From af24d3b04e9d93906ed3c5a6262972fecfe5388a Mon Sep 17 00:00:00 2001
From: Cursor Agent <cursoragent@cursor.com>
Date: Tue, 3 Nov 2026 13:38:46 +0000
Subject: [PATCH 1/2] Publish a replayable price check for the P111 span(7)
 query.

The triangular zero-frame continuation of PR #1525 keeps the original scatter outputs and does not beat the paid profile {1: 4, 8: 1}. The constructor rejects moving span(7) to the zero frame. No new kappa.

Co-authored-by: unpaidmoon <unpaidmoon@users.noreply.github.com>
---
 research/p111-line7-query-price/NOTICE.md     |  15 +
 research/p111-line7-query-price/README.md     |  82 +++++
 research/p111-line7-query-price/SOURCES.json  |  18 ++
 research/p111-line7-query-price/TASK.json     |  90 ++++++
 research/p111-line7-query-price/VERIFY.json   |  17 ++
 .../inputs/CENTRE-SEED.json                   | 172 +++++++++++
 .../inputs/word-base.json.gz                  | Bin 0 -> 57371 bytes
 research/p111-line7-query-price/verify.py     | 279 ++++++++++++++++++
 8 files changed, 673 insertions(+)
 create mode 100644 research/p111-line7-query-price/NOTICE.md
 create mode 100644 research/p111-line7-query-price/README.md
 create mode 100644 research/p111-line7-query-price/SOURCES.json
 create mode 100644 research/p111-line7-query-price/TASK.json
 create mode 100644 research/p111-line7-query-price/VERIFY.json
 create mode 100644 research/p111-line7-query-price/inputs/CENTRE-SEED.json
 create mode 100644 research/p111-line7-query-price/inputs/word-base.json.gz
 create mode 100644 research/p111-line7-query-price/verify.py

diff --git a/research/p111-line7-query-price/NOTICE.md b/research/p111-line7-query-price/NOTICE.md
new file mode 100644
index 0000000000..91d2acd964
--- /dev/null
+++ b/research/p111-line7-query-price/NOTICE.md
@@ -0,0 +1,15 @@
+SPDX-License-Identifier: Apache-2.0
+
+The pinned word and centre seed are byte copies of Rohan Arun's PR #1525 at
+`90d39a5603c7fbfd8d8d957e9732d9b6ebd6317f`, paths
+`research/p111-early-merge-query/inputs/word-base.json.gz` and
+`research/p111-early-merge-query/CENTRE-SEED.json`. That draft retains the
+PR1297 word, the PR1134 arithmetic, and the PR1060 physical model, with the
+notices in that package. Those predecessor files are not modified here.
+
+The containment test is the same subspace test as PR1060 `model.py`. This
+package reimplements that one predicate; it does not vendor or replay the
+PR1060 compiler.
+
+New checks and text: unpaidmoon, with substantial Cursor Grok assistance.
+Apache-2.0. No independent human review is claimed.
diff --git a/research/p111-line7-query-price/README.md b/research/p111-line7-query-price/README.md
new file mode 100644
index 0000000000..0e760cfa3b
--- /dev/null
+++ b/research/p111-line7-query-price/README.md
@@ -0,0 +1,82 @@
+# Line-span(7) query does not beat its zero-frame scatter
+
+**No new κ.** Selected conditional κ stays `781451/250000000`. Discussion #1166
+comment
+[19143427](https://github.com/CrocSwap/integer-mult-bounds/discussions/1166#discussioncomment-19143427)
+already stopped one triangular continuation of Rohan Arun's draft PR #1525 at
+`90d39a5603c7fbfd8d8d957e9732d9b6ebd6317f`, and left the evidence in local paths.
+This package replays that scatter identity from the pinned bytes and checks the
+constructor fact the handoff left open: `model.move` rejects a descent from
+`span(7)` to the zero frame.
+
+## Result
+
+Puncture 0 builds `q = (c61 + c63 + c31 + c256) / 2`. On the pinned word, the
+copied query is the line `span(7)`. The retained cut is 176 zero-frame centre
+ADDs, 22 from each of the eight centres. The triangular substitution
+
+- column 61 becomes twice itself,
+- columns 63, 31 and 256 each lose column 61,
+
+reproduces every original scatter linear form. Each of the 112 outputs is a
+vector on the 704 roles. This check does not replay section B. The corrected
+matrix has 230 nonzero ADD entries, exactly 54 more. Those 54 split by support:
+column 63 overlaps column 61 in 8 rows and cancels 4 of them (`+10`), while
+columns 31 and 256 are disjoint from column 61 (`+22` each). JoyboyBrian's
+handoff already recorded the 230-versus-176 census. The overlap split is checked
+here.
+
+All 62 dirty columns of `q` already appear in those original outputs. A final
+map that equals the original scatter therefore keeps every one of them. A final
+map that zeroes any of them does not deliver the original target outputs.
+
+The PR1060 constructor `move` admits a change only when the old frame is
+contained in the new one. `contained((7,), ())` is false, so that constructor
+rejects moving the query register from `span(7)` to the zero frame. The handoff
+priced the same conversion if a paid rank-1 copy is granted instead, and the
+profiles it named are `{1: 4, 8: 1}` and `{1: 5, 8: 1}`. For every positive
+integer power tariff those two multisets differ by exactly 1. The same strict
+increase holds for every tariff that gives rank 1 a positive price and prices
+no other rank differently. The 54 extra ADDs are further nonnegative scalar
+cost on this matrix.
+
+## What this does not show
+
+This does not price a scatter that consumes the line-7 query directly, a
+different correction matrix, whole-call owners, precision, tape, compiler, or
+outer admission. It does not replay section B and it does not change the
+selected frontier. The handoff's local scripts remain unpublished; these checks
+recompute the scatter identity from the pinned word and centre seed.
+
+## Reproduction
+
+Python 3.12, standard library only:
+
+```sh
+python3 -B research/p111-line7-query-price/verify.py
+python3 -B scripts/research_package.py --package research/p111-line7-query-price
+```
+
+Expected first line: `PASS_P111_LINE7_QUERY_PRICE delta_adds 54 dirty_visible 62 line_to_zero_move False NO_NEW_KAPPA`.
+
+The word SHA-256 is `e8e6e78ff7422275c38324499e1f33fb2ecd30de9503aef2b8f1ee80d8c4df8e`.
+Failure controls inside the verifier: omitting the three partner corrections
+changes an output, and the containment test rejects the line-to-zero move.
+
+## Open next questions
+
+1. Can a continuation whose 22 query receivers stay at `span(7)` until their
+   original final frames are restored beat `{1: 4, 8: 1}` after every restoration
+   copy is charged? The scalar cut does not record those final frames.
+2. Is there a correction other than this triangular substitution that preserves
+   the 112 output forms with no extra rank-1 child and fewer than 230 ADDs?
+
+## Credit
+
+Word, centre seed and query formula: Rohan Arun, PR #1525, with the retained
+PR1297 / PR1134 / PR1060 lineage in that package's NOTICE. The triangular
+relation, the 230-versus-176 census, and the conditional `{1: 4, 8: 1}` to
+`{1: 5, 8: 1}` bill are JoyboyBrian's, comment 19143427; that note labelled its
+checker local-only. Frame containment is the test in PR1060 `model.py`
+(`contained`). This replay and the support split were prepared by unpaidmoon
+with substantial Cursor Grok assistance. Apache-2.0.
diff --git a/research/p111-line7-query-price/SOURCES.json b/research/p111-line7-query-price/SOURCES.json
new file mode 100644
index 0000000000..75ea7c3d55
--- /dev/null
+++ b/research/p111-line7-query-price/SOURCES.json
@@ -0,0 +1,18 @@
+{
+  "schema_version": 1,
+  "base_commit": "7c49fe32c55de02c2c873655c804b16e4c3fef0a",
+  "files": [
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "3404fbdd5e7529a0674eef26114b5071e4586cec",
+      "sha256": "ead6cdc9d0af6d58e8a49744d8ec8c7c15e13d2ba93c276c434bcf9b51b93a81"
+    },
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "d59b5035e7b4cbaa9d688a1d32dd0d6eb79c466a",
+      "sha256": "9b8d0eea95b3bf0dfcb7938a732a6439b87a2685dec2a5ab9e525b3b34debbfa"
+    }
+  ]
+}
diff --git a/research/p111-line7-query-price/TASK.json b/research/p111-line7-query-price/TASK.json
new file mode 100644
index 0000000000..30af320040
--- /dev/null
+++ b/research/p111-line7-query-price/TASK.json
@@ -0,0 +1,90 @@
+{
+  "schema_version": 1,
+  "task_id": "joint-query-controller",
+  "priority_revision": 8,
+  "base_commit": "7c49fe32c55de02c2c873655c804b16e4c3fef0a",
+  "original_card": {
+    "id": "joint-query-controller",
+    "question": "Can a changed query demand or caller remove real work while satisfying native chronology and restoration?",
+    "starting_points": [
+      "docs/research/current-priorities.md",
+      "docs/research/research-family-status.md",
+      "certificates/selected-result.json",
+      "docs/research/pr-intake-evidence/pr5599-completion/PROOF-REVIEW.md"
+    ],
+    "methods": [
+      "Construct and independently check one source-bound instance of the stated first experiment.",
+      "Seek an exact counterexample or target-specific complete-budget obstruction to that same proposed change."
+    ],
+    "acceptance_gate": "A source-bound arbitrary-input identity and legal producer/consumer boundary with the complete paid and productive target invoice, including restoration, ownership, native alignment and extra charges. Price under the actual current model; historical ceiling.py assumptions must be established before use. A favorable optimistic relaxation keeps a route open but is not a completed supplier. A scoped local result remains useful; expansion requires the family-level budget gate.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "scripts/research_selected_baseline.py"
+      ],
+      "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+      "inspect": "Read revision 8, the selected review and live exact-source handoffs. Then follow this card's bounded first_experiment.",
+      "scope": "Source-bound orientation only, not a supplier replay or theorem proof."
+    },
+    "first_experiment": "Choose an exact caller and a new demand/interface hypothesis. Read the scoped #5617/#5631/#5649/#5747 and #5720/#5745 objections before rebuilding an excluded schedule. Compare the complete matched source/consumer protocols including all retained helper outputs. For an active-mode injection, first check #5745: its canonical delivery claim repays the eight removed centre jobs. Audit that exact claim or change its channel/feedback hypothesis; do not repeat the same free-injection search. Stop if the full favorable budget fails or the required restored output is unobservable.",
+    "bottleneck_link": "Judge the actual current supplier contract and complete signed target/paid bill; frozen-profile ceilings require an applicability proof.",
+    "allowed_variations": [
+      "One exact source head, helper/cut region or quantified proposition and changed hypothesis; check live handoffs first. Different seeds are not different scopes."
+    ],
+    "scope_change_triggers": [
+      "Changing source head, helper/cut domain, operation alphabet or caller boundary without recording the new scope.",
+      "Treating an archived proposal or local numerical pass as complete supplier admission."
+    ],
+    "overlap_terms": [
+      "query demand",
+      "active mode",
+      "5720",
+      "5745",
+      "5747",
+      "caller"
+    ],
+    "existing_checks": [
+      {
+        "scope": "PR #4166: author-checked installed producer/service/return/bridge connection; native-component comparison loses.",
+        "evidence": "research/qq16-caller-install/README.md",
+        "remaining": "Complete matched physical protocol bill, or changed source-compatible demand/circuit; no affordable supplier yet.",
+        "status": "author-checked",
+        "source_commit": "0b082d22a0e9a442d264ab0633e35ef26c790630",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      },
+      {
+        "scope": "Selected PR5599: complete helper-subspace construction and independent caller replay; five framework assumptions remain.",
+        "evidence": "docs/research/pr-intake-evidence/pr5599-completion/PROOF-REVIEW.md",
+        "remaining": "The next experiment must identify uncovered source-specific work. Successor archive intake does not transfer this admission.",
+        "status": "reviewed",
+        "source_commit": "09dd0965711ca7eeb169057a420abab1c9052137",
+        "selected_record_sha256": "2a0220e866417774606e0f991e41b9c1d26b1f43b97857238cf478dbc7d330b5"
+      }
+    ]
+  },
+  "scope_status": "refined",
+  "actual_scope": "For the exact PR #1525 puncture-0 / pivot-61 query at span(7), does the triangular zero-frame canonicalization (double column 61 and subtract it from columns 63, 31 and 256) deliver the original scatter outputs at a paid profile better than {1: 4, 8: 1}?",
+  "scope_change_reason": "The catalogue asks whether any changed query demand or caller can remove real work while satisfying native chronology and restoration. Comment 19143427 already stopped this one canonicalization with local-only evidence and left a broader successor open. This package narrows to that stopped candidate: it publishes a replay of the scatter identity and checks that PR1060 model.move rejects the span(7) to zero descent. It does not rerun the active-mode injection excluded by the card.",
+  "bottleneck_link": "A complete paid profile for this query has to price the frame that holds q and every scatter ADD. This triangular zero-frame continuation keeps the original scatter outputs and, once a rank-1 copy is granted in place of the rejected move, adds one rank-1 child plus 54 ADDs. It is not a saving under a positive rank-1 tariff.",
+  "budget_minutes": 60,
+  "stop_rule": "Stop once the pinned word shows that the triangular substitution preserves all 112 scatter outputs, hence all 62 dirty columns, and that presenting the span(7) query to the zero-frame cut requires one extra rank-1 child. Do not search other correction matrices, targets left at span(7), or outer admission in this session.",
+  "outcome": "negative-result",
+  "evidence": "research/p111-line7-query-price/verify.py recomputes q, the 176-entry cut, the 230-entry triangular correction, the +10/+22/+22 support split, equality of all 112 scatter forms, a nonzero witness for each of the 62 dirty columns, and the rejected span(7)-to-zero move. Both python3 -B and python3 -O -B print PASS_P111_LINE7_QUERY_PRICE. Section B, the Clifford compiler, Lean, and the selected frontier are not replayed. The 230-versus-176 census and the conditional profile bill were already stated in discussion comment 19143427.",
+  "author": "unpaidmoon",
+  "ai_assistance": "Prepared by unpaidmoon with substantial Cursor Grok assistance. No independent human review.",
+  "open_questions": [
+    {
+      "question": "Can a continuation whose 22 query receivers stay at span(7) until their original final frames are restored beat {1: 4, 8: 1} after every restoration copy is charged?",
+      "why_it_matters": "The zero-frame route loses because the constructor cannot move span(7) down to the zero frame. Leaving the receivers on the line might avoid that rank-1 copy, but only if restoration of the original final frames does not cost more.",
+      "first_step": "Recover the original final owner frame of each of the 22 query receivers from the pinned word and price one legal descent from span(7) to that frame.",
+      "blocked_by": "The scalar cut records frame None and does not store those final frames."
+    },
+    {
+      "question": "Is there a correction other than this triangular substitution that preserves the 112 output forms with no extra rank-1 child and fewer than 230 ADDs?",
+      "why_it_matters": "The triangular matrix is one exact continuation, not a proof that every output-preserving scatter costs 230 ADDs.",
+      "first_step": "Fix the four centre values at q in slot 61 and the three unchanged partners, and search integer combinations of those columns that match the 112 original output forms with fewer than 230 nonzeros.",
+      "blocked_by": "Any such matrix still has to present q at a frame the constructor can legally read. This session does not search that family."
+    }
+  ]
+}
diff --git a/research/p111-line7-query-price/VERIFY.json b/research/p111-line7-query-price/VERIFY.json
new file mode 100644
index 0000000000..2b22b6f727
--- /dev/null
+++ b/research/p111-line7-query-price/VERIFY.json
@@ -0,0 +1,17 @@
+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [
+    "research/p111-line7-query-price/inputs/word-base.json.gz",
+    "research/p111-line7-query-price/inputs/CENTRE-SEED.json"
+  ],
+  "commands": [
+    {
+      "argv": ["{python}", "-B", "{package}/verify.py"],
+      "timeout_seconds": 60,
+      "checks": "Recomputes q, the 176-entry cut, the triangular 230-entry correction, the exact +10/+22/+22 support split, equality of all 112 output forms on 704 coordinates, visibility of all 62 dirty columns, illegality of the span(7) to zero move, and the strict one-child profile increase. Omitting the partner correction must change an output."
+    }
+  ]
+}
diff --git a/research/p111-line7-query-price/inputs/CENTRE-SEED.json b/research/p111-line7-query-price/inputs/CENTRE-SEED.json
new file mode 100644
index 0000000000..d5bea849fd
--- /dev/null
+++ b/research/p111-line7-query-price/inputs/CENTRE-SEED.json
@@ -0,0 +1,172 @@
+{
+  "status": "PASS_SCOPED_NONNESTED_CENTRE_QUERY_NATIVE",
+  "puncture": 0,
+  "terms": [
+    {
+      "center": 61,
+      "weight": "1/2",
+      "frame": [
+        256,
+        128,
+        64,
+        32,
+        16,
+        8,
+        5,
+        3
+      ]
+    },
+    {
+      "center": 63,
+      "weight": "1/2",
+      "frame": [
+        256,
+        128,
+        64,
+        32,
+        17,
+        9,
+        4,
+        2
+      ]
+    },
+    {
+      "center": 31,
+      "weight": "1/2",
+      "frame": [
+        256,
+        128,
+        65,
+        33,
+        17,
+        9,
+        4,
+        2
+      ]
+    },
+    {
+      "center": 256,
+      "weight": "1/2",
+      "frame": [
+        256,
+        128,
+        65,
+        33,
+        16,
+        8,
+        5,
+        3
+      ]
+    }
+  ],
+  "query_frame": [
+    2,
+    5,
+    9,
+    16,
+    32,
+    64,
+    128,
+    256
+  ],
+  "transport_profile": {
+    "2": 4
+  },
+  "rank_mass": 8,
+  "omitted_source_coefficient": "2",
+  "dirty_columns": 62,
+  "dirty_coefficients": {
+    "239": "-1",
+    "225": "-1",
+    "237": "-1",
+    "224": "2",
+    "255": "-1",
+    "241": "-1",
+    "253": "-1",
+    "240": "1",
+    "242": "1",
+    "271": "-2",
+    "256": "1",
+    "261": "1",
+    "270": "1",
+    "351": "-3",
+    "340": "1",
+    "350": "1",
+    "336": "1",
+    "367": "-1",
+    "356": "1",
+    "366": "1",
+    "352": "1",
+    "383": "-1",
+    "379": "1",
+    "368": "1",
+    "399": "-2",
+    "388": "1",
+    "398": "1",
+    "395": "1",
+    "227": "1",
+    "283": "-1",
+    "287": "-2",
+    "280": "-1",
+    "272": "1",
+    "299": "-1",
+    "303": "-2",
+    "292": "1",
+    "302": "1",
+    "400": "1",
+    "403": "2",
+    "409": "1",
+    "402": "-1",
+    "411": "1",
+    "416": "1",
+    "419": "1",
+    "425": "1",
+    "418": "-1",
+    "421": "1",
+    "430": "1",
+    "417": "1",
+    "429": "1",
+    "243": "1",
+    "319": "-2",
+    "435": "1",
+    "441": "1",
+    "434": "-1",
+    "437": "1",
+    "446": "1",
+    "433": "1",
+    "445": "1",
+    "267": "-1",
+    "431": "-1",
+    "447": "-1"
+  },
+  "fixtures": [
+    {
+      "trial": 0,
+      "forward_and_inverse_transpose": true,
+      "streaming_peak_temporaries": 2,
+      "weighted_accumulations": 4,
+      "source_copies": 4,
+      "temporary_discards": 5
+    },
+    {
+      "trial": 1,
+      "forward_and_inverse_transpose": true,
+      "streaming_peak_temporaries": 2,
+      "weighted_accumulations": 4,
+      "source_copies": 4,
+      "temporary_discards": 5
+    }
+  ],
+  "optimistic_moment": "0.999971277929646601478394497346102075481621",
+  "optimistic_profile": {
+    "1": 2340,
+    "4": 130,
+    "3": 414,
+    "2": 508,
+    "5": 80,
+    "8": 7,
+    "7": 1
+  },
+  "optimistic_idle": 14274,
+  "scope": "Four source-stable whole-stream copies at nonnested frame transitions. Exact signed Pauli/global phase checks and two dense Gaussian fixtures in each orientation. The omitted source must be zero and dirty response compensated. Two-stream peak includes query accumulator and one live converted centre copy. Storage, all-size native recursion, nonmonotone owner hosting, full scatter and exact recovery/precision/analytic transfer are unadmitted. Favorable moment grants incompatible deletion/endpoint/hosting credits, not a new bound."
+}
\ No newline at end of file
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diff --git a/research/p111-line7-query-price/verify.py b/research/p111-line7-query-price/verify.py
new file mode 100644
index 0000000000..72c5ba62cd
--- /dev/null
+++ b/research/p111-line7-query-price/verify.py
@@ -0,0 +1,279 @@
+#!/usr/bin/env python3
+"""Price the PR1525 line-span(7) query against its zero-frame scatter.
+
+No new kappa. The triangular correction preserves every original scatter
+output, including all 62 dirty columns, and the constructor forbids moving
+that query from span(7) down to the zero frame.
+"""
+import gzip
+import hashlib
+import json
+from collections import Counter
+from fractions import Fraction as Q
+from pathlib import Path
+
+ROOT = Path(__file__).resolve().parent
+WORD_SHA = "e8e6e78ff7422275c38324499e1f33fb2ecd30de9503aef2b8f1ee80d8c4df8e"
+SEED_SHA = "228e178662fc01895bbcd8472a52114d3a3d11ea8c7ae44d99cd1c8cf9e89147"
+CENTRES_IN_QUERY = (61, 63, 31, 256)
+PARTNERS = (63, 31, 256)
+
+
+def require(condition, message):
+    if not condition:
+        raise AssertionError(message)
+
+
+def basis(rows):
+    pivots = {}
+    for value in rows:
+        while value:
+            bit = value.bit_length() - 1
+            if bit in pivots:
+                value ^= pivots[bit]
+            else:
+                pivots[bit] = value
+                break
+    for bit in sorted(pivots):
+        for other in pivots:
+            if other > bit and (pivots[other] >> bit) & 1:
+                pivots[other] ^= pivots[bit]
+    return tuple(pivots[bit] for bit in sorted(pivots))
+
+
+def contained(left, right):
+    """Span(left) is contained in span(right). Same test as PR1060 model.py."""
+    return len(basis(list(left) + list(right))) == len(basis(list(right)))
+
+
+def add_row(dst, scale, src):
+    for index, value in src.items():
+        total = dst.get(index, Q(0)) + scale * value
+        if total == 0:
+            dst.pop(index, None)
+        else:
+            dst[index] = total
+
+
+def apply_op(rows, event):
+    if event[0] == "add":
+        add_row(rows[event[1]], Q(event[3], event[4]), rows[event[2]])
+    else:
+        require(event[0] == "scale", event[0])
+        rows[event[1]] = {i: value * Q(event[2], event[3]) for i, value in rows[event[1]].items()}
+
+
+def scatter_matrix(word):
+    order = word["centers"]
+    require(order == [60, 61, 63, 224, 31, 240, 23, 256], order)
+    index = {centre: slot for slot, centre in enumerate(order)}
+    matrix = [[Q(0) for _ in order] for _ in range(112)]
+    receivers = {centre: [] for centre in order}
+    for event in word["cut"]:
+        require(event[0] == "add" and event[5] is None, event)
+        target = event[1] - 112
+        require(0 <= target < 112, event[1])
+        slot = index[event[2]]
+        matrix[target][slot] += Q(event[3], event[4])
+        receivers[event[2]].append(event[1])
+    return matrix, receivers
+
+
+def column_nnz(matrix, slot):
+    return sum(1 for row in matrix if row[slot])
+
+
+def triangular(matrix, index):
+    """Substitute q = (c61 + c63 + c31 + c256) / 2 for the c61 readout."""
+    query = index[61]
+    corrected = []
+    for row in matrix:
+        new_row = row[:]
+        original = row[query]
+        new_row[query] = 2 * original
+        for partner in PARTNERS:
+            new_row[index[partner]] = row[index[partner]] - original
+        corrected.append(new_row)
+    return corrected
+
+
+def support_delta(matrix, index, partner):
+    query = index[61]
+    slot = index[partner]
+    both = cancel = unequal = only_query = only_partner = 0
+    for row in matrix:
+        left, right = row[query], row[slot]
+        if left and right:
+            both += 1
+            if right - left == 0:
+                cancel += 1
+            else:
+                unequal += 1
+        elif left:
+            only_query += 1
+        elif right:
+            only_partner += 1
+    old = column_nnz(matrix, slot)
+    new = sum(1 for row in matrix if row[slot] - row[query])
+    return {
+        "partner": partner,
+        "old_nnz": old,
+        "new_nnz": new,
+        "delta": new - old,
+        "overlap": both,
+        "cancellations": cancel,
+        "unequal_overlap": unequal,
+        "only_query": only_query,
+        "only_partner": only_partner,
+    }
+
+
+def combine(matrix, vectors):
+    outputs = []
+    for row in matrix:
+        acc = {}
+        for slot, weight in enumerate(row):
+            if weight:
+                add_row(acc, weight, vectors[slot])
+        outputs.append(acc)
+    return outputs
+
+
+def endpoint_line(frame):
+    return next(
+        mask
+        for mask in range(1, 512)
+        if all((mask & vector).bit_count() % 2 == 0 for vector in frame)
+    )
+
+
+def main():
+    word_bytes = (ROOT / "inputs/word-base.json.gz").read_bytes()
+    seed_bytes = (ROOT / "inputs/CENTRE-SEED.json").read_bytes()
+    require(hashlib.sha256(word_bytes).hexdigest() == WORD_SHA, "word sha")
+    require(hashlib.sha256(seed_bytes).hexdigest() == SEED_SHA, "seed sha")
+    word = json.loads(gzip.decompress(word_bytes))
+    seed = json.loads(seed_bytes)
+    require(seed["puncture"] == 0, seed["puncture"])
+    require(seed["dirty_columns"] == 62, seed["dirty_columns"])
+    require([item["center"] for item in seed["terms"]] == list(CENTRES_IN_QUERY), seed["terms"])
+    require(all(item["weight"] == "1/2" for item in seed["terms"]), seed["terms"])
+
+    roles = 224 + word["report"]["R"]
+    require(roles == 704, roles)
+    rows = [{i: Q(1)} for i in range(roles)]
+    for event in word["precondition"] + word["A"]:
+        apply_op(rows, event)
+
+    query = {}
+    for item in seed["terms"]:
+        add_row(query, Q(item["weight"]), rows[item["center"]])
+    dirty = {i: value for i, value in query.items() if i >= 112}
+    require({str(i): str(value) for i, value in dirty.items()} == seed["dirty_coefficients"], "dirty census")
+    require(len(dirty) == 62, len(dirty))
+    beta = seed["puncture"]
+    for source in range(112):
+        if source == beta:
+            continue
+        expected = Q(sum(a * b for a, b in zip(word["root_lines"][beta], word["root_lines"][source])), 2)
+        require(query.get(source, Q(0)) == expected, source)
+
+    line = endpoint_line(seed["terms"][0]["frame"])
+    require(line == 7 and basis((line,)) == (7,), line)
+    require(contained((7,), ()) is False, "span(7) is not contained in the zero frame")
+    require(contained((), (7,)) is True, "the zero frame is contained in span(7)")
+
+    matrix, receivers = scatter_matrix(word)
+    index = {centre: slot for slot, centre in enumerate(word["centers"])}
+    require(all(len(receivers[centre]) == 22 and len(set(receivers[centre])) == 22 for centre in word["centers"]), "22 receivers")
+    require(sum(column_nnz(matrix, slot) for slot in range(8)) == 176, "S nnz")
+    for slot in range(8):
+        weights = Counter(str(row[slot]) for row in matrix if row[slot])
+        require(set(weights) <= {"1/4", "-1/4"}, weights)
+        require(sum(weights.values()) == 22, weights)
+
+    deltas = [support_delta(matrix, index, partner) for partner in PARTNERS]
+    require([item["delta"] for item in deltas] == [10, 22, 22], deltas)
+    require(sum(item["delta"] for item in deltas) == 54, deltas)
+    require(deltas[0]["cancellations"] == 4 and deltas[0]["overlap"] == 8, deltas[0])
+    require(deltas[1]["overlap"] == 0 and deltas[2]["overlap"] == 0, deltas[1:])
+
+    corrected = triangular(matrix, index)
+    corrected_nnz = sum(1 for row in corrected for value in row if value)
+    require(corrected_nnz == 230, corrected_nnz)
+    require(column_nnz(corrected, index[61]) == 22, "query column")
+    doubled = Counter(str(row[index[61]]) for row in corrected if row[index[61]])
+    require(doubled == Counter({"-1/2": 3, "1/2": 19}), doubled)
+
+    old_vectors = [rows[centre] for centre in word["centers"]]
+    new_vectors = [query if centre == 61 else rows[centre] for centre in word["centers"]]
+    old_outputs = combine(matrix, old_vectors)
+    new_outputs = combine(corrected, new_vectors)
+    require(old_outputs == new_outputs, "triangular image differs from the original scatter")
+
+    # The same identity fails if the partner correction is omitted.
+    uncorrected = [row[:] for row in matrix]
+    for row in uncorrected:
+        row[index[61]] = 2 * row[index[61]]
+    require(combine(uncorrected, new_vectors) != old_outputs, "missing partner correction should be visible")
+
+    witnesses = {}
+    for column in sorted(dirty):
+        hits = []
+        for target, form in enumerate(old_outputs):
+            coefficient = form.get(column, Q(0))
+            if coefficient:
+                hits.append((112 + target, str(coefficient)))
+                break
+        require(len(hits) == 1, column)
+        witnesses[str(column)] = {"output_row": hits[0][0], "coefficient": hits[0][1]}
+    require(len(witnesses) == 62, len(witnesses))
+
+    # One shared rank-1 copy takes span(7) to a zero-frame register. The
+    # comparator profile is the four already-paid rank-1 centre moves plus the
+    # rank-8 copy. The extra child is exactly one rank 1.
+    old_profile = {1: 4, 8: 1}
+    new_profile = {1: 5, 8: 1}
+    require(new_profile[1] - old_profile[1] == 1 and new_profile[8] == old_profile[8], "profile delta")
+    # For every tariff that sends rank 1 to a positive value and ignores no
+    # other change, the new multiset costs exactly that positive value more.
+    for exponent in range(1, 9):
+        old_mass = 4 * (1 ** exponent) + 8 ** exponent
+        new_mass = 5 * (1 ** exponent) + 8 ** exponent
+        require(new_mass - old_mass == 1, exponent)
+
+    receipt = {
+        "status": "PASS_P111_LINE7_QUERY_PRICE",
+        "word_sha256": WORD_SHA,
+        "seed_sha256": SEED_SHA,
+        "source_pr": 1525,
+        "source_head": "90d39a5603c7fbfd8d8d957e9732d9b6ebd6317f",
+        "endpoint_line": [7],
+        "move_line_to_zero_legal": False,
+        "move_zero_to_line_legal": True,
+        "scatter_nnz": 176,
+        "triangular_nnz": 230,
+        "scatter_add_delta": 54,
+        "partner_deltas": deltas,
+        "query_receivers": 22,
+        "dirty_columns": 62,
+        "dirty_columns_visible_in_original_outputs": 62,
+        "dirty_witnesses": witnesses,
+        "comparator_profile": old_profile,
+        "zero_frame_copy_profile": new_profile,
+        "profile_delta": {1: 1},
+        "no_new_kappa": True,
+    }
+    print(
+        receipt["status"],
+        "delta_adds", receipt["scatter_add_delta"],
+        "dirty_visible", receipt["dirty_columns_visible_in_original_outputs"],
+        "line_to_zero_move", receipt["move_line_to_zero_legal"],
+        "NO_NEW_KAPPA",
+        flush=True,
+    )
+    return receipt
+
+
+if __name__ == "__main__":
+    main()

From 916e18c55f0e4e1fc3a235440ea0bdbfb3d565e7 Mon Sep 17 00:00:00 2001
From: Cursor Agent <cursoragent@cursor.com>
Date: Tue, 3 Nov 2026 13:38:59 +0000
Subject: [PATCH 2/2] Pin the PR1525 word and centre seed at the publishing
 commit.

Those bytes are not on upstream main, so the source rows use an explicit head pin. The catalogue and selected record stay pinned at 7c49fe32.

Co-authored-by: unpaidmoon <unpaidmoon@users.noreply.github.com>
---
 research/p111-line7-query-price/SOURCES.json | 14 ++++++++++++++
 1 file changed, 14 insertions(+)

diff --git a/research/p111-line7-query-price/SOURCES.json b/research/p111-line7-query-price/SOURCES.json
index 75ea7c3d55..8f6aa74f1b 100644
--- a/research/p111-line7-query-price/SOURCES.json
+++ b/research/p111-line7-query-price/SOURCES.json
@@ -13,6 +13,20 @@
       "usage": "provenance",
       "git_blob": "d59b5035e7b4cbaa9d688a1d32dd0d6eb79c466a",
       "sha256": "9b8d0eea95b3bf0dfcb7938a732a6439b87a2685dec2a5ab9e525b3b34debbfa"
+    },
+    {
+      "path": "research/p111-line7-query-price/inputs/word-base.json.gz",
+      "usage": "input",
+      "pin": "head:af24d3b04e9d93906ed3c5a6262972fecfe5388a:research/p111-line7-query-price/inputs/word-base.json.gz",
+      "git_blob": "eacf8c773cb50637f93a762342b3b5f0853fe29a",
+      "sha256": "e8e6e78ff7422275c38324499e1f33fb2ecd30de9503aef2b8f1ee80d8c4df8e"
+    },
+    {
+      "path": "research/p111-line7-query-price/inputs/CENTRE-SEED.json",
+      "usage": "input",
+      "pin": "head:af24d3b04e9d93906ed3c5a6262972fecfe5388a:research/p111-line7-query-price/inputs/CENTRE-SEED.json",
+      "git_blob": "d5bea849fdde3bb43d38ff44d7b5a2c34e754954",
+      "sha256": "228e178662fc01895bbcd8472a52114d3a3d11ea8c7ae44d99cd1c8cf9e89147"
     }
   ]
 }