From e47d1dd9e38241b902545dbc41d1bbe7fa0c4bcd Mon Sep 17 00:00:00 2001 From: Pierre Date: Sat, 17 Oct 2026 19:31:41 -0700 Subject: [PATCH 1/3] Compose rank-seven supplier with T16 for improved conditional kappa --- .../CANONICAL-INPUTS.json | 2625 + .../CERTIFICATE.json | 8510 ++ .../t16-rank7-provider-composition/CREDITS.md | 11 + .../DISPATCH-RULE.json | 4 + .../EXPECTED-PROFILE-PRICE.json | 14 + .../EXPECTED.json | 22 + .../INPUT-PINS.json | 17 + .../LOCAL-PINS.json | 9 + .../MATERIALIZE.json | 7872 ++ .../PLAN-3413.json | 85660 ++++++++++++++++ .../PREDECESSOR-COLORING.py | 470 + .../t16-rank7-provider-composition/PROOF.md | 27 + .../t16-rank7-provider-composition/README.md | 47 + .../SOURCE-ORIGINS.json | 112 + .../SOURCES.json | 3156 + .../t16-rank7-provider-composition/TASK.json | 72 + .../VERIFY.json | 604 + .../coloring.py | 100 + .../derived-overlay.tar.gz | Bin 0 -> 4119635 bytes .../materialize.py | 105 + .../price_profile.py | 53 + .../reconstruct.py | 329 + .../t16-rank7-provider-composition/replay.py | 101 + .../ASSEMBLY.json | 345 + .../work/complex-nine-native/DATA-PHASES.json | 1 + .../multicold/engines/base_two_moment.py | 63 + .../vendor/multicold/engines/moment.py | 113 + .../vendor/multicold/engines/outer.py | 58 + .../inputs/ROUND20-PARENT-TEMPLATE.json.gz | Bin 0 -> 393948 bytes .../vendor/PR3133-PROVIDERS.json | 842 + .../coupled-carrier-cap740/words/base.json.gz | Bin 0 -> 72538 bytes .../words/extra.json.gz | Bin 0 -> 72537 bytes .../frontier1094-idle-star-ceiling/analyze.py | 324 + .../allocation/vendor/PLAN.json.gz | Bin 0 -> 29933 bytes .../allocation/vendor/TEMPLATE.json.gz | Bin 0 -> 1124331 bytes .../allocation/vendor/independent_owners.py | 111 + .../vendor/preload_move.py | 133 + .../research/t16-owner-audit-seed67/verify.py | 430 + .../test_materialize.py | 40 + .../test_reconstruct.py | 111 + .../t16-rank7-provider-composition/verify.py | 92 + 41 files changed, 112583 insertions(+) create mode 100644 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119, + 5, + 213 + ], + [ + 180, + 111, + 5, + 174 + ], + [ + 180, + 113, + 5, + 191 + ], + [ + 180, + 114, + 5, + 3 + ], + [ + 180, + 126, + 5, + 6 + ], + [ + 180, + 133, + 5, + 194 + ], + [ + 180, + 136, + 5, + 193 + ], + [ + 180, + 140, + 5, + 194 + ], + [ + 180, + 141, + 5, + 15 + ] + ] +} diff --git a/research/t16-rank7-provider-composition/CREDITS.md b/research/t16-rank7-provider-composition/CREDITS.md new file mode 100644 index 0000000000..c8bf7d03aa --- /dev/null +++ b/research/t16-rank7-provider-composition/CREDITS.md @@ -0,0 +1,11 @@ +# Attribution and scope + +This construction combines the current rank-seven local supplier with a newly allocated sixteen-replica schedule. It does not invent the local word, native projector compiler, controller, moment engines, or outer argument. + +- [PR3413](https://github.com/CrocSwap/integer-mult-bounds/pull/3413), exact head `391d02ced8e620d8f06aeda1ebe02f099d37af92`, supplies the admitted T16 comparison and the literal call chronology retained in `PLAN-3413.json`. +- [PR3403](https://github.com/CrocSwap/integer-mult-bounds/pull/3403), retained by PR3413, supplies deterministic regular bipartite edge coloring of pattern flows. `PREDECESSOR-COLORING.py` is its exact retained verifier; `coloring.py` extracts its three generic coloring functions and generalizes the width loop from five classes to the supplied count-vector length. The original verifier and upstream explanations remain unchanged. +- [PR3133](https://github.com/CrocSwap/integer-mult-bounds/pull/3133) and [PR3148](https://github.com/CrocSwap/integer-mult-bounds/pull/3148) supply both actual rank-seven words, their native interfaces, and the complete paid local profile. All previous source and research credits in that ancestry remain applicable. +- `research/t16-owner-audit-seed67/verify.py` and `research/rank7-joint-endframes/allocation/vendor/independent_owners.py` supply independent literal owner and current-provider checks. Their code is loaded unchanged from authenticated inputs. +- `research/frontier1094-idle-star-ceiling/analyze.py` and the retained multicold engines supply independent rational profile pricing. Its ancestral outer price is labeled separately from the changed physical/controller admission and modern outer result. + +New work is the six-width chronological allocation certificate, its source-bound deterministic reconstruction, compact-helper correspondence, and combination of these existing scientific interfaces. Solver discovery is not part of verification. No private optimizer, orchestration script, or research notebook is required for replay. diff --git a/research/t16-rank7-provider-composition/DISPATCH-RULE.json b/research/t16-rank7-provider-composition/DISPATCH-RULE.json new file mode 100644 index 0000000000..152990015c --- /dev/null +++ b/research/t16-rank7-provider-composition/DISPATCH-RULE.json @@ -0,0 +1,4 @@ +{ + "rule": "extra on (stage,replica)=(0,0); gauge44 on all other143calls", + "reason": "Exercise both authenticated providers under unchanged upstream reconstructor; actual widths and local paid profiles identical." +} diff --git a/research/t16-rank7-provider-composition/EXPECTED-PROFILE-PRICE.json b/research/t16-rank7-provider-composition/EXPECTED-PROFILE-PRICE.json new file mode 100644 index 0000000000..5f492d6122 --- /dev/null +++ b/research/t16-rank7-provider-composition/EXPECTED-PROFILE-PRICE.json @@ -0,0 +1,14 @@ +{ + "native": { + "endpoint": "69086128517542103751/40000000000000000000000", + "endpoint_decimal": "0.001727153212938552593775", + "kappa": "344835059606577/200000000000000000", + "kappa_decimal": "0.001724175298032885" + }, + "conservative": { + "endpoint": "863576604972635276219/500000000000000000000000", + "endpoint_decimal": "0.001727153209945270552438", + "kappa": "431043823762479/250000000000000000", + "kappa_decimal": "0.001724175295049916" + } +} \ No newline at end of file diff --git a/research/t16-rank7-provider-composition/EXPECTED.json b/research/t16-rank7-provider-composition/EXPECTED.json new file mode 100644 index 0000000000..d1ba499828 --- /dev/null +++ b/research/t16-rank7-provider-composition/EXPECTED.json @@ -0,0 +1,22 @@ +{ + "owner_canonical_sha256": "b177136dfa0be42d6b54796e6ae45afb2151f72a9a1fd67821acefdf278011ad", + "idle": { + "1": 4376, + "3": 1090, + "5": 458, + "48": 6078 + }, + "profile": { + "1": 354728, + "2": 104256, + "3": 33922, + "4": 14688, + "5": 3338, + "8": 1152, + "48": 6078 + }, + "rank_mass": 1041408, + "deficit": 5120, + "roles": 58752, + "calls": 144 +} diff --git a/research/t16-rank7-provider-composition/INPUT-PINS.json b/research/t16-rank7-provider-composition/INPUT-PINS.json new file mode 100644 index 0000000000..6f215fd1b1 --- /dev/null +++ b/research/t16-rank7-provider-composition/INPUT-PINS.json @@ -0,0 +1,17 @@ +{ + "research/coupled-carrier-cap740/words/base.json.gz": "300a9b8ad1d554f0e6f84f43f3f5fd870a5b4e5f81ad856900b6e8999684892e", + "research/coupled-carrier-cap740/words/extra.json.gz": "495d030f1e03b90e954dad3043994f03293d41b9ed220a3beaef849df435d3f0", + "research/rank7-joint-endframes/vendor/preload_move.py": "c8fda4674644fcd5cbf39b6645ce148a21daa90a998b678cbe51f970b78b0044", + "research/t16-owner-audit-seed67/verify.py": "f6e27f76c9ccb87b3ce6c5e673588338a09847d22771da7b3f28579661c9404b", + "research/complex-k492-owner-repair/vendor/multicold/vendor/pr558/vendor/pr552/complex-global/vendor535/inputs/ROUND20-PARENT-TEMPLATE.json.gz": "025448abdf2012d327e50a009084e1501690d05e650300d2982836aa0350ae00", + "research/community-k492-audit/pr622/replay/baseline558/complex-global/base/work/complex-nine-native/DATA-PHASES.json": "c5916ff312678f12aba403847643fbbc29f643acec60bdf836fa56cd3e8251fa", + "research/frontier1094-idle-star-ceiling/analyze.py": "d9768cff06d5e19e75b2ccc4d03ff5bc2d93098f3192c167d3f208c802877bbc", + "research/community-frontier1094-audit/ASSEMBLY.json": "1122cb3a575f8c788345fc1bf4c108ac7c3250fb81a5988671f5eb04b3ab3045", + "research/complex-k492-owner-repair/vendor/multicold/engines/moment.py": "81cbc864e106418fc7854322746f72180cb8110ff39f74450a3b8d55a82c1482", + "research/complex-k492-owner-repair/vendor/multicold/engines/base_two_moment.py": "aee70c242a2f1d225528fabe2002e1564d1dc884797c07d28a831c7878ee9098", + "research/complex-k492-owner-repair/vendor/multicold/engines/outer.py": "c1ebb52163a7219504c728a5c2b098bf1e50bf20148a2879c5a74c3cadc7c03c", + "research/rank7-joint-endframes/allocation/vendor/independent_owners.py": "77a848729159e271ba64f403dfd59dddb13044b17b2950fa56700f442e2fe461", + "research/rank7-joint-endframes/allocation/vendor/PLAN.json.gz": "d566cfb87b71639d4138e1f89b543e2dd6a7772070226a2a14c799a6835bf21e", + "research/rank7-joint-endframes/allocation/vendor/TEMPLATE.json.gz": "21297b20f1f2dc76eb9dd8124416068c3cb096bab9df17fa4da19bc68dfe082e", + "research/coupled-carrier-cap740/vendor/PR3133-PROVIDERS.json": "52eb0d85caa7b2d4a93acdf5011f52b793f61ddca86235fb03cd9a09397ad4cd" +} diff --git a/research/t16-rank7-provider-composition/LOCAL-PINS.json b/research/t16-rank7-provider-composition/LOCAL-PINS.json new file mode 100644 index 0000000000..53fcaafc92 --- /dev/null +++ b/research/t16-rank7-provider-composition/LOCAL-PINS.json @@ -0,0 +1,9 @@ +{ + "coloring.py": "0e43ba559f0552001b2271ea2eb0be968a372f6643bf1d3d14cf4779b82d5642", + "PLAN-3413.json": "27d6a1886d3f42b7bcc3dbf10d4e669524383227fa5e19c3453ca2eb6953e2d8", + "CERTIFICATE.json": 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+ "4": 142, + "5": 82, + "8": 8 + }, + "orientation_program_sha256": { + "forward": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8", + "backward": "f36c5831106f5637102c6bedeec76ed2b223c6671ce42fd0eceed9ef24725b23" + }, + "artifact_semantic_sha256": { + "CANONICAL-WORD.json.gz": "4ddb29fb9bc6f27e0c0fbfcf19a2a93a3496ad900d0f6d89059d0305c9576c0c", + "LOCAL-PROGRAMS.json.gz": "9f41d53659e9be84e20c661560c5687abbf5cd0660cdecbe01ad5eb29e6b8ee3", + "LOCAL-CHECKS.json": "18f09b79835aa352f04d27041d86d1338c5ad0094b888588c1c05af2dc399ffd", + "INDEPENDENT-LOCAL-REPLAY.json": "2d4680965c62db1fde1236c4857b19bf7bc97af58805e6b4109afbc452f0fdd8", + "CLIFFORD-RECIPES.json": "d0768f2164d5f64a2fdbec422f1cfde4e400818792f1904ca541958377243731", + "CLIFFORD-REVIEW.json": "4960fd1215509b5347ef7f0092868f79aea0f8e24fb84352da9a1033e4394007", + "RESIDUAL-ADAPTERS.json": "c682e9ff1b347f89771c6800f46ad98c2bb92b91c5c88452d53a9e7f0180c35f" + } + } + }, + "source_plan_sha256": "1dec4ca3af6d45d82286005cae4c5e56e7253adefb117d797da55c55c891af08", + "assignment_sha256": "37ef882e53a16a58e17ac965c6e0464f7df069522d30081c13b36549d9286480", + "source_owners_sha256": "32ca30cd1c652ef6ad43657273a08a157e1df3545e759ab36306a0d0b516fb4a", + "assignment_content_sha256": "cab19dc26106dd2008702a4b0e582e7ed09641d309802778cd6dad684bec0556", + "replica_lift": { + "groups": 2, + "source_replicas": 8, + "replicas": 16, + "parent_template_content_sha256": "8904bbbf46dfbf1c6df0e43479a23913fc59a410e879188112e88f16c850ede8", + "owners_file_sha256": "37ef882e53a16a58e17ac965c6e0464f7df069522d30081c13b36549d9286480", + "window_semantics": "strict physical source-event touch intervals, including bridges", + "schedule_content_sha256": "ef9b70f30251e90ca15f54e7802cedf9b2d23bdc150e8f2bc18c916d0f2f2312" + } +} diff --git a/research/t16-rank7-provider-composition/PREDECESSOR-COLORING.py b/research/t16-rank7-provider-composition/PREDECESSOR-COLORING.py new file mode 100644 index 0000000000..bc2898cdb1 --- /dev/null +++ b/research/t16-rank7-provider-composition/PREDECESSOR-COLORING.py @@ -0,0 +1,470 @@ +"""Reconstruct distinct-call T16 owners from exact pattern flows.""" + +import argparse +import gzip +import hashlib +import json +from collections import Counter, defaultdict, deque +from pathlib import Path +from typing import NamedTuple + +HERE = Path(__file__).resolve().parent +ROOT = HERE.parent.parent +PREFIX = "research/complex-t16-rare-pattern-exchanges/data/" +WIDTHS = (4, 5, 7, 8, 9) +INVENTORY = (56, 32, 30, 122, 240) +EXPECTED = {"old": {1: 2431, 17: 1, 48: 4887}, "new": {1: 2429, 5: 1, 14: 1, 48: 4887}} + + +class Group(NamedTuple): + capacity: int + times: tuple + keys: tuple + + +class Model(NamedTuple): + calls: tuple + widths: tuple + groups: tuple + windows: dict + pairs: tuple + sides: tuple + + +def need(ok, message): + if not ok: + raise ValueError(message) + + +def integer(value, low, high): + need(type(value) is int and low <= value <= high, "integer domain") + return value + + +def unique_object(pairs): + result = {} + for key, value in pairs: + need(key not in result, "duplicate JSON key") + result[key] = value + return result + + +def read_json(path): + need(not path.is_symlink() and path.is_file(), "regular JSON input") + need(path.stat().st_size <= 8_000_000, "JSON size bound") + return json.loads(path.read_bytes(), object_pairs_hook=unique_object) + + +def sources(root=ROOT): + pins = read_json(HERE / "SOURCES.json") + need(len(pins["files"]) <= 10, "source inventory bound") + decoded = {} + for pin in pins["files"]: + if pin["usage"] != "input": + continue + path = root / pin["path"] + need(not any(p.is_symlink() for p in (path, *path.parents)), "linked source") + decoded[pin["path"]] = read_json(path) + need( + hashlib.sha256(path.read_bytes()).hexdigest() == pin["sha256"], + "source bytes: " + pin["path"], + ) + manifest = decoded["research/community-frontier1094-audit/SELECTED-SOURCE.json"] + for name in ("PLAN.json", "SPEC.json"): + path = PREFIX + name + need( + hashlib.sha256((root / path).read_bytes()).hexdigest() + == manifest["files"][path], + "selected source binding", + ) + spec = decoded[PREFIX + "SPEC.json"] + need( + hashlib.sha256((root / (PREFIX + "PLAN.json")).read_bytes()).hexdigest() + == spec["data"]["plan_sha256"], + "SPEC plan binding", + ) + return decoded[PREFIX + "PLAN.json"], spec + + +def source_model(plan, spec): + need( + (plan["T"], plan["M"], plan["L"], plan["live"]) == (16, 73, 9, 14336), + "selected template", + ) + ports = plan["provider_registry"]["gauge44"]["ports"] + need(len(ports) == len(set(ports)) == 112, "port stock") + calls = tuple(tuple(integer(x, 0, 15) for x in call) for call in plan["order"]) + need( + len(calls) == 144 + and set(calls) == {(s, r) for s in range(9) for r in range(16)}, + "call set", + ) + entries = plan["per_call_widths"] + need(len(entries) == 144, "width list count") + bycall = {(r["stage"], r["replica"]): tuple(r["widths"]) for r in entries} + need(set(bycall) == set(calls), "width call set") + widths = tuple(bycall[c] for c in calls) + for values in widths: + need(len(values) == 480 and all(type(w) is int for w in values), "width domain") + need(Counter(values) == dict(zip(WIDTHS, INVENTORY)), "per-call inventory") + need( + {int(w): n for w, n in spec["providers"]["gauge44"]["inventory"].items()} + == dict(zip(WIDTHS, INVENTORY)), + "SPEC inventory", + ) + need(spec["call_order"] == plan["order"], "SPEC chronology") + pairs = tuple(integer(plan["pairs"][str(c)], 0, 3) for c in range(18)) + sides = tuple(integer(plan["sides"][str(c)], 0, 1) for c in range(18)) + grouped, windows = defaultdict(list), {} + need(len(plan["windows"]) == 288, "window count") + for key, (capacity, times) in plan["windows"].items(): + owner, child = map(int, key.split(",")) + need( + key == f"{owner},{child}" and 0 <= owner < 16 and 0 <= child < 18, + "window key", + ) + need(type(capacity) is int and capacity in (8, 16, 32, 48), "capacity") + need(1 <= len(times) <= 144, "window size") + times = tuple(integer(t, 0, 143) for t in times) + need(tuple(sorted(set(times))) == times, "ordered unique window") + windows[owner, child] = (capacity, frozenset(times)) + grouped[capacity, times].append((owner, child)) + groups = tuple( + Group(c, t, tuple(sorted(keys))) for (c, t), keys in sorted(grouped.items()) + ) + need( + len(groups) == 144 and all(len(g.keys) == 2 for g in groups), "group inventory" + ) + return Model(calls, widths, groups, windows, pairs, sides) + + +def family(model, owner, child, port): + return owner * 896 + (2 * model.pairs[child] + model.sides[child]) * 112 + port + + +def check_geometry(model): + for t, (stage, replica) in enumerate(model.calls): + eligible = [ + family(model, owner, child, 0) + for (owner, child), (_, times) in model.windows.items() + if t in times + ] + need(len(eligible) == len(set(eligible)), "two eligible children on one family") + active = max(0, (stage - 1) // 2) + need( + all( + owner != replica or model.pairs[child] != active + for (owner, child), (_, times) in model.windows.items() + if t in times + ), + "active data pair eligible", + ) + + +def pattern_inventory(cert, model): + patterns, allocation = (cert[k] for k in ("patterns", "allocation")) + need(1 <= len(patterns) <= 12 and 1 <= len(allocation) <= 1728, "inventory bound") + residuals = [] + for capacity, counts, multiplicity in patterns: + need(type(capacity) is int and capacity in (8, 16, 32, 48), "pattern capacity") + need(len(counts) == 5, "pattern dimension") + for n in counts: + integer(n, 0, 12) + integer(multiplicity, 1, 32256) + residuals.append(capacity - sum(w * n for w, n in zip(WIDTHS, counts))) + need(residuals[-1] >= 0, "overfull pattern") + totals, bins, idle, seen = Counter(), Counter(), Counter(), set() + for g, p, n in allocation: + integer(g, 0, 143) + integer(p, 0, len(patterns) - 1) + integer(n, 1, 224) + need((g, p) not in seen, "duplicate allocation") + seen.add((g, p)) + need(model.groups[g].capacity == patterns[p][0], "allocation capacity") + totals[p] += n + bins[g] += n + if residuals[p]: + idle[residuals[p]] += n + need(all(bins[g] == 224 for g in range(144)), "all bins allocated") + need( + [totals[p] for p in range(len(patterns))] == [p[2] for p in patterns], + "pattern inventory", + ) + return dict(idle) + + +def check_certificate(cert, model, expected): + need(pattern_inventory(cert, model) == expected, "attaining idle profile") + patterns, allocation, flow = (cert[k] for k in ("patterns", "allocation", "flow")) + need(len(flow) <= 30000, "flow bound") + demands, supplies, degrees, seen = Counter(), Counter(), Counter(), set() + for a, t, k, n in flow: + integer(a, 0, len(allocation) - 1) + integer(t, 0, 143) + integer(k, 0, 4) + integer(n, 1, 240) + need((a, t, k) not in seen, "duplicate flow") + seen.add((a, t, k)) + g, _p, count = allocation[a] + need(t in model.groups[g].times, "flow outside window") + demands[t, k] += n + supplies[a, k] += n + degrees[a, t] += n + need(degrees[a, t] <= count, "one call exceeds pattern bin count") + need( + all(demands[t, k] == INVENTORY[k] for t in range(144) for k in range(5)), + "per-call demand", + ) + need( + all( + supplies[a, k] == n * patterns[p][1][k] + for a, (_, p, n) in enumerate(allocation) + for k in range(5) + ), + "pattern width balance", + ) + + +def regular_graph(demands, counts, multiplicity): + """Make the time-to-slot multigraph regular using dummy slots and times.""" + times = sorted(demands) + slots = [k for k, n in enumerate(counts) for _ in range(n)] + size = max(len(times), len(slots)) + need(size <= 144, "graph vertex bound") + matrix = [[0] * size for _ in range(size)] + for k in range(5): + columns = [j for j, width in enumerate(slots) if width == k] + remaining = {j: multiplicity for j in columns} + for i, t in enumerate(times): + count = demands[t][k] + for j in columns: + amount = min(count, remaining[j]) + matrix[i][j] += amount + remaining[j] -= amount + count -= amount + need(count == 0, "slot supply exhausted") + need(not any(remaining.values()), "unfilled real slot") + row_defect = [multiplicity - sum(row) for row in matrix] + col_defect = [multiplicity - sum(row[j] for row in matrix) for j in range(size)] + for i in range(size): + for j in range(len(slots), size): + amount = min(row_defect[i], col_defect[j]) + matrix[i][j] += amount + row_defect[i] -= amount + col_defect[j] -= amount + need(not any(row_defect) and not any(col_defect), "regularization") + return matrix, times, slots + + +def perfect_matching(matrix): + """Bounded alternating-path matching on positive support, without recursion.""" + size = len(matrix) + left, right = [-1] * size, [-1] * size + for start in range(size): + queue, previous, endpoint = deque([start]), {}, None + for _ in range(size): + if not queue or endpoint is not None: + break + i = queue.popleft() + for j in range(size): + if matrix[i][j] <= 0 or j in previous: + continue + previous[j] = i + if right[j] == -1: + endpoint = j + break + queue.append(right[j]) + need(endpoint is not None, "regular graph has no perfect matching") + for _ in range(size): + i = previous[endpoint] + old = left[i] + left[i], right[endpoint] = endpoint, i + if old == -1: + break + endpoint = old + else: + raise ValueError("alternating path exceeded vertex bound") + return left + + +def colour_pattern(demands, counts, multiplicity): + if not any(counts): + return [[] for _ in range(multiplicity)] + matrix, times, slots = regular_graph(demands, counts, multiplicity) + bins = [] + for _ in range(multiplicity): + if len(bins) == multiplicity: + break + match = perfect_matching(matrix) + amount = min(matrix[i][j] for i, j in enumerate(match)) + values = sorted( + (times[i], slots[j]) for i, j in enumerate(match) if j < len(slots) + ) + need(len({t for t, _ in values}) == len(values), "repeated time in colour") + bins.extend([values] * amount) + for i, j in enumerate(match): + matrix[i][j] -= amount + need( + len(bins) == multiplicity and not any(any(row) for row in matrix), + "colour exhaustion", + ) + return bins + + +def expand(cert, model): + demands = defaultdict(lambda: defaultdict(lambda: [0] * 5)) + for a, t, k, n in cert["flow"]: + demands[a][t][k] = n + available = { + (t, k): deque(h for h, w in enumerate(values) if w == width) + for t, values in enumerate(model.widths) + for k, width in enumerate(WIDTHS) + } + rows, used = [], Counter() + for a, (g, p, n) in enumerate(cert["allocation"]): + coloured = colour_pattern(demands[a], cert["patterns"][p][1], n) + for values in coloured: + owner, child = model.groups[g].keys[used[g] // 112] + port = used[g] % 112 + used[g] += 1 + offset = 0 + for t, k in values: + need(bool(available[t, k]), "literal helper shortage") + rows.append( + ( + t, + available[t, k].popleft(), + owner, + child, + port, + offset, + WIDTHS[k], + ) + ) + offset += WIDTHS[k] + need(all(not q for q in available.values()), "unassigned helper") + return sorted(rows) + + +def check_rows(rows, model): + need(len(rows) == 69120, "literal helper count") + seen, families, bins = set(), set(), defaultdict(list) + for t, h, owner, child, port, offset, width in rows: + integer(t, 0, 143) + integer(h, 0, 479) + integer(owner, 0, 15) + integer(child, 0, 17) + integer(port, 0, 111) + integer(offset, 0, 48) + need((t, h) not in seen, "duplicate literal helper") + seen.add((t, h)) + need(type(width) is int and width == model.widths[t][h], "literal width") + need((owner, child) in model.windows, "literal owner") + need(t in model.windows[owner, child][1], "literal window") + f = family(model, owner, child, port) + need((t, f) not in families, "two helpers on one family in one call") + families.add((t, f)) + stage, replica = model.calls[t] + need( + owner != replica or model.pairs[child] != max(0, (stage - 1) // 2), + "literal active data pair", + ) + bins[owner, child, port].append((offset, width)) + idle = Counter() + for (owner, child), (capacity, _) in model.windows.items(): + for port in range(112): + used = 0 + for offset, width in sorted(bins[owner, child, port]): + need(offset == used, "literal overlap or prefix gap") + used += width + need(used <= capacity, "literal overfull bin") + if used < capacity: + idle[capacity - used] += 1 + return dict(sorted(idle.items())) + + +def verify(root=ROOT, certificate=None): + model = source_model(*sources(root)) + check_geometry(model) + cert = read_json(HERE / "CERTIFICATE.json") if certificate is None else certificate + need( + cert["schema_version"] == 1 and set(cert["profiles"]) == set(EXPECTED), "schema" + ) + result = {} + for name, expected in EXPECTED.items(): + profile = cert["profiles"][name] + check_certificate(profile, model, expected) + rows = expand(profile, model) + idle = check_rows(rows, model) + need(idle == expected, "literal profile") + digest = hashlib.sha256( + json.dumps(rows, separators=(",", ":")).encode() + ).hexdigest() + result[name] = { + "idle": {str(r): n for r, n in idle.items()}, + "helpers": len(rows), + "assignment_sha256": digest, + "pattern_flow_rows": len(profile["flow"]), + } + return { + "schema_version": 1, + "calls": 144, + "bins": 32256, + "profiles": result, + "one_helper_per_family_per_call": True, + "active_data_pairs_excluded": True, + "scope": "Finite hosting on supplied selected windows; no complete physical admission.", + } + + +def export_owners(output, model, certificate): + output = output.resolve() + need(not output.is_relative_to(ROOT), "owner output must be outside the checkout") + output.mkdir(parents=True, exist_ok=False) + for name, profile in certificate["profiles"].items(): + rows = expand(profile, model) + need(check_rows(rows, model) == EXPECTED[name], "exported owner profile") + owners = [] + for t, h, owner, child, port, offset, width in rows: + stage, replica = model.calls[t] + owners.append( + { + "time": t, + "helper": h, + "stage": stage, + "replica": replica, + "owner_replica": owner, + "child": child, + "port": port, + "offset": offset, + "width": width, + "copy": owner * 112 + port, + "family": family(model, owner, child, port), + } + ) + data = json.dumps(owners, sort_keys=True, separators=(",", ":")).encode() + (output / f"OWNERS-{name}.json.gz").write_bytes(gzip.compress(data, mtime=0)) + + +def main(): + parser = argparse.ArgumentParser(description=__doc__) + parser.add_argument("--root", type=Path, default=ROOT) + parser.add_argument("--certificate", type=Path, default=HERE / "CERTIFICATE.json") + parser.add_argument( + "--owners-dir", type=Path, help="New external directory for literal owner maps" + ) + parser.add_argument("--write", action="store_true") + args = parser.parse_args() + certificate = read_json(args.certificate) + result = verify(args.root, certificate) + if args.write: + (HERE / "RESULT.json").write_text(json.dumps(result, indent=2) + "\n") + else: + need(result == read_json(HERE / "RESULT.json"), "complete receipt equality") + if args.owners_dir is not None: + export_owners(args.owners_dir, source_model(*sources(args.root)), certificate) + print("PASS_T16_DISTINCT_CALL_ATTAINMENT", json.dumps(result, sort_keys=True)) + + +if __name__ == "__main__": + main() diff --git a/research/t16-rank7-provider-composition/PROOF.md b/research/t16-rank7-provider-composition/PROOF.md new file mode 100644 index 0000000000..e7283e0b37 --- /dev/null +++ b/research/t16-rank7-provider-composition/PROOF.md @@ -0,0 +1,27 @@ +# Literal allocation argument + +The source-bound frame replay of each of the two words yields the same ordered 408 helper widths and the same local profile. Retained literal helper registers, sorted after removing the 72 retired registers, define compact helper IDs. This changes the local supplier relative to PR3413's 480-helper word, so its fixed-inventory packing ceiling does not apply. + +The actual event-derived T16 windows form 144 groups, each with two owner/child pairs and 224 physical ports. The certificate supplies 181 group/pattern allocations and 1,167 nonzero integer flows. Verification checks every group bin total, pattern capacity, six-width supply, 144-call demand, actual event window, and the requirement that a call uses at most one slot in each physical bin. + +For an allocation of n identical bins, make a bipartite multigraph from eligible call times to the pattern's width-labeled slots. Real slot degree is n; every call degree is at most n. Dummy vertices and edges make the graph n-regular. Repeated perfect matchings decompose it into n bins. Thus no bin contains two helpers from one call, and every slot has the prescribed width. The inherited deterministic coloring implementation fixes the literal assignment without any optimizer. + +At each call, the authenticated geometry checks that eligible children cannot alias the same physical family. Coloring therefore enforces family uniqueness as well as width capacity. The original independent auditor then checks all 58,752 literal roles, offsets, physical families, active pairs, and actual source-event windows. A second checker consumes both current native provider interfaces and the modern fill format. + +The reconstructed idle profile is 4,376 H1 + 1,090 H3 + 458 H5 + 6,078 H48. Adding 144 actual local profiles gives the stored complete rank profile, with mass 1,041,408 and deficit 5,120. Two rational engines certify its complex endpoint 0.001727153212938552593775. The profile and owner checks do not by themselves establish changed-provider controller, private-stock, precision, or outer admission; those are separate reproducible obligations. + +Dispatch is explicit: call (0,0) uses `extra`, and the remaining 143 calls use `gauge44`. Both have the same authenticated ordered widths and local bill. This exercises both providers in the unchanged upstream reconstruction. + +## Complete finite admission + +The owner/profile argument is composed with the authenticated current-provider admission, including 91 private cleanup families, physical charts, controller and prefix charges, the exact discovery ledger, both rational outer engines and the release audit. The terminal release status is `PASS_RELEASE`, with +`κ = 0.001727153212938552593775 - 10^-46 - 10^-70`. +The source-bound native receipt SHA256 is +`f90cafe84385533a0eeb96356f385b646f402ff85cd05154c47a81c783023d9d`. +It authenticates native artifacts produced by a prior fresh PR3148 replay; this composition reuses that cache and freshly checks the changed T16 owner/controller/outer construction. + +The original full-admission run used the following historical serialized input identities: fill `5cb9df8fefd24cb4b4ad9b703945b5d2a3258889c6a076b1ea8a92f21b18ace2`, order `2fdb5e6aaa9cdfbb176388ce5e09a98fa67d0f4fa9412899efdc1138b55570fc`, and dispatch `b0a46813f0140014c1c4719e401714549779591ae4d145e67eb77a27575465fe`. These bind the explicit two-provider rule above. The public reconstructor emits equivalent decoded inputs using canonical JSON serialization, so its byte hashes differ. Every fresh replay binds its own reconstructed bytes; the historical hashes are not an acceptance shortcut. The retained release audit reports 63 exact outer inequalities and 17 rejecting outer controls, together with the retained provider, parent-lift, geometry and evidence checks. A release receipt is not substituted for execution by the source-closed admission runner. + +This is complete finite admission under the inherited analytic and implementation hypotheses. It does not establish the remaining all-size compiler, common-label/mutable-source realization, precision/tape or exact-recovery obligations, nor improve the stronger T740 global endpoint. + +The complex endpoint realizes approximately 99.84828790129842536% of the current 408-helper word packing cap (the exact rational root interval in PR3361). This comparison uses the changed word, not the ancestral 480-helper ceiling, and is not a proof of T16 optimality. diff --git a/research/t16-rank7-provider-composition/README.md b/research/t16-rank7-provider-composition/README.md new file mode 100644 index 0000000000..bc74246335 --- /dev/null +++ b/research/t16-rank7-provider-composition/README.md @@ -0,0 +1,47 @@ +# Rank-seven local supplier composed with the T16 chronology + +This candidate replaces PR3413's 480-helper local supplier with the authenticated 408-helper rank-seven supplier from PR3133/PR3148, then constructs a new allocation on PR3413's actual sixteen-replica chronology. It is a changed local-word composition, not another seed in PR3413's attained fixed-inventory packing envelope. + +**Complete finite admission passes.** The modern conditional exponent is +`κ = 0.001727153212938552593775 - 10^-46 - 10^-70`, improving the admitted T16 construction in PR3413. This remains below the supported T740 construction and is a scoped T16 improvement, not a global frontier claim. + +The complex profile endpoint is `0.001727153212938552593775`, versus PR3413's `0.001676895884165954931459`. The complete admission freshly reconstructs this allocation, parent lift, physical/controller invoice, discovery ledger and modern outer release. It authenticates and reuses the two current native providers from a completed fresh PR3148 native replay; this run does not claim to rebuild those native providers again. The ancestral T16 pricing routine separately reports `0.001724175298032885` under its older outer adapter; that diagnostic is not the admitted modern exponent. + +The certificate reconstructs all 58,752 helper occurrences across 144 complete calls. Its 181 group/pattern allocations and 1,167 nonzero flows are checked in exact integer arithmetic, then deterministically expanded by the credited bipartite edge-coloring algorithm. Verification uses no optimizer. Independent source-derived owner checks cover both actual local providers. + +| Quantity | Value | +| --- | --- | +| Idle profile | `4376 H1 + 1090 H3 + 458 H5 + 6078 H48` | +| Full paid profile | `{1:354728,2:104256,3:33922,4:14688,5:3338,8:1152,48:6078}` | +| Rank mass / deficit | `1,041,408 / 5,120` | +| Compact helpers per call | `408` | +| Dispatch | `(0,0): extra`; remaining 143 calls: `gauge44` | + +`SOURCE-ORIGINS.json` identifies exact historical Git objects for all fifteen unchanged scientific inputs. Their verbatim copies in `source-inputs/` make these checks independent of a checkout, historical refs, private directories or an optimizer installation. `PLAN-3413.json` is the retained geometry/chronology input; its old provider metadata is not reused as a new native binding. Reconstruction emits modern `FILL.json.gz`, `ORDER.json` and `DISPATCH.json` for the separate admission adapter. + +## Reproduce + +From this directory with Python 3.12, numpy 2.3.5 and sympy 1.14.0 (including its mpmath dependency; tested with mpmath 1.3.0): + +```sh +python3 -I -Werror -B reconstruct.py +python3 -I -Werror -B price_profile.py +python3 -I -Werror -B test_reconstruct.py +python3 -I -O -Werror -B test_reconstruct.py +python3 -I -Werror -B test_materialize.py +python3 -I -Werror -B verify.py --work /absolute/new/external/admission +``` + +The last command runs complete finite admission and writes its receipts outside the checkout. `MATERIALIZE.json` authenticates the canonical source files listed in `VERIFY.json` plus the compressed derived overlay; the registered package exporter includes all required files. Native cache reuse is explicit and does not replace owner/controller/physical/outer execution. + +Use `reconstruct.py --output /absolute/new/owned/directory` to save the literal owners, source geometry, modern fill and audit receipts. The output directory must not already exist. No source is rewritten. + +Nine test groups exercise valid reconstruction and reject duplicate/missing flow, fractional or Boolean counts, width/bin corruption, unavailable windows, literal role time/width/family faults, source-byte corruption, mismatched native widths and duplicate JSON keys. + +`PROOF.md` explains the exact allocation argument. `CREDITS.md` preserves the predecessor algorithms and provider ancestry. PR3390 and the earlier T16 work remain valid historical branch improvements; this composition uses the newer PR3413 chronology and current rank-seven supplier rather than claiming those predecessors as new work. + +## Open next questions + +1. Can the same allocation recipe reduce replicas further while retaining actual source windows, provider bindings and the complete bill? The present result establishes this specific T16 construction, not an optimum over changed local words or architectures. +2. Can a changed recursive interface improve the global T740 endpoint? This T16 architecture comparison does not establish that claim, and another fixed-inventory allocation is not a new mechanism. +3. 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Report the word's packing cap from ceiling.ceiling() and the fraction of it realized; label packing gains as such.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Locate the selected packing source in the review and check live PRs for the same residual problem.", + "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay." + }, + "first_experiment": "Define an unclaimed canonical domain and a favorable bound before starting a new search.", + "bottleneck_link": "An actual paid-profile gain can improve the frontier up to the other supplier cap.", + "allowed_variations": [ + "One bounded residual packing instance or exact relaxation.", + "If the coverage law, template or guard changes, derive an applicable fully charged replacement bound instead of applying the incumbent ceiling outside its scope." + ], + "scope_change_triggers": [ + "Rerunning an existing search with only a different seed as a separate mathematical contribution." + ], + "overlap_terms": [ + "T16", + "owner exchange", + "packing" + ], + "existing_checks": [ + { + "scope": "Packing-independent ceiling for the selected paid profile under the one-unpaid-coordinate coverage and halving guard.", + "evidence": "docs/research/community-efficient1000-review.md", + "remaining": "A changed word or model requires new pricing; a local packing search must name uncovered scope.", + "status": "reviewed", + "source_commit": "836b19bfa309ceafbc8ee32a15e8c4b10dde7e11", + "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + } + ] + }, + "scope_status": "changed", + "actual_scope": "Compose the current 408-helper rank-seven native supplier with the admitted PR3413 T16 call chronology using a six-width integer pattern-flow certificate, then replay complete changed-provider physical/controller/outer admission with authenticated native-cache reuse.", + "scope_change_reason": "PR3413 reaches the fixed 480-helper envelope. This changes the local supplier and width inventory rather than rerunning an owner-exchange seed.", + "bottleneck_link": "The lower-mass 408-helper supplier and a new chronological allocation improve the finite T16 endpoint; no global T740 frontier claim.", + "budget_minutes": 20, + "stop_rule": "Freeze the first exact positive chronological candidate; reject on any full paid admission failure; do not silently waive provider, private-stock, or precision costs.", + "outcome": "completed", + "evidence": "CERTIFICATE.json; source origins and pins; deterministic reconstruction of 58,752 roles; both-provider independent owner checks; dual-engine profile pricing; complete admission and PASS_RELEASE at kappa = 0.001727153212938552593775 - 10^-46 - 10^-70. The complete admission authenticates and reuses the native cache from a fresh PR3148 replay.", + "author": "User-directed contribution with OpenAI Codex assistance", + "ai_assistance": "OpenAI Codex assisted with bounded allocation discovery, exact scientific reconstruction, source audits and tests. Solver tooling is not part of verification.", + "open_questions": [ + { + "question": "Can a changed recursive interface improve the global T740 endpoint rather than only the T16 architecture?", + "why_it_matters": "This T16 combination remains below the independently supported T740 baseline.", + "first_step": "Derive a complete cost ledger for one named changed interface before a bounded construction.", + "blocked_by": "Requires a changed scientific mechanism and its native realization." + } + ] +} diff --git a/research/t16-rank7-provider-composition/VERIFY.json b/research/t16-rank7-provider-composition/VERIFY.json new file mode 100644 index 0000000000..b60c6fff76 --- /dev/null +++ b/research/t16-rank7-provider-composition/VERIFY.json @@ -0,0 +1,604 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [ + "numpy==2.3.5", + "sympy==1.14.0" + ], + "inputs": [ + "LICENSE", + "research/adaptive-kernel-demotion/inputs/PR589-EXPECTED.json", + 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"timeout_seconds": 600, + "checks": "Reconstruct the literal allocation and run unchanged complete provider/controller/physical/outer admission from Git-free authenticated sources. Native providers explicitly reused." + } + ] +} diff --git a/research/t16-rank7-provider-composition/coloring.py b/research/t16-rank7-provider-composition/coloring.py new file mode 100644 index 0000000000..3c81633444 --- /dev/null +++ b/research/t16-rank7-provider-composition/coloring.py @@ -0,0 +1,100 @@ +"""Deterministic regular bipartite edge coloring from PR3403/PR3413. + +Original source retained/authenticated by PR3413 at commit +391d02ced8e620d8f06aeda1ebe02f099d37af92. This six-width adaptation +changes only range(5) to range(len(counts)); no optimization is performed. +Apache-2.0, inherited attribution retained in CREDITS.md. +""" + +from collections import deque + + +def need(condition, message): + if not condition: + raise ValueError(message) + + +def regular_graph(demands, counts, multiplicity): + """Make the time-to-slot multigraph regular using dummy slots and times.""" + times = sorted(demands) + slots = [k for k, n in enumerate(counts) for _ in range(n)] + size = max(len(times), len(slots)) + need(size <= 144, "graph vertex bound") + matrix = [[0] * size for _ in range(size)] + for k in range(len(counts)): + columns = [j for j, width in enumerate(slots) if width == k] + remaining = {j: multiplicity for j in columns} + for i, t in enumerate(times): + count = demands[t][k] + for j in columns: + amount = min(count, remaining[j]) + matrix[i][j] += amount + remaining[j] -= amount + count -= amount + need(count == 0, "slot supply exhausted") + need(not any(remaining.values()), "unfilled real slot") + row_defect = [multiplicity - sum(row) for row in matrix] + col_defect = [multiplicity - sum(row[j] for row in matrix) for j in range(size)] + for i in range(size): + for j in range(len(slots), size): + amount = min(row_defect[i], col_defect[j]) + matrix[i][j] += amount + row_defect[i] -= amount + col_defect[j] -= amount + need(not any(row_defect) and not any(col_defect), "regularization") + return matrix, times, slots + + +def perfect_matching(matrix): + """Bounded alternating-path matching on positive support, without recursion.""" + size = len(matrix) + left, right = [-1] * size, [-1] * size + for start in range(size): + queue, previous, endpoint = deque([start]), {}, None + for _ in range(size): + if not queue or endpoint is not None: + break + i = queue.popleft() + for j in range(size): + if matrix[i][j] <= 0 or j in previous: + continue + previous[j] = i + if right[j] == -1: + endpoint = j + break + queue.append(right[j]) + need(endpoint is not None, "regular graph has no perfect matching") + for _ in range(size): + i = previous[endpoint] + old = left[i] + left[i], right[endpoint] = endpoint, i + if old == -1: + break + endpoint = old + else: + raise ValueError("alternating path exceeded vertex bound") + return left + + +def colour_pattern(demands, counts, multiplicity): + if not any(counts): + return [[] for _ in range(multiplicity)] + matrix, times, slots = regular_graph(demands, counts, multiplicity) + bins = [] + for _ in range(multiplicity): + if len(bins) == multiplicity: + break + match = perfect_matching(matrix) + amount = min(matrix[i][j] for i, j in enumerate(match)) + values = sorted( + (times[i], slots[j]) for i, j in enumerate(match) if j < len(slots) + ) + need(len({t for t, _ in values}) == len(values), "repeated time in colour") + bins.extend([values] * amount) + for i, j in enumerate(match): + matrix[i][j] -= amount + need( + len(bins) == multiplicity and not any(any(row) for row in matrix), + "colour exhaustion", + ) + return bins diff --git a/research/t16-rank7-provider-composition/derived-overlay.tar.gz b/research/t16-rank7-provider-composition/derived-overlay.tar.gz new file mode 100644 index 0000000000000000000000000000000000000000..a192b51749af94eeeedb54e7018a0a6874c50100 GIT binary patch literal 4119635 zcmV)7K*zryiwFP!00002|Lna9d?ZJ8Fm3`E5D;v0-|aOpGrKcV--omf)~>X+V7)6# zTH7Gxp^xg-?2cxJ>Cv8EPGbWGhcf{J31=XX4~LKgFsBXVkAWmW67v5zj1wTi0mp%l z>*M;rS5@6z-P5C$v6k=q|B_9xr0(jfS5@zRuU_q&UYfgXwy`j~dvN@=i{|Y}f)l$vm8GEkCmZqE~$!Glr{;kIYuMfkY^K;Eyb1{%L-J(3Jqd=fkC`T4rRx841-v* z?*+Q2Ilf_fhPkc2MPMy1&CV~TV40pmWKY&Z8vwMOz|?(*sDwmO80e89Ye8s-p@Xk< zqUvf8SxP`cjVMOs=vJ_0V70q}*M>FQw}0QN zzzA*C_w*o8NazqhQVfd(vTBAQu`SP$4Z|`l%>+WyWiPZ8m25Sjd*}A-0T7XM%+1ec z3u@SMNQe@6W+;2AV<~>1gg$XJ!?1l@(-c4QOvNz-jKs^tSbXAaKG z=4LNX!Hg6Dz_Mjq)?~|+9a}acU4_N9RZaE)V#^MV&;j^7RkH~IF9%j=YNo6yrmy>3 z4CbB#dxy9D?)JUKFwX6pnVp}7|Lj|8?A?zzx-dJxclzlWi7Te20onS{ovH?kZ|cM% 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