From cd37bdf943876f81a60522e13cf838a464ed3104 Mon Sep 17 00:00:00 2001 From: Cinna Davis <1337isnot1337@users.noreply.github.com> Date: Wed, 14 Oct 2026 19:03:05 -0500 Subject: [PATCH] Research exact selected BIT ADD route invoice --- .../OVERLAP.json | 48 + .../README.md | 106 + .../RESULT.json | 4104 +++++++++ .../ROUTES.json | 8110 +++++++++++++++++ .../SOURCES.json | 131 + .../TASK.json | 82 + .../VERIFY.json | 44 + .../verify.py | 406 + 8 files changed, 13031 insertions(+) create mode 100644 research/selected-bit-add-route-invoice-seed96e4cc/OVERLAP.json create mode 100644 research/selected-bit-add-route-invoice-seed96e4cc/README.md create mode 100644 research/selected-bit-add-route-invoice-seed96e4cc/RESULT.json create mode 100644 research/selected-bit-add-route-invoice-seed96e4cc/ROUTES.json create mode 100644 research/selected-bit-add-route-invoice-seed96e4cc/SOURCES.json create mode 100644 research/selected-bit-add-route-invoice-seed96e4cc/TASK.json create mode 100644 research/selected-bit-add-route-invoice-seed96e4cc/VERIFY.json create mode 100644 research/selected-bit-add-route-invoice-seed96e4cc/verify.py diff --git a/research/selected-bit-add-route-invoice-seed96e4cc/OVERLAP.json b/research/selected-bit-add-route-invoice-seed96e4cc/OVERLAP.json new file mode 100644 index 0000000000..fb74e6067e --- /dev/null +++ b/research/selected-bit-add-route-invoice-seed96e4cc/OVERLAP.json @@ -0,0 +1,48 @@ +{ + "searched_at_utc": "2026-10-14T23:39:40Z", + "query": [ + "selected low-class invocation", + "fixed-tape allocation", + "selected routing invoice", + "restricted ADD", + "selected-stock-envelope" + ], + "coverage": { + "open_prs": 444, + "discussions": 892, + "complete_pagination": true, + "warnings": [] + }, + "narrow_cached_exact_term_result": { + "searched_at_utc": "2026-10-14T23:40:40Z", + "open_pr_match": { + "number": 2195, + "head": "3a1cf78a1ba6322129e42d80c50d21765524d612", + "relationship": "source package and released handoff" + }, + "competing_discussion_matches": 0 + }, + "related_predecessors": [ + { + "pr": 2157, + "head": "eb1bf93950e9b14f7fadca7892866e9f29a26ad3", + "relationship": "exact route catalogue supplier" + }, + { + "pr": 2171, + "head": "416aac58960660edced905dc7d914c126d357290", + "relationship": "controlled ADD preparation costs" + }, + { + "pr": 2188, + "head": "77bb4e8cfe3e8c89f6e281eaf948454ee487796a", + "relationship": "mixed weight descriptor; no competing claim" + } + ], + "limits": "find_overlap searches open PR bodies, discussion claims and selected local READMEs, not code diffs; results are leads, not a novelty certificate. Recheck before any later PR.", + "discussion_2179_direct_snapshot": { + "updated_at_utc": "2026-10-14T23:17:10Z", + "comments": 0, + "body_status": "released handoff; original author left next task open" + } +} diff --git a/research/selected-bit-add-route-invoice-seed96e4cc/README.md b/research/selected-bit-add-route-invoice-seed96e4cc/README.md new file mode 100644 index 0000000000..deaa2ec016 --- /dev/null +++ b/research/selected-bit-add-route-invoice-seed96e4cc/README.md @@ -0,0 +1,106 @@ +# Selected BIT same-family ADD route invoice + +**Partial, conditional cost result. No new supplier, kappa, or multiplication theorem.** + +## Result + +For the pinned PR589 selected owner layout, this package reconstructs every +same-family helper ADD in the 288 selected local calls. Each event receives the +three chart actions specified by PR2195's restricted-fibre XOR procedure: +target alignment, source alignment, and target return. The verifier replays +each captured route word over exact rationals, checks its selected GL64 chart +map and dyadic primitive bill, then sums the route actions in chronological +event order. + +| Item | Exact result | +|---|---:| +| Selected local calls | 288 | +| Same-family ADD events | 11,072 | +| Target/source/return route actions | 33,216 | +| Distinct used route types | 43 | +| Ordinary route operations | 19,398,656 | +| Double-half operations | 3,407,872 | +| Negations | 417,792 | +| Controlled shifts | 4,177,920 | +| Constant shifts | 1,097,728 | +| Low permutations | 321,408 | + +The ordinary route bill per selected call ranges from 18,432 to 103,552; the +median is recorded exactly in [RESULT.json](RESULT.json). These numbers are +the route compiler's charged primitive inventory, not a count of completed +recursive child executions. + +The concrete first event is stage 0, replica 0, local position 19422: family +451, target role 243 on axes 1..8, source role 244 on axes 9..16. Its three +route bills are 192 ordinary operations for the target, 512 for the source, +and 192 for the target return, plus the exact dyadic and permutation counts +in [RESULT.json](RESULT.json). + +## Scan-sharing screen + +The selected word has 3,456 `(call, family)` groups for 11,072 ADDs. If each +group could be processed with one family selection scan, the arithmetic +ceiling would remove 7,616 repeated selection scans. This is not an admitted +saving. In family 451, the same-family ADDs at positions 19422 and 19448 are +separated by an ADD at position 19424 that also changes role 243. The exact +three-operation control shows that moving the later family ADD across this +update changes role 244 on a valid dirty input. A correct cache would have to +retain and update the intermediate payload state and pay for its restoration. +No such cache is claimed here. + +## Exact scope and limits + +The route inputs are the selected base files pinned in [SOURCES.json](SOURCES.json). +The 43 used route records are captured from Jose Manuel's PR #2157 at exact +head `eb1bf93950e9b14f7fadca7892866e9f29a26ad3` and independently rebound to +the selected owner supports and exact matrix products by this verifier. +PR #2195 at `3a1cf78a1ba6322129e42d80c50d21765524d612` supplies the selected +owner schedule and the restricted-fibre three-route formula. + +This is the route component of the #2179 handoff. It does not price the +whole-family selector `C_select(q) V_F`, the payload XOR term, fixed-tape +parking, descriptor installation, precision, the ordinary recursive children, +or restoration. Therefore it is not a complete selected low-class invocation +bill and does not establish admission to a recursive moment. The selected +conditional kappa remains `0.001672660197076918`. + +The 43 route records are a small captured input, not an independent replay of +PR #2157's full 1,123-type catalogue. The present verifier checks every used +word against its exact selected map and bill. It does not search for cheaper +route words. + +## Reproduce + +From the repository root: + +```sh +python3 scripts/research_package.py --package research/selected-bit-add-route-invoice-seed96e4cc --check-only +python3.12 scripts/research_package.py --package research/selected-bit-add-route-invoice-seed96e4cc +``` + +The registered verifier runs normally and with Python optimization enabled. +It uses exact `Fraction` arithmetic and includes controls for a corrupted +route word, an omitted target-return action, and naive reordering across an +intervening owner update. `OVERLAP.json` records the complete refreshed PR and +Discussion search used for the claim; it is not a novelty certificate. + +## Open next questions + +See [TASK.json](TASK.json). The next required step is to attach whole-family +selection, payload XOR, depth-first parking, descriptors, and recursive child +costs to one selected low-class invocation. A separate construction question +is whether any persistent family cache can preserve the exact chronological +word while charging the retained state and restoration. + +## Credit + +This package builds on Jose Manuel's PR589 selected tuning and PR #2195's +owner-packet integration; Jose Manuel's PR #2157 supplies the selected route +compiler and PR #2171 the controlled-ADD preparation interface. Commdata2338's +PR #2188 was checked as nearby descriptor work, but its implementation is not +imported. The retained upstream depth-first parking schedule and PR1627/PR490 +work remain their authors' contributions. + +Prepared by OpenAI Codex with substantial AI assistance in scope selection, +mathematical analysis, implementation, verification, and writing. No +independent human review is claimed. New work is Apache-2.0. diff --git a/research/selected-bit-add-route-invoice-seed96e4cc/RESULT.json b/research/selected-bit-add-route-invoice-seed96e4cc/RESULT.json new file mode 100644 index 0000000000..1971458bb7 --- /dev/null +++ b/research/selected-bit-add-route-invoice-seed96e4cc/RESULT.json @@ -0,0 +1,4104 @@ +{ + "base_commit": "0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2", + "calls": 288, + "calls_receipt_sha256": "27291e14065d61c75d07e0218e35134b85fb0bacc19a0ae3cf524dc1db078910", + "family_groups": 3456, + "first_event": { + "family": 451, + "position": 19422, + "replica": 0, + "source_role": 244, + "source_route": "host:9,10,11,12,13,14,15,16", + "stage": 0, + "target_role": 243, + "target_route": "host:1,2,3,4,5,6,7,8:7", + "three_route_bill": { + "constant_shift": 256, + "low_permutation": 18, + "negation": 256, + "ordinary": 896 + } + }, + "naive_family_scan_reduction": 7616, + "negative_controls": [ + "route-word mutation rejected by exact chart replay", + "omitted target-return direction changes the invoice", + "naive same-family ADD reordering changes role-244 output" + ], + "new_kappa": false, + "noncommutation_control": { + "baseline_output_role244": 1, + "family": 451, + "intervening_event": [ + 1, + 243, + 236, + 1, + 266, + 0 + ], + "intervening_position": 19424, + "positions": [ + 19422, + 19448, + 26620, + 26642 + ], + "reordered_output_role244": 0 + }, + "per_call_invoices": [ + { + "family_groups": 9, + "replica": 0, + "route_bill": { + "constant_shift": 7680, + "controlled_shift": 30336, + "double_half": 24576, + "low_permutation": 1026, + "negation": 2944, + "ordinary": 57600 + }, + "same_family_adds": 28, + "stage": 0 + }, + { + "family_groups": 9, + "replica": 1, + "route_bill": { + "constant_shift": 7680, + "controlled_shift": 30336, + "double_half": 24576, + "low_permutation": 1026, + "negation": 2944, + "ordinary": 57600 + }, + "same_family_adds": 28, + "stage": 0 + }, + { + "family_groups": 9, + "replica": 2, + "route_bill": { 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2157, + "author": "jmbarrancoml", + "head": "eb1bf93950e9b14f7fadca7892866e9f29a26ad3", + "use": "Source for the exact selected route words and bill semantics captured as the 43 used route records in ROUTES.json; verifier replays and binds each captured word to the selected chart." + }, + { + "pr": 2195, + "author": "jmbarrancoml", + "head": "3a1cf78a1ba6322129e42d80c50d21765524d612", + "use": "Selected same-family owner layout, local word, restricted-fibre XOR formula, and handoff scope." + }, + { + "pr": 2171, + "author": "jmbarrancoml", + "head": "416aac58960660edced905dc7d914c126d357290", + "use": "Controlled ADD preparation cost is acknowledged but remains outside this route-only receipt." + }, + { + "pr": 2188, + "author": "commdata2338", + "head": "77bb4e8cfe3e8c89f6e281eaf948454ee487796a", + "use": "Concurrent descriptor work considered during overlap check; no implementation imported." + } + ], + "external_artifacts": [ + { + "path": "ROUTES.json", + "sha256": "4dc53efa6768b44316e2ee661fb8df07cf956a35cb6f35981d00cd2f7b4f44ac", + "source_pr": 2157, + "source_commit": "eb1bf93950e9b14f7fadca7892866e9f29a26ad3", + "source_catalogue_sha256": "63d467f79e7e13fffd1f3de277dd5c6372cdac87f3fcd24b36a69149d300f81f" + } + ] +} diff --git a/research/selected-bit-add-route-invoice-seed96e4cc/TASK.json b/research/selected-bit-add-route-invoice-seed96e4cc/TASK.json new file mode 100644 index 0000000000..d827a13996 --- /dev/null +++ b/research/selected-bit-add-route-invoice-seed96e4cc/TASK.json @@ -0,0 +1,82 @@ +{ + "schema_version": 1, + "task_id": "selected-stock-envelope", + "priority_revision": 4, + "base_commit": "0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2", + "original_card": { + "id": "selected-stock-envelope", + "question": "What explicit uniform stock envelope does the actual selected stopped producer supply at one bootstrap stage?", + "starting_points": [ + "research/selected-bootstrap-stock-audit/README.md", + "research/bootstrap-cutoff-time-space-split/README.md", + "certificates/selected-result.json", + "docs/research/community-efficient1000-review.md" + ], + "methods": [ + "Derive a source-bound reserve recurrence at the actual selected atom widths, separating parent stock from completed inner borrowing.", + "Find an exact missing implication or counterexample to a proposed selected-stage stock envelope." + ], + "acceptance_gate": "Bind every coefficient and depth factor to the selected producer and state the width domain. Compare a proved envelope with the sufficient cutoff guard; a large numerical headroom or a historical m=120 coefficient is not a selected m=73 proof.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read #1956/#1965/#1990 in the batch review and the stock-audit source boundary. Its actual selected coefficient remains uncomputed.", + "scope": "Source-bound orientation only. Read the named package and review before relying on its local evidence; this command is not its replay or supplier admission." + }, + "first_experiment": "Choose one of the fourteen recorded stages, pin its producer, and derive the parent reserve and depth coefficient. Stop with a precise source-level missing lemma if that coefficient cannot yet be bounded; do not rerun the already checked headroom arithmetic as a new result.", + "bottleneck_link": "This reduces a concrete inherited implementation obligation without confusing unchanged kappa arithmetic with a completed theorem.", + "allowed_variations": [ + "One stage or one explicit reserve/depth implication.", + "An independently checked same-domain proof repair, retaining all remaining assumptions." + ], + "scope_change_triggers": [ + "Importing the historical 57604 or 252 allowance without a selected-producer binding.", + "Calling a conditional fit lemma a full outer-proof adoption." + ], + "overlap_terms": [ + "selected stock", + "stock envelope", + "bootstrap cutoff", + "1956", + "1965", + "1990" + ] + }, + "scope_status": "changed", + "actual_scope": "Source-pinned route invoice for the selected PR589 same-family ADD actions: reconstruct all 11,072 matching events in 288 calls and charge the target, source, and target-return GL64 chart routes per event. This is a finite route component, not a full low-class invocation.", + "scope_change_reason": "Rather than pursue the generic uniform stock-envelope question, I followed PR2195\u2019s explicitly released #2179 handoff: its selected row layout is in place, while the concrete fixed-tape routing invoice remains open. I checked and set aside the centre-sharing suggestion because PR2076 explicitly leaves a persistent centre bank open, and the QQ16 suggestion because PR2153/PR2189 occupy its transcript-capacity line.", + "bottleneck_link": "Recursive supplier admission needs a charged selected invocation. This package fixes the exact chart-route term while keeping whole-family selection, payload XOR, parking, descriptors, precision, recursive child cost, and restoration separate.", + "budget_minutes": 60, + "stop_rule": "Exhaust all 288 calls and one exact scan-reorder control. Stop without a kappa claim if the whole-family selection or recursive child and wrapper costs remain unbound; do not extend to an unbounded schedule search.", + "outcome": "partial", + "evidence": "verify.py replays the pinned selected owner schedule against 43 captured PR2157 route records. It certifies 11,072 same-family ADDs, 33,216 ordered route actions, 19,398,656 ordinary route operations and the exact interleaving control for family 451. The full invocation remains unpriced.", + "author": "OpenAI Codex", + "ai_assistance": "Substantial OpenAI Codex assistance in scope selection, exact route compilation, implementation, verification, and writing. No independent human review or proof-assistant formalization is claimed.", + "open_questions": [ + { + "question": "Can the scan, controlled-XOR, depth-first parking, descriptor, and recursive child terms be closed for one selected low-class invocation?", + "why_it_matters": "The exact route-operation census is only one additive component of the physical invocation bill and does not establish time admission.", + "first_step": "Bind PR2171 preparation to the exact family-451 packet and instantiate the upstream fixed-tape schedule with explicit V_F, V_f, markers, descriptors, and child interfaces.", + "blocked_by": "A completed row-level scan and restoration contract plus an admitted cost for the ordinary recursive callees." + }, + { + "question": "Can a stateful family cache share scans while preserving the selected chronological ADD word?", + "why_it_matters": "The naive grouping ceiling removes 7,616 repeated family selections, but family 451 has intervening operations on the same owner roles.", + "first_step": "Specify a persistent cache state for the exact sequence at positions 19422, 19424, and 19448, then price its writes and restoration on arbitrary payloads.", + "blocked_by": "No complete cache interface or spectator-restoration cost is supplied." + } + ], + "seed": "96e4cc54f6b42661a96b916ab0d83929", + "track": "recursive-interfaces", + "selector_suggestions": [ + "centre-path-sharing", + "joint-query-controller", + "connector-alphabet-change" + ], + "selected_record_sha256": "10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32", + "discussion_claim": "https://github.com/CrocSwap/integer-mult-bounds/discussions/2179#discussioncomment-18936389" +} diff --git a/research/selected-bit-add-route-invoice-seed96e4cc/VERIFY.json b/research/selected-bit-add-route-invoice-seed96e4cc/VERIFY.json new file mode 100644 index 0000000000..501394aaf1 --- /dev/null +++ b/research/selected-bit-add-route-invoice-seed96e4cc/VERIFY.json @@ -0,0 +1,44 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [ + "research/community-frontier1094-audit/ASSEMBLY.json", + "research/community-hyperplane599-audit/pr589/bit589/v9/hosted/GLOBAL-TEMPLATE.json.gz", + "research/community-hyperplane599-audit/pr589/bit589/v9/hosted/GLOBAL.json", + "research/community-hyperplane599-audit/pr589/bit589/v9/nine/GEOMETRY.json", + "research/e8-bit-p111-tuned/tune/EXPECTED.json", + "research/e8-bit-p111-tuned/tune/bitE8mut-p111-tuned.json.gz", + "research/idle-axis-hosting/PROOF.md", + "research/pr589-five-helper-hosting/PROOF.md", + "research/pr589-five-helper-hosting/RESULT.json", + "research/pr589-five-helper-hosting/SOURCES.json", + "research/pr589-five-helper-hosting/verify.py", + "upstream/build/sections/02-streams.tex", + "upstream/build/sections/04-swap.tex" + ], + "commands": [ + { + "argv": [ + "{python}", + "-I", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 120, + "checks": "Exact source pins, all 43 route words and dyadic bills, every selected same-family ADD in all 288 calls, target-return invoices, the first selected event, and three negative controls." + }, + { + "argv": [ + "{python}", + "-I", + "-O", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 120, + "checks": "Repeat the same receipt and controls with Python optimization enabled; the verifier does not rely on assert." + } + ] +} diff --git a/research/selected-bit-add-route-invoice-seed96e4cc/verify.py b/research/selected-bit-add-route-invoice-seed96e4cc/verify.py new file mode 100644 index 0000000000..98f171eb25 --- /dev/null +++ b/research/selected-bit-add-route-invoice-seed96e4cc/verify.py @@ -0,0 +1,406 @@ +#!/usr/bin/env python3 +"""Replay the selected same-family ADD route invoice on pinned inputs.""" + +from collections import Counter, defaultdict +from fractions import Fraction as F +from hashlib import sha256 +import gzip +import json +from pathlib import Path +import sys + + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parents[1] +BASE = "0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2" +SELECTED_SHA256 = "10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32" +ROUTE_SHA256 = "4dc53efa6768b44316e2ee661fb8df07cf956a35cb6f35981d00cd2f7b4f44ac" +ROUTE_HEAD = "eb1bf93950e9b14f7fadca7892866e9f29a26ad3" + + +def need(condition, message): + if not condition: + raise ValueError(message) + + +def canonical(value): + return json.dumps(value, sort_keys=True, separators=(",", ":")) + + +def digest(value): + return sha256(canonical(value).encode()).hexdigest() + + +def eye(n): + return [[F(i == j) for j in range(n)] for i in range(n)] + + +def transpose(matrix): + return [list(col) for col in zip(*matrix)] + + +def multiply(left, right): + rows, inner, cols = len(left), len(right), len(right[0]) + need(len(left[0]) == inner, "matrix dimensions") + out = [[F(0) for _ in range(cols)] for _ in range(rows)] + for i, row in enumerate(left): + for k, x in enumerate(row): + if x: + for j, y in enumerate(right[k]): + if y: + out[i][j] += x * y + return out + + +def replay(word, n=64): + matrix = eye(n) + for kind, dest, src, coefficient in word: + coefficient = F(coefficient) + for row in matrix: + if kind == "swap": + row[dest], row[src] = row[src], row[dest] + elif kind == "scale": + row[dest] *= coefficient + elif kind == "add": + row[dest] += coefficient * row[src] + else: + raise ValueError("unknown route factor") + return matrix + + +def column_word(matrix): + """The exact Gaussian column compiler used for inverse directions.""" + n = len(matrix) + reduced = [list(row) for row in matrix] + word = [] + for col in range(n): + pivot = next((row for row in range(col, n) if reduced[row][col]), None) + need(pivot is not None, "inverse route is singular") + if pivot != col: + reduced[col], reduced[pivot] = reduced[pivot], reduced[col] + word.append(("swap", pivot, col, F(1))) + diagonal = reduced[col][col] + if diagonal != 1: + reduced[col] = [x / diagonal for x in reduced[col]] + word.append(("scale", col, col, diagonal)) + for row in range(n): + if row == col: + continue + coefficient = reduced[row][col] + if coefficient: + reduced[row] = [x - coefficient * y for x, y in zip(reduced[row], reduced[col])] + word.append(("add", col, row, coefficient)) + need(reduced == eye(n), "Gaussian inverse endpoint") + need(replay(word, n) == matrix, "Gaussian route factor product") + return word + + +def bill(word): + counts = Counter({ + "ordinary": 0, + "double_half": 0, + "negation": 0, + "controlled_shift": 0, + "constant_shift": 0, + "low_permutation": len(word), + }) + for kind, dest, src, coefficient in word: + coefficient = F(coefficient) + numerator, denominator = abs(coefficient.numerator), coefficient.denominator + need(numerator & (numerator - 1) == 0, "dyadic numerator") + need(denominator & (denominator - 1) == 0, "dyadic denominator") + if kind == "swap": + counts["ordinary"] += 64 + elif kind == "add": + counts["ordinary"] += 128 * (src > dest) + counts["double_half"] += 128 * (denominator.bit_length() - 1) + counts["controlled_shift"] += 64 + elif kind == "scale": + counts["double_half"] += 64 * (numerator.bit_length() + denominator.bit_length() - 2) + counts["negation"] += 64 * (coefficient < 0) + counts["constant_shift"] += 64 + else: + raise ValueError("unknown bill operation") + return dict(counts) + + +def basis(port): + q = port["q"] + complement = port["complement_columns"] + return [[F(q[i], 2)] + [F(x) for x in complement[i]] for i in range(8)] + + +def expected_route_matrix(record, geometry): + slots = record["slots"] + need(len(slots) == 8 and len(set(slots)) == 8, "eight distinct hosted axes") + permutation = list(range(64)) + domain, image = set(range(8)), set(slots) + for i, s in zip(sorted(domain - image), sorted(image - domain)): + permutation[i], permutation[s] = s, i + need(record["permutation"] == permutation, "route support permutation") + pi = [[F(i == permutation[j]) for j in range(64)] for i in range(64)] + local = min(slots) < 8 + if not local: + need(record["port"] is None, "nonlocal route has no port") + sigma = pi + expected = transpose(pi) + else: + need(isinstance(record["port"], int) and 0 <= record["port"] < len(geometry["ports"]), + "selected local route port") + need(slots == list(range(1, 9)), "selected local route support") + port = geometry["ports"][record["port"]] + b = basis(port) + embedded_b = eye(64) + embedded_bt = eye(64) + for i in range(8): + for j in range(8): + embedded_b[i][j] = b[i][j] + embedded_bt[i][j] = b[j][i] + sigma = multiply(embedded_b, pi) + expected = multiply(transpose(pi), embedded_bt) + identity = eye(64) + need(multiply(expected, sigma) == identity, "route inverse on right") + need(multiply(sigma, expected) == identity, "route inverse on left") + return expected + + +def validate_route(key, record, geometry): + need(record["family"] == "hosted", "hosted route record") + expected = expected_route_matrix(record, geometry) + word = [(k, i, j, F(c)) for k, i, j, c in record["word"]] + need(replay(word) == expected, "route word matches selected chart") + need(record["bill"] == bill(word), "route bill matches word") + need(key.startswith("host:"), "hosted route key") + key_slots = [int(x) for x in key.split(":")[1].split(",")] + key_port = int(key.split(":")[2]) if key.count(":") == 2 else None + need(key_slots == record["slots"] and key_port == record["port"], "route key binding") + return expected + + +def source_bytes(path): + return (ROOT / path).read_bytes() + + +def load_inputs(): + manifest = json.loads((HERE / "SOURCES.json").read_text()) + need(manifest["base_commit"] == BASE, "exact research base") + selected_source = next( + entry for entry in manifest["files"] + if entry["path"] == "certificates/selected-result.json" + ) + for entry in manifest["files"]: + raw = source_bytes(entry["path"]) + need(sha256(raw).hexdigest() == entry["sha256"], "source pin: " + entry["path"]) + need(selected_source["sha256"] == SELECTED_SHA256, "selected-record pin") + route_raw = (HERE / "ROUTES.json").read_bytes() + need(sha256(route_raw).hexdigest() == ROUTE_SHA256, "captured predecessor route pin") + routes_file = json.loads(route_raw) + need(routes_file["predecessor_commit"] == ROUTE_HEAD, "route compiler head") + need(routes_file["predecessor_pr"] == 2157, "route compiler predecessor") + routes = routes_file["routes"] + paths = {entry["path"]: ROOT / entry["path"] for entry in manifest["files"]} + template = json.loads(gzip.decompress(paths[ + "research/community-hyperplane599-audit/pr589/bit589/v9/hosted/GLOBAL-TEMPLATE.json.gz" + ].read_bytes())) + geometry = json.loads(paths[ + "research/community-hyperplane599-audit/pr589/bit589/v9/nine/GEOMETRY.json" + ].read_bytes()) + return manifest, routes, template, geometry + + +def route_key(call, role, children): + family, route = call["owners"][role] + need(role >= 222 and route[0] == "hosted", "same-family ADD uses hosted owners") + _, child, offset, width = route + entry = children[child] + first, last = entry["source_level"], entry["target_level"] + pending = list(range(1 if first == -1 else 8 + 7 * first, 8 + 7 * last)) + slots = pending[offset:offset + width] + need(width == 8 and len(slots) == 8, "complete width-eight owner") + port = family % 111 + return "host:" + ",".join(map(str, slots)) + (f":{port}" if min(slots) < 8 else "") + + +def xor_add(vector, event): + need(event[0] == 1 and event[3] == 1, "unit F2 ADD event") + vector[event[1]] ^= vector[event[2]] + + +def noncommutation_control(template): + call = next(c for c in template["calls"] if c["stage"] == 0 and c["replica"] == 0) + program = template["local_programs"][call["orientation"]] + first, middle, second = program[19422], program[19424], program[19448] + need(first[:3] == [1, 243, 244], "first selected family ADD") + need(middle[:3] == [1, 243, 236], "intervening update of the target role") + need(second[:3] == [1, 244, 243], "second selected family ADD") + baseline = [0] * 661 + baseline[236] = 1 + reordered = baseline.copy() + for event in (first, middle, second): + xor_add(baseline, event) + for event in (first, second, middle): + xor_add(reordered, event) + need(baseline != reordered and baseline[244] == 1 and reordered[244] == 0, + "family scan grouping must preserve intervening state") + return { + "family": 451, + "positions": [19422, 19448, 26620, 26642], + "intervening_position": 19424, + "intervening_event": middle, + "baseline_output_role244": baseline[244], + "reordered_output_role244": reordered[244], + } + + +def compute_receipt(routes, template, geometry): + children = {e["idx"]: e for e in template["schedule"] if e["kind"] == "idle"} + route_matrices = {} + inverse_bills = {} + for key, record in routes.items(): + matrix = validate_route(key, record, geometry) + route_matrices[key] = matrix + inverse = transpose(matrix) + need(multiply(matrix, inverse) == eye(64) and multiply(inverse, matrix) == eye(64), + "orthogonal selected route") + inverse_bills[key] = bill(column_word(inverse)) + + total = Counter() + calls = [] + groups = 0 + route_keys = set() + first_event = None + for call in template["calls"]: + owners = call["owners"] + program = template["local_programs"][call["orientation"]] + bill_call = Counter() + by_family = Counter() + add_count = 0 + for position, event in enumerate(program): + if event[0] != 1: + continue + target, source = event[1:3] + if target < 222 or source < 222 or owners[target][0] != owners[source][0]: + continue + target_key = route_key(call, target, children) + source_key = route_key(call, source, children) + need(target_key in routes and source_key in routes, "selected route present") + route_keys.update((target_key, source_key)) + bill_call.update(routes[target_key]["bill"]) + bill_call.update(routes[source_key]["bill"]) + bill_call.update(inverse_bills[target_key]) + by_family[owners[target][0]] += 1 + add_count += 1 + if (call["stage"], call["replica"], position) == (0, 0, 19422): + first_event = { + "stage": 0, + "replica": 0, + "position": position, + "family": owners[target][0], + "target_role": target, + "source_role": source, + "target_route": target_key, + "source_route": source_key, + "three_route_bill": dict(Counter(routes[target_key]["bill"]) + + Counter(routes[source_key]["bill"]) + + Counter(inverse_bills[target_key])), + } + groups += len(by_family) + total.update(bill_call) + calls.append({ + "stage": call["stage"], + "replica": call["replica"], + "same_family_adds": add_count, + "family_groups": len(by_family), + "route_bill": dict(sorted(bill_call.items())), + }) + + need(len(calls) == 288, "all selected calls") + adds = sum(c["same_family_adds"] for c in calls) + need(adds == 11072, "selected same-family ADD census") + need(len(route_keys) == 43 == len(routes), "exact used route-type inventory") + route_actions = 3 * adds + ordinary = sorted(c["route_bill"].get("ordinary", 0) for c in calls) + med = F(ordinary[143] + ordinary[144], 2) + stage0 = next(c for c in calls if (c["stage"], c["replica"]) == (0, 0)) + need(stage0["same_family_adds"] == 28, "selected stage-zero call count") + need(first_event is not None, "selected event 19422") + controls = noncommutation_control(template) + totals = dict(sorted(total.items())) + expected_totals = { + "ordinary": 19398656, + "double_half": 3407872, + "negation": 417792, + "controlled_shift": 4177920, + "constant_shift": 1097728, + "low_permutation": 321408, + } + need(totals == expected_totals, "complete selected route invoice") + return { + "status": "PASS_SELECTED_BIT_ADD_ROUTE_INVOICE", + "base_commit": BASE, + "selected_record_sha256": SELECTED_SHA256, + "route_predecessor_commit": ROUTE_HEAD, + "calls": len(calls), + "same_family_adds": adds, + "route_actions": route_actions, + "route_types": len(routes), + "family_groups": groups, + "naive_family_scan_reduction": adds - groups, + "per_call_ordinary": { + "min": ordinary[0], + "median": str(med), + "max": ordinary[-1], + "stage0_replica0": stage0["route_bill"]["ordinary"], + }, + "route_bill": totals, + "first_event": first_event, + "noncommutation_control": controls, + "negative_controls": [ + "route-word mutation rejected by exact chart replay", + "omitted target-return direction changes the invoice", + "naive same-family ADD reordering changes role-244 output", + ], + "per_call_invoices": calls, + "scope": "Conditional exact chart-route bill for the selected same-family ADD subset; scans, XOR payload cost, fixed-tape wrapper, recursive child costs, descriptors, precision and restoration remain unpriced.", + "new_kappa": False, + "calls_receipt_sha256": digest(calls), + } + + +def run_controls(routes, geometry, receipt): + first_key = receipt["first_event"]["target_route"] + mutated = json.loads(json.dumps(routes[first_key])) + mutated["word"] = mutated["word"][:-1] + rejected = False + try: + validate_route(first_key, mutated, geometry) + except (ValueError, IndexError, StopIteration): + rejected = True + need(rejected, "mutated route word must fail") + direct = Counter() + for key in (receipt["first_event"]["target_route"], receipt["first_event"]["source_route"]): + direct.update(routes[key]["bill"]) + need(direct != receipt["first_event"]["three_route_bill"], "omitted target return is detected") + + +def main(): + manifest, routes, template, geometry = load_inputs() + need(len(routes) == 43, "captured route subset size") + receipt = compute_receipt(routes, template, geometry) + run_controls(routes, geometry, receipt) + result_path = HERE / "RESULT.json" + if "--write" in sys.argv: + result_path.write_text(json.dumps(receipt, indent=2, sort_keys=True) + "\n") + else: + expected = json.loads(result_path.read_text()) + need(receipt == expected, "stored result receipt") + print( + "PASS_SELECTED_BIT_ADD_ROUTE_INVOICE " + f"adds={receipt['same_family_adds']} routes={receipt['route_actions']} " + f"types={receipt['route_types']} ordinary={receipt['route_bill']['ordinary']} " + f"groups={receipt['family_groups']} controls={len(receipt['negative_controls'])} no_new_kappa" + ) + + +if __name__ == "__main__": + main()