diff --git a/research/k-adjoint-boundary-price/PROOF.md b/research/k-adjoint-boundary-price/PROOF.md new file mode 100644 index 0000000000..2f8ee44be0 --- /dev/null +++ b/research/k-adjoint-boundary-price/PROOF.md @@ -0,0 +1,92 @@ +# One K/adjoint round trip on register 333 + +## Pinned boundary + +PR #4002 freezes forty recipe descriptors and sixteen warps on four binary +maps. One of those maps is the credited source witness + +```text +G = (1, 2, 8, 32, 44, 128, 59, 66, 489). +``` + +The new-version sign-+1 warp with those columns has entrance +`(266, 138, 74, 30, 1)`, terminal `(426, 96, 24, 6, 1)`, and coverage rows +for providers `base` and `extra` at register `333`, index `4`. The matching +sign-−1 descriptor swaps that entrance and terminal. This package prices that +pair and no other warp. + +## Operators + +Columns are images of the standard basis. Write `P_G|x> = |Gx>`, +`Z_t|x> = (-1)^{t·x}|x>`, and `D|x> = i^{wt(x)}|x>`. The source canonical +lift and the normalized section are + +```text +K_G|x> = i^{q(Q_G)(Gx)}|Gx>, +J_G|x> = i^{wt(Gx)-wt(x)}|Gx>, +Q_G = I + G^{-T} G^{-1}. +``` + +The quadratic value is the source polar form modulo 4. PR #4002 proves +`K_G = J_G Z_{t_G}` with + +```text +(t_G)_j = [q(Q_G)(G e_j) - wt(G e_j) + 1]_4 / 2, +``` + +and the cocycle + +```text +K_H K_G = K_{HG} Z_{t_G + G^t t_H + t_{HG}}. +``` + +Masks add by XOR. Those identities are used here only for this `G`. + +## The round trip + +Direct inversion gives + +```text +G^{-1} = (1, 2, 28, 4, 79, 8, 130, 32, 431), +t_G = 144, t_{G^{-1}} = 68. +``` + +The identity has tag 0, so + +```text +K_{G^{-1}} K_G = Z_{144 + G^t 68} = Z_{256}. +``` + +`256 = 2^8`, so the character is the single coordinate sign on bit 8. It is +not the identity: the states with that bit set, 256 of the 512 addresses, +pick up phase `2` modulo 4, which is a factor `-1`. + +The same permutation round trip under `J` is `J_{G^{-1}} J_G = J_I`. The +section phase of `J_I` is `wt(x) - wt(x) = 0`. Substituting `J` for `K` on +this pair therefore deletes `Z_256` and disagrees on those 256 states. The +binary permutation of either product is the identity, so the deleted object +is only that central character. + +## What the recipe already records, and what it does not + +The sign-+1 descriptor stores `phase = 3` and + +```text +linear_Z4 = (1, 2, 2, 0, 2, 2, 3, 2, 2). +``` + +That Z4 vector is not the coboundary mask `144`. Paying the published +`linear_Z4` field does not display `Z_256`, and deleting the coboundary is a +separate change. + +The descriptor's `rank` field is `0`. This note does not read that field as a +free child. Helper return, routing and tape are absent, so those charges are +unknown. Unknown charges are not zero. The sign itself is an exact factor +`±1`, so this boundary adds no further denominator. + +The uncompensated `J` pair is consequently not a zero-cost rewrite of the +`K` pair. This is not a complete supplier invoice, a scalar-addition saving, +or a change of selected κ. + +The old-version descriptors on the same register use the same columns with a +shorter entrance. They are not part of this pair. diff --git a/research/k-adjoint-boundary-price/README.md b/research/k-adjoint-boundary-price/README.md new file mode 100644 index 0000000000..9c8f7fef44 --- /dev/null +++ b/research/k-adjoint-boundary-price/README.md @@ -0,0 +1,76 @@ +# Price of one K/adjoint round trip + +**Partial ledger. No new κ.** Selected conditional κ stays +`0.001672660197076918`. + +## Scope and evidence + +Original card: `independent-moment`, scope **changed**. The card asks for an +independent check of one changed supplier claim and its physical ledger. The +session handoff is the unpaid physical boundary in discussion #1166 comment +19036235, left by PR #4002. The catalogue method used is that card's frame +reconstruction: one coordinated substitution and its single-change control. + +The pinned boundary is the new-version witness warp on register `333`, index +`4`, together with the adjoint descriptor that swaps its entrance and +terminal. Both use + +```text +G = (1, 2, 8, 32, 44, 128, 59, 66, 489). +``` + +`K_{G^{-1}} K_G = Z_{256}` and `J_{G^{-1}} J_G = J_I`. The single-change +control deletes only `Z_{256}`. The binary product stays the identity, and +256 of 512 states change sign. [PROOF.md](PROOF.md) records the tags +`t_G = 144` and `t_{G^{-1}} = 68`. + +The published `linear_Z4` on the sign-+1 gate is not the mask `144`. Helper, +routing and tape charges are absent from the descriptor and stay unknown. +The exact sign adds no denominator. A favorable complete bill is not +established. No native expansion and no κ change. + +`RECIPES.json` is the byte-identical `source/RECIPES.json` from PR #4002 at +`d593941ea0a4926021cba9d01fe60500579e464f`, SHA256 +`64b85f6aef485026eebaec7acddb41999f57e074b0dfde8077b6543700cd684b`. That +commit is not required as a Git object in this clone. The checker rejects any +other bytes. It does not import PR #4002's verifier. + +## Reproduce + +From the repository root, CPython 3.12: + +```sh +python3.12 -B scripts/research_package.py --package research/k-adjoint-boundary-price +``` + +Direct check: + +```sh +python3.12 -B research/k-adjoint-boundary-price/verify.py +``` + +Expected marker: `PASS_K_ADJOINT_BOUNDARY_PRICE` with +`central_child=Z_256`, `states_wrong_under_J=256`, +`favorable_complete_bill=false`, and `new_kappa=false`. + +## Open next questions + +1. Can `Z_{256}` be absorbed by an adjacent paid gate on register `333`? + First step: name the predecessor and successor of index `4` in the + PR #3945 schedule and multiply those three operators. Blocked here + because this descriptor has no neighboring gates. +2. What helper, routing and tape tariff does this warp pay in the emitter? + First step: read the owner row for register `333` in the PR #3945 + native inventory. Blocked because those fields are not in `RECIPES.json`. + +## Credit + +Chris R / Clear1nsight, PR #3987, for the canonical lift and the inverse +witness. ToikY, PR #4002, for the explicit tag formula, the frozen four-map +inventory, and the open pricing question. Dugongue, PR #3945 / #3929, and the +native lineage named in that package, for the recipe convention. The tag +arithmetic on this one pair was recomputed here and does not import that +checker. + +Prepared by unpaidmoon with substantial Cursor Grok assistance. Apache-2.0. +No independent human or formal-kernel review is claimed. diff --git a/research/k-adjoint-boundary-price/RECIPES.json b/research/k-adjoint-boundary-price/RECIPES.json new file mode 100644 index 0000000000..a24e14593f --- /dev/null +++ b/research/k-adjoint-boundary-price/RECIPES.json @@ -0,0 +1,4236 @@ +{ + "items": [ + { + "kind": "warp", + "G_columns": [ + 1, + 2, + 4, + 54, + 72, + 8, + 130, + 16, + 284 + ], + "entrance": [ + 257, + 161, + 70, + 19, + 13 + ], + "terminal": [ + 260, + 132, + 75, + 42, + 25 + ], + "sign": 1, + "recipe": { + "rank": 0, + "left": { + "matrix_rows": [ + 265, + 202, + 396, + 184, + 128, + 136, + 16, + 64, + 384 + ], + "offset": 426, + "quadratic_rows": [ + 264, + 200, + 392, + 119, + 184, + 152, + 202, + 246, + 5 + ], + "linear_Z4": [ + 0, + 2, + 0, + 2, + 1, + 2, + 1, + 1, + 0 + ], + "phase": 1 + }, + "right": null + }, + "coverage": [ + { + "provider": "base", + "kind": "warp", + "index": 42, + "register": 1, + "version": "new", + "sign": 1 + 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"b1fea0c94436b236cc2b7d41a7be032811b94c81", + "sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129" + }, + { + "path": "docs/research/agent-task-catalog.json", + "usage": "provenance", + "git_blob": "67f085acd86acd7d4e03922d9cf4b26bca66fed5", + "sha256": "47b42433f5a85809a3aadd29c2c339da2c6ed728e4f7762df6b88bccb7874cf0" + } + ] +} diff --git a/research/k-adjoint-boundary-price/TASK.json b/research/k-adjoint-boundary-price/TASK.json new file mode 100644 index 0000000000..6b74a78f29 --- /dev/null +++ b/research/k-adjoint-boundary-price/TASK.json @@ -0,0 +1,72 @@ +{ + "schema_version": 1, + "task_id": "independent-moment", + "priority_revision": 6, + "base_commit": "bb4bccbf42844d2801487450727c2f63e10d1d0f", + "original_card": { + "id": "independent-moment", + "question": "Does one changed supplier or assembly claim lack a source-bound independent check of a specific new implication?", + "starting_points": [ + "certificates/selected-result.json", + "research/rank7-joint-endframes/README.md", + "docs/research/research-family-status.md" + ], + "methods": [ + "Independently reconstruct a coordinated frame/circuit change and its single-change control, then derive the complete rank and physical ledger.", + "Implement certified moment inequalities through a different exact enclosure method." + ], + "acceptance_gate": "Demonstrate independence, source binding, positive cases and semantic failure controls. Name the existing checks and the missing coverage. More digits or another equivalent evaluation of an unchanged root is not by itself new verification coverage.", + "first_step": { + "command": [ + "python3", + "-B", + "scripts/research_baseline.py" + ], + "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY", + "inspect": "Read #2979 joint rank-7 end-frame proposal and the revision-6 evidence status. Its claimed kappa is not selected. Compare coordinated changes with the losing single-change controls and locate the complete physical ledger; an aggregate moment alone does not validate the mechanism.", + "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay." + }, + "first_experiment": "Prioritize a bounded independent audit of #2979: reconstruct one joint group and its single-lowering control, check the declared frames/chronology, then trace changed children, idle widths and cleanup buffers into the complete invoice and both supplier caps. Choose one still-missing implication after checking existing audits. Stop with exact unresolved dependencies if full admission exceeds the session; do not launch a new lowering census on an unvalidated premise or substitute extra root digits for mechanism checking.", + "bottleneck_link": "Independent pricing prevents unsupported frontier claims and can reveal genuine accounting slack.", + "allowed_variations": [ + "Reconstruct either a source ledger or a numeric enclosure with a different method." + ], + "scope_change_triggers": [ + "Importing the primary function and calling its output independent verification.", + "Promoting #2979 from merged source archive to validated supplier solely from author PASS receipts or aggregate pricing." + ], + "overlap_terms": [ + "independent moment", + "rank histogram", + "exact enclosure", + "2979", + "rank7 joint endframes", + "paired extraction", + "joint lowering" + ] + }, + "scope_status": "changed", + "actual_scope": "Price the new-version K/adjoint round trip of the credited 9-bit witness on register 333, index 4, and record the unpaid central character Z_256.", + "scope_change_reason": "The eligible handoff is the unpaid physical boundary left by PR #4002, not a #2979 rank-group audit. The card method used is one coordinated substitution, the single-change control that drops Z_256, and the partial physical ledger of that pair.", + "bottleneck_link": "A J substitution that deletes a nontrivial central character is not a free rewrite of the native lift. The complex supplier still has no priced replacement for this boundary.", + "budget_minutes": 60, + "stop_rule": "Stop after this one round trip. Do not expand the native alphabet once helper, routing or tape charges are unknown.", + "outcome": "partial", + "evidence": "Independent recomputation of t_G=144, t_inv=68 and Z_256 on all 512 states. The J product is the identity phase and disagrees on 256 states. linear_Z4 is a different charge. Helper, routing and tape remain unknown.", + "author": "unpaidmoon", + "ai_assistance": "Substantial Cursor Grok assistance for the verifier, proof note and packaging. No independent human or formal-kernel review.", + "open_questions": [ + { + "question": "Can Z_256 be absorbed by an adjacent paid gate on register 333?", + "why_it_matters": "A neighboring gate could pay the central character without a new child. This descriptor cannot show that.", + "first_step": "Name the predecessor and successor of index 4 in the PR #3945 schedule and multiply the three operators.", + "blocked_by": "RECIPES.json has no neighboring gates for this warp." + }, + { + "question": "What helper, routing and tape tariff does this warp pay in the emitter?", + "why_it_matters": "Those unknown charges block a favorable complete bill. They are not zero.", + "first_step": "Read the owner row for register 333 in the PR #3945 native inventory.", + "blocked_by": "Those fields are absent from the frozen descriptor." + } + ] +} diff --git a/research/k-adjoint-boundary-price/VERIFY.json b/research/k-adjoint-boundary-price/VERIFY.json new file mode 100644 index 0000000000..151b26c5d7 --- /dev/null +++ b/research/k-adjoint-boundary-price/VERIFY.json @@ -0,0 +1,18 @@ +{ + "schema_version": 1, + "status": "ready", + "python": "3.12", + "requirements": [], + "inputs": [], + "commands": [ + { + "argv": [ + "{python}", + "-B", + "{package}/verify.py" + ], + "timeout_seconds": 120, + "checks": "Witness tags 144 and 68, round-trip character Z_256 on all 512 states, J-substitution mismatch on 256 states, and rejection of a zero defect." + } + ] +} diff --git a/research/k-adjoint-boundary-price/verify.py b/research/k-adjoint-boundary-price/verify.py new file mode 100644 index 0000000000..7542ad46e1 --- /dev/null +++ b/research/k-adjoint-boundary-price/verify.py @@ -0,0 +1,239 @@ +#!/usr/bin/env python3 +"""Price one actual K/adjoint round trip from the frozen native-lift recipes. + +The quadratic form and tag formula are the statements in PR #4002's proof. +This file does not import that package. Apache-2.0. +""" +from __future__ import annotations + +import hashlib +import json +from pathlib import Path + +HERE = Path(__file__).resolve().parent +RECIPES_SHA256 = "64b85f6aef485026eebaec7acddb41999f57e074b0dfde8077b6543700cd684b" +WITNESS = (1, 2, 8, 32, 44, 128, 59, 66, 489) +WIDTH = 9 +STATES = 1 << WIDTH + + +def fail(message): + raise SystemExit("FAIL_K_ADJOINT_BOUNDARY_PRICE " + message) + + +def unique_object(pairs): + result = {} + for key, value in pairs: + if key in result: + fail("duplicate JSON key " + str(key)) + result[key] = value + return result + + +def load_recipes(): + raw = (HERE / "RECIPES.json").read_bytes() + if hashlib.sha256(raw).hexdigest() != RECIPES_SHA256: + fail("RECIPES.json bytes differ from the PR #4002 pin") + data = json.loads(raw, object_pairs_hook=unique_object) + items = data["items"] + if len(items) != 40: + fail("expected 40 recipe descriptors") + return items + + +def invert_columns(columns): + width = len(columns) + rows = [sum(((columns[j] >> i) & 1) << j for j in range(width)) | (1 << (width + i)) + for i in range(width)] + for col in range(width): + pivot = next((row for row in range(col, width) if (rows[row] >> col) & 1), None) + if pivot is None: + fail("singular binary map") + rows[col], rows[pivot] = rows[pivot], rows[col] + for row in range(width): + if row != col and (rows[row] >> col) & 1: + rows[row] ^= rows[col] + return tuple(sum(((rows[i] >> (width + j)) & 1) << i for i in range(width)) + for j in range(width)) + + +def apply_columns(columns, state): + out = 0 + bit = 0 + while state: + if state & 1: + out ^= columns[bit] + state >>= 1 + bit += 1 + return out + + +def quadratic_rows(columns): + inverse = invert_columns(columns) + width = len(columns) + rows = [] + for i in range(width): + row = 0 + for j in range(width): + diagonal = 1 if i == j else 0 + gram = (inverse[i] & inverse[j]).bit_count() & 1 + row |= (diagonal ^ gram) << j + rows.append(row) + return tuple(rows) + + +def quadratic_value(rows, state): + total = 0 + for i, row in enumerate(rows): + if (state >> i) & 1: + higher = row & state & ~((1 << (i + 1)) - 1) + total += (row >> i) & 1 + total += 2 * higher.bit_count() + return total % 4 + + +def tag_mask(columns, rows=None): + rows = quadratic_rows(columns) if rows is None else rows + mask = 0 + for j, column in enumerate(columns): + # wt(e_j) = 1, so the input correction in the proof is +1. + difference = (quadratic_value(rows, column) - (column.bit_count() - 1)) % 4 + if difference not in (0, 2): + fail("phase-section difference is not an even residue") + mask |= (difference // 2) << j + return mask + + +def canonical_phase(columns, rows, state): + return quadratic_value(rows, apply_columns(columns, state)) + + +def section_phase(columns, state): + image = apply_columns(columns, state) + return (image.bit_count() - state.bit_count()) % 4 + + +def pin_boundary(items): + warps = [item for item in items if item.get("kind") == "warp"] + maps = {tuple(item["G_columns"]) for item in warps} + if len(warps) != 16 or len(maps) != 4 or WITNESS not in maps: + fail("frozen warp inventory is not the four changed-interface maps") + witness = [item for item in warps if tuple(item["G_columns"]) == WITNESS] + if len(witness) != 4: + fail("witness map does not have four frozen descriptors") + for item in witness: + if any(row.get("register") != 333 or row.get("index") != 4 for row in item["coverage"]): + fail("witness map is not confined to register 333 index 4") + forward_rows = [item for item in witness + if item["sign"] == 1 and item["entrance"] == [266, 138, 74, 30, 1] + and item["terminal"] == [426, 96, 24, 6, 1]] + if len(forward_rows) != 1: + fail("new-version sign-+1 boundary not unique") + forward = forward_rows[0] + backward = None + for item in warps: + if (tuple(item["G_columns"]) == WITNESS and item["sign"] == -1 + and item["entrance"] == forward["terminal"] + and item["terminal"] == forward["entrance"]): + backward = item + break + if backward is None: + fail("matching adjoint descriptor is absent") + providers = sorted({(row["provider"], row["version"]) for row in forward["coverage"]}) + if providers != [("base", "new"), ("extra", "new")]: + fail("new-version owner rows are not the two providers") + return forward, backward + + +def round_trip(): + items = load_recipes() + forward, backward = pin_boundary(items) + columns = WITNESS + inverse = invert_columns(columns) + rows = quadratic_rows(columns) + inverse_rows = quadratic_rows(inverse) + tag = tag_mask(columns, rows) + inverse_tag = tag_mask(inverse, inverse_rows) + # Masks add by XOR. t_I = 0, so ell(G, G^{-1}) = t_G XOR G^t t_{G^{-1}}. + pulled = sum(((column & inverse_tag).bit_count() % 2) << j + for j, column in enumerate(columns)) + defect = tag ^ pulled + if (tag, inverse_tag, defect) != (144, 68, 256): + fail("credited witness tags were not recomputed") + if defect.bit_count() != 1 or defect != 1 << 8: + fail("round-trip support is not the single coordinate 8") + j_wrong = 0 + for state in range(STATES): + k_phase = (canonical_phase(columns, rows, state) + + canonical_phase(inverse, inverse_rows, apply_columns(columns, state))) % 4 + j_phase = (section_phase(columns, state) + + section_phase(inverse, apply_columns(columns, state))) % 4 + expected = (2 * ((defect & state).bit_count() % 2)) % 4 + if k_phase != expected or j_phase != 0: + fail("round-trip phase identity failed at state " + str(state)) + if k_phase != j_phase: + j_wrong += 1 + image = apply_columns(inverse, apply_columns(columns, state)) + if image != state: + fail("binary round trip is not the identity") + if j_wrong != 256: + fail("J substitution does not miss exactly the odd states of bit 8") + # The recipe's own Z4 linear field is a different charge from the coboundary. + linear = forward["recipe"]["left"]["linear_Z4"] + if linear == [(tag >> j) & 1 for j in range(WIDTH)]: + fail("linear_Z4 collapsed onto the coboundary; the separation is gone") + if any(entry not in (0, 1, 2, 3) for entry in linear): + fail("linear_Z4 left the Z4 alphabet") + controls(columns, rows) + return { + "register": 333, + "index": 4, + "version": "new", + "providers": ["base", "extra"], + "sign_pair": [1, -1], + "tag": tag, + "inverse_tag": inverse_tag, + "central_child": "Z_256", + "support_coordinate": 8, + "support_weight": 1, + "states": STATES, + "states_wrong_under_J": j_wrong, + "binary_round_trip": "identity", + "recipe_phase": forward["recipe"]["left"]["phase"], + "recipe_linear_Z4": linear, + "linear_Z4_equals_coboundary": False, + "recipe_rank_field": forward["recipe"]["rank"], + "helper_routing_tape": "unknown", + "precision_extra_denominator": 0, + "favorable_complete_bill": False, + "new_kappa": False, + "adjoint_descriptor_sign": backward["sign"], + } + + +def controls(columns, rows): + # Dropping the weight-one correction selects a different mask. + broken = 0 + for j, column in enumerate(columns): + difference = (quadratic_value(rows, column) - column.bit_count()) % 4 + if difference in (0, 2): + broken |= (difference // 2) << j + if broken == 144: + fail("control did not move the tag") + # A zero defect is the J product, which is not the K product. + if any((2 * ((0 & state).bit_count() % 2)) % 4 + == (canonical_phase(columns, rows, state) + + canonical_phase(invert_columns(columns), + quadratic_rows(invert_columns(columns)), + apply_columns(columns, state))) % 4 + for state in (256,)): + fail("control accepted a zero central child") + + +def main(): + invoice = round_trip() + print("PASS_K_ADJOINT_BOUNDARY_PRICE " + json.dumps(invoice, sort_keys=True)) + + +if __name__ == "__main__": + main()