From b895ae7770a97276ae0e9c13fb0c51cbed4fd00a Mon Sep 17 00:00:00 2001 From: ToikY <27568617+ToikY@users.noreply.github.com> Date: Mon, 26 Oct 2026 15:10:27 -0700 Subject: [PATCH] Bind actual G20 route markers to conditional ROW cover words --- research/g20-route-word-binding/NOTICE | 18 + research/g20-route-word-binding/ORACLE.json | 1120 + research/g20-route-word-binding/PROOF.md | 137 + research/g20-route-word-binding/README.md | 37 + research/g20-route-word-binding/RESULT.json | 93907 ++++++++++++++++ research/g20-route-word-binding/SOURCES.json | 89 + research/g20-route-word-binding/TASK.json | 100 + research/g20-route-word-binding/VERIFY.json | 47 + research/g20-route-word-binding/oracle.py | 368 + .../g20-route-word-binding/source/CALLS.json | 1262 + .../source/CONTROLLER.json | 2175 + .../source/GLOBAL.jsonl.gz | Bin 0 -> 1895549 bytes .../g20-route-word-binding/source/PORTS.json | 18875 ++++ .../g20-route-word-binding/source/WORDS.json | 48152 ++++++++ research/g20-route-word-binding/verify.py | 271 + 15 files changed, 166558 insertions(+) create mode 100644 research/g20-route-word-binding/NOTICE create mode 100644 research/g20-route-word-binding/ORACLE.json create mode 100644 research/g20-route-word-binding/PROOF.md create mode 100644 research/g20-route-word-binding/README.md create mode 100644 research/g20-route-word-binding/RESULT.json create mode 100644 research/g20-route-word-binding/SOURCES.json create mode 100644 research/g20-route-word-binding/TASK.json create mode 100644 research/g20-route-word-binding/VERIFY.json create mode 100644 research/g20-route-word-binding/oracle.py create mode 100644 research/g20-route-word-binding/source/CALLS.json create mode 100644 research/g20-route-word-binding/source/CONTROLLER.json create mode 100644 research/g20-route-word-binding/source/GLOBAL.jsonl.gz create mode 100644 research/g20-route-word-binding/source/PORTS.json create mode 100644 research/g20-route-word-binding/source/WORDS.json create mode 100644 research/g20-route-word-binding/verify.py diff --git a/research/g20-route-word-binding/NOTICE b/research/g20-route-word-binding/NOTICE new file mode 100644 index 0000000000..ef603b281d --- /dev/null +++ b/research/g20-route-word-binding/NOTICE @@ -0,0 +1,18 @@ +Retained source notice from PR #5798 (the following credits describe predecessor work): + +New G20 global boundary checker, rational port certificates and proof: +Ali Romman with substantial OpenAI Codex assistance. No subagents. Apache-2.0. + +The construction is PR5708, building on PR5679, Dugongue PR5657/5665 and +ai-nanachi PR5512. The local all-address proof is PR5782. Their complete source +attribution and limitations remain in source/PROOF.md, source/NATIVE-README.md, +source/NATIVE-PROOF.md and source/NOTICE-*.md. The controller, native involution, +helper retirement/split, query accounting and positive finite-fee schema are +source contributions. This package claims the separate global boundary audit +and explicit port/interface witnesses, not those constructions. + +Named ROW/P2 contract and earlier schedule: JoyboyBrian with substantial OpenAI Codex assistance. Retain ai-nanachi, Chris R/Clear1nsight, rohanarun, Maxime Fleury, Cinna Davis, zxv, Jacob Alan Sussman, Mark/Matarener and the native/E8/ordinary/ROW/routing/precision/tape lineage in the pinned ROW-generator README. + +New finite dyadic words and certificate: ToikY with substantial OpenAI Codex assistance, using separate primary, independent-oracle and read-only proof/review contexts. Apache-2.0. No predecessor construction, physical ABI implementation or complete supplier admission is claimed. + +The above finite dyadic words are predecessor work from PR5801, frozen here as WORDS.json. New marker-to-word binding, conditional cover-model ledger and reflected-address audit: ToikY with substantial OpenAI Codex assistance in separate primary, independent-oracle and proof-review contexts. No physical lowering, complete supplier or predecessor construction credit is claimed. Apache-2.0. diff --git a/research/g20-route-word-binding/ORACLE.json b/research/g20-route-word-binding/ORACLE.json new file mode 100644 index 0000000000..611ea84eb1 --- /dev/null +++ b/research/g20-route-word-binding/ORACLE.json @@ -0,0 +1,1120 @@ +{ + "bank_phase_counts": [ + { + "bank": 0, + "count": 111, + "phase": "ENTRY" + }, + { + "bank": 0, + "count": 111, + "phase": "RETURN" + }, + { + "bank": 1, + "count": 111, + "phase": "ENTRY" + }, + { + "bank": 1, + "count": 111, + "phase": "RETURN" + }, + { + "bank": 2, + "count": 111, + "phase": "ENTRY" + }, + { + "bank": 2, + "count": 111, + "phase": "RETURN" + }, + { + "bank": 3, + "count": 111, + "phase": "ENTRY" + }, + { + "bank": 3, + "count": 111, + "phase": "RETURN" + }, + { + "bank": 4, + "count": 111, + "phase": "ENTRY" + }, + { + "bank": 4, + "count": 111, + "phase": "RETURN" + }, + { + "bank": 5, + "count": 111, + "phase": "ENTRY" + }, + { + "bank": 5, + "count": 111, + "phase": "RETURN" + }, + { + "bank": 6, + "count": 111, + "phase": "ENTRY" + }, + { + "bank": 6, + "count": 111, + "phase": "RETURN" + }, + { + "bank": 7, + "count": 111, + "phase": "ENTRY" + }, + { + "bank": 7, + "count": 111, + "phase": "RETURN" + }, + { + "bank": 8, + "count": 111, + "phase": "ENTRY" + }, + { + "bank": 8, + "count": 111, + "phase": "RETURN" + }, + { + "bank": 9, + "count": 111, + "phase": "ENTRY" + }, + { + "bank": 9, + "count": 111, + "phase": "RETURN" + }, + { + "bank": 10, + "count": 111, + "phase": "ENTRY" + }, + { + "bank": 10, + "count": 111, + "phase": "RETURN" + }, + { + "bank": 11, + "count": 111, + "phase": "ENTRY" + }, + { + "bank": 11, + "count": 111, + "phase": "RETURN" + }, + { + "bank": 12, + "count": 111, + "phase": "ENTRY" + }, + { + "bank": 12, + "count": 111, + "phase": "RETURN" + }, + { + "bank": 13, + "count": 111, + "phase": "ENTRY" + }, + { + "bank": 13, + "count": 111, + "phase": "RETURN" + }, + { + "bank": 14, + "count": 111, + "phase": "ENTRY" + }, + { + "bank": 14, + "count": 111, + "phase": "RETURN" + }, + { + "bank": 15, + "count": 111, + "phase": "ENTRY" + }, + { + "bank": 15, + "count": 111, + "phase": "RETURN" + }, + { + "bank": 16, + "count": 111, + "phase": "ENTRY" + }, + { + "bank": 16, + "count": 111, + "phase": "RETURN" + }, + { + "bank": 17, + "count": 111, + "phase": "ENTRY" + }, + { + "bank": 17, + "count": 111, + "phase": "RETURN" + }, + { + "bank": 18, + "count": 111, + "phase": "ENTRY" + }, + { + "bank": 18, + "count": 111, + "phase": "RETURN" + }, + { + "bank": 19, + "count": 111, + "phase": "ENTRY" + }, + { + "bank": 19, + "count": 111, + "phase": "RETURN" + }, + { + "bank": 20, + "count": 111, + "phase": "ENTRY" + }, + { + "bank": 20, + "count": 111, + "phase": "RETURN" + }, + { + "bank": 21, + "count": 111, + "phase": "ENTRY" + }, + { + "bank": 21, + "count": 111, + "phase": "RETURN" + }, + { + "bank": 22, + "count": 111, + "phase": "ENTRY" + }, + { + "bank": 22, + "count": 111, + "phase": "RETURN" + }, + { + "bank": 23, + "count": 111, + "phase": "ENTRY" + }, + { + "bank": 23, + "count": 111, + "phase": "RETURN" + }, + { + "bank": 24, + "count": 111, + "phase": "ENTRY" + }, + { + "bank": 24, + "count": 111, + "phase": "RETURN" + }, + { + "bank": 25, + "count": 111, + "phase": "ENTRY" + }, + { + "bank": 25, + "count": 111, + "phase": "RETURN" + }, + { + "bank": 26, + "count": 111, + "phase": "ENTRY" + }, + { + "bank": 26, + "count": 111, + "phase": "RETURN" + }, + { + "bank": 27, + "count": 111, + "phase": "ENTRY" + }, + { + "bank": 27, + "count": 111, + "phase": "RETURN" + }, + { + "bank": 28, + "count": 111, + "phase": "ENTRY" + }, + { + "bank": 28, + "count": 111, + "phase": "RETURN" + }, + { + "bank": 29, + "count": 111, + "phase": "ENTRY" + }, + { + "bank": 29, + "count": 111, + "phase": "RETURN" + }, + { + "bank": 30, + "count": 222, + "phase": "ENTRY" + }, + { + "bank": 30, + "count": 222, + "phase": "RETURN" + }, + { + "bank": 31, + "count": 222, + "phase": "ENTRY" + }, + { + "bank": 31, + "count": 222, + "phase": "RETURN" + } + ], + "cover_conjugations": 111, + "cover_recipe": "One retained cover route g->g W^-1 at ENTRY and g->g W at RETURN. (g W^-1)P(g W^-1)^-1=g Q g^-1.", + "cover_word_instances": 7548, + "cover_words_per_marker": 1, + "event_count": 317004, + "event_join_columns": [ + "event_index", + "call_index", + "stage", + "owner", + "port", + "phase", + "direction", + "word_sha256" + ], + "event_join_sha256": "91383314869a40a96ced928dc857b9f32ac02b11eb7cb45853b1092d10291eb0", + "half_count_scope": "Both native halves are normalized by the same changed cover matrix. They do not duplicate this cover-route word.", + "named_P2_kernel_counts": [ + { + "N": 127, + "coefficient_counts": [ + { + "coefficient": "-1", + "count": 9974580, + "primitive": "ordered_shift" + }, + { + "coefficient": "-1/2", + "count": 1580388, + "primitive": "ordered_shift" + }, + { + "coefficient": "-2", + "count": 811784, + "primitive": "ordered_shift" + }, + { + "coefficient": "-3", + "count": 427482, + "primitive": "ordered_shift" + }, + { + "coefficient": "-3/2", + "count": 60452, + "primitive": "ordered_shift" + }, + { + "coefficient": "-4", + "count": 12954, + "primitive": "ordered_shift" + }, + { + "coefficient": "1", + "count": 9974580, + "primitive": "ordered_shift" + }, + { + "coefficient": "1/2", + "count": 1580388, + "primitive": "ordered_shift" + }, + { + "coefficient": "2", + "count": 811784, + "primitive": "ordered_shift" + }, + { + "coefficient": "3", + "count": 427482, + "primitive": "ordered_shift" + }, + { + "coefficient": "3/2", + "count": 60452, + "primitive": "ordered_shift" + }, + { + "coefficient": "4", + "count": 12954, + "primitive": "ordered_shift" + }, + { + "coefficient": "-1", + "count": 4162552, + "primitive": "unit_scale" + }, + { + "coefficient": "-1/2", + "count": 64770, + "primitive": "unit_scale" + }, + { + "coefficient": "-1/4", + "count": 198628, + "primitive": "unit_scale" + }, + { + "coefficient": "-2", + "count": 64770, + "primitive": "unit_scale" + }, + { + "coefficient": "-4", + "count": 198628, + "primitive": "unit_scale" + }, + { + "coefficient": "1/2", + "count": 2111502, + "primitive": "unit_scale" + }, + { + "coefficient": "1/4", + "count": 237490, + "primitive": "unit_scale" + }, + { + "coefficient": "2", + "count": 2111502, + "primitive": "unit_scale" + }, + { + "coefficient": "4", + "count": 237490, + "primitive": "unit_scale" + } + ], + "f": 1 + }, + { + "N": 254, + "coefficient_counts": [ + { + "coefficient": "-1", + "count": 39898320, + "primitive": "ordered_shift" + }, + { + "coefficient": "-1/2", + "count": 6321552, + "primitive": "ordered_shift" + }, + { + "coefficient": "-2", + "count": 3247136, + "primitive": "ordered_shift" + }, + { + "coefficient": "-3", + "count": 1709928, + "primitive": "ordered_shift" + }, + { + "coefficient": "-3/2", + "count": 241808, + "primitive": "ordered_shift" + }, + { + "coefficient": "-4", + "count": 51816, + "primitive": "ordered_shift" + }, + { + "coefficient": "1", + "count": 39898320, + "primitive": "ordered_shift" + }, + { + "coefficient": "1/2", + "count": 6321552, + "primitive": "ordered_shift" + }, + { + "coefficient": "2", + "count": 3247136, + "primitive": "ordered_shift" + }, + { + "coefficient": "3", + "count": 1709928, + "primitive": "ordered_shift" + }, + { + "coefficient": "3/2", + "count": 241808, + "primitive": "ordered_shift" + }, + { + "coefficient": "4", + "count": 51816, + "primitive": "ordered_shift" + }, + { + "coefficient": "-1", + "count": 16650208, + "primitive": "unit_scale" + }, + { + "coefficient": "-1/2", + "count": 259080, + "primitive": "unit_scale" + }, + { + "coefficient": "-1/4", + "count": 794512, + "primitive": "unit_scale" + }, + { + "coefficient": "-2", + "count": 259080, + "primitive": "unit_scale" + }, + { + "coefficient": "-4", + "count": 794512, + "primitive": "unit_scale" + }, + { + "coefficient": "1/2", + "count": 8446008, + "primitive": "unit_scale" + }, + { + "coefficient": "1/4", + "count": 949960, + "primitive": "unit_scale" + }, + { + "coefficient": "2", + "count": 8446008, + "primitive": "unit_scale" + }, + { + "coefficient": "4", + "count": 949960, + "primitive": "unit_scale" + } + ], + "f": 2 + } + ], + "native_address_halves": 2, + "negative_controls": { + "duplicate_bank_same_coefficient_counts": { + "actual_cover_diagonals": { + "0": [ + "2", + "2", + "2", + "2", + "2", + "2", + "2", + "2" + ], + "1": [ + "1/2", + "1/2", + "1/2", + "1/2", + "1/2", + "1/2", + "1/2", + "1/2" + ] + }, + "banks": [ + 1, + 0 + ], + "call_index": 1, + "marker_count": 4, + "port": 0, + "same_word_and_coefficient_histogram": true, + "source_events": [ + 21391, + 21502, + 36407, + 36518 + ], + "stage": 1 + }, + "omit_second": { + "actual": { + "15": "2" + }, + "axis": 0, + "expected": { + "15": "1" + }, + "port": 0 + }, + "unreflected": { + "actual": { + "14": "1" + }, + "axis": 0, + "expected": { + "15": "1" + }, + "port": 1 + }, + "wrong_cover_direction": { + "actual": {}, + "axis": 0, + "expected": { + "0": "1" + }, + "port": 2 + }, + "wrong_return_same_factor_count": { + "actual_cover_diagonals": { + "0": [ + "1/4", + "1/4", + "1/4", + "1/4", + "1/4", + "1/4", + "1/4", + "1/4" + ], + "1": [ + "1", + "1", + "1", + "1", + "1", + "1", + "1", + "1" + ] + }, + "call_index": 1, + "elementary_call_count": 32, + "marker_count": 4, + "port": 0 + } + }, + "paired_basis_columns": 1776, + "paired_basis_order": "x0..x7; x15..x8; physical D=diag(W,J W J)", + "route_count": 7548, + "scope": "Conditional finite cover-route word binding and coefficient counts. The source marker does not implement a full physical route. Low cache/carry/permutation, ROW borrow/pad/return, coefficient preparation, head motion, tape tariffs and full compiler admission remain open.", + "source_sha256": { + "CALLS.json": "30dcc37cdade6b2dc05478837eca28b696894d1c4782bac6a1caab5e7f56c9e8", + "CONTROLLER.json": "39ac84fb848b908f7ba051fae4556d507900c421dc5d23501a9c0cb1d61fd08d", + "GLOBAL.jsonl.gz": "86e7ce6aff05409410ef4bbc00ff1b29b8c1606383549c7e15242b327e39c235", + "PORTS.json": "a53a49c938a46c5a9da8c05ffdec4c2ef2dd906dd94c009d6fa451af4ed350e9", + "WORDS.json": "c74b8446503425fb4964921e8651b3931f917c62a21565d9569e9f6399ea571b" + }, + "stage_layouts": [ + { + "active": [ + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 7 + ], + "ordinal": 0, + "spectator_count": 119, + "stage": 0 + }, + { + "active": [ + 0, + 8, + 9, + 10, + 11, + 12, + 13, + 14 + ], + "ordinal": 1, + "spectator_count": 119, + "stage": 1 + }, + { + "active": [ + 0, + 15, + 16, + 17, + 18, + 19, + 20, + 21 + ], + "ordinal": 2, + "spectator_count": 119, + "stage": 3 + }, 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"spectator_count": 119, + "stage": 19 + }, + { + "active": [ + 0, + 78, + 79, + 80, + 81, + 82, + 83, + 84 + ], + "ordinal": 11, + "spectator_count": 119, + "stage": 21 + }, + { + "active": [ + 0, + 85, + 86, + 87, + 88, + 89, + 90, + 91 + ], + "ordinal": 12, + "spectator_count": 119, + "stage": 23 + }, + { + "active": [ + 0, + 92, + 93, + 94, + 95, + 96, + 97, + 98 + ], + "ordinal": 13, + "spectator_count": 119, + "stage": 25 + }, + { + "active": [ + 0, + 99, + 100, + 101, + 102, + 103, + 104, + 105 + ], + "ordinal": 14, + "spectator_count": 119, + "stage": 27 + }, + { + "active": [ + 0, + 106, + 107, + 108, + 109, + 110, + 111, + 112 + ], + "ordinal": 15, + "spectator_count": 119, + "stage": 29 + }, + { + "active": [ + 0, + 113, + 114, + 115, + 116, + 117, + 118, + 119 + ], + "ordinal": 16, + "spectator_count": 119, + "stage": 31 + }, + { + "active": [ + 0, + 120, + 121, + 122, + 123, + 124, + 125, + 126 + ], + "ordinal": 17, + "spectator_count": 119, + "stage": 32 + } + ], + "stage_phase_counts": [ + { + "count": 222, + "phase": "ENTRY", + "stage": 1 + }, + { + "count": 222, + "phase": "RETURN", + "stage": 1 + }, + { + "count": 222, + "phase": "ENTRY", + "stage": 3 + }, + { + "count": 222, + "phase": "RETURN", + "stage": 3 + }, + { + "count": 222, + "phase": "ENTRY", + "stage": 5 + }, + { + "count": 222, + "phase": "RETURN", + "stage": 5 + }, + { + "count": 222, + "phase": "ENTRY", + "stage": 7 + }, + { + "count": 222, + "phase": "RETURN", + "stage": 7 + }, + { + "count": 222, + "phase": "ENTRY", + "stage": 9 + }, + { + "count": 222, + "phase": "RETURN", + "stage": 9 + }, + { + "count": 222, + "phase": "ENTRY", + "stage": 11 + }, + { + "count": 222, + "phase": "RETURN", + "stage": 11 + }, + { + "count": 222, + "phase": "ENTRY", + "stage": 13 + }, + { + "count": 222, + "phase": "RETURN", + "stage": 13 + }, + { + "count": 222, + "phase": "ENTRY", + "stage": 15 + }, + { + "count": 222, + "phase": "RETURN", + "stage": 15 + }, + { + "count": 222, + "phase": "ENTRY", + "stage": 17 + }, + { + "count": 222, + "phase": "RETURN", + "stage": 17 + }, + { + "count": 222, + "phase": "ENTRY", + "stage": 19 + }, + { + "count": 222, + "phase": "RETURN", + "stage": 19 + }, + { + "count": 222, + "phase": "ENTRY", + "stage": 21 + }, + { + "count": 222, + "phase": "RETURN", + "stage": 21 + }, + { + "count": 222, + "phase": "ENTRY", + "stage": 23 + }, + { + "count": 222, + "phase": "RETURN", + "stage": 23 + }, + { + "count": 222, + "phase": "ENTRY", + "stage": 25 + }, + { + "count": 222, + "phase": "RETURN", + "stage": 25 + }, + { + "count": 222, + "phase": "ENTRY", + "stage": 27 + }, + { + "count": 222, + "phase": "RETURN", + "stage": 27 + }, + { + "count": 222, + "phase": "ENTRY", + "stage": 29 + }, + { + "count": 222, + "phase": "RETURN", + "stage": 29 + }, + { + "count": 222, + "phase": "ENTRY", + "stage": 31 + }, + { + "count": 222, + "phase": "RETURN", + "stage": 31 + }, + { + "count": 222, + "phase": "ENTRY", + "stage": 32 + }, + { + "count": 222, + "phase": "RETURN", + "stage": 32 + } + ], + "status": "PASS_G20_ROUTE_WORD_BINDING_ORACLE", + "word_products": 222 +} diff --git a/research/g20-route-word-binding/PROOF.md b/research/g20-route-word-binding/PROOF.md new file mode 100644 index 0000000000..9dbbe42fde --- /dev/null +++ b/research/g20-route-word-binding/PROOF.md @@ -0,0 +1,137 @@ +# Route-marker binding under one declared ROW-cover model + +This joins the exact G20 route records from Ali Romman's PR #5798 at +`eaa9cc8c15d8e994d7b81b0cda3f6dd63b0db826` to the frozen RIGHT words of the +preceding `g20-normalizer-dyadic-words` package. The source already supplies +the complete endpoint/marker audit and its full finite bill. The new statement +is a marker-to-word join with an explicit conditional direction convention. +It neither recertifies the whole source nor identifies a physical marker ABI. + +## Three actions that must be kept distinct + +For one port write `Q=diag(1,0,...,0)` and let W and W^-1 be the authenticated +eight-dimensional normalizers. The inherited native interface gives +`P = W Q W^-1`. The preceding package's words have exact RIGHT products W +and W^-1; ADD[i,j,a] updates row coordinate j from coordinate i. In particular, +executing such a word on a cover row v means vW or vW^-1, respectively. + +The identities here are rational. Dyadic words also remain invertible over +odd-modulus local rings under the admitted unit-P2 contracts, because their +scalings are signed powers of two. This does not widen native admissibility: +the inherited native theorem retains its sufficient guard `gcd(q,12)=1`, +its own modulus/prime hypotheses and all framework assumptions. Matrix algebra +alone supplies neither admission for every odd composite nor physical tariffs. + +Native address operators instead act on column vectors. For a physical +16-coordinate address x define `d_i=x_i-x_(15-i)`, i=0,...,7. The source map +H_P is + +``` +x_i <- x_i - (P d)_i, +x_(15-i) <- x_(15-i) + (P d)_i. +``` + +In the paired ordering `(x_0,...,x_7; x_15,...,x_8)` its matrix is +`[[I-P,P],[P,I-P]]`. Let J reverse eight coordinates. Applying W to both +paired halves is `diag(W,W)` in that paired ordering, and therefore + +``` +D_W = diag(W, J W J) +``` + +in the physical contiguous ordering `(x_0,...,x_15)`. From `P W = W Q`, block +multiplication gives `H_P D_W = D_W H_Q`, hence +`D_W^-1 H_P D_W = H_Q`. These are identities of native column-address maps. +For function transport `T_M F(x)=F(M^-1 x)`, the corresponding pullback rule +is `T_M T_N=T_(MN)`; it must not be silently read as row-word execution. + +## Conditional ROW direction and restoration + +The chosen ROW-cover model is the retained row-route convention: a single +invertible cover matrix g is updated on the right to `h=gS`; an available +local projector P then acts globally with projector `h P h^-1` and returns +the complete cover h and exposed spectators unchanged. This restoration is +an inherited native/ROW contract, not a consequence of matrix conjugacy. +Desired global projector Q therefore requires + +``` +S = W^-1, +h P h^-1 = g W^-1 (W Q W^-1) W g^-1 = g Q g^-1. +``` + +Under this declared model, an ENTRY marker selects the frozen inverse_word, +and a RETURN marker selects forward_word. The returning cover is exactly +`g W^-1 W = g`, on arbitrary cover entries. Neither word is transposed or +silently reversed: each is executed in its certified RIGHT chronological +order. A return word is the literal reverse-and-inverse of its entry word. + +The stage embedding and tensor lanes preserve this identity. Use the selected +eight active indices for that thick-stage ordinal, extend W by identity on +the other 119 ambient coordinates, and tensor with I_f for f>=1. For N=127f, +each factor is applied to all N cover rows and f lanes at its certified +source/destination addresses. Thus all inactive cover coordinates remain +unchanged, and the inverse pair restores the full chosen cover. + +This is **one** GL-cover word for one owner-marker. The global projector +`g Q g^-1` already determines both native paired halves through the formula +for H above. Executing two independent words on two physical address halves +would be a different lowering. It is not an additional factor of two in this +single-cover model. Distinct owner banks in the stream remain distinct routes. + +## Discriminating exact source examples + +Port 2 has W equal to twice the permutation with +`e_0 -> e_2 -> e_1 -> e_0`. Hence `P=e_2 e_2^T`. Using forward_word at ENTRY +would give `W P W^-1=e_1 e_1^T`, whereas the correct inverse entry gives Q. +This separates the two direction choices on actual source data. + +Port 1 has W equal to twice the swap of coordinates 0 and 1. Its P selects +coordinate 1. The correct physical D_W maps both paired coordinates together. +The naive contiguous `diag(W,W)` instead gives +`D_naive^-1 H_P D_naive e_0 = e_14`, while `H_Q e_0=e_15`. +Thus omitting the reflected second-half ordering is a real operator error, +even though the isolated eight-dimensional W product remains correct. + +## Exact incidence versus assumed execution semantics + +Each authenticated route record contains stage, physical owner, port and +ENTRY/RETURN phase. The finite join must check its complete source position +against CALLS, including the appropriate source/target bank, every port, +phase block, and the absence of paid route markers at stage zero. A program +identifier must bind the actual frozen word and its certified port matrix, +not merely agree with an aggregate count or an unrelated catalogue index. + +The retained nonzero stages contribute `17*2 banks*111 ports*2 phases=7,548` +markers. Under the single-cover interpretation above this is 7,548 selected +word instances, with 3,774 in each direction. The marker fields themselves +do not encode right-multiplication, a physical head map or this ENTRY ABI. +Accordingly the incidence join can be exact while the direction-to-physical- +execution implication remains explicitly conditional. + +A coefficient histogram must be rebuilt from the selected actual words. +For each selected word every local ADD or SCALE produces `N*f=127*f^2` +named cover-kernel calls. Each port uses both words in two banks over 17 +nonzero stages, so a histogram already combining both directions is multiplied +by `34*N*f`, without a second paired-half multiplier. The preceding 7,992 +catalogue cross-product instances are a different inventory. Their operation +counts are not an already admitted budget for these source markers. + +The coefficient counts can form a positive symbolic tariff expression under +the named primitive contracts. Actual P2 tape movement, coefficient preparation, +head placement, complete low-cache COPY/CLEAR, carry correction, low-type +commit, padding, return workspace and their prices remain unknown. Unknown +costs are not zero. No absorption into the source's finite fee, new kappa, +ordinary compiler, native admission or selected-frontier change follows. + +The inherited all-address native identities and full caller audit remain +authenticated dependencies. This conditional join does not replace them or +establish that the physical PAID_PORT_ROUTE implementation follows the chosen +single-cover model. + +Credit: Ali Romman and retained G20/native/controller contributors for the +source data and paired-address interface; ToikY with OpenAI Codex assistance +for the preceding RIGHT factor words; JoyboyBrian and Chris R/Clear1nsight +for the retained ROW/P2 interface and its explicit implementation obligations. +This scoped proof/audit was prepared by ToikY with substantial OpenAI Codex +assistance in separate primary, oracle and review contexts. Retain NOTICE and +all predecessor credit. Apache-2.0. diff --git a/research/g20-route-word-binding/README.md b/research/g20-route-word-binding/README.md new file mode 100644 index 0000000000..ba3814a073 --- /dev/null +++ b/research/g20-route-word-binding/README.md @@ -0,0 +1,37 @@ +# Exact G20 route-marker to normalizer-word binding + +This fills the specific incidence and direction gap left by [PR #5801](https://github.com/CrocSwap/integer-mult-bounds/pull/5801). It binds the actual PAID_PORT_ROUTE records from Ali Romman's [PR #5798](https://github.com/CrocSwap/integer-mult-bounds/pull/5798), head eaa9cc8c15d8e994d7b81b0cda3f6dd63b0db826, to the frozen RIGHT words at eb92cbdf211f0c3717ff6fa71af47ec38f8e412d. The source audit already establishes the complete global endpoint, marker placements and retained fee. Those are predecessor results, not new claims here. [Canonical claim](https://github.com/CrocSwap/integer-mult-bounds/discussions/5777#discussioncomment-19205398). + +The stream markers identify stage, owner, port and phase. They do not supply a physical lowering or specify a word direction. This certificate gives an explicit **conditional single-ROW-cover plan**: with local projector P=WQW^-1 and native cut h=gS, choose ENTRY S=W^-1 and RETURN W. Then hPh^-1=gQg^-1 and the borrowed cover returns to g. This is a model-qualified interpretation, not a newly decoded instruction hidden in the source marker. + +Native address halves are a different notion from owner banks. The native pairing is x_i with x_(15-i). In physical contiguous order, applying W to both paired halves is diag(W,JWJ), with J the eight-coordinate reversal. It is generally not diag(W,W). The proof and independent oracle distinguish this column-address conjugation, function pullback and ROW right update. One cover-matrix word changes both native halves through the cover encoding; a second full ROW word per native half is not charged by this declared model. + +## Exact evidence and scope + +The actual stream contains **7,548** route markers, each bound to one word under this cover plan: 3,774 in each direction. RESULT.json retains every event/call/stage/owner/port/phase/program binding and coefficient ledger. The selected words total **202,640 ADDs and 73,916 SCALEs**. Lifting their factors gives **25,735,280 ordered_shift and 9,387,332 unit_scale calls times f^2**, without another native-half factor. Seven recomputed controls reject missing markers, owner/phase/direction/program/stage misbinding and source drift. ORACLE.json independently scans the source stream, checks the join and tests the exact cover and paired-address identities. The independent checks include 222 word products, 111 cover conjugations, 1,776 literal paired basis columns and all 18 ordinal layouts. Two further controls preserve aggregate counts while breaking actual bank restoration. Neither checker imports the other or a predecessor implementation. + +Only nonzero thick stages have internal route markers. Stage embedding uses the actual thick-stage ordinal in the 18-stage inventory, central coordinate 0 and its seven-coordinate block in dimension 127. This is the same chosen compatible layout as #5801; a retained literal physical head map is still unproved. + +Positive coefficient counts describe the declared single-cover plan. For N=127f they lift every factor across all N cover-matrix rows and f lanes. Each coefficient retains a named positive ordered_shift or unit_scale tariff, potentially dependent on radix, width and tape parameters. These symbolic counts are not a unit-cost model, a complete route invoice or absorption into the source's finite fee. + +This package does not rerun or newly admit the full native/global caller. Its physical head map, old-low cache COPY/CLEAR, carries, low-type commit, padding, movement, restoration schedule, primitive implementation and tariffs remain open. Compiler, stock, precision/tape, analytic recovery and all five inherited framework assumptions remain. No new kappa, selected-frontier change or full multiplication theorem follows. + +## Reproduction + +Python 3.12 and the standard library suffice: + +```sh +python3.12 -B scripts/research_package.py --package research/g20-route-word-binding +``` + +The registered commands run normal/optimized primary checks and the separate optimized oracle. Frozen package-local inputs authenticate by raw SHA256 and Git blob identity. Default runs compare complete canonical JSON receipts, preserving numeric-type distinctions. Explicit --emit generates a candidate on stdout and never rewrites a receipt. Injected faults are controls, not allegations about predecessor code. + +SOURCES.json separates main-context provenance from vendored unmerged input origins. Committed-byte/source-history checks cover the declared main ancestry; raw source bindings do not claim those input heads are publication ancestors. Official export and read-only Git-free empty-PATH replay are separate integrity checks, not scientific acceptance. TASK.json records the changed formal-interface-lemma scope. No Lean build or native replay ran. + +## Open next questions + +Bind this conditional cover plan to the retained literal physical route and price all caches, carries, low-type commit, padding, movement and return. The source markers alone cannot choose among physical lowering models. Prove that missing ABI and coefficient-specific tariffs before importing the counts into the source's full caller invoice. The structured next question and blocker are recorded in TASK.json. + +## Credit + +Ali Romman with substantial Codex assistance supplied the G20 construction/audits and rational normalizer witnesses; retain Dugongue, ai-nanachi, PR #5679/#5708/#5782 and all source credits. JoyboyBrian supplied the earlier ROW generator and named P2 schedule, with its retained predecessors. PR #5801's ToikY/Codex operation words are frozen predecessor work in this package. The new contribution is the exact marker-to-word binding, explicit conditional cover convention and independent reflected-address audit, by ToikY with substantial OpenAI Codex assistance using separate primary/oracle/proof-review contexts. Classical conjugation is not claimed as a new general theorem. Apache-2.0; full attribution is in NOTICE. diff --git a/research/g20-route-word-binding/RESULT.json b/research/g20-route-word-binding/RESULT.json new file mode 100644 index 0000000000..7d83c80328 --- /dev/null +++ b/research/g20-route-word-binding/RESULT.json @@ -0,0 +1,93907 @@ +{ + "RIGHT_word_convention": "RIGHT product E1...Em=W; ADD[i,j,a]=I+a*e_i*e_j^T; row[j]+=a*row[i]", + "bank_phase_counts": [ + [ + 0, + "ENTRY", + 111 + ], + [ + 0, + "RETURN", + 111 + ], + [ + 1, + "ENTRY", + 111 + ], + [ + 1, + "RETURN", + 111 + ], + [ + 2, + "ENTRY", + 111 + ], + [ + 2, + "RETURN", + 111 + ], + [ + 3, + "ENTRY", + 111 + ], + [ + 3, + "RETURN", + 111 + ], + [ + 4, + "ENTRY", + 111 + ], + [ + 4, + "RETURN", + 111 + ], + [ + 5, + "ENTRY", + 111 + ], + [ + 5, + "RETURN", + 111 + ], + [ + 6, + "ENTRY", + 111 + ], + [ + 6, + "RETURN", + 111 + ], + [ + 7, + "ENTRY", + 111 + ], + [ + 7, + "RETURN", + 111 + ], + [ + 8, + "ENTRY", + 111 + ], + [ + 8, + "RETURN", + 111 + ], + [ + 9, + "ENTRY", + 111 + 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111 + ], + [ + 25, + "ENTRY", + 111 + ], + [ + 25, + "RETURN", + 111 + ], + [ + 26, + "ENTRY", + 111 + ], + [ + 26, + "RETURN", + 111 + ], + [ + 27, + "ENTRY", + 111 + ], + [ + 27, + "RETURN", + 111 + ], + [ + 28, + "ENTRY", + 111 + ], + [ + 28, + "RETURN", + 111 + ], + [ + 29, + "ENTRY", + 111 + ], + [ + 29, + "RETURN", + 111 + ], + [ + 30, + "ENTRY", + 222 + ], + [ + 30, + "RETURN", + 222 + ], + [ + 31, + "ENTRY", + 222 + ], + [ + 31, + "RETURN", + 222 + ] + ], + "coefficient_histogram": { + "ADD": { + "-1": 78540, + "-1/2": 12444, + "-2": 6392, + "-3": 3366, + "-3/2": 476, + "-4": 102, + "1": 78540, + "1/2": 12444, + "2": 6392, + "3": 3366, + "3/2": 476, + "4": 102 + }, + "SCALE": { + "-1": 32776, + "-1/2": 510, + "-1/4": 1564, + "-2": 510, + "-4": 1564, + "1/2": 16626, + "1/4": 1870, + "2": 16626, + "4": 1870 + } + }, + "conditional_coefficient_bill": "For each observed word coefficient a, count[a]*(127*f)*f*C_kind(a); no physical leaf tariff is asserted", + 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"docs/research/research-family-status.md", + "certificates/selected-result.json", + "research/gate-operand-parity-lean/README.md", + "research/staged544-certified-endpoint/README.md", + "research/unconditional-batched-crt/README.md" + ], + "methods": [ + "Formalize a missing boundary lemma identified by the selected review.", + "Audit a formal theorem-to-certificate binding independently." + ], + "acceptance_gate": "State the exact formalized proposition and remaining assumptions; avoid duplicate arithmetic formalizations already present.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_selected_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Resolve the current selected review, separate complex/ordinary BIT/admitted BIT/outer budgets, and compare the card against live handoffs before starting. Historical ceilings require exact source/model equivalence.", + "scope": "Source-binding orientation only; not a scientific replay or all-size proof. Materialize selected inputs if this checkout is sparse." + }, + "first_experiment": "Write one missing statement with quantified hypotheses, actual caller and existing coverage. A compact-switch lemma is a candidate only after its mathematical contract is reviewed. Establish a bounded proof plan before a separately budgeted proof-assistant build; do not rerun large Lean jobs as orientation.", + "bottleneck_link": "A missing interface proof can reduce the conditional gap even if it does not change kappa.", + "allowed_variations": [ + "Narrow to one formal lemma or one theorem-to-certificate binding." + ], + "scope_change_triggers": [ + "Formalizing already-covered arithmetic and claiming the full multiplication theorem." + ], + "overlap_terms": [ + "hyperplane end", + "formal interface", + "Lean binding", + "3807", + "3857", + "4100", + "gate-operand-parity-lean", + "staged544-certified-endpoint", + "unconditional-batched-crt" + ], + "existing_checks": [ + { + "scope": "PR #3807: scoped gate-operand parity formalization.", + "evidence": "research/gate-operand-parity-lean/README.md", + "remaining": "Exact theorem-to-caller binding and genuinely uncovered interface lemmas.", + "status": "author-checked", + "source_commit": "4c3530f42a6abcc48e7a6bcffd6c901911dc8269", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #3857: certified real-power moment/endpoint arithmetic.", + "evidence": "research/staged544-certified-endpoint/README.md", + "remaining": "Uniform algorithmic implications, not another endpoint digit.", + "status": "author-checked", + "source_commit": "ef4315b8caa605e47a2515004845eb2d2ed71a86", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "scope": "PR #4100: compact-switch formalization proposed as future validation.", + "evidence": "research/unconditional-batched-crt/README.md", + "remaining": "Audit the statement and assumptions before a formal proof campaign.", + "status": "author-checked", + "source_commit": "337d04939571a637aeab54a0f58f54fde811663a", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + } + ] + }, + "scope_status": "changed", + "actual_scope": "Bind actual G20 route markers to frozen RIGHT normalizer words under a declared single-ROW-cover model, with exact phase/owner/direction and paired reflection identities.", + "scope_change_reason": "The released PR5801 catalogue explicitly leaves actual source incidence and retained cover direction open; audit this particular binding gap rather than expanding physical implementation.", + "bottleneck_link": "Closes a specific catalogue-to-source incidence/direction gap; a conditional plan cannot stand in for physical ROW/tape realization.", + "budget_minutes": 60, + "stop_rule": "Freeze by22:40UTC; narrow to a documented binding obstruction if the exact source schema or declared cover convention cannot be justified. No physical tape tariff or new kappa claim.", + "outcome": "completed", + "evidence": "RESULT:7548 exact event bindings,202640 ADD and73916 SCALE factors, conditional f1P2counts25735280/9387332;7recomputed semantic/source controls. Independent oracle and frozen transport verification recorded separately. Independent oracle:222wordproducts,111coverconjugations,1776pairedcolumns,18layouts; five algebraic/owner/restoration controls. BotheventjoinSHA91383314869a40a96ced928dc857b9f32ac02b11eb7cb45853b1092d10291eb0.", + "author": "ToikY", + "ai_assistance": "Substantial OpenAI Codex assistance, separate primary/oracle/proof-review contexts.", + "open_questions": [ + { + "question": "Can this conditional single-cover plan be bound to the retained literal physical ROW route and fully priced?", + "why_it_matters": "Markers do not identify physical lowering, and named operation counts do not discharge cache/carry/type-commit/padding/tape costs.", + "first_step": "Bind one owner-marker to the actual ROW head map, preserve borrowed g and spectators, then price every cache, carry, low-type commit, padding and return.", + "blocked_by": "Physical primitive/head-map ABI and tariffs remain unproved." + } + ], + "started_at": "2026-10-26T21:55:17.606266+00:00", + "science_cutoff": "2026-10-26T22:40:17.606266+00:00", + "finish_by": "2026-10-26T22:55:17.606266+00:00", + "source_head": "eaa9cc8c15d8e994d7b81b0cda3f6dd63b0db826", + "claim_expires": "2026-10-26T23:20:00Z" +} diff --git a/research/g20-route-word-binding/VERIFY.json b/research/g20-route-word-binding/VERIFY.json new file mode 100644 index 0000000000..35a551578d --- /dev/null +++ b/research/g20-route-word-binding/VERIFY.json @@ -0,0 +1,47 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [], + "commands": [ + { + "argv": [ + "{python}", + "-I", + "-W", + "error", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 120, + "checks": "Exact source marker-to-word binding and conditional cover-model ledger with explicit semantic controls and strict canonical receipt." + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-W", + "error", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 120, + "checks": "Exact source marker-to-word binding and conditional cover-model ledger with explicit semantic controls and strict canonical receipt." + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-W", + "error", + "-B", + "{package}/oracle.py" + ], + "timeout_seconds": 120, + "checks": "Independent event join, cover roundtrip and physical reflected-pair identities; strict canonical oracle receipt." + } + ] +} diff --git a/research/g20-route-word-binding/oracle.py b/research/g20-route-word-binding/oracle.py new file mode 100644 index 0000000000..a1c150efc1 --- /dev/null +++ b/research/g20-route-word-binding/oracle.py @@ -0,0 +1,368 @@ +#!/usr/bin/env python3 +"""Independent join and paired-address oracle for the actual G20 route markers. + +ToikY with substantial OpenAI Codex assistance in a separate implementation +context. Ali Romman supplied the frozen global caller and port witnesses; +the frozen ToikY dyadic words are predecessor data. Apache-2.0. Retain NOTICE. +No primary verifier, predecessor implementation or mutable result is imported. +""" +import argparse +from collections import Counter +from fractions import Fraction as F +from hashlib import sha1, sha256 +import gzip +import json +from pathlib import Path + + +HERE = Path(__file__).resolve().parent +PINS = { + "GLOBAL.jsonl.gz": (1895549, + "86e7ce6aff05409410ef4bbc00ff1b29b8c1606383549c7e15242b327e39c235", + "2290f206fe550af3738ab1219bb127bc09c65bbb"), + "PORTS.json": (311085, + "a53a49c938a46c5a9da8c05ffdec4c2ef2dd906dd94c009d6fa451af4ed350e9", + "aeffcdb444f564d247aff2265f9aebc424bce14f"), + "CALLS.json": (18903, + "30dcc37cdade6b2dc05478837eca28b696894d1c4782bac6a1caab5e7f56c9e8", + "9ee8c26f321ee3d420976fab69075c0c05db12ce"), + "CONTROLLER.json": (23753, + "39ac84fb848b908f7ba051fae4556d507900c421dc5d23501a9c0cb1d61fd08d", + "89c400d5970024b3debe870c36ce43889beed001"), + "WORDS.json": (640895, + "c74b8446503425fb4964921e8651b3931f917c62a21565d9569e9f6399ea571b", + "c3466c486097794afcdaba7ad3b3a26f517fb09c"), +} + + +def need(condition, message): + if not condition: + raise ValueError(message) + + +def canonical(value): + return json.dumps(value, sort_keys=True, separators=(",", ":"), + allow_nan=False).encode() + + +def digest(value): + return sha256(canonical(value)).hexdigest() + + +def source(name): + raw = (HERE / "source" / name).read_bytes() + size, checksum, blob = PINS[name] + need(len(raw) == size and sha256(raw).hexdigest() == checksum, + "Oracle exact raw source: " + name) + need(sha1(b"blob " + str(len(raw)).encode() + b"\0" + raw).hexdigest() == blob, + "Oracle exact source Git blob: " + name) + if name.endswith(".gz"): + return [json.loads(line) for line in gzip.decompress(raw).splitlines()] + return json.loads(raw) + + +def eye(n=8): + return [[F(i == j) for j in range(n)] for i in range(n)] + + +def multiply(a, b): + n = len(a) + return [[sum((a[i][k] * b[k][j] for k in range(n) + if a[i][k] and b[k][j]), F(0)) + for j in range(n)] for i in range(n)] + + +def apply(matrix, vector): + return [sum((a * x for a, x in zip(row, vector)), F(0)) for row in matrix] + + +def p2_event(event): + need(type(event) is list and event and event[0] in ("ADD", "SCALE"), + "Oracle explicit P2 factor opcode") + kind = event[0] + need(len(event) == (4 if kind == "ADD" else 3), "Oracle factor arity") + positions = event[1:3] if kind == "ADD" else event[1:2] + need(all(type(i) is int and 0 <= i < 8 for i in positions), + "Oracle factor coordinate") + need(type(event[-1]) is str, "Oracle exact rational coefficient") + q = F(event[-1]) + need(q and str(q) == event[-1] and q.denominator & (q.denominator - 1) == 0, + "Oracle dyadic factor coefficient") + if kind == "ADD": + need(positions[0] != positions[1], "Oracle distinct ADD coordinates") + return kind, positions[0], positions[1], q + n = abs(q.numerator) + need(n & (n - 1) == 0, "Oracle dyadic unit scale") + return kind, positions[0], positions[0], q + + +def word_matrix(word): + result = eye() + for event in word: + kind, i, j, q = p2_event(event) + elementary = eye() + elementary[i][j] = q + result = multiply(result, elementary) + return result + + +def paired_basis(matrix, vector, mode="reflected"): + first = apply(matrix, vector[:8]) + if mode == "omit_second": + return first + vector[8:] + if mode == "unreflected": + return first + apply(matrix, vector[8:]) + return first + list(reversed(apply(matrix, list(reversed(vector[8:]))))) + + +def native(projector, vector): + differences = [vector[i] - vector[15 - i] for i in range(8)] + correction = apply(projector, differences) + output = vector[:] + for i in range(8): + output[i] -= correction[i] + output[15 - i] += correction[i] + return output + + +def compact(vector): + return {str(i): str(x) for i, x in enumerate(vector) if x} + + +def algebra(ports, words): + q = [[F(i == j == 0) for j in range(8)] for i in range(8)] + failures = {} + histograms = {} + word_hashes = {} + need([p["port"] for p in ports] == [p["port"] for p in words] == list(range(111)), + "Oracle exact port inventory") + for port, witness in zip(ports, words): + w = [[F(x) for x in row] for row in port["normalizer"]] + wi = [[F(x) for x in row] for row in port["inverse"]] + need(word_matrix(witness["forward_word"]) == w + and word_matrix(witness["inverse_word"]) == wi, + "Oracle frozen word to actual port matrix") + need(multiply(w, wi) == eye() == multiply(wi, w), "Oracle both port inverses") + # Reconstruct the orthogonal line projector directly from the literal + # first source column, independently of W Q W^-1. + line = [row[0] for row in w] + norm = sum((x * x for x in line), F(0)) + need(norm > 0, "Oracle nonzero actual source line") + projector = [[x * y / norm for y in line] for x in line] + need(all(sum((line[i] * w[i][j] for i in range(8)), F(0)) == 0 + for j in range(1, 8)), "Oracle literal source complement orthogonality") + need(multiply(projector, w) == multiply(w, q), + "Oracle actual line/complement normalizer") + need(multiply(multiply(wi, projector), w) == q, + "Oracle cover ENTRY inverse, RETURN forward") + if "wrong_cover_direction" not in failures: + changed = multiply(multiply(w, projector), wi) + if changed != q: + axis = next(j for j in range(8) + if any(changed[i][j] != q[i][j] for i in range(8))) + failures["wrong_cover_direction"] = { + "port": port["port"], "axis": axis, + "expected": compact([q[i][axis] for i in range(8)]), + "actual": compact([changed[i][axis] for i in range(8)])} + for direction in ("forward", "inverse"): + word = witness[direction + "_word"] + word_hashes[(port["port"], direction)] = digest(word) + histograms[(port["port"], direction)] = Counter( + (p2_event(event)[0], str(p2_event(event)[3])) for event in word) + for axis in range(16): + x = [F(i == axis) for i in range(16)] + expected = native(q, x) + actual = paired_basis(wi, native(projector, paired_basis(w, x))) + need(actual == expected, "Oracle every literal paired address basis column") + for bad in ("unreflected", "omit_second"): + if bad not in failures: + changed = paired_basis(wi, native(projector, + paired_basis(w, x, bad)), bad) + if changed != expected: + failures[bad] = {"port": port["port"], "axis": axis, + "expected": compact(expected), + "actual": compact(changed)} + need(set(failures) == {"unreflected", "omit_second", "wrong_cover_direction"}, + "Oracle discriminating actual-port direction/reflection/half controls") + return histograms, word_hashes, failures + + +def layouts_for(stages, words): + layouts = [] + for ordinal, stage in enumerate(stages): + active = [0] + list(range(1 + 7 * ordinal, 8 + 7 * ordinal)) + actual = words["placements"][ordinal] + need(actual == {"active_indices": active, "ordinal": ordinal, "stage": stage}, + "Oracle chosen layout binds stage ordinal, not raw stage ID") + spectators = set(range(127)) - set(active) + need(len(set(active)) == 8 and len(spectators) == 119, + "Oracle all inactive stage coordinates") + for f in (1, 2): + lifted = {c * f + lane for c in active for lane in range(f)} + need(len(lifted) == 8 * f + and len(set(range(127 * f)) - lifted) == 119 * f, + "Oracle tensor lanes and spectator completeness") + layouts.append({"stage": stage, "ordinal": ordinal, "active": active, + "spectator_count": len(spectators)}) + need(len(words["placements"]) == len(stages), "Oracle no additional layout") + return layouts + + +def cover_controls(join, calls, ports, words): + # Choose the two distinct actual owner banks for stage1/port0. Reassign one + # ENTRY to the other bank while retaining all four words and every count. + call_index = 1 + banks = [calls[call_index]["source_bank"], calls[call_index]["target_bank"]] + need(len(set(banks)) == 2, "Oracle distinct actual owner banks") + rows = [row for row in join if row[1] == call_index and row[4] == 0] + need(len(rows) == 4, "Oracle concrete four-marker control scope") + w = [[F(x) for x in row] for row in ports[0]["normalizer"]] + wi = [[F(x) for x in row] for row in ports[0]["inverse"]] + matrices = {"forward": w, "inverse": wi} + + def endpoint(reassign=False, wrong_return=False): + covers = {bank: eye() for bank in banks} + assignments = [] + for row in rows: + bank, direction = row[3] // 111, row[6] + if reassign and row[5] == "ENTRY" and bank == banks[1]: + bank = banks[0] + if wrong_return and row[5] == "RETURN" and bank == banks[1]: + direction = "inverse" + covers[bank] = multiply(covers[bank], matrices[direction]) + assignments.append((bank, direction)) + return covers, assignments + + good, good_assignments = endpoint() + bad, bad_assignments = endpoint(reassign=True) + phase, phase_assignments = endpoint(wrong_return=True) + need(all(matrix == eye() for matrix in good.values()), + "Oracle actual two-bank cover restoration") + need(Counter(direction for bank, direction in good_assignments) + == Counter(direction for bank, direction in bad_assignments), + "Oracle owner control retains every word/coefficient multiplicity") + need(any(matrix != eye() for matrix in bad.values()), + "Oracle duplicate-bank control fails actual cover restoration") + lengths = {direction: len(words[0][direction + "_word"]) + for direction in ("forward", "inverse")} + need(sum(lengths[d] for b, d in good_assignments) + == sum(lengths[d] for b, d in phase_assignments), + "Oracle phase control retains total elementary call count") + need(any(matrix != eye() for matrix in phase.values()), + "Oracle wrong RETURN control fails actual cover restoration") + return { + "duplicate_bank_same_coefficient_counts": { + "call_index": call_index, "stage": calls[call_index]["stage"], + "port": 0, "source_events": [row[0] for row in rows], + "banks": banks, "marker_count": 4, + "same_word_and_coefficient_histogram": True, + "actual_cover_diagonals": {str(bank): [str(bad[bank][i][i]) + for i in range(8)] for bank in banks}}, + "wrong_return_same_factor_count": { + "call_index": call_index, "port": 0, "marker_count": 4, + "elementary_call_count": sum(lengths[d] for b, d in good_assignments), + "actual_cover_diagonals": {str(bank): [str(phase[bank][i][i]) + for i in range(8)] for bank in banks}}, + } + + +def run(): + events, ports, calls, controller, words = (source(name) for name in PINS) + need(len(events) == 317004 and len(calls) == 18, "Oracle exact stream and calls") + stages = controller["invoice"]["thick_stages"] + need(controller["ambient_rank"] == 127 + and [call["stage"] for call in calls] == stages + and len(set(stages)) == 18 and stages[0] == 0, + "Oracle actual thick-stage order") + layouts = layouts_for(stages, words) + histograms, word_hashes, controls = algebra(ports["port_interfaces"]["ports"], + words["ports"]) + by_stage = {call["stage"]: (i, call) for i, call in enumerate(calls)} + join, seen, counts = [], set(), Counter() + stage_phase, bank_phase = Counter(), Counter() + for event_index, event in enumerate(events): + if event[0] != "PAID_PORT_ROUTE": + continue + need(len(event) == 5, "Oracle actual route arity") + _, stage, owner, port, phase = event + need(type(stage) is int and stage in by_stage and stage != 0 + and phase in ("ENTRY", "RETURN"), + "Oracle actual route stage and phase") + call_index, call = by_stage[stage] + need(type(owner) is int and type(port) is int and 0 <= port < 111, + "Oracle actual route owner and port") + bank, residue = divmod(owner, 111) + need(residue == port and bank in (call["source_bank"], call["target_bank"]), + "Oracle source-call owner/port join") + start = call["core_begin"] - 222 if phase == "ENTRY" else call["core_end"] + need(start <= event_index < start + 222, "Oracle route call-boundary interval") + key = (call_index, bank, port, phase) + need(key not in seen, "Oracle unique actual route incidence") + seen.add(key) + direction = "inverse" if phase == "ENTRY" else "forward" + word_hash = word_hashes[(port, direction)] + join.append([event_index, call_index, stage, owner, port, phase, + direction, word_hash]) + counts.update(histograms[(port, direction)]) + stage_phase[(stage, phase)] += 1 + bank_phase[(bank, phase)] += 1 + wanted = {(i, bank, port, phase) + for i, call in enumerate(calls) if call["stage"] != 0 + for bank in (call["source_bank"], call["target_bank"]) + for port in range(111) for phase in ("ENTRY", "RETURN")} + need(seen == wanted and len(join) == 7548, "Oracle every actual route exactly once") + controls.update(cover_controls(join, calls, ports["port_interfaces"]["ports"], + words["ports"])) + named = [] + for f in (1, 2): + n = 127 * f + named.append({"f": f, "N": n, + "coefficient_counts": [{"primitive": "ordered_shift" if kind == "ADD" + else "unit_scale", "coefficient": value, + "count": count * n * f} + for (kind, value), count in sorted(counts.items())]}) + return { + "status": "PASS_G20_ROUTE_WORD_BINDING_ORACLE", + "source_sha256": {name: row[1] for name, row in PINS.items()}, + "event_count": len(events), "route_count": len(join), + "event_join_columns": ["event_index", "call_index", "stage", "owner", "port", + "phase", "direction", "word_sha256"], + "event_join_sha256": digest(join), + "stage_phase_counts": [{"stage": stage, "phase": phase, "count": count} + for (stage, phase), count in sorted(stage_phase.items())], + "bank_phase_counts": [{"bank": bank, "phase": phase, "count": count} + for (bank, phase), count in sorted(bank_phase.items())], + "word_products": 222, "cover_conjugations": 111, "paired_basis_columns": 1776, + "stage_layouts": layouts, + "paired_basis_order": "x0..x7; x15..x8; physical D=diag(W,J W J)", + "cover_recipe": "One retained cover route g->g W^-1 at ENTRY and g->g W " + "at RETURN. (g W^-1)P(g W^-1)^-1=g Q g^-1.", + "cover_word_instances": len(join), "cover_words_per_marker": 1, + "native_address_halves": 2, + "half_count_scope": "Both native halves are normalized by the same changed " + "cover matrix. They do not duplicate this cover-route word.", + "named_P2_kernel_counts": named, "negative_controls": controls, + "scope": "Conditional finite cover-route word binding and coefficient counts. " + "The source marker does not implement a full physical route. Low " + "cache/carry/permutation, ROW borrow/pad/return, coefficient preparation, " + "head motion, tape tariffs and full compiler admission remain open.", + } + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--emit", action="store_true", + help="Print a candidate receipt without writing files") + args = parser.parse_args() + value = run() + if args.emit: + print(json.dumps(value, indent=2, sort_keys=True)) + else: + need(canonical(json.loads((HERE / "ORACLE.json").read_bytes())) == canonical(value), + "Oracle complete retained receipt") + print(json.dumps({"status": value["status"], "routes": value["route_count"], + "event_join_sha256": value["event_join_sha256"]}, sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/g20-route-word-binding/source/CALLS.json b/research/g20-route-word-binding/source/CALLS.json new file mode 100644 index 0000000000..9ee8c26f32 --- /dev/null +++ b/research/g20-route-word-binding/source/CALLS.json @@ -0,0 +1,1262 @@ +[ + { + "stage": 0, + "pair": 0, + "source_bank": 0, + "target_bank": 1, + "old_direction_inverse": false, + "new_direction_inverse": true, + "helper_old_owner_begin": 3552, + "core_begin": 6597, + "core_end": 21391, + "owned_global_indices": [ + 11022, + 11023, + 11024, + 11025, + 11026, + 11027, + 11028, + 11029, + 11030, + 11031, + 11032, + 11033, + 11034, + 11035, + 11036, + 11037, + 11038, + 11039, + 11040, + 11041, + 11042, + 11043, + 11044, + 11045, + 11046, + 11047, + 11048, + 11049, + 11050, + 11051, + 11052, + 11053, + 11054, + 11055, + 11056, + 11057, + 11058, + 11059, + 11060, + 11061, + 11062, + 11063, + 11064, + 11065, + 11066, + 11067, + 11068, + 11069 + ], + "retained_helper_count": 415, + "paid": { + "1": 1281, + "2": 1338, + "4": 57, + "5": 102, + "6": 10, + "3": 58 + } + }, + { + "stage": 1, + "pair": 0, + "source_bank": 1, + "target_bank": 0, + "old_direction_inverse": true, + 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+ "-1" + ], + [ + "SCALE", + 1, + "-1" + ], + [ + "ADD", + 0, + 1, + "1" + ], + [ + "ADD", + 1, + 0, + "-1" + ], + [ + "ADD", + 0, + 1, + "1" + ] + ], + "matrix": [ + [ + "3", + "1" + ], + [ + "2", + "1" + ] + ] + }, + "word_convention": "RIGHT product E1...Em=W; ADD[i,j,a]=I+a*e_i*e_j^T; row[j]+=a*row[i]", + "wrong_direction_witness_port": 1 +} diff --git a/research/g20-route-word-binding/verify.py b/research/g20-route-word-binding/verify.py new file mode 100644 index 0000000000..c66c7bdb68 --- /dev/null +++ b/research/g20-route-word-binding/verify.py @@ -0,0 +1,271 @@ +#!/usr/bin/env python3 +"""Bind actual G20 route markers to frozen RIGHT words under a cover plan. + +ToikY with substantial OpenAI Codex assistance. Apache-2.0. +Retains Ali Romman's G20 source credit and the S3 word/ROW lineage in NOTICE. +This checker does not import sibling code or implement physical tape primitives. +""" +from collections import Counter +from copy import deepcopy +from fractions import Fraction as Q +from hashlib import sha256 +from pathlib import Path +import argparse +import gzip +import json + + +HERE = Path(__file__).resolve().parent +PINS = { + "GLOBAL.jsonl.gz": "86e7ce6aff05409410ef4bbc00ff1b29b8c1606383549c7e15242b327e39c235", + "PORTS.json": "a53a49c938a46c5a9da8c05ffdec4c2ef2dd906dd94c009d6fa451af4ed350e9", + "CALLS.json": "30dcc37cdade6b2dc05478837eca28b696894d1c4782bac6a1caab5e7f56c9e8", + "CONTROLLER.json": "39ac84fb848b908f7ba051fae4556d507900c421dc5d23501a9c0cb1d61fd08d", + "WORDS.json": "c74b8446503425fb4964921e8651b3931f917c62a21565d9569e9f6399ea571b", +} +COLUMNS = ["event_index", "call_index", "stage", "owner", "port", "phase", + "direction", "word_sha256", "stage_ordinal", "owner_bank"] + + +def need(condition, reason): + if not condition: + raise ValueError(reason) + + +def canonical(value): + return json.dumps(value, sort_keys=True, separators=(",", ":"), allow_nan=False).encode() + + +def digest(value): + return sha256(canonical(value)).hexdigest() + + +def authenticate(name, raw): + need(sha256(raw).hexdigest() == PINS[name], "source bytes: " + name) + + +def right_product(word): + matrix = [[Q(i == j) for j in range(8)] for i in range(8)] + for operation in word: + opcode, i = operation[:2] + need(type(i) is int and 0 <= i < 8, "program coordinate") + if opcode == "ADD": + need(len(operation) == 4, "program ADD arity") + j, coefficient = operation[2], Q(operation[3]) + need(type(j) is int and 0 <= j < 8 and i != j and coefficient + and coefficient.denominator & (coefficient.denominator - 1) == 0, + "program dyadic ADD") + for row in matrix: + row[j] += coefficient * row[i] + else: + need(opcode == "SCALE" and len(operation) == 3, "program SCALE arity") + coefficient = Q(operation[2]) + numerator, denominator = abs(coefficient.numerator), coefficient.denominator + need(numerator > 0 and numerator & (numerator - 1) == 0 + and denominator & (denominator - 1) == 0, "program dyadic-unit SCALE") + for row in matrix: + row[i] *= coefficient + return matrix + + +def programs(words, ports): + need([record["port"] for record in words["ports"]] == list(range(111)) + == [record["port"] for record in ports["port_interfaces"]["ports"]], + "all source program ports") + references, by_hash, catalogue = {}, {}, [] + for record, source in zip(words["ports"], ports["port_interfaces"]["ports"]): + need(record["line"] == source["line"] and record["complement"] == source["complement"], + "source port geometry binding") + for direction, target in (("forward", "normalizer"), ("inverse", "inverse")): + word = record[direction + "_word"] + # These are dependency checks, not a claim to newly construct S3. + need(right_product(word) == [[Q(value) for value in row] for row in source[target]], + "frozen RIGHT word matrix binding") + word_hash = digest(word) + references[record["port"], direction] = word_hash + by_hash[word_hash] = word + catalogue.append({"port": record["port"], "direction": direction, + "word_sha256": word_hash, "operations": len(word)}) + return references, by_hash, catalogue + + +def expected_routes(events, calls, stages): + """Independently build every marker's receiver from declared core boundaries.""" + need([call["stage"] for call in calls] == stages + == [0, 1, *range(3, 32, 2), 32], "source thick-call stages") + expected = {} + for ordinal, call in enumerate(calls): + stage = call["stage"] + need(call["source_bank"] != call["target_bank"], "distinct call banks") + if stage == 0: + continue + for phase, start in (("ENTRY", call["core_begin"] - 222), + ("RETURN", call["core_end"])): + for bank_position, bank in enumerate((call["source_bank"], call["target_bank"])): + for port in range(111): + index = start + bank_position * 111 + port + need(0 <= index < len(events) and index not in expected, "disjoint route intervals") + owner = 111 * bank + port + expected[index] = (ordinal, stage, owner, port, phase, bank) + need(events[index] == ["PAID_PORT_ROUTE", stage, owner, port, phase], + "actual source route interval") + actual = {index for index, event in enumerate(events) if event[0] == "PAID_PORT_ROUTE"} + need(actual == set(expected), "actual marker interval bijection") + return expected + + +def make_manifest(events, calls, stages, references, expected): + manifest = [] + for index, event in enumerate(events): + if event[0] != "PAID_PORT_ROUTE": + continue + ordinal, stage, owner, port, phase, bank = expected[index] + direction = "inverse" if phase == "ENTRY" else "forward" + manifest.append([index, ordinal, stage, owner, port, phase, direction, + references[port, direction], ordinal, bank]) + return manifest + + +def tally(manifest, by_hash): + """Recompute the coefficient bill from bound words, never an inherited total.""" + histograms = {"ADD": Counter(), "SCALE": Counter()} + phase_stage, bank_phase, port_direction = Counter(), Counter(), Counter() + for row in manifest: + index, call_index, stage, owner, port, phase, direction, word_hash, ordinal, bank = row + need(word_hash in by_hash, "known concrete program hash") + phase_stage[stage, phase] += 1 + bank_phase[bank, phase] += 1 + port_direction[port, direction] += 1 + for operation in by_hash[word_hash]: + histograms[operation[0]][str(Q(operation[-1]))] += 1 + histogram = {kind: dict(sorted(counter.items(), key=lambda item: Q(item[0]))) + for kind, counter in histograms.items()} + return { + "coefficient_histogram": histogram, + "scalar_word_operations": {kind: sum(counter.values()) for kind, counter in histograms.items()}, + "stage_phase_counts": [[stage, phase, count] + for (stage, phase), count in sorted(phase_stage.items())], + "bank_phase_counts": [[bank, phase, count] + for (bank, phase), count in sorted(bank_phase.items())], + "port_direction_counts": [[port, direction, count] + for (port, direction), count in sorted(port_direction.items())], + "conditional_named_primitive_counts_times_f_squared": { + kind: {coefficient: 127 * count for coefficient, count in counter.items()} + for kind, counter in histogram.items()}, + } + + +def validate_manifest(manifest, expected, references, placements): + indices = [row[0] for row in manifest] + need(len(indices) == len(set(indices)) and set(indices) == set(expected), + "route-event coverage") + for row in manifest: + index, call_index, stage, owner, port, phase, direction, word_hash, ordinal, bank = row + source_call, source_stage, source_owner, source_port, source_phase, source_bank = expected[index] + need(call_index == source_call and stage == source_stage, "source call/stage binding") + need(owner == source_owner and port == source_port and bank == source_bank + and owner == 111 * bank + port, "owner bank/port binding") + need(phase == source_phase, "source route phase") + need(direction == ("inverse" if source_phase == "ENTRY" else "forward"), + "single-cover route direction") + need(word_hash == references[port, direction], "bound concrete port program") + need(ordinal == source_call and placements[ordinal]["stage"] == stage, + "stage ordinal binding") + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--emit", action="store_true", help="emit candidate only; never write files") + args = parser.parse_args() + raw = {name: (HERE / "source" / name).read_bytes() for name in PINS} + for name, content in raw.items(): + authenticate(name, content) + decoded = gzip.decompress(raw["GLOBAL.jsonl.gz"]) + events = [json.loads(line) for line in decoded.splitlines()] + ports, calls, controller, words = (json.loads(raw[name]) for name in + ("PORTS.json", "CALLS.json", "CONTROLLER.json", "WORDS.json")) + need(len(events) == ports["events"] == 317004 + and sha256(decoded).hexdigest() == ports["stream_sha256"], "retained stream receipt") + stages = controller["invoice"]["thick_stages"] + placements = words["placements"] + need([record["stage"] for record in placements] == stages, "S3 placement stages") + for ordinal, record in enumerate(placements): + need(record["ordinal"] == ordinal and record["active_indices"] + == [0] + list(range(1 + 7 * ordinal, 8 + 7 * ordinal)), "S3 compatible placement") + references, by_hash, catalogue = programs(words, ports) + expected = expected_routes(events, calls, stages) + manifest = make_manifest(events, calls, stages, references, expected) + bill = tally(manifest, by_hash) + validate_manifest(manifest, expected, references, placements) + need(len(manifest) == 7548, "source-specific marker count") + need(all(count == 34 for _, _, count in bill["port_direction_counts"]) + and len(bill["port_direction_counts"]) == 222, "observed per-port direction multiplicity") + need(all(bill["coefficient_histogram"][kind] + == {coefficient: 34 * count for coefficient, count in counts.items()} + for kind, counts in words["operation_histogram_both_directions"].items()), + "actual marker histogram versus S3 words") + controls = [] + + def reject(name, reason, mutate): + changed = deepcopy(manifest) + mutate(changed) + # Recompute a coherent bill before testing the source join. A stale + # aggregate receipt/hash is not the rejection mechanism. + rebuilt = tally(changed, by_hash) + try: + validate_manifest(changed, expected, references, placements) + except ValueError as error: + need(str(error) == reason, "control rejected for unintended reason: " + name) + controls.append({"name": name, "reason": str(error), "rejected": True, + "recomputed_bill_sha256": digest(rebuilt)}) + else: + raise ValueError("semantic control accepted: " + name) + + reject("omitted_marker", "route-event coverage", lambda rows: rows.pop(0)) + reject("wrong_owner", "owner bank/port binding", lambda rows: rows[0].__setitem__(3, rows[0][3] + 1)) + + def wrong_phase(rows): + rows[0][5:8] = ["RETURN", "forward", references[rows[0][4], "forward"]] + + def wrong_direction(rows): + rows[0][6:8] = ["forward", references[rows[0][4], "forward"]] + + reject("coherently_rebound_wrong_phase", "source route phase", wrong_phase) + reject("coherently_rebound_wrong_direction", "single-cover route direction", wrong_direction) + reject("foreign_port_program", "bound concrete port program", + lambda rows: rows[0].__setitem__(7, references[1, "inverse"])) + wrong_ordinal = next(index for index, row in enumerate(manifest) if row[2] == 3) + reject("raw_stage_as_ordinal", "stage ordinal binding", + lambda rows: rows[wrong_ordinal].__setitem__(8, 3)) + try: + authenticate("GLOBAL.jsonl.gz", raw["GLOBAL.jsonl.gz"] + b" ") + except ValueError as error: + need(str(error) == "source bytes: GLOBAL.jsonl.gz", "source control reason") + controls.append({"name": "source_corruption", "reason": str(error), "rejected": True}) + else: + raise ValueError("source corruption accepted") + result = { + "schema": "g20-route-word-binding/1", "source_raw_sha256": PINS, + "source_stream_sha256": ports["stream_sha256"], "source_events": len(events), + "marker_count": len(manifest), "single_cover_word_instances": len(manifest), + "manifest_columns": COLUMNS, "manifest": manifest, + "manifest_sha256": digest(manifest), + "event_join_sha256": digest([row[:8] for row in manifest]), + "program_catalogue": catalogue, "placements": placements, + "cover_convention": "Declared single ROW cover g->gS: P=WQW^-1, ENTRY S=W^-1, RETURN S=W; one word per marker", + "RIGHT_word_convention": words["word_convention"], + "multiplicity": "Observed 17 nonzero stages * 2 owner banks * 111 ports * 2 phases; no extra paired-half multiplier", + "conditional_coefficient_bill": "For each observed word coefficient a, count[a]*(127*f)*f*C_kind(a); no physical leaf tariff is asserted", + "source_dependency_scope": "5798 endpoint/native/marker audit and S3 factor construction are retained dependencies, not new whole-caller acceptance", + "physical_scope": "Exact source-event to program manifest under the declared single-cover plan; physical ROW schedule, tape/cache/carry/type/borrow/padding and full bill remain open", + **bill, "failure_controls": controls, + } + if not args.emit: + need(canonical(result) == canonical(json.loads((HERE / "RESULT.json").read_text(encoding="utf-8"))), + "frozen canonical RESULT.json comparison") + print(json.dumps(result, sort_keys=True, indent=2)) + print("PASS_G20_ROUTE_WORD_BINDING") + + +if __name__ == "__main__": + main()

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