): + """Bounds for (rank/width)**(1-saving), with proper positive rank.""" + require(type(rank) is int and type(width) is int and 0 < rank < width, + 'improper recursive child') + saving = rational(saving, 'saving') + require(0 <= saving < 1, 'saving outside [0,1)') + lo, hi = log_bounds(Q(width, rank)) + elo = exp_bounds(saving*lo)[0] + ehi = exp_bounds(saving*hi)[1] + return Q(rank, width)*elo, Q(rank, width)*ehi + + +def normalize_children(children, width): + require(type(children) is dict and children, 'empty/nonobject child inventory') + result = {} + for key, count in children.items(): + if type(key) is str: + require(key.isascii() and key.isdigit() and str(int(key)) == key, + 'invalid child rank key') + rank = int(key) + else: + require(type(key) is int, 'invalid child rank type') + rank = key + require(rank not in result, 'duplicate normalized child rank') + require(0 < rank < width and type(count) is int and count > 0, + 'invalid child rank/count') + result[rank] = count + return result + + +def supplier_bounds(width, stock, children, saving, *, bad_fraction=Q(0), + fallback_children_per_edge=0): + """Reusable bound for complete ideal children plus entire rank-one fallback. + + stock is the number of ambient roles per vertex. The bad contribution + is added in full, without subtracting any ideal child it might replace. + Domains too wide for the exp enclosure are rejected rather than guessed. + """ + require(type(width) is int and width >= 2 and type(stock) is int and stock > 0, + 'invalid width/stock') + children = normalize_children(children, width) + saving = rational(saving, 'saving') + bad_fraction = rational(bad_fraction, 'bad fraction') + require(0 <= bad_fraction <= 1, 'bad fraction outside [0,1]') + require(type(fallback_children_per_edge) is int and fallback_children_per_edge >= 0, + 'invalid fallback multiplicity') + require((bad_fraction == 0) == (fallback_children_per_edge == 0), + 'partial fallback specification') + lower = upper = Q(0) + for rank, count in children.items(): + lo, hi = power_ratio_bounds(rank, width, saving) + lower += Q(count, stock)*lo + upper += Q(count, stock)*hi + fallback_lo = fallback_hi = Q(0) + edges = sum(children.values()) + if bad_fraction: + lo, hi = power_ratio_bounds(1, width, saving) + factor = bad_fraction*Q(fallback_children_per_edge*edges, stock) + fallback_lo, fallback_hi = factor*lo, factor*hi + mass = sum(rank*count for rank, count in children.items()) + contaminated_mass = Q(mass)+bad_fraction*fallback_children_per_edge*edges + return dict(width=width, stock=stock, saving=saving, edge_count=edges, + rank_mass=mass, ambient_rank_mass=width*stock, + ideal_lower=lower, ideal_upper=upper, + fallback_lower=fallback_lo, fallback_upper=fallback_hi, + bad_fraction=bad_fraction, + fallback_children_per_edge=fallback_children_per_edge, + total_lower=lower+fallback_lo, total_upper=upper+fallback_hi, + characteristic_gap_lower=1-upper-fallback_hi, + contaminated_rank_mass=contaminated_mass, + rank_gap=width*stock-contaminated_mass) + + +def require_contraction(bounds): + require(bounds['total_upper'] < 1, 'contaminated characteristic does not contract') + require(bounds['contaminated_rank_mass'] < bounds['ambient_rank_mass'], + 'contaminated rank moment does not contract') + return bounds + + +def certify_bit_supplier(width, stock, children, coarse_saving, *, + atom=ATOM, ordinary_saving=OLD): + """Selected compiler: full 32m^2 fallback, fixed bad fraction, stopped saving.""" + coarse = rational(coarse_saving, 'coarse saving') + atom = rational(atom, 'atom') + ordinary = rational(ordinary_saving, 'ordinary saving') + require(0 < coarse < 1 and 0 < atom < 1 and 0 < ordinary < 1, + 'bit saving/atom domain') + bounds = require_contraction(supplier_bounds(width, stock, children, coarse, + bad_fraction=BAD, fallback_children_per_edge=32*width*width)) + require(Q(2*width**3, 2**80) < BAD, 'fixed-prime bad-class allowance') + effective = (1-atom)*coarse+atom*ordinary + require(effective < atom < 1-effective, 'adapter and row tolls not subordinate') + return dict(bounds, effective_saving=effective, atom=atom, + ordinary_saving=ordinary, + prime_bad_fraction_upper=Q(2*width**3, 2**80)) + + +def js(value): + if type(value) is Q: + return str(value) + if type(value) is dict: + return {str(k): js(v) for k, v in value.items()} + if type(value) in (list, tuple): + return [js(v) for v in value] + return value + diff --git a/research/precision-certificate/inputs/paired-cube-bit-physical-input.json b/research/precision-certificate/inputs/paired-cube-bit-physical-input.json new file mode 100644 index 0000000000..8014fc2a23 --- /dev/null +++ b/research/precision-certificate/inputs/paired-cube-bit-physical-input.json @@ -0,0 +1,99 @@ +{ + "R": 19788, + "W_per_vertex": 21548, + "changed_operation_frames": 2884, + "checks": { + "donor_frames_inside_gauges": true, + "gauge_read_window": true, + "operation_frames_nondegenerate_and_spanning": true, + "pair_chronology": true, + "partner_chronology": true, + "phase_one_closure": true, + "register_contents": true, + "role_chains_nested": true, + "target_chains_nested_in_read_order": true, + "telescoping_deficit": true + }, + "child_histogram": { + "1": 125448, + "2": 62908, + "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": 13272, + "60": 2200 + }, + "deficit_per_vertex": 1936, + "f2_replay": { + "lanes": 64, + "registers": 18028, + "rejected_controls": [ + "alias_onto_live_register", + "omitted_recipient_read", + "read_before_donor_death" + ], + "seeds_restored_and_y_plus_x": true + }, + "h": 24, + "late_pairs": 1760, + "local_histogram": { + "1": 35656, + "2": 18916, + "3": 9872, + "4": 2990, + "5": 2600, + "6": 1220, + "7": 1104, + "8": 934, + "9": 604, + "10": 836, + "11": 386, + "12": 1440, + "13": 530, + "14": 1078, + "15": 410, + "16": 1072, + "17": 388, + "18": 444, + "19": 306, + "21": 2840, + "22": 3544 + }, + "loss": 528, + "m": 72, + "operations": 41288, + "pairs": 1760, + "physical_R": 18028, + "physical_gauge_histogram": { + "20": 2200 + }, + "rank_per_vertex": 1549520, + "source_data_histogram": { + "1": 1760, + "2": 880, + "20": 880, + "22": 880 + }, + "target_data_histogram": { + "1": 4400, + "20": 880, + "21": 880 + }, + "v": 1760 +} diff --git a/research/precision-certificate/inputs/paired-cube-complex-input.json b/research/precision-certificate/inputs/paired-cube-complex-input.json new file mode 100644 index 0000000000..26d8a8f4a0 --- /dev/null +++ b/research/precision-certificate/inputs/paired-cube-complex-input.json @@ -0,0 +1,82 @@ +{ + "R": 13042, + "W_per_vertex": 15682, + "c": 21249, + "child_histogram": { + "1": 70488, + "10": 3501, + "11": 468, + "12": 1467, + "13": 114, + "14": 465, + "15": 537, + "16": 672, + "17": 7557, + "18": 8910, + "19": 495, + "2": 58386, + "20": 1056, + "21": 0, + "22": 0, + "3": 25443, + "4": 16539, + "5": 13215, + "54": 2310, + "6": 6420, + "7": 3264, + "8": 3957, + "9": 1797 + }, + "copied_centers_already": true, + "deficit_per_vertex": 1320, + "h": 22, + "loss": 440, + "m": 66, + "matched": 11364, + "matching_frames": "coordinate", + "phase1_operations": 9496, + "q": 3157, + "rank_per_vertex": 1033692, + "remaining_internal_histogram": [ + 8262, + 18216, + 17262, + 8481, + 5513, + 4405, + 2140, + 1088, + 1319, + 599, + 1167, + 156, + 489, + 38, + 155, + 179, + 224, + 2519, + 330, + 165, + 352, + 0, + 0 + ], + "selected_rank_histogram": { + "18": 2310 + }, + "selected_roles": 2310, + "source_data_histogram": { + "1": 1320, + "18": 1320, + "2": 1320 + }, + "target_data_histogram": { + "0": 6270, + "1": 3960, + "18": 1320 + }, + "total_M_operations": 32971, + "untouched_non_source_roles": 5834, + "v": 1320 +} diff --git a/research/precision-certificate/inputs/paired-cube-sinks-input.json b/research/precision-certificate/inputs/paired-cube-sinks-input.json new file mode 100644 index 0000000000..3b6f7b6f54 --- /dev/null +++ b/research/precision-certificate/inputs/paired-cube-sinks-input.json @@ -0,0 +1,82 @@ +{ + "R": 13042, + "W_per_vertex": 13328, + "child_histogram": { + "1": 88155, + "10": 2589, + "11": 987, + "12": 3555, + "13": 642, + "14": 2142, + "15": 3255, + "16": 330, + "17": 132, + "18": 7788, + "19": 5334, + "2": 45525, + "20": 1551, + "3": 29427, + "4": 10830, + "5": 7044, + "6": 4407, + "7": 2559, + "8": 3675, + "9": 1323 + }, + "deficit_per_vertex": 1320, + "h": 22, + "local_histogram": { + "1": 24105, + "10": 855, + "11": 327, + "12": 1179, + "13": 212, + "14": 710, + "15": 1073, + "16": 103, + "17": 44, + "19": 1778, + "2": 12952, + "20": 517, + "3": 9793, + "4": 3603, + "5": 2346, + "6": 1462, + "7": 850, + "8": 1220, + "9": 440 + }, + "loss": 440, + "m": 66, + "pairs": 2310, + "physical_R": 10688, + "physical_gauge_histogram": {}, + "rank_per_vertex": 878328, + "sinks": 44, + "source_data_histogram": { + "1": 1320, + "18": 1320, + "2": 1320 + }, + "target_data_histogram": { + "0": 6323, + "1": 3960, + "10": 8, + "11": 2, + "12": 6, + "13": 2, + "14": 4, + "15": 12, + "16": 7, + "18": 1276, + "2": 23, + "3": 16, + "4": 7, + "5": 2, + "6": 7, + "7": 3, + "8": 5, + "9": 1 + }, + "v": 1320 +} diff --git a/research/precision-certificate/profile_binding.py b/research/precision-certificate/profile_binding.py new file mode 100644 index 0000000000..d50eba2e98 --- /dev/null +++ b/research/precision-certificate/profile_binding.py @@ -0,0 +1,115 @@ +"""Pinned native-profile consistency gate, separate from independent arithmetic. + +Apache-2.0. Prepared with substantial OpenAI Codex assistance. +This module imports no producer. Native answers are comparison targets for +input wiring, not an implementation of geometry or scalar verification. +""" +import gzip +import hashlib +import json +from pathlib import Path + +PIN = '7fb2194801e3a10f54772c7f0d5505035a4fc0ad' +PACKAGE = 'research/paired-cube-local-168/' +SELECT = PACKAGE+'selected/complex/' +INPUT_NAMES = ('paired-cube-complex-input.json', 'paired-cube-sinks-input.json', + 'paired-cube-bit-physical-input.json') +NATIVE_HASHES = {'research/paired-cube-local-168/certificate.json': '1e72ed46c81f1fada5adc71da38145f155872912fd39546b3294130cd0eeb9ed', 'research/paired-cube-local-168/SOURCE.json': '30c3878dde69a4ed29beed26856d1015ad3180da464d96154e5b005f728847bf', 'research/paired-cube-local-168/selected/complex/profile-before.json.gz': '89a46f6c9bc2e49a903a44952539034165acbc26ef6b7f14504554299ca8e2c6', 'research/paired-cube-local-168/selected/complex/profile.json.gz': '9d470b72ae31e2debd945b61481bde9c68df93054013f657cb331e0e49b53105', 'research/paired-cube-local-168/selected/complex/sinks.json': 'f4d0c85db8bc90b4c0ad243adb5332e0da6fa1a8db1be6b1ad58d93a5e19fdbe', 'certificates/paired-cube-bit-physical-input.json': '6735294e8639da09eb3eb2234cbc5814298442a6c946b5534bcf6e48903547f3'} +DIAGNOSTICS = {'numerical_complex_root', 'gauge_cost_rejections', + 'gauge_trial_saving', 'gauge_selection'} + +def require(condition, message): + if not condition: + raise ValueError(message) + +def canonical(value): + return hashlib.sha256(json.dumps(value, sort_keys=True, separators=(',', ':')).encode()).hexdigest() + +def positive_bins(hist, maximum): + require(type(hist) is dict, 'native component histogram object') + out = {} + for key, count in hist.items(): + require(type(key) is str and key.isascii() and key.isdigit() and str(int(key)) == key, + 'native component rank key') + rank = int(key) + require(0 <= rank <= maximum and type(count) is int and count >= 0, + 'native component rank/count') + if rank and count: + out[key] = count + return out + +def bind_objects(native, inputs): + """Pure consistency check; mathematical mutations bypass byte hash guards.""" + require(set(inputs) == set(INPUT_NAMES), 'precision input names') + logical = inputs['paired-cube-complex-input.json'] + physical = inputs['paired-cube-sinks-input.json'] + bit = inputs['paired-cube-bit-physical-input.json'] + expected_logical = {k:v for k,v in native['logical'].items() if k not in DIAGNOSTICS} + require(logical == expected_logical, 'native logical scalar profile mismatch') + require(tuple(logical[k] for k in ('h', 'v', 'R', 'c', 'q', 'matched', 'total_M_operations', 'loss')) + == (22, 1320, 13042, 21249, 3157, 11364, 32971, 440), 'native scalar dimensions') + require(logical['R'] == logical['c']+logical['q']-logical['matched'], 'native logical role identity') + published = native['certificate']['complex']['physical']['physical'] + profile = native['certificate']['complex']['profile'] + sink = native['sinks'] + require(published['terminal_sinks'] == profile['terminal_sinks'] == sink['eligible_count'] == 44, + 'native terminal population') + require(physical['sinks'] == 44, 'native copied terminal population') + for key in ('h', 'v', 'R', 'pairs', 'physical_R', 'loss', 'm', 'W_per_vertex', + 'rank_per_vertex', 'deficit_per_vertex'): + require(type(physical[key]) is int and physical[key] == published[key], + 'native physical dimension mismatch: '+key) + require((physical['m'],physical['W_per_vertex'],physical['rank_per_vertex'], + physical['deficit_per_vertex'],physical['physical_R']) == (66,13328,878328,1320,10688), + 'native final stock/rank') + require(physical['R'] == logical['R'] and physical['pairs'] == profile['reuse_pairs'] == 2310, + 'native logical/alias coupling') + require(physical['physical_R'] == physical['R']-physical['pairs']-physical['sinks'] == profile['R'], + 'native physical role recount') + require(profile['scalar_role_reserve'] == logical['R'] and profile['c'] == logical['c'] + and profile['q'] == logical['q'] and profile['total_M_operations'] == logical['total_M_operations'], + 'native full scalar charge inventory') + component_sha256 = {} + for field in ('local_histogram', 'source_data_histogram', 'target_data_histogram', + 'physical_gauge_histogram', 'child_histogram'): + maximum = 65 if field == 'child_histogram' else 22 + ours = positive_bins(physical[field], maximum) + require(ours == positive_bins(published[field], maximum), 'native '+field+' mismatch') + component_sha256[field] = canonical(ours) + require(positive_bins(physical['local_histogram'],22) == positive_bins(sink['local_histogram'],22), + 'native selected sink local histogram mismatch') + require(positive_bins(physical['target_data_histogram'],22) == positive_bins(sink['target_histogram'],22), + 'native selected sink target histogram mismatch') + require(positive_bins(physical['child_histogram'],65) == positive_bins(sink['child_histogram'],65) + == positive_bins(profile['child_histogram'],65), 'native selected sink paid inventory mismatch') + before = native['profile_before_terminal'] + require((before['R'],before['physical_R'],before['pairs'],before['W_per_vertex'],before['rank_per_vertex']) + == (13042,10732,2310,13372,881232), 'native pre-terminal physical stock') + require(before['source_data_histogram'] == published['source_data_histogram'], 'native source inventory changed') + require(bit == native['bit'], 'native unchanged bit profile mismatch') + native_zero = published['target_data_histogram'].get('0',0) + ours_zero = physical['target_data_histogram'].get('0',0) + require(type(native_zero) is int and type(ours_zero) is int and native_zero >= 0 and ours_zero >= 0, + 'native zero-rank diagnostics') + return dict(status='pinned_native_profile_binding_pass',upstream_commit=PIN, + paid_component_sha256=component_sha256,logical_profile_sha256=canonical(logical), + bit_profile_sha256=canonical(bit),zero_rank_target_events=dict(native=native_zero, + independent_literal_recount=ours_zero,difference=ours_zero-native_zero), + scope='Native input consistency only. Positive rank bins and all paid dimensions agree. ' + 'Zero-rank events create no child, rank mass or characteristic charge; full c/M scalar ' + 'charges remain paid. Native scalar_replay metadata is not copied or treated as fresh evidence.') + +def load_native(root): + root = Path(root) + for path, expected in NATIVE_HASHES.items(): + require(hashlib.sha256((root/path).read_bytes()).hexdigest() == expected, + 'native source byte mismatch: '+path) + read = lambda name: json.loads((root/name).read_bytes()) + zipped = lambda name: json.loads(gzip.decompress((root/name).read_bytes())) + return dict(certificate=read(PACKAGE+'certificate.json'), logical=zipped(SELECT+'profile-before.json.gz'), + profile_before_terminal=zipped(SELECT+'profile.json.gz'), sinks=read(SELECT+'sinks.json'), + bit=read('certificates/paired-cube-bit-physical-input.json')) + +def check_native_inputs(root, inputs): + require(len(NATIVE_HASHES) == 6, 'complete native binding pin set') + return bind_objects(load_native(root), inputs) diff --git a/research/precision-certificate/test_native.py b/research/precision-certificate/test_native.py new file mode 100644 index 0000000000..cac9d59d5d --- /dev/null +++ b/research/precision-certificate/test_native.py @@ -0,0 +1,31 @@ +"""Native wiring controls exercise scientific fields, bypassing source hashes.""" +import copy +import json +import unittest +import verify as V +import profile_binding as P + +class NativeBindingControls(unittest.TestCase): + @classmethod + def setUpClass(cls): + cls.native=P.load_native(V.HERE.parents[1]) + cls.inputs={n:json.loads((V.HERE/'inputs'/n).read_bytes()) for n in P.INPUT_NAMES} + def test_full_native_binding(self): + result=P.bind_objects(self.native,self.inputs) + self.assertEqual(result['zero_rank_target_events'],{'native':6270,'independent_literal_recount':6323,'difference':53}) + def test_positive_paid_component_changed(self): + inputs=copy.deepcopy(self.inputs);inputs['paired-cube-sinks-input.json']['target_data_histogram']['1']-=1 + with self.assertRaisesRegex(ValueError,'native target_data_histogram mismatch'):P.bind_objects(self.native,inputs) + def test_logical_reserve_collapsed(self): + inputs=copy.deepcopy(self.inputs);inputs['paired-cube-complex-input.json']['R']=10688 + with self.assertRaisesRegex(ValueError,'logical scalar profile'):P.bind_objects(self.native,inputs) + def test_terminal_removal_count_changed(self): + inputs=copy.deepcopy(self.inputs);inputs['paired-cube-sinks-input.json']['sinks']=43 + with self.assertRaisesRegex(ValueError,'copied terminal population'):P.bind_objects(self.native,inputs) + def test_zero_rank_is_reported_without_paid_child(self): + inputs=copy.deepcopy(self.inputs);inputs['paired-cube-sinks-input.json']['target_data_histogram']['0']+=1 + before=P.bind_objects(self.native,self.inputs);after=P.bind_objects(self.native,inputs) + self.assertEqual(before['paid_component_sha256'],after['paid_component_sha256']) + self.assertEqual(after['zero_rank_target_events']['difference'],54) + +if __name__=='__main__':unittest.main() diff --git a/research/precision-certificate/test_precision.py b/research/precision-certificate/test_precision.py new file mode 100644 index 0000000000..c03aa325d6 --- /dev/null +++ b/research/precision-certificate/test_precision.py @@ -0,0 +1,68 @@ +"""Mathematical and source-binding controls for the standalone refinement.""" +import copy +import json +import unittest +import verify as V + + +class PrecisionControls(unittest.TestCase): + @classmethod + def setUpClass(cls): + read = lambda name: json.loads((V.HERE/'inputs'/name).read_bytes()) + cls.complex = read('paired-cube-sinks-input.json') + cls.bit = read('paired-cube-bit-physical-input.json') + cls.scalar = read('paired-cube-complex-input.json') + + def test_recomputed_certificate(self): + self.assertEqual(V.regenerate(), json.loads((V.HERE/'certificate.json').read_bytes())) + + def test_supplier_successors_fail_characteristic(self): + result = V.arithmetic(self.complex, self.bit, self.scalar) + for side in ('complex', 'bit'): + self.assertGreaterEqual(V.Q(result['supplier_successors'][side]['total_lower']), 1) + + def test_headline_successor_fails_compact_layer(self): + bridge = V.A.reconstruct_bridge(self.scalar, self.complex) + effective = (1-V.ATOM)*V.COARSE+V.ATOM*V.M.OLD + with self.assertRaisesRegex(ValueError, 'compact_phase_layer_above_kappa'): + V.A.balanced_assembly(bridge, effective, V.COMPLEX, V.KAPPA+V.Q(1,V.GRID), + eta=V.ETA,beta=V.BETA,phase_gap=V.PHASE_GAP) + + def test_omit_paid_child(self): + row = copy.deepcopy(self.bit) + rank = next(k for k,n in row['local_histogram'].items() if int(k)>0 and n>0) + row['local_histogram'][rank] -= 1 + with self.assertRaisesRegex(ValueError, 'Paid child reconstruction'): + V.paid_profile(row) + + def test_wrong_positive_router_charge(self): + bridge = V.A.reconstruct_bridge(self.scalar, self.complex) + bridge['literal_charge'] = bridge['E']+1 + effective = (1-V.ATOM)*V.COARSE+V.ATOM*V.M.OLD + with self.assertRaisesRegex(ValueError, 'literal_scalar_guard'): + V.A.balanced_assembly(bridge,effective,V.COMPLEX,V.KAPPA, + eta=V.ETA,beta=V.BETA,phase_gap=V.PHASE_GAP) + + def test_duplicate_rank_and_bool_rejected(self): + with self.assertRaisesRegex(ValueError, 'duplicate normalized child rank'): + V.M.normalize_children({'2':1,2:1},72) + with self.assertRaisesRegex(ValueError, 'invalid child rank/count'): + V.M.normalize_children({'2':True},72) + + def test_wrong_revision_label(self): + manifest = json.loads((V.HERE/'SOURCE.json').read_bytes()) + manifest['upstream_commit'] = '0'*40 + with self.assertRaisesRegex(ValueError, 'Wrong upstream revision label'): + V.check_source_manifest(manifest,lambda name:(V.HERE/name).read_bytes()) + + def test_modified_raw_input(self): + manifest = json.loads((V.HERE/'SOURCE.json').read_bytes()) + def modified(name): + data=(V.HERE/name).read_bytes() + return data+b' ' if name.startswith('inputs/') else data + with self.assertRaisesRegex(ValueError, 'Source byte mismatch: inputs/'): + V.check_source_manifest(manifest,modified) + + +if __name__ == '__main__': + unittest.main() diff --git a/research/precision-certificate/verify.py b/research/precision-certificate/verify.py new file mode 100644 index 0000000000..8dd8dc2a48 --- /dev/null +++ b/research/precision-certificate/verify.py @@ -0,0 +1,144 @@ +#!/usr/bin/env python3 +"""Finite precision refinement from pinned inventories, without producer imports. + +Copyright 2026 Muhammed Ali Mehmood. Apache-2.0. +Prepared with substantial OpenAI Codex assistance. +""" +import argparse +from collections import Counter +from fractions import Fraction as Q +from hashlib import sha256 +import json +from pathlib import Path +import sys + +import independent_moments as M +import independent_assembly as A + +HERE = Path(__file__).resolve().parent +if hasattr(sys, 'set_int_max_str_digits'): + sys.set_int_max_str_digits(100000) +PIN = '7fb2194801e3a10f54772c7f0d5505035a4fc0ad' +GRID = 10**24 +COMPLEX = Q(132438677973141606647, 200000000000000000000000) +COARSE = Q(82503172294962610849, 125000000000000000000000) +ATOM = Q(659615384207882296543, 1000000000000000000000000) +KAPPA = Q(659180578557294852359, 1000000000000000000000000) +ETA = BETA = PHASE_GAP = Q(1, GRID) +BASELINE = Q(659180578557293, 1000000000000000000) +FIXED_HASHES = { + 'inputs/paired-cube-sinks-input.json': 'aeb7b2c053f6eacd55837c4c597a9cb3626d681495b783cc6310789e35b5fc9a', + 'inputs/paired-cube-bit-physical-input.json': '6735294e8639da09eb3eb2234cbc5814298442a6c946b5534bcf6e48903547f3', + 'inputs/paired-cube-complex-input.json': '9adcc1e7da7222e19dce989cd6f86200997a677642b4c2a580aaae0c0a31a855', + 'independent_moments.py': '4d398b4600f7aeaf73a36c68ebc9727de0451399512769282684ae9d4804f594', + 'independent_assembly.py': '99584fe21922926ed9766ec5bc75a06ae531f396bf41ef87baafde248e1f9b9b', + 'LICENSE': 'c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4', +} +SOURCE_FILES = set(FIXED_HASHES) | {'verify.py', 'test_precision.py', 'README.md', 'PROOF.md', 'NOTICE', 'profile_binding.py', 'test_native.py'} + + +def check_source_manifest(manifest, read_bytes): + A.require(manifest['upstream_commit'] == PIN, 'Wrong upstream revision label') + hashes = manifest['source_sha256'] + A.require(type(hashes) is dict and set(hashes) == SOURCE_FILES, 'Incomplete source closure') + for name, expected in FIXED_HASHES.items(): + A.require(hashes[name] == expected, 'Wrong frozen source pin: ' + name) + for name, expected in hashes.items(): + A.require(sha256(read_bytes(name)).hexdigest() == expected, 'Source byte mismatch: ' + name) + + +def paid_profile(row): + """Reconstruct every paid child, then compare the frozen complete inventory.""" + h, v, roles, loss = (row[k] for k in ('h', 'v', 'physical_R', 'loss')) + A.require(all(type(x) is int and x > 0 for x in (h, v, roles)), 'Invalid physical dimensions') + A.require(type(loss) is int and loss >= 0, 'Invalid loss') + for key in ('R', 'pairs'): + A.require(type(row[key]) is int and row[key] >= 0, 'Invalid logical/pair stock') + sinks = row.get('sinks', 0) + A.require(type(sinks) is int and sinks >= 0, 'Invalid sink count') + A.require(roles == row['R'] - row['pairs'] - sinks, 'Physical role recount') + width, stock = 3*h, 2*v+roles + children = Counter() + for name in ('local_histogram', 'source_data_histogram', 'target_data_histogram'): + for rank, count in A.component_histogram(row[name], h).items(): + children[rank] += 3*count + for rank, count in A.component_histogram(row['physical_gauge_histogram'], h-1).items(): + children[3*rank] += count + children[2] += 2*v + children = dict(sorted(children.items())) + A.require(children == M.normalize_children(row['child_histogram'], width), 'Paid child reconstruction') + mass = sum(rank*count for rank, count in children.items()) + deficit = width*stock-mass + A.require((width, stock, mass, deficit) == (row['m'], row['W_per_vertex'], + row['rank_per_vertex'], row['deficit_per_vertex']), 'Dimension and rank recount') + A.require(deficit == 2*v-3*loss > 0, 'Shared-core telescoping deficit') + return dict(width=width, stock=stock, children=children, mass=mass, deficit=deficit) + + +def arithmetic(complex_row, bit_row, scalar_row): + cp, bp = paid_profile(complex_row), paid_profile(bit_row) + complex_bound = M.require_contraction(M.supplier_bounds( + cp['width'], cp['stock'], cp['children'], COMPLEX)) + bit_bound = M.certify_bit_supplier(bp['width'], bp['stock'], bp['children'], COARSE, atom=ATOM) + threshold = COARSE/(1+COARSE-M.OLD) + A.require(ATOM-Q(1, GRID) <= threshold < ATOM, 'Atom is not first strict grid point') + successors = {} + for side, p, saving in (('complex', cp, COMPLEX), ('bit', bp, COARSE)): + bounds = M.supplier_bounds(p['width'], p['stock'], p['children'], saving+Q(1, GRID), + bad_fraction=M.BAD if side == 'bit' else Q(0), + fallback_children_per_edge=32*p['width']**2 if side == 'bit' else 0) + A.require(bounds['total_lower'] >= 1, side + ' supplier successor not rejected') + successors[side] = dict(saving=saving+Q(1, GRID), total_lower=bounds['total_lower']) + bridge = A.reconstruct_bridge(scalar_row, complex_row) + assembled = A.balanced_assembly(bridge, bit_bound['effective_saving'], COMPLEX, + KAPPA, eta=ETA, beta=BETA, phase_gap=PHASE_GAP) + minimum = assembled['minimum_margin'] + A.require(KAPPA < minimum <= KAPPA+Q(1, GRID), 'Headline strict grid interval') + try: + A.balanced_assembly(bridge, bit_bound['effective_saving'], COMPLEX, + KAPPA+Q(1, GRID), eta=ETA, beta=BETA, phase_gap=PHASE_GAP) + except ValueError as error: + A.require('compact_phase_layer_above_kappa' in str(error), 'Wrong headline successor failure') + else: + raise ValueError('Headline successor accepted') + A.require(KAPPA > BASELINE, 'Refinement does not improve pinned headline') + return A.serialize(dict(schema_version=1, upstream_commit=PIN, kappa=KAPPA, + pinned_baseline_kappa=BASELINE, improvement=KAPPA-BASELINE, + supplier_grid=GRID, atom_grid=GRID, headline_grid=GRID, + phase_gap=PHASE_GAP, complex_profile=cp, bit_profile=bp, + complex=complex_bound, bit=bit_bound, atom_threshold=threshold, + supplier_successors=successors, headline_successor=KAPPA+Q(1, GRID), + headline_successor_rejected=True, finite_bridge=bridge, assembly=assembled, + scope='Independent exact arithmetic from pinned stored inventories. Local schedule, phases, uniform compiler, analytic and fixed-tape interfaces remain proof obligations.')) + + +def regenerate(): + manifest_raw = (HERE/'SOURCE.json').read_bytes() + check_source_manifest(json.loads(manifest_raw), lambda name: (HERE/name).read_bytes()) + read = lambda name: json.loads((HERE/'inputs'/name).read_bytes()) + result = arithmetic(read('paired-cube-sinks-input.json'), + read('paired-cube-bit-physical-input.json'), + read('paired-cube-complex-input.json')) + result['source_manifest_sha256'] = sha256(manifest_raw).hexdigest() + return result + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--write', action='store_true', help='write the recomputed precision certificate') + parser.add_argument('--native-inputs', action='store_true', help='also bind every copied profile to pinned native181 components') + args = parser.parse_args() + if args.native_inputs: + import profile_binding as P + print(json.dumps(P.check_native_inputs(HERE.parents[1], {name: json.loads((HERE/'inputs'/name).read_bytes()) for name in P.INPUT_NAMES}),sort_keys=True)) + text = json.dumps(regenerate(), indent=2, sort_keys=True)+'\n' + path = HERE/'certificate.json' + if args.write: + path.write_bytes(text.encode('utf-8')) + else: + A.require(path.read_bytes() == text.encode('utf-8'), 'Stored precision certificate differs') + print('PASS conditional precision kappa=' + str(KAPPA) + '; exact supplier moments, paid inventories, finite bridge, all 47 inequalities and next-grid controls') + + +if __name__ == '__main__': + main() diff --git a/research/terminal-sinks/README.md b/research/terminal-sinks/README.md new file mode 100644 index 0000000000..d23e08116f --- /dev/null +++ b/research/terminal-sinks/README.md @@ -0,0 +1,66 @@ +# Terminal sinks on the paired-cube complex word + +This applies the terminal-sink lemma of PR #166 by jamesyc (closed by its author) to the complex word and checks it +independently here. `sinks_gate.py`'s own frame scans, replay and controls carry the soundness argument; they do +not use #166's checker. Gate, audit and integration by eumemic with Anthropic Claude assistance. + +## The substitution + +A sink is an auxiliary role `z` with these properties: + +- it starts at frame 0 with no gauge: no source injection, not a donor or recipient; +- it is written only as a destination, `z <- z + b*a`, never as a control, and never in phase one; +- its write frames are nested, `0 <= F_1 <= ... <= F_k <= U`, where `U` is the frame of its single side root + `y_t += c*z` (`t` in `T`); +- it has a pivot `p` in `T` with no deferred old-value read of `p` between the phase cut and `z`'s last write. + +The sink is deleted and replaced by three steps: + +1. at the phase cut, after the copied-centre scatter: `y_t -= y_p` for `t` in `T - p`, at frame 0; +2. at each original write time: `y_p += c*b*a`, at frame `F_i`; +3. right after the last write: `y_t += y_p` for `t` in `T - p`, at frame `U`. + +Each sink removes one physical register and, per core, one child `r = rank U` and one child `h - r`. The deficit is +unchanged. + +## Checks (`sinks_gate.py`) + +1. The frozen layer passes #161's checker (`scripts/paired_cube_physical.py`, unchanged) and matches its frozen + record. +2. Every condition above is recomputed for every sink from the regenerated word, the layer and the read schedule. + Target groups of different sinks are disjoint. +3. The literal stage word has every frame step nested, forward and literally reflected. This covers X ports, + Y ports and physical slots: time-0 and deferred reads, injections, ops, the centre scatter, side-root reads, + K on the sources and full-frame inverses. +4. The unsubstituted word's literal per-stage histogram equals #161's record over three stages. The substituted + word's histogram is that minus `[r]` and `[h - r]` per sink. +5. A dirty-scratch replay mod 2^61-1 gives `(X, Y + X, Z)` forward and `(X - Y, Y, Z)` reflected. +6. Four controls are rejected: + - a sandwich raised before the centre scatter; + - an omitted post-shear; + - an uncomplemented reflected pivot write; + - a post-shear moved after its pivot's first correction. + +## Results (p11N1d_J0TEc3u: J0 pair module, TE triple module, climb3u Q module, the depth-4 maximum-weight layer) + +| | W | complex AC | +|---|---|---| +| layer | 13,702 | 3273661/5e9 = 6.547322e-4 | +| + 47 sinks | 13,655 | 6563200/1e10 = 6.563200e-4 (+0.243%) | + +The same rule gave 42 sinks on p11N1b_TB31 (6479443/1e10 -> 6493335/1e10) and on p11N1_Qb01 +(6466544/1e10 -> 6480380/1e10). + +**Why only 47.** Only all-eight (disjoint) roots are sinks here. Of the 165 roots, 118 have retained producer +consumers, 14 are source-injection roles, and 14 are written in phase one; some roots fail more than one test. +The face0 sinks that meet the conditions (10 here) fail the frame scan: the post-shear at their rank-19 `U` raises target +registers above later rank-18 reads, so the target chains stop nesting. + +## Use + + python3 research/terminal-sinks/sinks_gate.py # check against certificates/paired-cube-sinks-input.json + python3 research/terminal-sinks/sinks_gate.py --write # refreeze + python3 research/terminal-sinks/sinks_gate.py --tree=T --work=W --layer=L --sinks=S.json [--out=X.json] + +`sinks.json` is `{"sinks": [[role, pivot], ...]}`. When it is present, `scripts/paired_cube_network.py` prices the +complex profile from `checked_sinks_record()` instead of #161's record. diff --git a/research/terminal-sinks/sinks.json b/research/terminal-sinks/sinks.json new file mode 100644 index 0000000000..8ba0b59242 --- /dev/null +++ b/research/terminal-sinks/sinks.json @@ -0,0 +1 @@ +{"sinks": [[10570, 40], [10930, 72], [10846, 88], [10197, 120], [10961, 136], [10556, 160], [10546, 168], [10539, 224], [9448, 272], [10829, 296], [10920, 344], [10966, 432], [10578, 456], [10782, 464], [10926, 472], [10928, 488], [10959, 536], [10849, 560], [10592, 568], [10934, 576], [10786, 584], [10936, 592], [10589, 608], [10927, 640], [10744, 664], [9418, 672], [10537, 712], [10955, 728], [10921, 776], [10838, 792], [10969, 800], [10945, 840], [10820, 848], [10790, 880], [10747, 904], [10075, 928], [10784, 952], [10833, 960], [10543, 976], [10968, 1016], [10951, 1024], [10953, 1088], [10952, 1128], [10824, 1136], [9454, 1184], [10845, 1240], [10958, 1304]]} \ No newline at end of file diff --git a/research/terminal-sinks/sinks_gate.py b/research/terminal-sinks/sinks_gate.py new file mode 100644 index 0000000000..7ed910e59d --- /dev/null +++ b/research/terminal-sinks/sinks_gate.py @@ -0,0 +1,541 @@ +#!/usr/bin/env python3 +"""Terminal-sink substitution (PR #166) on the paired-cube complex word with its frozen physical layer. + +The substitution is the terminal-sink lemma of PR #166 by jamesyc (closed by its author), independently audited +here: this gate's own frame scans, replay and controls carry the soundness argument and do not use #166's checker. +Gate, audit and integration by eumemic with Anthropic Claude assistance. Apache-2.0. + +Sink. An auxiliary role z that starts at frame 0 with no gauge (no source injection, not a donor or recipient), +is written only as a destination (z <- z + b*a, never a control), never in phase one, at frames +0 <= F_1 <= ... <= F_k <= U (the frame of its single side root, read y_t += c*z for t in T), and has a pivot p in T +with no deferred old-value read of p between the phase cut and z's last write. Then z is deleted and: + 1. at the phase cut, after the copied-centre scatter: y_t -= y_p for t in T - p, at frame 0; + 2. at each original write time: y_p += c*b*a, at frame F_i; + 3. right after the last write: y_t += y_p for t in T - p, at frame U. +Ledger per sink: one physical register fewer and, per core, one child r = rank U and one child h - r fewer; the +deficit is unchanged. + +Checks (sinks_record), from the regenerated word, the frozen layer (references/paired-cube/physical) and sinks.json: + - every sink satisfies the conditions above, recomputed from the word, the layer and the read schedule + (#161's: a recipient is read at its frozen read op, an unpaired gauge at the phase cut), and target groups of + different sinks are disjoint; + - the literal substituted stage word (X ports, Y ports, physical slots; time-0 and deferred reads, injections, + ops, the centre scatter, side-root reads, K on the sources, full-frame inverses) has every frame step nested, + forward and literally reflected; + - the unsubstituted word's literal per-stage histogram equals #161's record over three stages, and the + substituted word's is that minus [r] and [h - r] per sink; the change is booked per register class + (auxiliary slots and centre copies: local; X: source data; Y: target data) onto #161's record; + - a dirty-scratch replay mod 2^61-1 gives (X, Y + X, Z) forward and (X - Y, Y, Z) reflected; + - controls that must be rejected: a sandwich raised before the centre scatter, an omitted post-shear, an + uncomplemented reflected pivot write, and a post-shear moved after its pivot's first correction. +The record has the shape of paired_cube_physical.physical() with the sinks applied (plus a 'sinks' entry), so +paired_cube_network.py prices it as the complex profile. + +Why all-eight roots only: on this word the face0 sinks that meet the conditions fail the frame scan, because the +post-shear at their rank-19 U raises target registers above later rank-18 reads. + +usage: sinks_gate.py [--write] (frozen check against certificates/paired-cube-sinks-input.json) + sinks_gate.py --tree=T --work=W --layer=L --sinks=S.json [--out=X.json] (dumped word; pipeline use) +""" +import json +import random +import sys +from collections import Counter +from functools import lru_cache +from pathlib import Path + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +SINKS = HERE / 'sinks.json' +OUTPUT = ROOT / 'certificates/paired-cube-sinks-input.json' +P = (1 << 61) - 1 + + +def require(condition, message): + if not condition: + raise AssertionError(message) + + +def sinks_record(g, witness, word, record, frames_in, pairs_in, sinks_in, base): + """Apply and check the substitution; base = paired_cube_physical.physical(...) of the same layer.""" + h, v, R = g['h'], g['v'], record['R'] + + @lru_cache(maxsize=None) + def basis(rows): + b, mask = {}, 0 + for x in rows: + mm = x & mask + while mm: + p = mm.bit_length() - 1 + x ^= b[p] + mm ^= 1 << p + if x: + p = x.bit_length() - 1 + for k in list(b): + if b[k] >> p & 1: + b[k] ^= x + b[p] = x + mask |= 1 << p + return tuple(b[p] for p in sorted(b, reverse=True)) + + @lru_cache(maxsize=None) + def perp(U): + U = basis(U) + piv = {r.bit_length() - 1: r for r in U} + out = [] + for j in range(h): + if j not in piv: + x = 1 << j + for p, r in piv.items(): + if r >> j & 1: + x |= 1 << p + out.append(x) + return basis(tuple(out)) + + @lru_cache(maxsize=None) + def contained(Aa, Bb): + rb = basis(Bb) + return len(basis(rb + tuple(Aa))) == len(rb) + + ZERO, FULL = (), basis(tuple(1 << i for i in range(h))) + inputs, labels = g['inputs'], g['labels'] + roots = [dict(r, node=r['node'] + 1) for r in g['roots']] + args = [None] + [None if a is None else (a[0] + 1, a[1] + 1) for a in g['args']] + ann = witness['annihilators'] + ops = [tuple(o) for o in word['ops']] + coef = [tuple(c) for c in word['opcoeff']] + require(all(ca == 1 for ca, cb in coef), 'Every operation is a shear dest += cb*control') + frames = [perp(tuple(ann[x])) for _, _, x in ops] + for i, F in frames_in: + frames[i] = basis(tuple(F)) + pairs = [(int(a), int(b)) for a, b, _ in pairs_in] + deadline = {int(b): (None if t is None else int(t)) for _, b, t in pairs_in} + phase1 = sorted(word['phase1']) + pset = set(phase1) + rest = [i for i in range(len(ops)) if i not in pset] + position = {i: k for k, i in enumerate(phase1 + rest)} + sources = {int(x): s for x, s in word['sources'].items()} + rootroles = word['rootroles'] + selected = [z['role'] for z in word['selected']] + gauge_targets = {z['role']: z['targets'] for z in word['selected']} + merge = {b: a for a, b in pairs} + live = sorted(set(range(R)) - set(merge)) + slot = {s: i for i, s in enumerate(live)} + X = lambda t: t + Y = lambda t: v + t + A = lambda s: 2 * v + slot[merge.get(s, s)] + NREG = 2 * v + len(live) + + # exact responses of the unsubstituted word (every retained read keeps its original column) + inv = lambda x: pow(x % P, P - 2, P) + HALF, THIRD, SIXTH = inv(2), inv(3), inv(6) + cseed, dseed, rootframe, rootorder, span = {}, {}, {}, [], {} + for x in range(1, len(args)): + span[x] = basis((inputs[x - 1],)) if args[x] is None else basis(span[args[x][0]] + span[args[x][1]]) + for r, s in zip(roots, rootroles): + if r['kind'] == 'center': + c = [0] * h + c[r['coordinate']] = 1 + cseed[s] = c + rootframe[s] = span[r['node']] + else: + dseed[s] = {t: (HALF if q == '1/2' else P - HALF) for t, q in zip(r['targets'], r['coefficients'])} + rootframe[s] = perp(basis(tuple(inputs[t] for t in r['targets']))) + rootorder.append((s, r['targets'])) + cvec, dpart = [None] * R, [dict() for _ in range(R)] + for s, c in cseed.items(): + cvec[s] = list(c) + for s, d in dseed.items(): + dpart[s] = dict(d) + for (a, b, x), (ca, cb) in zip(reversed(ops), reversed(coef)): + if cvec[a] is not None: + cvec[b] = [(cb * u) % P for u in cvec[a]] if cvec[b] is None else [(w + cb * u) % P for w, u in zip(cvec[b], cvec[a])] + if dpart[a]: + db = dpart[b] + for t, u in dpart[a].items(): + db[t] = (db.get(t, 0) + cb * u) % P + scatter = [[THIRD if c in labels[t] else (P - SIXTH) for t in range(v)] for c in range(h)] + deferred = set(selected) + + def reach(s, mode): + if mode == 'seed': + return sorted(dseed.get(s, {})) + return list(range(v)) if cvec[s] is not None else sorted(t for t, u in dpart[s].items() if u) + + read_op = {s: (deadline[s] if deadline.get(s) is not None else rest[0]) for s in selected} + require(all(op not in pset for op in read_op.values()), 'Deferred read inside phase one') + reads_at = {} + for s in reversed(selected): + reads_at.setdefault(read_op[s], []).append(s) + gauge = {z['role']: perp(basis(tuple(z['annihilator']))) for z in word['selected']} + leaf_of = {s: x for x, s in sources.items()} + first_read = {} + for s in selected: + for t in gauge_targets[s]: + first_read[t] = min(first_read.get(t, 1 << 60), position[read_op[s]]) + + # sinks: recompute and check every condition + sink = {} + for s, p in sinks_in: + js = [j for j, r in enumerate(rootroles) if r == s] + require(len(js) == 1 and roots[js[0]]['kind'] == 'side', 'Sink %d: exactly one side root' % s) + j = js[0] + T = list(roots[j]['targets']) + require(len(set(roots[j]['coefficients'])) == 1, 'Sink %d: one root coefficient' % s) + require(s not in merge and s not in set(merge.values()) and s not in deferred, 'Sink %d: no pair, no gauge' % s) + require(s not in sources.values() and s not in cseed, 'Sink %d: no source injection, not a centre' % s) + W_ = [i for i, (a, b, x) in enumerate(ops) if a == s] + require(W_ and not any(b == s for a, b, x in ops), 'Sink %d: destination-only writes' % s) + require(all(i not in pset for i in W_), 'Sink %d: no write in phase one' % s) + U = rootframe[s] + path = [ZERO] + [frames[i] for i in W_] + [U] + require(all(contained(p0, p1) for p0, p1 in zip(path, path[1:])), 'Sink %d: write frames nested into U' % s) + require(cvec[s] is None and dpart[s] == dseed[s], 'Sink %d: response equals its root seed' % s) + last = max(position[i] for i in W_) + require(p in T and first_read.get(p, 1 << 60) > last, 'Sink %d: pivot corrected before the last write' % s) + sink[s] = dict(T=T, c=p, writes=W_, U=U, coeff=roots[j]['coefficients'][0]) + targets = [t for z in sink.values() for t in z['T']] + require(len(targets) == len(set(targets)), 'Target groups of different sinks are disjoint') + + def build(active, control=None, ctl_sink=None, ctl_op=None): + sink_of_write = {i: s for s, z in active.items() for i in z['writes']} + last_write = {z['writes'][-1]: s for s, z in active.items()} + W, fwd_ops = [], [] + + def op_event(i): + a, b, x = ops[i] + fwd_ops.append(i) + return ('op', A(a), A(b), coef[i][1], frames[i]) + for s in range(R): + if s not in deferred and s not in active: + W.append(('read', A(s), s, -1, 'resp', ZERO, 'Y', reach(s, 'resp'))) + for s, xnode in sorted(leaf_of.items()): + W.append(('inj', A(s), X(xnode - 1), 1, basis((inputs[xnode - 1],)))) + if control == 'early_raise': + z = active[ctl_sink] + W += [('ysh', Y(t), Y(z['c']), -1, frames[z['writes'][0]]) for t in z['T'] if t != z['c']] + for i in phase1: + W.append(op_event(i)) + for s in cseed: + W.append(('centre', A(s), s, 1, rootframe[s], ZERO, 'Y')) + for s, z in active.items(): # 1. pre-shears at the phase cut, frame 0 + if not (control == 'early_raise' and s == ctl_sink): + W += [('ysh', Y(t), Y(z['c']), -1, ZERO) for t in z['T'] if t != z['c']] + for i in rest: + for s in reads_at.get(i, ()): + W.append(('read', A(s), s, -1, 'resp', gauge[s], 'Y', gauge_targets[s])) + if i in sink_of_write: # 2. pivot writes at the original write frames + s = sink_of_write[i] + k = coef[i][1] * (HALF if active[s]['coeff'] == '1/2' else P - HALF) % P + W.append(('yw', Y(active[s]['c']), A(ops[i][1]), k, frames[i])) + else: + W.append(op_event(i)) + posts = [last_write[i]] if i in last_write and not (control == 'late_post' and last_write[i] == ctl_sink) else [] + if control == 'late_post' and i == ctl_op: + posts.append(ctl_sink) + for s in posts: # 3. post-shears after the last write, frame U + if not (control == 'omit_post' and s == ctl_sink): + z = active[s] + W += [('ysh', Y(t), Y(z['c']), +1, z['U']) for t in z['T'] if t != z['c']] + for s, tg in rootorder: + if s not in active: + W.append(('read', A(s), s, 1, 'seed', rootframe[s], 'Y', tg)) + for b0 in range(0, v, 8): + qs = [inputs[b0 + k] for k in range(8)] + K2 = [[1 if (qs[i] ^ qs[j]).bit_count() == 6 else -1 if (qs[i] ^ qs[j]).bit_count() == 2 else 0 + for j in range(8)] for i in range(8)] + for parity in (0, 1): + S = [k for k in range(8) if k.bit_count() % 2 == parity] + Tg = [k ^ 7 for k in S] + Tm = [[K2[j][i] * HALF % P for i in S] for j in Tg] + regs = [X(b0 + k) for k in S] + W.append(('ktr', regs, Tm, basis(tuple(qs[k] for k in S)), 'X')) + W += [('kd', Y(b0 + Tg[k]), X(b0 + S[k]), 1, perp(basis((qs[Tg[k]],)))) for k in range(4)] + W.append(('ktr', regs, [[Tm[l][k] for l in range(4)] for k in range(4)], FULL, 'X')) + W += [('op', A(ops[i][0]), A(ops[i][1]), -coef[i][1], FULL) for i in reversed(fwd_ops)] + W += [('inj', A(s), X(x - 1), -1, FULL) for s, x in sorted(leaf_of.items(), reverse=True)] + return W + + swapXY = lambda r: r + v if r < v else (r - v if r < 2 * v else r) + + def reflect(e): + k = e[0] + if k == 'read': + _, a, s, sg, mode, F, bank, tg = e + return ('read', a, s, -sg, mode, perp(F), 'X' if bank == 'Y' else 'Y', tg) + if k == 'centre': + _, a, s, sg, F, G, bank = e + return ('centre', a, s, -sg, perp(F), perp(G), 'X' if bank == 'Y' else 'Y') + if k == 'inj': + return ('inj', e[1], swapXY(e[2]), -e[3], perp(e[4])) + if k == 'op': + return ('op', e[1], e[2], -e[3], perp(e[4])) + if k == 'ysh': + return ('ysh', swapXY(e[1]), swapXY(e[2]), -e[3], perp(e[4])) + if k == 'yw': + return ('yw', swapXY(e[1]), e[2], (P - e[3]) % P, perp(e[4])) + if k == 'ktr': + M = e[2] + return ('ktr', [swapXY(r) for r in e[1]], [[M[l][kk] for l in range(4)] for kk in range(4)], perp(e[3]), + 'Y' if e[4] == 'X' else 'X') + if k == 'kd': + return ('kd', swapXY(e[1]), swapXY(e[2]), -e[3], perp(e[4])) + raise ValueError(k) + + def ends(active): + removed = {A(s) for s in active} + st, fi = [None] * NREG, [None] * NREG + for t in range(v): + st[X(t)], st[Y(t)] = basis((inputs[t],)), ZERO + fi[X(t)], fi[Y(t)] = FULL, perp(basis((inputs[t],))) + for s in live: + st[A(s)], fi[A(s)] = gauge.get(s, ZERO), FULL + for r in removed: + st[r] = fi[r] = ZERO + rs, rf = [None] * NREG, [None] * NREG + for r in range(NREG): + rs[swapXY(r)], rf[swapXY(r)] = perp(fi[r]), perp(st[r]) + for r in removed: + rs[r] = rf[r] = ZERO + return removed, (st, fi), (rs, rf) + + def framescan(events, st, fin, removed): + """Per-stage children split by register class: local (slots and centre copies), source (X), target (Y).""" + cur = list(st) + H = {'local': Counter(), 'source': Counter(), 'target': Counter()} + cls = lambda r: 'source' if r < v else ('target' if r < 2 * v else 'local') + + def promote(r, F): + require(r not in removed, 'Deleted sink touched') + old = cur[r] + if old is F: + return + require(contained(old, F), 'Frame step not nested (register %d, %d -> %d)' % (r, len(old), len(F))) + if len(F) > len(old): + H[cls(r)][len(F) - len(old)] += 1 + cur[r] = F + for e in events: + k = e[0] + if k == 'read': + _, a, s, sg, mode, F, bank, tg = e + promote(a, F) + for t in tg: + promote((0 if bank == 'X' else v) + t, F) + elif k == 'centre': + _, a, s, sg, F, G, bank = e + require(contained(G, F) or contained(F, G), 'Centre frames comparable') + promote(a, F) + H['local'][abs(len(F) - len(G))] += 1 + for t in range(v): + promote((0 if bank == 'X' else v) + t, G) + elif k in ('inj', 'op', 'ysh', 'yw', 'kd'): + require(e[1] != e[2], 'Distinct registers') + promote(e[1], e[4]) + promote(e[2], e[4]) + elif k == 'ktr': + for r in e[1]: + promote(r, e[3]) + for r in range(NREG): + if r not in removed: + promote(r, fin[r]) + return H + + def run_scalar(events, xin, yin, zin): + bank, a = {'X': list(xin), 'Y': list(yin)}, list(zin) + pend = {'X': [0] * h, 'Y': [0] * h} + + def flush(bnk): + B = bank[bnk] + for kk in range(h): + f = pend[bnk][kk] + if f: + row = scatter[kk] + for t in range(v): + B[t] = (B[t] + f * row[t]) % P + pend[bnk][kk] = 0 + + def get(r): + if r < 2 * v: + bnk = 'X' if r < v else 'Y' + flush(bnk) + return bank[bnk][r % v] + return a[r - 2 * v] + + def add(r, val): + if r < 2 * v: + B = bank['X' if r < v else 'Y'] + B[r % v] = (B[r % v] + val) % P + else: + a[r - 2 * v] = (a[r - 2 * v] + val) % P + for e in events: + k = e[0] + if k == 'read': + _, ar, s, sg, mode, F, bnk, tg = e + val = a[ar - 2 * v] + c = cseed.get(s) if mode == 'seed' else cvec[s] + d = dseed.get(s, {}) if mode == 'seed' else dpart[s] + if c is not None: + for kk, u in enumerate(c): + if u: + pend[bnk][kk] = (pend[bnk][kk] + sg * u * val) % P + B = bank[bnk] + for t, u in d.items(): + B[t] = (B[t] + sg * u * val) % P + elif k == 'centre': + _, ar, s, sg, F, G, bnk = e + val = a[ar - 2 * v] + for kk, u in enumerate(cseed[s]): + if u: + pend[bnk][kk] = (pend[bnk][kk] + sg * u * val) % P + elif k in ('inj', 'op', 'ysh', 'yw', 'kd'): + add(e[1], e[3] * get(e[2])) + elif k == 'ktr': + regs, M = e[1], e[2] + vals = [get(r) for r in regs] + for kk, r in enumerate(regs): + add(r, sum(M[kk][l] * vals[l] for l in range(4)) % P - vals[kk]) + flush('X') + flush('Y') + return bank['X'], bank['Y'], a + + def replay(Wf, removed, seed): + rng = random.Random(seed) + x0 = [rng.randrange(P) for _ in range(v)] + y0 = [rng.randrange(P) for _ in range(v)] + z0 = [rng.randrange(P) for _ in live] + keep = [i for i, s in enumerate(live) if A(s) not in removed] + xf, yf, zf = run_scalar(Wf, x0, y0, z0) + fwd = xf == x0 and all((yf[t] - y0[t] - x0[t]) % P == 0 for t in range(v)) and all(zf[i] == z0[i] for i in keep) + xr, yr, zr = run_scalar([reflect(e) for e in reversed(Wf)], x0, y0, z0) + ref = all((xr[t] - x0[t] + y0[t]) % P == 0 for t in range(v)) and yr == y0 and all(zr[i] == z0[i] for i in keep) + return fwd, ref + + # the unsubstituted word: its literal per-stage histogram is #161's record over three stages + removed0, (st0, fi0), _ = ends({}) + H0 = framescan(build({}), st0, fi0, removed0) + cover = Counter({int(r): n for r, n in base['child_histogram'].items()}) + cover.subtract(Counter(3 * len(gauge[s]) for s in live if s in gauge)) + cover[2] -= 2 * v + require(all(n >= 0 and n % 3 == 0 for n in cover.values()), 'Cover children are a three-stage multiple') + require(sum(H0.values(), Counter()) == Counter({r: n // 3 for r, n in cover.items() if n}), + 'Literal per-stage histogram of the unsubstituted word = #161 record / 3') + # the substituted word + removed, (st, fi), (rst, rfi) = ends(sink) + W = build(sink) + Hf = framescan(W, st, fi, removed) + Hr = framescan([reflect(e) for e in reversed(W)], rst, rfi, removed) + require(sum(Hf.values(), Counter()) == sum(Hr.values(), Counter()), 'Reflected per-stage histogram') + delta = sum(H0.values(), Counter()) + delta.subtract(sum(Hf.values(), Counter())) + expect = Counter() + for z in sink.values(): + expect[len(z['U'])] += 1 + expect[h - len(z['U'])] += 1 + require(+delta == expect and not -delta, 'Per-stage histogram drops [r] and [h - r] per sink') + fwd, ref = replay(W, removed, 166) + require(fwd and ref, 'Dirty-scratch replay forward (X, Y+X, Z) and reflected (X-Y, Y, Z)') + controls = {} + + def rejected(Wc): + try: + framescan(Wc, st, fi, removed) + framescan([reflect(e) for e in reversed(Wc)], rst, rfi, removed) + except AssertionError: + return True + return not all(replay(Wc, removed, 168)) + s0 = next(iter(sink)) + controls['early_raise'] = rejected(build(sink, 'early_raise', s0)) + controls['omit_post_shear'] = rejected(build(sink, 'omit_post', s0)) + bad = [reflect(e) for e in reversed(W)] + j = next(j for j, e in enumerate(bad) if e[0] == 'yw' and 3 <= len(e[4]) <= h - 3) + bad[j] = bad[j][:4] + (perp(bad[j][4]),) + try: + framescan(bad, rst, rfi, removed) + controls['uncomplemented_reflected_pivot_write'] = False + except AssertionError: + controls['uncomplemented_reflected_pivot_write'] = True + pc, sl, tl = min((first_read[t], s, t) for s, z in sink.items() for t in z['T'] if t in first_read) + moved = dict(sink) + moved[sl] = dict(sink[sl], c=tl) + controls['post_shear_after_pivot_correction'] = rejected(build(moved, 'late_post', sl, (phase1 + rest)[pc])) + require(all(controls.values()), 'Every control is rejected') + # the substituted record, in physical()'s format + rec = json.loads(json.dumps(base)) + for name, cls in (('local_histogram', 'local'), ('source_data_histogram', 'source'), ('target_data_histogram', 'target')): + Hc = Counter({int(r): n for r, n in base[name].items()}) + Hc.update(Hf[cls]) + Hc.subtract(H0[cls]) + require(all(n >= 0 for n in Hc.values()), 'Nonnegative %s children' % cls) + rec[name] = {str(r): n for r, n in sorted(Hc.items()) if n} + m = 3 * h + C = Counter({int(r): n for r, n in base['child_histogram'].items()}) + for r, n in expect.items(): + C[r] -= 3 * n + C = Counter({r: n for r, n in C.items() if n}) + require(min(C.values()) > 0, 'Positive children') + rec['child_histogram'] = {str(r): C[r] for r in sorted(C)} + rec['physical_R'] = base['physical_R'] - len(sink) + rec['W_per_vertex'] = base['W_per_vertex'] - len(sink) + rec['rank_per_vertex'] = sum(r * n for r, n in C.items()) + rec['deficit_per_vertex'] = rec['W_per_vertex'] * m - rec['rank_per_vertex'] + require(rec['deficit_per_vertex'] == base['deficit_per_vertex'], 'Deficit unchanged') + rec['sinks'] = len(sink) + rec['sink_substitution'] = dict( + lemma='terminal-sink lemma of PR #166 by jamesyc (closed by its author), independently audited here', sinks=[[s, z['c']] for s, z in sink.items()], + root_ranks={str(r): n for r, n in sorted(Counter(len(z['U']) for z in sink.values()).items())}, + per_stage_removed={str(r): n for r, n in sorted(expect.items())}, events=len(W), + forward_and_reflected_nested=True, replay_seed=166, replay_forward=fwd, replay_reflected=ref, + controls_rejected=controls) + return rec + + +def checked_sinks_record(): + """Regenerate the word, check the frozen layer with #161's checker, apply sinks.json, compare the frozen record.""" + sys.path.insert(0, str(ROOT / 'scripts')) + import paired_cube_physical as PCP + g, witness, word, record = PCP.regenerated_word() + frames_in = json.loads((PCP.REF / 'frames.json').read_text())['frames'] + pairs_in = json.loads((PCP.REF / 'pairs.json').read_text())['pairs'] + base = PCP.physical(g, witness, word, record, frames_in, pairs_in) + require(json.loads(PCP.OUTPUT.read_text()) == json.loads(json.dumps(base)), 'Frozen physical input differs') + result = sinks_record(g, witness, word, record, frames_in, pairs_in, json.loads(SINKS.read_text())['sinks'], base) + require(json.loads(OUTPUT.read_text()) == json.loads(json.dumps(result)), 'Frozen sinks input differs') + return result + + +def main(): + flags = dict(a.split('=', 1) if '=' in a else (a, True) for a in sys.argv[1:]) + if '--work' in flags: + tree = Path(flags['--tree']).resolve() + sys.path.insert(0, str(tree / 'scripts')) + import paired_cube_physical as PCP + g, witness, word, record = (json.loads((Path(flags['--work']) / n).read_text()) for n in + ('graph.json', 'frames.json', 'selection.json', 'record.json')) + frames_in = json.loads((Path(flags['--layer']) / 'frames.json').read_text())['frames'] + pairs_in = json.loads((Path(flags['--layer']) / 'pairs.json').read_text())['pairs'] + base = PCP.physical(g, witness, word, record, frames_in, pairs_in) + result = sinks_record(g, witness, word, record, frames_in, pairs_in, + json.loads(Path(flags['--sinks']).read_text())['sinks'], base) + if '--out' in flags: + Path(flags['--out']).write_text(json.dumps(result, indent=2, sort_keys=True) + '\n') + else: + sys.path.insert(0, str(ROOT / 'scripts')) + import paired_cube_physical as PCP + g, witness, word, record = PCP.regenerated_word() + frames_in = json.loads((PCP.REF / 'frames.json').read_text())['frames'] + pairs_in = json.loads((PCP.REF / 'pairs.json').read_text())['pairs'] + base = PCP.physical(g, witness, word, record, frames_in, pairs_in) + result = sinks_record(g, witness, word, record, frames_in, pairs_in, json.loads(SINKS.read_text())['sinks'], base) + text = json.dumps(result, indent=2, sort_keys=True) + '\n' + if '--write' in flags: + OUTPUT.write_text(text) + else: + require(OUTPUT.read_text() == text, 'Frozen sinks input differs') + print('PASS terminal sinks: %d sinks (root ranks %s), W %d -> %d, deficit %d; nested forward and reflected, ' + 'replay and %d controls rejected' % (result['sinks'], result['sink_substitution']['root_ranks'], + base['W_per_vertex'], result['W_per_vertex'], + result['deficit_per_vertex'], len(result['sink_substitution']['controls_rejected']))) + + +if __name__ == '__main__': + main() diff --git a/scripts/experiments/joint_dual_reclaim_compiler.py b/scripts/experiments/joint_dual_reclaim_compiler.py index 1eb8dea9fa..4b658dc692 100644 --- a/scripts/experiments/joint_dual_reclaim_compiler.py +++ b/scripts/experiments/joint_dual_reclaim_compiler.py @@ -18,6 +18,7 @@ from changed_graph import graph from collections import defaultdict,Counter,deque import argparse,json,time,struct +from bisect import bisect_left, insort def independent(rows,vec): for row in rows: @@ -117,10 +118,26 @@ def compile_(h,matching=True,reclaim=False,dirty=True): edges,chosen,right,stats=match(blocks,uses,matching) print('matched',len(chosen),'seconds',time.time()-t0,flush=True,file=sys.stderr) slots=[];frames=[];ops=[];events=[];hist=Counter();assign={};sources={};retired=set();stats['regions']=len(blocks);stats['matched']=len(chosen);stats['multi_node_regions']=sum(len(b['nodes'])>1 for b in blocks) + # Keep the original descending-rank, ascending-slot selection order. + # A retired anchor can move during clearing: raise_ updates this index too. + retired_by_rank=[[] for _ in range(h+1)] + def retire_add(s): + assert s not in retired + retired.add(s);insort(retired_by_rank[blocks[frames[s]]['rank']],s) + def retire_remove(s): + bucket=retired_by_rank[blocks[frames[s]]['rank']] + i=bisect_left(bucket,s);assert i> 31 else code // 2 + def use_value(code): return roots[code & 0x7fffffff]['node'] if code >> 31 else args[code // 2][code & 1] + succ, direct, indeg = [[] for _ in args], [[] for _ in args], [0] * n + for x in sorted(active): + if args[x]: + for y in args[x]: succ[y].append(x); indeg[x] += 1 + for j, r in enumerate(roots): direct[r['node']].extend(rann[j]) + assert len(set(arcs.values())) == len(arcs), 'one donor per use' + for x, code in arcs.items(): + assert args[x] and use_value(code) in args[x] and code not in (2 * x, 2 * x + 1), 'a donor carries one of its own operands' + t = use_node(code) + if t is None: direct[x].extend(rann[code & 0x7fffffff]) + else: succ[x].append(t); indeg[t] += 1 + heap = [x for x in sorted(active) if indeg[x] == 0]; heapq.heapify(heap); topo = [] + while heap: + x = heapq.heappop(heap); topo.append(x) + for y in succ[x]: + indeg[y] -= 1 + if indeg[y] == 0: heapq.heappush(heap, y) + assert len(topo) == len(active), 'the generalized dependency graph is acyclic' + ann, rank = [None] * n, [0] * n + for x in reversed(topo): + ann[x] = basis(direct[x] + [z for y in succ[x] for z in ann[y]]); rank[x] = h - len(ann[x]) + assert contained(spans[x], perp(ann[x], h)), ('value span outside its frame', x) + index = {x: i for i, x in enumerate(topo)} + if repository_order: + dag = [[] for _ in args]; constraint = [[] for _ in args]; padded = {} + for x in sorted(active): + if args[x]: + for y in args[x]: dag[y].append(x) + for j, r in enumerate(roots): constraint[r['node']].extend(rann[j]) + pre = [None] * n + for x in sorted(active, reverse=True): + pre[x] = basis(constraint[x] + [z for y in dag[x] for z in pre[y]]) + cover = g.get('side_padding_mask', 0) + for u in spans[x]: cover |= u + padded[x] = perp(pre[x] + tuple(1 << j for j in range(h) if not cover >> j & 1), h) + order = sorted(active, key=lambda x: (len(padded[x]), x)) + else: + order = sorted(active, key=lambda x: (rank[x], index[x])) + position = {x: i for i, x in enumerate(order)} + for x in order: + for y in succ[x]: assert position[y] > position[x] + uses = [[] for _ in args] + for x in order: + if args[x]: + for j, y in enumerate(args[x]): uses[y].append(2 * x + j) + for j, r in enumerate(roots): uses[r['node']].append((1 << 31) | j) + donors = [x for x in order if args[x]] + H = Counter() + for x in order: + r, degree = rank[x], len(uses[x]); assert degree > 0, ('unused input', x) + H[r] += degree - 1 + if args[x]: + H[h - r] += 1 + for y in args[x]: + assert contained(ann[x], ann[y]) + H[r - rank[y]] += 1 + else: H[1] += 1; H[r - 1] += 1 + for j, rt in enumerate(roots): + x = rt['node']; r = rank[x]; top = len(rframe[j]); assert r <= top + if rt.get('kind', 'side') == 'center': + assert r == top + H[r] += 1; H[h - r] += 1 + else: H[top - r] += 1; H[h - top] += 1 + for x, code in arcs.items(): + value, t = use_value(code), use_node(code); rv, rd = rank[value], rank[x] + top = rank[t] if t is not None else len(rframe[code & 0x7fffffff]) + assert top >= rd >= rv + H[h - rd] -= 1; H[rv] -= 1; H[top - rv] -= 1; H[top - rd] += 1 + assert min(H.values()) >= 0 + R = len(donors) + q - len(arcs) + mass = sum(r * c for r, c in H.items()); assert mass == h * R + ell, (mass, h * R + ell) + source = Counter({int(r): c for r, c in g['source_data_histogram'].items()}) + assert sum(r * c for r, c in source.items()) == v * (h - 1) + m, W = 3 * h, 2 * v + R + children = Counter({r: 3 * c for r, c in H.items() if r}) + children.update({r: 3 * c for r, c in source.items() if r}) + children.update({r: 3 * c for r, c in targetH.items() if r}) + children[2] += 2 * v + cmass = sum(r * c for r, c in children.items()); deficit = W * m - cmass + assert deficit == 2 * v - 3 * ell + profile = dict(h=h, v=v, R=R, q=q, c=len(donors), matched=len(arcs), loss=ell, selected_roles=0, + selected_rank_histogram={}, remaining_internal_histogram=[H[r] for r in range(h + 1)], + source_data_histogram=dict(source), target_data_histogram=dict(targetH), copied_centers_already=True, + m=m, W_per_vertex=W, rank_per_vertex=cmass, deficit_per_vertex=deficit, + child_histogram=dict(children), matching_frames='coordinate') + witness = dict(matching_arcs=[[x, c] for x, c in arcs.items()], annihilators=ann, order=order) + return profile, witness diff --git a/scripts/paired_cube/graph.py b/scripts/paired_cube/graph.py index a440598df4..580ae3baa6 100644 --- a/scripts/paired_cube/graph.py +++ b/scripts/paired_cube/graph.py @@ -13,8 +13,9 @@ class Graph: - def __init__(self, p): + def __init__(self, p, local=None): self.p = p + self.local = local self.h = 2*p self.cubes = list(combinations(range(p), 3)) self.labels = [tuple(2*i+b for i, b in zip(I, bits)) @@ -69,6 +70,8 @@ def module(self, data, inputs): return [image[x] for x in data['roots']] def local_channels(self): + if self.local is not None: + return self.configured_local_channels(self.local) for I in self.cubes: edges = {} for ii, jj in combinations(range(3), 2): @@ -94,6 +97,62 @@ def local_channels(self): self.A[I, I[ii], a] = self.add(*ids) self.F[I] = self.add(self.A[I, I[0], 0], self.A[I, I[0], 1]) + def configured_local_channels(self, cfg): + """The same 13 outputs per cube (positions 0,1,2 of I) by a configured circuit: + A[i,a] = sum of the ports with bit i = a; 'e': two edges along direction d, 'fd': two face diagonals. + G[j,k,m] = [bits (j,k) = (0,m)] - [bits (j,k) = (1,1-m)], [.] summing the third bit r; 'e': edges along r, + 'l': long-diagonal differences, 's': differences at fixed r. F = A[f,0] + A[f,1]. + Signed pairs take the smaller port as minuend so equal differences are shared.""" + A_cfg = {tuple(int(c) for c in k.split(',')): v for k, v in cfg['A'].items()} + G_cfg = {tuple(int(c) for c in k.split(',')): v for k, v in cfg['G'].items()} + + def signed(xa, xb): + return (self.add(xa, xb, -1), 1) if xa < xb else (self.add(xb, xa, -1), -1) + + def combine(t1, t2): + (n1, s1), (n2, s2) = t1, t2 + if s1 == 1: + return self.add(n1, n2, s2) + assert s2 == 1, 'negated local output' + return self.add(n2, n1, -1) + for I in self.cubes: + def at(values): + bits = [0]*3 + for q, b in values.items(): + bits[q] = b + return self.source[I, tuple(bits)] + + def edge(d, fixed): + return self.add(at({**fixed, d: 0}), at({**fixed, d: 1})) + for j, k in combinations(range(3), 2): + r = 3-j-k + for mode in range(2): + u, v = 0, mode + kind = G_cfg[j, k, mode] + if kind == 'e': + node = self.add(edge(r, {j: u, k: v}), edge(r, {j: 1-u, k: 1-v}), -1) + else: + assert kind in ('l', 's') + far = (1, 0) if kind == 'l' else (0, 1) + node = combine(signed(at({j: u, k: v, r: 0}), at({j: 1-u, k: 1-v, r: far[0]})), + signed(at({j: u, k: v, r: 1}), at({j: 1-u, k: 1-v, r: far[1]}))) + self.G[I, I[j], I[k], mode] = node + for i in range(3): + j, k = [q for q in range(3) if q != i] + for a in range(2): + kind = A_cfg[i, a] + if kind == 'fd': + n1 = self.add(at({i: a, j: 0, k: 0}), at({i: a, j: 1, k: 1})) + n2 = self.add(at({i: a, j: 0, k: 1}), at({i: a, j: 1, k: 0})) + else: + d = int(kind[1]) + assert kind[0] == 'e' and d != i + o = j if d == k else k + n1, n2 = edge(d, {i: a, o: 0}), edge(d, {i: a, o: 1}) + self.A[I, I[i], a] = self.add(n1, n2) + f = cfg['F'] + self.F[I] = self.add(self.A[I, I[f], 0], self.A[I, I[f], 1]) + def center_channels(self): # Route each cube total to maximal binary-tree intervals avoiding I. nodes = [] diff --git a/scripts/paired_cube/modules.py b/scripts/paired_cube/modules.py index f590aa7edd..85b1397ec5 100644 --- a/scripts/paired_cube/modules.py +++ b/scripts/paired_cube/modules.py @@ -123,3 +123,230 @@ def restricted_triples(p): source_author='eumemic', contract='Root indexed by J sums input I exactly when I and J are disjoint.') return result + + +# ---- Generalized restrictions for other p / other #117-format sources (eumemic, Claude assistance; Apache-2.0). +# Same contracts and checks as restricted_triples/restricted_pairs above; the defaults of those functions are +# keep = 0..p-1 (triples) and keep = 0..n-1, pin = 23, out = 22 (pairs) on the PR117 h24 witness. +def _source_witness(path): + return json.loads(gzip.decompress(Path(path).read_bytes())) + +def restricted_triples_from(path, keep): + w = _source_witness(path) + keep = sorted(keep); p = len(keep); rename = {x: j for j, x in enumerate(keep)} + labels = list(combinations(range(p), 3)); index = {t: i+1 for i, t in enumerate(labels)} + args = [(0, 0)] + [(0, 0)] * len(labels); supports = [0] + [1 << i for i in range(len(labels))] + intern = {s: i for i, s in enumerate(supports) if s} + old_labels = list(combinations(range(w['h']), 3)) + def new(t): return tuple(rename[x] for x in t) if all(x in rename for x in t) else None + image = [0] + [index.get(new(t), 0) for t in old_labels] + for aa, bb in zip(w['args'][::2], w['args'][1::2]): + a, b = image[aa], image[bb] + if not a or not b: + image.append(a or b); continue + assert not supports[a] & supports[b] + s = supports[a] | supports[b] + if s not in intern: + intern[s] = len(args); args.append((a, b)); supports.append(s) + image.append(intern[s]) + roots = [image[x] for t, x in zip(old_labels, w['D']) if new(t) is not None] + for J, r in zip(labels, roots): + assert r and supports[r] == sum(1 << i for i, I in enumerate(labels) if not set(I) & set(J)) + active = set(range(len(labels)+1)); stack = roots[:] + while stack: + x = stack.pop() + if x in active: continue + active.add(x); stack.extend(args[x]) + order = sorted(active); rename2 = {x: i for i, x in enumerate(order)} + return dict(kind='disjoint_triples', p=p, input_labels=labels, target_labels=labels, input_count=len(labels), + args=[[rename2[a], rename2[b]] for x in order for a, b in [args[x]]], roots=[rename2[x] for x in roots], + source='exact zero restriction of a pinned #117-format witness to kept points', kept=keep, + contract='Root indexed by J sums input I exactly when I and J are disjoint.') + +def restricted_pairs_from(path, keep, pin, out): + w = _source_witness(path) + keep = sorted(keep); n = len(keep) + assert pin not in keep and out not in keep and pin != out + rename = {x: j for j, x in enumerate(keep)} + oldtriples = list(combinations(range(w['h']), 3)); pairs = list(combinations(range(n), 2)) + pid = {q: i for i, q in enumerate(pairs)} + args = [None]*len(pairs); support = [1 << i for i in range(len(pairs))]; by = {s: i for i, s in enumerate(support)} + image = [None] + for t in oldtriples: + rest = tuple(x for x in t if x != pin) + ok = pin in t and len(rest) == 2 and all(x in rename for x in rest) + image.append(pid[tuple(sorted(rename[x] for x in rest))] if ok else None) + for aa, bb in zip(w['args'][::2], w['args'][1::2]): + a, b = image[aa], image[bb] + if a is None or b is None: + image.append(a if b is None else b); continue + assert not support[a] & support[b] + s = support[a] | support[b] + if s not in by: + by[s] = len(args); args.append([a, b]); support.append(s) + image.append(by[s]) + oldroots = {t: x for t, x in zip(oldtriples, w['D'])} + roots = [image[oldroots[tuple(sorted((keep[i], keep[j], out)))]] for i, j in pairs] + for (i, j), r in zip(pairs, roots): + expected = sum(1 << k for k, (a, b) in enumerate(pairs) if i not in (a, b) and j not in (a, b)) + assert r is not None and support[r] == expected + active = set(range(len(pairs))); stack = list(roots) + while stack: + x = stack.pop() + if x in active: continue + active.add(x) + if args[x] is not None: stack.extend(args[x]) + ids = sorted(active); ren = {x: i for i, x in enumerate(ids)} + args = [None if args[x] is None else [ren[y] for y in args[x]] for x in ids] + return dict(kind='pair_disjoint', n=n, input_count=len(pairs), input_labels=pairs, output_labels=pairs, + args=args, roots=[ren[x] for x in roots], kept=keep, pin=pin, out=out, + source='zero restriction of a pinned #117-format witness: inputs {a,b,pin}, outputs D_{i,j,out}') + + +# ---- Direct pair-module source (PMOD lane; eumemic, Claude assistance; Apache-2.0). +def pair_module_from(path, n): + """Zero-based pair-disjoint module given as JSON {input_count, args, roots}; same contract as restricted_pairs(n): + additions combine disjoint supports and root (i,j) sums exactly the inputs {a,b} disjoint from {i,j}.""" + d = json.loads(Path(path).read_text()) + pairs = list(combinations(range(n), 2)) + assert d['input_count'] == len(pairs) == len(d['roots']) + support = [] + for x, a in enumerate(d['args']): + if x < len(pairs): + assert a is None + support.append(1 << x) + else: + assert a is not None and 0 <= a[0] < x and 0 <= a[1] < x and not support[a[0]] & support[a[1]] + support.append(support[a[0]] | support[a[1]]) + for (i, j), r in zip(pairs, d['roots']): + assert support[r] == sum(1 << k for k, (a, b) in enumerate(pairs) if i not in (a, b) and j not in (a, b)) + return dict(kind='pair_disjoint', n=n, input_count=len(pairs), input_labels=pairs, output_labels=pairs, + args=[None if a is None else list(a) for a in d['args']], roots=list(d['roots']), + source='Direct pair module JSON; contract checked above') + + +# ---- Direct triple-module source (TMOD lane; eumemic, Claude assistance; Apache-2.0). +def triple_module_from(path, p): + """One-based disjoint-triples module given as JSON (the layout of restricted_triples(p)); same contract: + additions combine disjoint supports and the root indexed by J sums input I exactly when I and J are disjoint.""" + d = json.loads(Path(path).read_text()) + labels = list(combinations(range(p), 3)) + assert d['input_count'] == len(labels) == len(d['roots']) + assert [tuple(x) for x in d['input_labels']] == labels == [tuple(x) for x in d['target_labels']] + args = d['args'] + assert all(list(a) == [0, 0] for a in args[:len(labels) + 1]) + support = [0] + [1 << i for i in range(len(labels))] + for x in range(len(labels) + 1, len(args)): + a, b = args[x] + assert 0 < a < x and 0 < b < x and not support[a] & support[b] + support.append(support[a] | support[b]) + for J, r in zip(labels, d['roots']): + assert support[r] == sum(1 << i for i, I in enumerate(labels) if not set(I) & set(J)) + return dict(kind='disjoint_triples', p=p, input_labels=labels, target_labels=labels, input_count=len(labels), + args=[list(a) for a in args], roots=list(d['roots']), + source='Direct triple module JSON; contract checked above', + contract='Root indexed by J sums input I exactly when I and J are disjoint.') + + +# ---- Direct all-but-one source (QMOD lane; eumemic, Claude assistance; Apache-2.0). +def all_but_one_from(path, n): + """Zero-based all-but-one module given as JSON {input_count, args, roots}; same contract as all_but_one(n): + additions combine disjoint supports and root i sums exactly the inputs other than i.""" + d = json.loads(Path(path).read_text()) + assert d['input_count'] == n == len(d['roots']) + support = [] + for x, a in enumerate(d['args']): + if x < n: + assert a is None + support.append(1 << x) + else: + assert a is not None and 0 <= a[0] < x and 0 <= a[1] < x and not support[a[0]] & support[a[1]] + support.append(support[a[0]] | support[a[1]]) + full = (1 << n) - 1 + assert all(support[r] == full ^ (1 << i) for i, r in enumerate(d['roots'])) + return dict(kind='all_but_one', n=n, input_count=n, input_labels=list(range(n)), output_labels=list(range(n)), + args=[None if a is None else list(a) for a in d['args']], roots=list(d['roots']), + source='Direct all-but-one module JSON; contract checked above') + + +# ---- Output merging (pmerge.py variants; eumemic, Claude assistance; Apache-2.0). +def merge_outputs(g, G, variant): + """Replace #144's single-target channels of each port T=(I,b) -- face2 P[I,I2,1-b2] (1/2), edge02 + Q[I,I0,I2,b0^b2] ((2b0-1)/2), edge12 Q[I,I1,I2,b1^b2] ((2b1-1)/2) -- by signed sums read with coefficient 1/2. + w02: face2 + (2b0-1)*edge02, one node per (b0,b2) shared by the ports b1=0,1; edge12 stays single. The decoder + contribution is unchanged and Graph.add asserts disjoint supports.""" + from fractions import Fraction + side = [r for r in g['roots'] if r['kind'] == 'side'] + centre = [r for r in g['roots'] if r['kind'] != 'side'] + if variant.startswith('f8:'): + # per-class fold orders: port t folds its face2, edge02, edge12 singles in order PERMS[code[t % 8]] + perms = [(0, 1, 2), (0, 2, 1), (1, 0, 2), (1, 2, 0), (2, 0, 1), (2, 1, 0)] + code = variant[3:] + assert len(code) == 8 and all(ch in '012345' for ch in code) + names = ('face2', 'edge02', 'edge12') + single = {} + keep = [] + for r in side: + if r['channel'] in names: + assert len(r['targets']) == 1 + single[r['targets'][0], r['channel']] = (r['node'], Fraction(r['coefficients'][0])) + else: + keep.append(r) + new = [] + for t in range(g['v']): + parts = [single[t, ch] for ch in names] + order = perms[int(code[t % 8])] + node, c0 = parts[order[0]] + for k in order[1:]: + nd, c = parts[k] + sg = c / c0 + assert sg in (1, -1) + node = G.add(node, nd, int(sg)) + new.append(dict(node=node, targets=[t], coefficients=[str(c0)], kind='side', channel='fused')) + return dict(g, roots=keep + new + centre, args=G.a, signs=G.signs) + if variant == 'pf': + # PR #163's fold rule: each port's three single-target channels face2, edge02, edge12 become one signed + # sum, folded left with the positive-coefficient channels first (in that channel order), then the negatives. + names = ('face2', 'edge02', 'edge12') + single = {} + keep = [] + for r in side: + if r['channel'] in names: + assert len(r['targets']) == 1 + single[r['targets'][0], r['channel']] = (r['node'], Fraction(r['coefficients'][0])) + else: + keep.append(r) + new = [] + for t in range(g['v']): + parts = [single[t, ch] for ch in names] + order = [k for k in range(3) if parts[k][1] > 0] + [k for k in range(3) if parts[k][1] < 0] + node, c0 = parts[order[0]] + for k in order[1:]: + nd, c = parts[k] + sg = c / c0 + assert sg in (1, -1) + node = G.add(node, nd, int(sg)) + new.append(dict(node=node, targets=[t], coefficients=[str(c0)], kind='side', channel='fused')) + return dict(g, roots=keep + new + centre, args=G.a, signs=G.signs) + specs = {'w02': [('face2', 'edge02')], 'w12': [('face2', 'edge12')], + 's': [('face2', 'edge02', 'edge12')]}[variant] + chan = {c: k for k, spec in enumerate(specs) for c in spec} + found = {} + keep = [] + for r in side: + if r['channel'] in chan: + assert all(Fraction(c) == Fraction(r['coefficients'][0]) for c in r['coefficients']) + found[chan[r['channel']], tuple(r['targets']), r['channel']] = (r['node'], Fraction(r['coefficients'][0])) + else: + keep.append(r) + new = [] + for k, tg in sorted({(k, tg) for k, tg, _ in found}): + parts = [found[k, tg, ch] for ch in specs[k]] + node, c0 = parts[0] + for nd, c in parts[1:]: + sg = c / c0 + assert sg in (1, -1) + node = G.add(node, nd, int(sg)) + new.append(dict(node=node, targets=list(tg), coefficients=[str(c0)] * len(tg), kind='side', channel=variant)) + new.sort(key=lambda r: -len(r['targets'])) # multi-target roots before singles (target chains ascend) + return dict(g, roots=keep + new + centre, args=G.a, signs=G.signs) diff --git a/scripts/paired_cube/verify.py b/scripts/paired_cube/verify.py index 9b0d6be233..000bd2d381 100644 --- a/scripts/paired_cube/verify.py +++ b/scripts/paired_cube/verify.py @@ -147,7 +147,7 @@ def each(bits): assert contained(A,current[t]);Y[len(current[t])-len(A)]+=1;current[t]=A for t,q in enumerate(inputs):assert contained((q,),current[t]);Y[len(current[t])-1]+=1 assert dict(Y)=={int(k):c for k,c in record['target_data_histogram'].items()} - assert record['selected_roles']==len(seen)==4840 and birth==Counter({20:4840}) + assert record['selected_roles']==len(seen)==2310 and birth==Counter({18:2310}) return dict(signed_scalar_pairs_checked=scalar_pairs,scalar_H_exact=True,K_involution_and_inverse_exact=True, decoder_identity_exact=True,conservative_source_supports=True,K_source_itinerary_verified=True, full_backward_intersections=True,physical_signed_M_replayed=True, diff --git a/scripts/paired_cube_assembly.py b/scripts/paired_cube_assembly.py new file mode 100644 index 0000000000..43007488ad --- /dev/null +++ b/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/scripts/paired_cube_bit_physical.py b/scripts/paired_cube_bit_physical.py new file mode 100644 index 0000000000..a05126c498 --- /dev/null +++ b/scripts/paired_cube_bit_physical.py @@ -0,0 +1,420 @@ +#!/usr/bin/env python3 +"""Physical paired-cube bit word: per-operation frames, deferred old-value reads and compensated register reuse. + +Prepared by eumemic with Anthropic Claude assistance. Apache-2.0. The bit word, its decoder, exact frames and +ledger are the paired-cube bit word of research/paired-cube-bit (PR144's bit ledger). Frame descent under PR130's +general Clifford frames follows PR131; compensated birth-cut reuse follows jamesyc's PR124; deadline (late) reads +follow PR143. Frozen input: references/paired-cube/bit-physical (the word with per-operation frames, read times +and pairs; its exact frames; the partner-pair chronology). + +Checks, from the package graph and the frozen word only, with the package checker's exact integer algebra: + * exact frames; the mod-2 decoder and the source, root and centre geometry of the package checker; + * register contents: every operation leaves its node's support in its destination (an addition combines the + supports of its two operands, a copy starts from an empty register), every source role starts with its leaf; + * every operation frame is G-nondegenerate and contains its node's span, and every role chain + start -> operation frames (execution order: phase one first) -> root frame -> full space + is nested and ascending, with each recipient's chain spliced after its donor's last operation; phase one is + the centre closure and gauged roles are untouched in it; + * gauges: targets are the response support, frames G-nondegenerate; every gauge is read after phase one and no + later than its role's first operation; + * pairs: a matching; the donor is not a root role and its last operation precedes the recipient's read; the + recipient is gauged; the donor's last frame lies in the recipient's gauge; + * target chains nested in the actual read chronology; the partner-pair chronology; + * the spliced recount: W = 2v + R - pairs, recipients' gauge exteriors dropped, deficit 2v - 3 loss; + * an exact 64-lane F2 replay of the aliased word with arbitrary dirty scratch and time-ordered old-value reads + restores every register and source and adds x to y, for two seeds; omitting one recipient's read, reading a + late recipient at the phase cut before its donor's last write, or aliasing a recipient onto a live register + is rejected. +Writes certificates/paired-cube-bit-physical-input.json with --write; otherwise checks it. +""" +import argparse +from collections import Counter, defaultdict +import gzip +import json +from pathlib import Path +import random +import sys + +ROOT = Path(__file__).resolve().parents[1] +BIT = ROOT / 'research/paired-cube-bit' +REF = ROOT / 'references/paired-cube/bit-physical' +OUTPUT = ROOT / 'certificates/paired-cube-bit-physical-input.json' +P = 12 +LANES = 64 +sys.path.insert(0, str(BIT)) + + +def require(condition, message): + if not condition: + raise AssertionError(message) + + +def read_json(path): + data = path.read_bytes() + return json.loads(gzip.decompress(data) if path.suffix == '.gz' else data) + + +def loaded(folder=None, package=BIT / 'out'): + """The package checker's exact algebra on the package graph and a physical word folder; without a frozen + physical word, the package word itself (operation frames = node frames, no pairs).""" + from check_paired_cube_bit import Checker # refuses python -O + + def find(name): + path = folder / ('%s_p%d.json' % (name, P)) + return path if path.exists() else path.with_suffix('.json.gz') + if folder is None: + folder = REF if (REF / ('word_p%d.json.gz' % P)).exists() else package + chk = Checker.__new__(Checker) + chk.mut = None + chk.g = read_json(package / ('graph_p%d.json' % P)) + chk.prof = read_json(package / ('profile_p%d.json' % P)) + chk.w, chk.fr, chk.k = (read_json(find(name)) for name in ('word', 'frames', 'kchron')) + chk.h, chk.v = chk.g['h'], chk.g['v'] + return chk + + +def physical(chk): + from check_paired_cube_bit import dot, reduce_rows + chk.frames() + chk.decoder() + chk.geometry() + g, w, h, v = chk.g, chk.w, chk.h, chk.v + dim, sub, nondeg = chk.dimf, chk.sub, chk.nondeg + args, sup, nf = g['args'], chk.sup, chk.nf + ops = [tuple(o) for o in w['ops']] + opf = w.get('op_frame') or [nf[x] for _, _, x in ops] + require(len(opf) == len(ops) and all(f in dim for f in opf), 'Operation frames') + roots, rootroles, rf, full = g['roots'], w['rootroles'], w['root_frame'], w['full_frame'] + sources = {int(x): s for x, s in w['sources'].items()} + rootroles_set = set(rootroles) + R = 1 + max(max(max(a, b) for a, b, _ in ops), max(rootroles), max(sources.values())) + phase1 = sorted(w['phase1']) + pset = set(phase1) + rest = [i for i in range(len(ops)) if i not in pset] + order = phase1 + rest + position = {i: k for k, i in enumerate(order)} + cut = len(phase1) + # Phase one is the closure of the centre roots' last operations under per-role precedence. + previous, pred = {}, [] + for i, (a, b, _) in enumerate(ops): + pred.append((previous.get(a, -1), previous.get(b, -1))) + previous[a] = previous[b] = i + stack = [previous[s] for r, s in zip(roots, rootroles) if r['kind'] == 'center' and s in previous] + closure = set() + while stack: + i = stack.pop() + if i not in closure: + closure.add(i) + stack.extend(j for j in pred[i] if j >= 0) + require(closure == pset, 'Phase one is the centre closure') + # Register contents along the execution order. + content = [0] * R + for x, s in sources.items(): + content[s] = 1 << x + role_ops = defaultdict(list) + for i in order: + a, b, x = ops[i] + require(a != b, 'Gate ports') + if content[a]: + require(args[x] is not None and {content[a], content[b]} == {sup[y] for y in args[x]}, 'Addition operands') + else: + require(content[b] == sup[x], 'Copied value') + content[a] |= content[b] + role_ops[a].append(i) + role_ops[b].append(i) + require(all(l == sorted(l) for l in role_ops.values()), 'Execution order keeps every role order') + require(all(s in role_ops or s in rootroles_set for s in range(R)), 'Every role is used') + # Operation frames: moved frames are G-nondegenerate and contain their node's span. + chi = chk.chi + span = {} + + def node_span(x): + stack = [x] + while stack: + y = stack[-1] + if y in span: + stack.pop() + elif args[y] is None: + span[y] = [chi[y]] + stack.pop() + elif all(z in span for z in args[y]): + span[y] = reduce_rows(span[args[y][0]] + span[args[y][1]], h)[0] + stack.pop() + else: + stack.extend(z for z in args[y] if z not in span) + return span[x] + moved = 0 + for f, (_, _, x) in zip(opf, ops): + if f != nf[x]: + moved += 1 + require(all(chk.in_frame(u, f) for u in node_span(x)), 'Node span inside operation frame') + used = set(opf) | set(rf) | set(w['source_frame']) | {z['frame'] for z in w['gauges']} + used |= {e['mix_frame'] for e in chk.k['entries']} + require(all(nondeg(f) for f in used), 'G-nondegenerate frames') + # Starts, gauges and root frames. + start = {s: w['source_frame'][x] for x, s in sources.items()} + rootframe = {} + for j, s in enumerate(rootroles): + require(s not in rootframe, 'Duplicate root role') + rootframe[s] = rf[j] + co = [0] * R + for r, s in zip(roots, rootroles): + for t in r['targets']: + co[s] |= 1 << t + for i in reversed(order): + a, b, _ = ops[i] + co[b] |= co[a] + touched = {s for i in phase1 for s in ops[i][:2]} + gauge = {} + for z in w['gauges']: + s = z['role'] + require(s not in gauge and s not in start and s not in touched and s in role_ops, 'Gauged role') + require(sum(1 << t for t in z['targets']) == co[s], 'Gauge targets are the response support') + require(dim[z['frame']] == z['dim'] > 0, 'Gauge dimension') + gauge[s] = z + start[s] = z['frame'] + # Read chronology: before position p means before the operation order[p]; ties in reverse selection order. + reads = {int(s): t for s, t in w.get('reads', {}).items()} + require(set(reads) <= set(gauge), 'Reads of gauged roles only') + when = {} + for k, z in enumerate(reversed(w['gauges'])): + s = z['role'] + t = reads.get(s, cut) + require(cut <= t <= position[role_ops[s][0]], 'Gauge read after phase one and before the first operation') + when[s] = (t, k) + # Pairs. + pairs = [tuple(p) for p in w.get('pairs', [])] + donors = {a: b for a, b in pairs} + merge = {b: a for a, b in pairs} + require(len(donors) == len(merge) == len(pairs) and not set(donors) & set(merge), 'Pair matching') + for a, b in pairs: + require(a in role_ops and a not in rootframe and b in gauge, 'Pair kinds') + last = role_ops[a][-1] + require(position[last] < when[b][0], 'Donor dies before the recipient read') + require(sub(opf[last], gauge[b]['frame']), 'Donor frame inside recipient gauge') + + def chain(s): + return [start.get(s)] + [opf[i] for i in role_ops[s]] + ([rootframe[s]] if s in rootframe else []) + [full] + # Role chains, spliced at every pair, and the local recount. + local = Counter() + for s in range(R): + if s in merge: + continue + seq = chain(s) + if seq[0] is not None and s not in gauge: + local[1] += 1 # source injection at + if s in donors: + seq = seq[:-1] + chain(donors[s]) + prev = seq[0] + d0 = 0 if prev is None else dim[prev] + for f in seq[1:]: + require(prev is None or sub(prev, f), 'Role chain nesting') + require(dim[f] >= d0, 'Ascending role chain') + if dim[f] > d0: + local[dim[f] - d0] += 1 + prev, d0 = f, dim[f] + for r, f in zip(roots, rf): + if r['kind'] == 'center': + local[dim[f]] += 1 # copied-centre transform + # Partner-pair chronology on the source registers. + labels = [set(l) for l in g['labels']] + source, members = Counter(), Counter() + for e in chk.k['entries']: + c, d, mix, cap = e['carrier'], e['passive'], e['mix_frame'], e['deliver_frame'] + require(len(labels[c] & labels[d]) == 1, 'Orthogonal partner pair') + require(dim[mix] == 2 and chk.in_frame(chi[c], mix) and chk.in_frame(chi[d], mix), 'Mix frame') + require(sub(mix, cap) and all(dot(chk.cov[t], u) == 0 for t in e['receivers'] for u in chk.B[cap]), + 'Delivery frame inside the receiver caps') + require(e['carrier_chain'] == [w['source_frame'][c], mix, cap, full] and + e['passive_chain'] == [w['source_frame'][d], mix, full], 'Partner chains') + for ch in (e['carrier_chain'], e['passive_chain']): + for f1, f2 in zip(ch, ch[1:]): + require(sub(f1, f2), 'Nested partner chain') + source[dim[f2] - dim[f1]] += 1 + members[c] += 1 + members[d] += 1 + require(all(members[s] == 1 for s in range(v)), 'Each source in one partner pair') + # Target chains in the actual read chronology: gauge reads, side caps in root order, partner deliveries. + events = defaultdict(list) + for s in sorted(when, key=when.get): + for t in gauge[s]['targets']: + events[t].append(gauge[s]['frame']) + deliveries = defaultdict(list) + for e in chk.k['entries']: + deliveries[e['deliver_after_root']].append(e) + for j, r in enumerate(roots): + if r['kind'] == 'side': + for t in r['targets']: + events[t].append(rf[j]) + for e in deliveries.get(j, ()): + require(sorted(e['receivers']) == sorted(r['targets']), 'Delivery after the receivers own root') + for t in e['receivers']: + events[t].append(e['deliver_frame']) + require(set(deliveries) <= set(range(len(roots))), 'Delivery roots') + target = Counter() + for t in range(v): + prev, d0 = None, 0 + for f in events[t]: + require(prev is None or sub(prev, f), 'Target chain nesting') + require(all(dot(chk.cov[t], u) == 0 for u in chk.B[f]), 'Target frame inside the cap') + if dim[f] > d0: + target[dim[f] - d0] += 1 + prev, d0 = f, dim[f] + require(d0 <= h - 1, 'Target chain below the cap') + if d0 < h - 1: + target[h - 1 - d0] += 1 + # The PR144 bit ledger with the spliced chains. + m, loss = 3 * h, chk.prof['loss'] + children = Counter() + for part in (local, source, target): + for r, n in part.items(): + if r and n: + children[r] += 3 * n + tails = Counter(z['dim'] for s, z in gauge.items() if s not in merge) + for d, n in tails.items(): + children[3 * d] += n + children[2] += 2 * v + W = 2 * v + R - len(pairs) + rank = sum(r * n for r, n in children.items()) + require(W * m - rank == 2 * v - 3 * loss, 'Telescoping deficit') + require(all(0 < r < m for r in children), 'Proper children') + replay = f2_replay(chk, ops, order, cut, R, sources, when, pairs, role_ops, position) + srt = lambda c: {r: n for r, n in sorted(c.items()) if n} + return dict(h=h, v=v, R=R, physical_R=R - len(pairs), pairs=len(pairs), + late_pairs=sum(when[b][0] > cut for _, b in pairs), operations=len(ops), + changed_operation_frames=moved, m=m, W_per_vertex=W, rank_per_vertex=rank, + deficit_per_vertex=W * m - rank, loss=loss, local_histogram=srt(local), + physical_gauge_histogram=srt(tails), source_data_histogram=srt(source), + target_data_histogram=srt(target), child_histogram=srt(children), f2_replay=replay, + checks=dict(register_contents=True, operation_frames_nondegenerate_and_spanning=True, + role_chains_nested=True, phase_one_closure=True, gauge_read_window=True, + pair_chronology=True, donor_frames_inside_gauges=True, + target_chains_nested_in_read_order=True, partner_chronology=True, + telescoping_deficit=True)) + + +def f2_replay(chk, ops, order, cut, R, sources, when, pairs, role_ops, position): + g, w, v = chk.g, chk.w, chk.v + roots, rootroles = g['roots'], w['rootroles'] + # Exact F2 response of every role's content before its first operation (all reads after the producer). + response = [0] * R + for r, s in zip(roots, rootroles): + for t in r['targets']: + response[s] ^= 1 << t + for i in reversed(order): + a, b, _ = ops[i] + response[b] ^= response[a] + gauged = sorted(when, key=when.get) + merge = {b: a for a, b in pairs} + centres = [(r, s) for r, s in zip(roots, rootroles) if r['kind'] == 'center'] + sides = [(j, r, s) for j, (r, s) in enumerate(zip(roots, rootroles)) if r['kind'] == 'side'] + deliveries = defaultdict(list) + for e in chk.k['entries']: + deliveries[e['deliver_after_root']].append(e) + + def run(seed, omit=None, early=None, alias=None): + rng = random.Random(seed) + slot = list(range(R)) + for b, a in merge.items(): + slot[b] = a + if alias: + slot[alias[0]] = alias[1] + x = [rng.getrandbits(LANES) for _ in range(v)] + y0 = [rng.getrandbits(LANES) for _ in range(v)] + z0 = {s: rng.getrandbits(LANES) for s in set(slot)} + z, y, X = dict(z0), list(y0), list(x) + at = defaultdict(list) + for s in gauged: + if s != omit: + at[cut if s == early else when[s][0]].append(s) + + def read(s): + value, mask = z[slot[s]], response[s] + while mask: + low = mask & -mask + y[low.bit_length() - 1] ^= value + mask ^= low + + def gate(i): + a, b, _ = ops[i] + require(slot[a] != slot[b], 'Aliased gate ports') + z[slot[a]] ^= z[slot[b]] + for s in range(R): + if s not in when: + read(s) + for leaf, s in sources.items(): + z[slot[s]] ^= X[leaf] + for i in order[:cut]: + gate(i) + for r, s in centres: + for t in r['targets']: + y[t] ^= z[slot[s]] + for p in range(cut, len(order)): + for s in at.get(p, ()): + read(s) + gate(order[p]) + for j, r, s in sides: + for t in r['targets']: + y[t] ^= z[slot[s]] + for e in deliveries.get(j, ()): + X[e['carrier']] ^= X[e['passive']] + for t in e['receivers']: + y[t] ^= X[e['carrier']] + for e in chk.k['entries']: + X[e['carrier']] ^= X[e['passive']] + for i in reversed(order): + gate(i) + for leaf, s in sources.items(): + z[slot[s]] ^= X[leaf] + return z == z0 and X == x, all(y[t] == y0[t] ^ x[t] for t in range(v)) + + def rejected(**control): + try: + return run(7, **control)[1] is False + except AssertionError: + return True + result = {'seed1': run(1), 'seed2': run(2)} + require(all(r == (True, True) for r in result.values()), 'Aliased dirty-scratch F2 replay') + controls = {} + if pairs: + b = next(b for _, b in pairs if response[b]) + controls['omitted_recipient_read'] = rejected(omit=b) + late = [b for a, b in pairs if response[b] and any(ops[i][0] == a and position[i] >= cut for i in role_ops[a])] + if late: + controls['read_before_donor_death'] = rejected(early=late[0]) + b = pairs[0][1] + t = position[role_ops[b][0]] + live = next(s for s in range(R) if s not in merge and s != pairs[0][0] and role_ops[s] and + position[role_ops[s][0]] < t < position[role_ops[s][-1]] and b not in + {c for i in role_ops[s] for c in ops[i][:2]}) + controls['alias_onto_live_register'] = rejected(alias=(b, live)) + require(all(controls.values()), 'Replay control accepted') + return dict(lanes=LANES, seeds_restored_and_y_plus_x=True, rejected_controls=sorted(controls), + registers=len(set(range(R)) - set(merge))) + + +def checked_record(): + result = physical(loaded()) + require(json.loads(OUTPUT.read_text()) == json.loads(json.dumps(result)), 'Frozen bit physical input differs') + return result + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--write', action='store_true') + parser.add_argument('--word', type=Path, help='physical word folder (default: the frozen input)') + parser.add_argument('--package', type=Path, default=BIT / 'out', help='package folder with graph and profile') + a = parser.parse_args() + result = physical(loaded(a.word, a.package)) + text = json.dumps(result, indent=2, sort_keys=True) + '\n' + if a.write: + OUTPUT.write_text(text) + elif a.word is None: + require(OUTPUT.read_text() == text, 'Frozen bit physical input differs') + print('PASS physical paired-cube bit word: %d operation frames moved, %d pairs (%d late), W %d, rank %d, ' + 'deficit %d' % (result['changed_operation_frames'], result['pairs'], result['late_pairs'], + result['W_per_vertex'], result['rank_per_vertex'], result['deficit_per_vertex']), flush=True) + + +if __name__ == '__main__': + main() diff --git a/scripts/paired_cube_network.py b/scripts/paired_cube_network.py index 63dab6d4e3..9d1aba904d 100644 --- a/scripts/paired_cube_network.py +++ b/scripts/paired_cube_network.py @@ -16,29 +16,56 @@ import sys from certify import require -from paired_cube_bit import reconstruct +from paired_cube_physical import checked_record +from paired_cube_bit_physical import checked_record as checked_bit_record + + +def bitcube_row(): + """Paired-cube bit word with partner-pair source mixing (research/paired-cube-bit, p = 12). Its standalone + checker recomputes the exact frames, the mod-2 decoder identity, every role and target chain, the + partner-pair chronology, G-nondegeneracy, a literal F2 replay and the ledger recount; the generator and + mutation controls run in research/paired-cube-bit.""" + folder = ROOT/'research/paired-cube-bit' + sys.path.insert(0,str(folder)) + from check_paired_cube_bit import Checker + checked = Checker(folder/'out',12).run() + row = json.loads((folder/'out/profile_p12.json').read_text()) + require((checked['roles'],checked['W'],checked['m'],checked['deficit']) == + (row['R'],row['W_per_vertex'],row['m'],row['deficit_per_vertex']),'Checked bit word profile') + return row from three_stage_cover_network import log_upper, exp_upper -from structured_bulk_assembly import assembly, halving, js +from structured_bulk_assembly import assembly as prefix_assembly, halving, js +from paired_cube_assembly import assembly if hasattr(sys,'set_int_max_str_digits'): sys.set_int_max_str_digits(0) ROOT = Path(__file__).resolve().parents[1] -AC = Q(4856569,10**10) -COARSE = Q(4617656,10**10) -ATOM = Q(1,1000) +SINKS = ROOT/'research/terminal-sinks' +AC = Q(6563200,10**10) +COARSE = Q(6600253,10**10) OLD = Q(384599,10**10) +ATOM = Q(int(COARSE/(1+COARSE-OLD)*10**12)+1,10**12) # first 10^-12 grid point above the toll edge (geckods, PR158) AB = (1-ATOM)*COARSE+ATOM*OLD BAD = Q(1,10**16) -PHASE_STOP = Q(1,10**6) +PHASE_STOP = Q(1,10**9) ASSEMBLY_BIT = min(AB,(1-PHASE_STOP)*AC-Q(1,10**10)) -KAPPA = Q(4609169,10**10) +KAPPA = Q(6558894,10**10) def clean(hist): return dict(sorted((int(r),n) for r,n in hist.items() if int(r) and n)) +def checked_complex_record(): + """#161's checked physical record; with research/terminal-sinks/sinks.json, the terminal-sink record on top.""" + if not (SINKS/'sinks.json').exists(): + return checked_record() + sys.path.insert(0,str(SINKS)) + from sinks_gate import checked_sinks_record + return checked_sinks_record() + + def shared_profile(row,complex_word): h,v,R,ell = (row[k] for k in ('h','v','R','loss')) m,W,H = 3*h,2*v+R,Counter() @@ -48,9 +75,9 @@ def shared_profile(row,complex_word): require(0 < r < h and n > 0,'Proper local gauges') H[3*r] += n if complex_word: - require((h,v,R,ell) == (24,1760,26417,528),'Paired-cube local dimensions') + require((h,v,R,ell) == (22,1320,13372,440),'Paired-cube local dimensions') require(R == row['c']+row['q']-row['matched'],'Compatible carrier roles') - require(selected == {20:4840},'Selected rank20 gauges') + require(selected == {18:2310},'Selected rank18 gauges') for r,n in enumerate(row['remaining_internal_histogram']): H[r] += 3*n parts = ('source_data_histogram','target_data_histogram') @@ -72,6 +99,30 @@ def shared_profile(row,complex_word): deficit_per_vertex=W*m-mass,child_multiplicities=H,maxchild=max(H),edge_count=sum(H.values())) +def bitcube_profile(row): + """Shared-core profile of the paired-cube bit word, in the complex word's ledger format.""" + h,v,R,ell = (row[k] for k in ('h','v','R','loss')) + require((h,v,R,ell) == (24,1760,19788,528),'Paired-cube bit dimensions') + m,W,H = 3*h,2*v+R,Counter() + selected = {int(r):n for r,n in row['selected_rank_histogram'].items()} + require(selected == {20:2200,21:1760} and sum(selected.values()) == row['selected_roles'],'Selected bit gauges') + for r,n in selected.items(): + H[3*r] += n + for name in ('remaining_internal_histogram','source_data_histogram','target_data_histogram'): + for r,n in row[name].items(): + H[int(r)] += 3*n + H[2] += 2*v + H = clean(H) + require(all(0 < r < m and n > 0 for r,n in H.items()),'Proper shared-core children') + mass = sum(r*n for r,n in H.items()) + require(H == clean(row['child_histogram']),'Saved complete child histogram') + require((m,W,mass,W*m-mass) == (row['m'],row['W_per_vertex'],row['rank_per_vertex'],row['deficit_per_vertex']), + 'Saved sharing dimensions and rank') + require(W*m-mass == 2*v-3*ell,'Shared-core telescoping deficit') + return dict(m=m,local_dimension=h,W_per_vertex=W,rank_per_vertex=mass,deficit_per_vertex=W*m-mass, + child_multiplicities=H,maxchild=max(H),edge_count=sum(H.values())) + + def exact_moment(p,saving): m,W = p['m'],p['W_per_vertex'] logs = {r:log_upper(Q(m,r)) for r in p['child_multiplicities']} @@ -81,8 +132,8 @@ def exact_moment(p,saving): log_upper_bounds=logs,rounding_denominator=1 << 120) -def bit_certificate(row): - p = shared_profile(row,False) +def bit_certificate(row,phys): + p = bit_physical_profile(phys,row) exact = exact_moment(p,COARSE) m,W = p['m'],p['W_per_vertex'] fallback = 32*m*m @@ -98,8 +149,45 @@ def bit_certificate(row): row_stock='O(w log e) internally borrowed radix-q digits; retained stopped wrapper restores them') -def complex_certificate(row): - p = shared_profile(row,True) +def physical_profile(phys,row): + """Shared-core profile of the physical word (paired_cube_physical.py): descended frames, compensated reuse.""" + h,v,R,ell = (row[k] for k in ('h','v','R','loss')) + shared_profile(row,True) + require((phys['h'],phys['v'],phys['R'],phys['loss']) == (h,v,R,ell),'Physical word dimensions') + return physical_counts(phys,h,v,ell) + + +def bit_physical_profile(phys,row): + """Shared-core profile of the physical bit word (paired_cube_bit_physical.py) over the checked package word.""" + h,v,ell = (row[k] for k in ('h','v','loss')) + bitcube_profile(row) + require((phys['h'],phys['v'],phys['loss']) == (h,v,ell),'Physical bit word dimensions') + return physical_counts(phys,h,v,ell) + + +def physical_counts(phys,h,v,ell): + require(phys['physical_R'] == phys['R']-phys['pairs']-phys.get('sinks',0) and phys['W_per_vertex'] == 2*v+phys['physical_R'], + 'Physical stock') + m,W,H = 3*h,phys['W_per_vertex'],Counter() + for name in ('local_histogram','source_data_histogram','target_data_histogram'): + for r,n in phys[name].items(): + H[int(r)] += 3*n + for d,n in phys['physical_gauge_histogram'].items(): + H[3*int(d)] += n + H[2] += 2*v + H = clean(H) + require(H == clean(phys['child_histogram']),'Saved physical child histogram') + require(all(0 < r < m and n > 0 for r,n in H.items()),'Proper shared-core children') + mass = sum(r*n for r,n in H.items()) + require((m,mass,W*m-mass) == (phys['m'],phys['rank_per_vertex'],phys['deficit_per_vertex']),'Saved physical rank') + require(W*m-mass == 2*v-3*ell,'Shared-core telescoping deficit') + return dict(m=m,local_dimension=h,W_per_vertex=W,rank_per_vertex=mass,deficit_per_vertex=W*m-mass, + child_multiplicities=H,maxchild=max(H),edge_count=sum(H.values()),physical_roles=phys['physical_R'], + reuse_pairs=phys['pairs'],late_reads=phys['late_pairs'],moved_operation_frames=phys['changed_operation_frames']) + + +def complex_certificate(row,phys): + p = physical_profile(phys,row) exact = exact_moment(p,AC) m = p['m'] n = m//2 @@ -148,12 +236,18 @@ def certificate(): def read(name): return json.loads((ROOT/'certificates'/name).read_text()) expected = read('paired-cube-input.json') - bit_row = reconstruct() + bit_row = bitcube_row() row = read('paired-cube-complex-input.json') - bit,phase = bit_certificate(bit_row),complex_certificate(row) + bit,phase = bit_certificate(bit_row,checked_bit_record()),complex_certificate(row,checked_complex_record()) bridge = finite_bridge(phase,bit,row) require(Q(read('copied-centers-network.json')['bit']['saving']) == OLD,'Retained ordinary leaf') result = assembly(ASSEMBLY_BIT,AC,bridge,KAPPA,beta=PHASE_STOP) + try: # control: the same inputs under PR23's original prefix 1-eps(1+c) do not reach KAPPA + prefix_assembly(ASSEMBLY_BIT,AC,bridge,KAPPA,beta=PHASE_STOP) + except AssertionError: + pass + else: + raise AssertionError('Original-prefix control accepted') result['parameters']['actual_bit_saving'] = AB require(ASSEMBLY_BIT <= AB,'Supported bit interface') for actual,key in ((bit['strict_gap'],'bit_moment_gap'),(phase['strict_gap'],'complex_moment_gap'), @@ -170,10 +264,15 @@ def read(name): sources += sorted(p for folder in ('scripts/paired_cube','references/paired-cube') for p in (ROOT/folder).rglob('*') if p.is_file() and '__pycache__' not in p.parts) sources += sorted((ROOT/'notes').glob('paired-cube-*.tex')) + sources += sorted(p for p in SINKS.rglob('*') if p.is_file() and '__pycache__' not in p.parts) + sources += sorted(p for p in (ROOT/'research/paired-cube-bit').rglob('*') + if p.is_file() and '__pycache__' not in p.parts) sources += [ROOT/p for p in ('scripts/three_stage_cover_network.py','scripts/structured_bulk_assembly.py', 'scripts/partial_gauge_bit.py','certificates/partial-gauge-bit-input.json', 'references/partial-gauge/pr97/SOURCE.json','certificates/copied-centers-network.json', - 'certificates/three-stage-cover-network.json','notes/general-clifford-frames.tex')] + 'certificates/three-stage-cover-network.json','notes/general-clifford-frames.tex', + 'references/semantic-bulk/rad20/reports/review-balanced-transform.md', + 'research/copied-fixed/balanced_assembly.py')] return dict(status='Conditional paired-cube multiplication witness',kappa=KAPPA,bit=bit,complex=phase, finite_bridge=bridge,assembly=result,predecessor_commit='6a9970a530119174507904e23592fd59ede19a5d', source_sha256={str(p.relative_to(ROOT)):sha256(p.read_bytes()).hexdigest() for p in sources}, @@ -187,7 +286,7 @@ def main(): p.add_argument('--output',type=Path,default=ROOT/'certificates/paired-cube-network.json') args = p.parse_args() args.output.write_text(json.dumps(js(certificate()),indent=2,sort_keys=True)+'\n') - print('PASS kappa=4609169/10000000000 = 4.609169e-4; both moments, shared cores, finite router and 47 strict constraints') + print('PASS kappa=6558894/10000000000 = 6.558894e-4; both moments, shared cores, finite router and 47 strict constraints') if __name__ == '__main__': diff --git a/scripts/paired_cube_physical.py b/scripts/paired_cube_physical.py new file mode 100644 index 0000000000..187bd31c59 --- /dev/null +++ b/scripts/paired_cube_physical.py @@ -0,0 +1,328 @@ +#!/usr/bin/env python3 +"""Physical frame descent and compensated birth-cut reuse on the selected paired-cube complex word. + +Prepared by eumemic with Anthropic Claude assistance. Apache-2.0. The signed word, frozen arcs, gauges, +chronology and shared-core accounting are icekylinx's PR144. Frame descent under PR130's general Clifford +frames and compensated birth-cut reuse follow PR131 and jamesyc's PR124; deadline (late) compensation reads +follow PR143. Frozen inputs: references/paired-cube/physical/{frames,pairs}.json. + +Checks, from the regenerated PR144 word and the frozen inputs only: + * every operation frame contains its node's value span, and every role chain + start -> operation frames -> root frame -> full space + is nested, with each recipient's chain spliced after its donor's last operation; + * every pair: donor ungauged, not a root, its last operation before the recipient's old-value read; the + recipient gauged and untouched before its read; donor last frame inside the recipient gauge; reads in + chronological order keep every target chain nested; + * the spliced positive-rank recount gives the shared-core profile with W = 2v + R - pairs and the unchanged + deficit 2v - 3 loss; + * an exact numeric replay mod 2^61-1 of the aliased signed word with arbitrary dirty scratch restores every + slot and adds x to y, for two seeds; omitting one recipient's read, reading a late recipient before its + donor's last operation, or flipping one signed coefficient is rejected. +Writes certificates/paired-cube-physical-input.json with --write; otherwise checks it. +""" +import argparse +from collections import Counter, defaultdict +import json +from pathlib import Path +import random +import sys +import tempfile + +from paired_cube.frames import basis, perp, contained + +ROOT = Path(__file__).resolve().parents[1] +REF = ROOT / 'references/paired-cube/physical' +OUTPUT = ROOT / 'certificates/paired-cube-physical-input.json' +P = (1 << 61) - 1 + + +def require(condition, message): + if not condition: + raise AssertionError(message) + + +def regenerated_word(): + from paired_cube_producer import regenerate + expected = json.loads((ROOT / 'certificates/paired-cube-complex-input.json').read_text()) + with tempfile.TemporaryDirectory(prefix='paired-cube-physical-') as d: + regenerate(expected, Path(d)) + return tuple(json.loads((Path(d) / name).read_text()) + for name in ('graph.json', 'frames.json', 'selection.json')) + (expected,) + + +def physical(g, witness, word, record, frames_in, pairs_in): + h, v, R = g['h'], g['v'], record['R'] + full = basis(1 << i for i in range(h)) + args = [None] + [None if a is None else (a[0] + 1, a[1] + 1) for a in g['args']] + inputs = g['inputs'] + roots = [dict(r, node=r['node'] + 1) for r in g['roots']] + ann = witness['annihilators'] + ops = [tuple(o) for o in word['ops']] + coef = [tuple(c) for c in word['opcoeff']] + phase1 = sorted(word['phase1']) + pset = set(phase1) + rest = [i for i in range(len(ops)) if i not in pset] + sources = {int(x): s for x, s in word['sources'].items()} + require(len(ops) == record['total_M_operations'], 'Operation count') + spans = [()] * len(args) + for x in range(1, len(args)): + spans[x] = (inputs[x - 1],) if args[x] is None else basis(spans[args[x][0]] + spans[args[x][1]]) + frames = [perp(tuple(ann[x]), h) for _, _, x in ops] # PR144's full backward-intersection frames + moved = set() + for i, F in frames_in: + require(i not in moved and basis(F) == tuple(F) != frames[i], 'Duplicate, noncanonical or unmoved frame') + frames[i] = tuple(F) + moved.add(i) + changed = len(moved) + for i, (_, _, x) in enumerate(ops): + require(contained(spans[x], frames[i]), 'Value span outside operation frame') + start = [()] * R + for x, s in sources.items(): + start[s] = (inputs[x - 1],) + gauge = {} + for z in word['selected']: + gauge[z['role']] = perp(tuple(z['annihilator']), h) + require(len(gauge[z['role']]) == z['rank'], 'Gauge rank') + start[z['role']] = gauge[z['role']] + rootframe, rootkind, rootann = {}, {}, {} + for r, s in zip(roots, word['rootroles']): + if r['kind'] == 'center': + U = spans[r['node']] + require(len(U) == h - 2, 'Centre frame rank') + A = perp(U, h) + else: + A = basis(inputs[t] for t in r['targets']) + U = perp(A, h) + require(s not in rootframe, 'Duplicate root role') + rootframe[s], rootkind[s], rootann[s] = U, r['kind'], A + role_ops = defaultdict(list) + for i, (a, b, _) in enumerate(ops): + require(a != b, 'Gate ports') + role_ops[a].append(i) + role_ops[b].append(i) + position = {i: k for k, i in enumerate(phase1 + rest)} + + def chain(s): + return [start[s]] + [frames[i] for i in role_ops[s]] + ([rootframe[s]] if s in rootframe else []) + [full] + + # Pairs and deadlines. + pairs = [(int(a), int(b)) for a, b, _ in pairs_in] + deadline = {int(b): (None if t is None else int(t)) for _, b, t in pairs_in} + donors = {a: b for a, b in pairs} + merge = {b: a for a, b in pairs} + require(len(donors) == len(merge) == len(pairs) and not set(donors) & set(merge), 'Pair aliases') + first = {s: l[0] for s, l in role_ops.items()} + for a, b in pairs: + require(a not in gauge and a not in rootframe, 'Donor kind') + require(b in gauge, 'Recipient kind') + last = role_ops[a][-1] + t = deadline[b] + if t is None: # read at the phase cut, after all of phase one + require(last in pset and first[b] not in pset, 'Early pair chronology') + else: # read immediately before operation t, the recipient's first operation + require(t == first[b] and t not in pset and position[last] < position[t], 'Late pair chronology') + require(contained(frames[last], gauge[b]), 'Donor frame outside recipient gauge') + # Chains, the spliced recount and the profile. + local = Counter() + for s in range(R): + seq = chain(s) + require(all(contained(A, B) for A, B in zip(seq, seq[1:])), 'Role chain nesting') + if s in merge: + continue + if s in sources.values(): + local[1] += 1 + if s in donors: + seq = seq[:-1] + chain(donors[s]) + dims = [len(F) for F in seq] + local.update(d1 - d0 for d0, d1 in zip(dims, dims[1:]) if d1 > d0) + for t in (s, donors.get(s)): + if t is not None and rootkind.get(t) == 'center': + local[len(rootframe[t])] += 1 + # Target chains along the actual read chronology (late reads move; sides last; inputs end). + cut = len(phase1) + when = {z['role']: (cut if deadline.get(z['role']) is None else position[deadline[z['role']]], k) + for k, z in enumerate(reversed(word['selected']))} + current = [full] * v + target = Counter() + for z in sorted(word['selected'], key=lambda z: when[z['role']]): + A = tuple(z['annihilator']) + for t in z['targets']: + require(contained(A, current[t]), 'Target chain order') + target[len(current[t]) - len(A)] += 1 + current[t] = A + for r, s in zip(roots, word['rootroles']): + if r['kind'] == 'side': + for t in r['targets']: + require(contained(rootann[s], current[t]), 'Side target order') + target[len(current[t]) - len(rootann[s])] += 1 + current[t] = rootann[s] + for t, q in enumerate(inputs): + require(contained((q,), current[t]), 'Target input') + target[len(current[t]) - 1] += 1 + require(dict(target) == {int(k): n for k, n in record['target_data_histogram'].items()}, 'Target histogram') + source = Counter({int(k): n for k, n in record['source_data_histogram'].items()}) + children = Counter({r: 3 * n for r, n in local.items() if r}) + children.update({r: 3 * n for r, n in source.items() if r}) + children.update({r: 3 * n for r, n in target.items() if r}) + tails = Counter(len(U) for s, U in gauge.items() if s not in merge) + children.update({3 * d: n for d, n in tails.items() if d}) + children[2] += 2 * v + m, W = 3 * h, 2 * v + R - len(pairs) + rank = sum(r * n for r, n in children.items()) + require(W * m - rank == 2 * v - 3 * record['loss'] == record['deficit_per_vertex'], 'Telescoping deficit') + require(all(0 < r < m for r in children), 'Proper children') + replay = scalar_replay(g, word, R, pairs, deadline, ops, coef, phase1, rest, sources, roots) + return dict(h=h, v=v, R=R, physical_R=R - len(pairs), pairs=len(pairs), + late_pairs=sum(t is not None for t in deadline.values()), changed_operation_frames=changed, + m=m, W_per_vertex=W, rank_per_vertex=rank, deficit_per_vertex=W * m - rank, loss=record['loss'], + local_histogram=dict(sorted(local.items())), physical_gauge_histogram=dict(sorted(tails.items())), + source_data_histogram=dict(sorted(source.items())), target_data_histogram=dict(sorted(target.items())), + child_histogram=dict(sorted(children.items())), scalar_replay=replay, + checks=dict(value_spans_inside_frames=True, role_chains_nested=True, pair_chronology=True, + donor_frames_inside_gauges=True, target_chains_nested_in_read_order=True, + telescoping_deficit=True)) + + +def scalar_replay(g, word, R, pairs, deadline, ops, coef, phase1, rest, sources, roots): + h, v, inputs, labels = g['h'], g['v'], g['inputs'], g['labels'] + inv = lambda a: pow(a % P, P - 2, P) + half, third, sixth = inv(2), inv(3), inv(6) + selected = [z['role'] for z in word['selected']] + deferred = set(selected) + cseed, dseed = {}, {} + for r, s in zip(roots, word['rootroles']): + if r['kind'] == 'center': + cseed[s] = [int(k == r['coordinate']) for k in range(h)] + else: + dseed[s] = {t: half if q == '1/2' else P - half for t, q in zip(r['targets'], r['coefficients'])} + cvec = [None] * R + dpart = [dict() for _ in range(R)] + for s, c in cseed.items(): + cvec[s] = list(c) + for s, d in dseed.items(): + dpart[s] = dict(d) + for (a, b, _), (ca, cb) in zip(reversed(ops), reversed(coef)): + if cvec[a] is not None: + cvec[b] = [(cb * u) % P for u in cvec[a]] if cvec[b] is None else \ + [(w + cb * u) % P for w, u in zip(cvec[b], cvec[a])] + for t, u in dpart[a].items(): + dpart[b][t] = (dpart[b].get(t, 0) + cb * u) % P + if ca != 1: + if cvec[a] is not None: + cvec[a] = [(ca * u) % P for u in cvec[a]] + dpart[a] = {t: (ca * u) % P for t, u in dpart[a].items()} + scatter = [[third if c in labels[t] else P - sixth for t in range(v)] for c in range(h)] + merge = {b: a for a, b in pairs} + late_at = defaultdict(list) + for b, t in deadline.items(): + if t is not None: + late_at[t].append(b) + leaf = {s: x for x, s in sources.items()} + cubes = [range(k, k + 8) for k in range(0, v, 8)] + + def run(seed, omit=None, early=None, flip=None): + rng = random.Random(seed) + live = sorted(set(range(R)) - set(merge)) + slot = {s: i for i, s in enumerate(live)} + alias = lambda s: slot[merge.get(s, s)] + x = [rng.randrange(P) for _ in range(v)] + z = [rng.randrange(P) for _ in live] + y0 = [rng.randrange(P) for _ in range(v)] + a, y, yc, chron = list(z), list(y0), [0] * h, [] + + def read(s, sign, seed_only=False): + val = a[alias(s)] + c = cseed.get(s) if seed_only else cvec[s] + d = dseed.get(s, {}) if seed_only else dpart[s] + if c is not None: + for k, u in enumerate(c): + yc[k] = (yc[k] + sign * u * val) % P + for t, u in d.items(): + y[t] = (y[t] + sign * u * val) % P + + def gate(i): + (dst, src, _), (ca, cb) = ops[i], coef[i] + cb = -cb if flip == i else cb + dd, ss = alias(dst), alias(src) + require(dd != ss, 'Aliased gate ports') + a[dd] = (ca * a[dd] + cb * a[ss]) % P + chron.append((dd, ss, ca, cb)) + for s in range(R): + if s not in deferred and s not in merge: + read(s, -1) + for s, xn in leaf.items(): + a[alias(s)] = (a[alias(s)] + x[xn - 1]) % P + chron.append((alias(s), None, xn - 1, None)) + for i in phase1: + gate(i) + for s in cseed: + read(s, +1, True) + for s in reversed(selected): + if s != omit and (deadline.get(s) is None or s == early): + read(s, -1) + for i in rest: + for s in late_at.get(i, ()): + if s != omit and s != early: + read(s, -1) + gate(i) + for s in dseed: + read(s, +1, True) + for cube in cubes: + qs = [inputs[t] for t in cube] + for i, t in enumerate(cube): + acc = sum(x[s] if (qs[i] ^ qs[j]).bit_count() == 6 else -x[s] if (qs[i] ^ qs[j]).bit_count() == 2 + else 0 for j, s in enumerate(cube)) + y[t] = (y[t] + acc * half) % P + for k in range(h): + if yc[k]: + for t in range(v): + y[t] = (y[t] + yc[k] * scatter[k][t]) % P + for dd, ss, ca, cb in reversed(chron): + if ss is None: + a[dd] = (a[dd] - x[ca]) % P + else: + a[dd] = (ca * (a[dd] - cb * a[ss])) % P + return a == z, all((y[t] - y0[t] - x[t]) % P == 0 for t in range(v)) + result = {'seed1': run(1), 'seed2': run(2)} + require(all(r == (True, True) for r in result.values()), 'Aliased dirty-scratch replay') + controls = {} + if pairs: + controls['omitted_recipient_read'] = run(3, omit=pairs[0][1]) + late = [b for b, t in deadline.items() if t is not None] + if late: + controls['late_read_before_donor_death'] = run(4, early=late[-1]) + controls['flipped_signed_operation'] = run(5, flip=next(i for i, c in enumerate(coef) if c[1] == -1)) + require(all(r[1] is False for r in controls.values()), 'Replay control accepted') + return dict(modulus='2^61-1', seeds_restored_and_y_plus_x=True, + rejected_controls=sorted(controls), slots=R - len(pairs)) + + +def checked_record(): + g, witness, word, record = regenerated_word() + frames_in = json.loads((REF / 'frames.json').read_text())['frames'] + pairs_in = json.loads((REF / 'pairs.json').read_text())['pairs'] + result = physical(g, witness, word, record, frames_in, pairs_in) + require(json.loads(OUTPUT.read_text()) == json.loads(json.dumps(result)), 'Frozen physical input differs') + return result + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument('--write', action='store_true') + a = parser.parse_args() + g, witness, word, record = regenerated_word() + frames_in = json.loads((REF / 'frames.json').read_text())['frames'] + pairs_in = json.loads((REF / 'pairs.json').read_text())['pairs'] + result = physical(g, witness, word, record, frames_in, pairs_in) + text = json.dumps(result, indent=2, sort_keys=True) + '\n' + if a.write: + OUTPUT.write_text(text) + else: + require(OUTPUT.read_text() == text, 'Frozen physical input differs') + print('PASS physical paired-cube word: %d operation frames moved, %d pairs (%d late), W %d, rank %d, deficit %d' + % (result['changed_operation_frames'], result['pairs'], result['late_pairs'], result['W_per_vertex'], + result['rank_per_vertex'], result['deficit_per_vertex']), flush=True) + + +if __name__ == '__main__': + main() diff --git a/scripts/paired_cube_producer.py b/scripts/paired_cube_producer.py index 3354975491..d278490673 100644 --- a/scripts/paired_cube_producer.py +++ b/scripts/paired_cube_producer.py @@ -13,8 +13,8 @@ from pathlib import Path import sys from paired_cube.graph import Graph -from paired_cube.modules import restricted_pairs, restricted_triples, all_but_one -from paired_cube.frames import compile_graph +from paired_cube.modules import restricted_pairs, restricted_triples, all_but_one, restricted_triples_from, restricted_pairs_from, pair_module_from, all_but_one_from, triple_module_from, merge_outputs +from paired_cube.closure import compile_closure from paired_cube.gauges import select from paired_cube.verify import verify @@ -33,12 +33,15 @@ def stage(message):print(message,file=sys.stderr,flush=True) frozen=reference/'matching-arcs.json' assert hashlib.sha256(frozen.read_bytes()).hexdigest()==pin['matching_arcs_sha256'] stage('Regenerating paired-cube signed DAG from inherited PR117 restrictions') - g=Graph(12).finish(restricted_triples(12),restricted_pairs(11),all_but_one(10)) + src=ROOT/'references/paired-cube/sources' + srcpin=json.loads((src/'SOURCE.json').read_text())['files'] + for name,digest in srcpin.items():assert hashlib.sha256((src/name).read_bytes()).hexdigest()==digest + _G=Graph(11,local=json.loads((src/'local_L1.json').read_text()));g=_G.finish(triple_module_from(src/'tmod_TE_TD_TB3_1_1_4_full_6.0617964e-4.json',11),pair_module_from(src/'pmod_J0_full_6.0666810e-4.json',10),all_but_one_from(src/'qmod_climb3u_best.json',9));g=merge_outputs(g,_G,'f8:00111100') g['matching_frames']='coordinate' binding={k:g[k] for k in ('inputs','labels','args','signs','roots','centers')} assert hashlib.sha256(json.dumps(binding,separators=(',',':')).encode()).hexdigest()==pin['graph_sha256'] stage('Replaying frozen carrier matching and full binary intersections') - baseline,witness=compile_graph(g,json.loads(frozen.read_text())) + baseline,witness=compile_closure(g,json.loads(frozen.read_text())) stage('Selecting chronological partial gauges and constructing signed physical M') actual,word=select(g,baseline,witness);actual=json.loads(json.dumps(actual)) for key in ('numerical_complex_root','status','gauge_selection',