Price the F0 adjacent ADD after the first rank-1 climb.

research/qq16-adjacent-add-bill/PROOF.md

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+# Frame bill for events 9894 and 9895
+
+The forward core and the canonical word are the pinned inputs named in
+`SOURCES.json`. Frames are lists of integer axes. Frame 0 is `[]` and frame 4
+is `[459]`.
+
+A climb from frame `a` to frame `b` of recorded rank `r` is legal only when
+every axis of `a` lies in the `F_2`-span of the axes of `b` and
+`r = |b| - |a| > 0`. It then sets that register's current frame to `b`.
+A scalar operation annotated with frame `f` is legal only when every `L`
+operand's current frame is already `f`. These are the checks in `verify.py`.
+
+Event 9894 is `['climb', 'A', 546, 0, 4, 1]`. It is the first climb in the
+word, so every register is still at `start`. `start[546] = 0` and
+`start[561] = 4`. Empty axes sit in the span of `[459]`, and `1 = 1 - 0`,
+so the climb is legal and leaves `L546` in frame 4. `L561` is not the
+climbed register.
+
+Event 9895 is `['scalar', ['add', ['L', 546], ['L', 561], -1, 1], 4]`.
+Both current frames equal 4, so the annotation is legal. The event does not
+write a new frame. No earlier scalar writes `L561`. The only earlier event
+that names 561 is the entrance wrapper
+`['residual_adapter', 'pre', 561, 4]`, which the same contract requires to
+repeat the entrance frame.
+
+The retained coefficient count for a positive numerator and a power-of-two
+denominator is: one clear, one step per bit after the leading bit, one step
+per `1` bit, one step per halving, then `+2` for the signed accumulation and
+the work clear. For absolute value 1 and denominator 1 that count is 4.
+The invoice's real-step total is twice that count, so 8. The same count
+applies to `+1`.
+
+The pair's rank histogram therefore gains one rank-1 child and no scalar
+rank child. Adding `L561` back, with coefficient `+1` and the same frame, is
+legal in that state and costs another 4 scalar steps. It restores the
+post-climb value of `L546` and leaves both frames at 4.
+
+The recipe table contains `(old, new) = (0, 4)` at rank 1 and does not
+contain `(4, 0)`. The published `final` vector puts both registers at frame
+1. The forward replay that applies every climb reaches that vector, so the
+word never uses a rank-decreasing climb to undo event 9894.
+
+No six-tape origin is read here. A zero frame delta is not a zero physical
+layout bill.

research/qq16-adjacent-add-bill/README.md

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+# Adjacent F0 ADD after the first rank-positive climb
+
+**Partial frame bill. No new κ.** Selected conditional κ stays
+`0.001672660197076918`.
+
+On the pinned forward core, event 9894 is the word's first climb:
+`L546` from frame 0 (`[]`) to frame 4 (`[459]`), rank 1. Event 9895 is
+`L546 -= L561` in frame 4. `L561` enters in frame 4 and is not climbed or
+written before that ADD. Both operands already sit in the annotated frame, so
+the retained nested-frame contract accepts the ADD with no second climb.
+
+The coefficient `-1/1` costs 4 scalar work steps and 8 real steps under the
+retained bit-clear / bit-add / halving count. The sign does not add a step.
+The climb is the pair's only rank child (`+1` at rank 1). Replaying every
+climb and every `L` scalar in the forward word reproduces `final`.
+
+The in-frame inverse `L546 += L561` is legal at the same 4-step cost and
+restores only the post-climb value. The pinned Clifford table has no child
+`(4, 0)`. Both registers end at frame 1, not at `L546`'s entrance frame 0.
+
+This does not assign six-tape windows, meter the climb's kernel, or price a
+consumer. Unknown physical layout cost is not zero. PR #3932 bound event 9894
+and left this ADD unpriced. PR #4114 ledgers rays `L359` and `L112`; it does
+not replay this pair.
+
+## Scope and evidence
+
+Task `joint-query-controller`, scope **refined** to this one pair. The card's
+allowed variation is one changed first pair. Base
+`bb4bccbf42844d2801487450727c2f63e10d1d0f`, priority revision 6. Pins are in
+[SOURCES.json](SOURCES.json). The argument is checked by
+[verify.py](verify.py), not by a separate prose proof.
+
+## Reproduce
+
+From the repository root, CPython 3.12:
+
+```sh
+python3.12 -B scripts/research_package.py --package research/qq16-adjacent-add-bill
+```
+
+Expected:
+
+```text
+PASS_QQ16_ADJACENT_ADD_BILL climb=9894 add=9895 frame=4 axis=459 rank_child=1 scalar_work=4 real_steps=8 climbs_before_pair=0 reverse_child=absent word_climbs=3486 word_scalars=20089 no_new_kappa
+PASS_REGISTERED_RESEARCH_PACKAGE research/qq16-adjacent-add-bill outcome=partial
+```
+
+Controls inside the verifier: the published final-frame vector, a unit / `3/1` /
+`1/2` work triple, rejection of the ADD with the climb deleted, and rejection
+if `L561` enters in frame 0.
+
+## Credit
+
+The forward word and frame table are the pinned joint-query / selected-replay
+sources. PR #3932 (Chris R / Clear1nsight) named event 9895 as the unpriced
+successor of event 9894. The nested-frame rule is the retained local checker
+contract. New check by unpaidmoon, with substantial Cursor Grok assistance.
+Apache-2.0. No independent human or formal-kernel review.
+
+## Open next questions
+
+1. What physical head moves does this ADD cost once `L546` and `L561` are
+   placed on real six-tape windows? Same-frame legality does not meter layout
+   or the climb's kernel. The blocker is PR #3932's unbound intervals and head
+   positions.
+2. Which cleanup child returns `L546` from frame 4 to entrance frame 0? The
+   in-frame inverse does not. The forward contract only admits strict rank
+   increases, and no recipe child `(4, 0)` is present.

research/qq16-adjacent-add-bill/SOURCES.json

@@ -0,0 +1,30 @@
+{
+  "schema_version": 1,
+  "base_commit": "bb4bccbf42844d2801487450727c2f63e10d1d0f",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "b1fea0c94436b236cc2b7d41a7be032811b94c81",
+      "sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "67f085acd86acd7d4e03922d9cf4b26bca66fed5",
+      "sha256": "47b42433f5a85809a3aadd29c2c339da2c6ed728e4f7762df6b88bccb7874cf0"
+    },
+    {
+      "path": "research/community-frontier1042-audit/selected-replay.tar.gz",
+      "usage": "input",
+      "git_blob": "6f4dc6fe7631d8aacf8081fcaecf32197181685b",
+      "sha256": "22c3f4dce4b897a1d423d1388801933e288b6a6b1906cb15e1b16a5eb68db754"
+    },
+    {
+      "path": "research/joint-query/certificate.json.gz",
+      "usage": "input",
+      "git_blob": "c6e876d8b48d768214deee265ade428f8983b566",
+      "sha256": "a5ed85fac5ebf3c091482a113ab0d351eb5a7892fe2841a35e16017ec1ff49f7"
+    }
+  ]
+}

research/qq16-adjacent-add-bill/TASK.json

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+{
+  "schema_version": 1,
+  "task_id": "joint-query-controller",
+  "priority_revision": 6,
+  "base_commit": "bb4bccbf42844d2801487450727c2f63e10d1d0f",
+  "original_card": {
+    "id": "joint-query-controller",
+    "question": "Can a literal QQ16 producer meet the proposed completed-output error budgets with dirty helpers and an affordable physical consumer?",
+    "starting_points": [
+      "docs/research/research-family-status.md",
+      "research/joint-query/README.md",
+      "research/joint-query/evidence/QQ16-SELECTED-WITNESS.md",
+      "research/joint-query/evidence/JOINT-QUERY-TRANSFER.md",
+      "docs/research/community-efficient1000-review.md",
+      "research/qq16-producer-defect-transfer/README.md"
+    ],
+    "methods": [
+      "Derive one literal producer's completed-output defects and intermediate dirty-helper bounds, with its physical bill.",
+      "Design or audit one consumer, retention or hosting boundary and its complete cost for the pinned producer/decoder."
+    ],
+    "acceptance_gate": "Name the changed premise of the fixed F0/B1 observation obstruction. Show exactly which query is recovered, legal native reads and restoration, and a full favorable budget including cover maps, helpers and endpoints. Local inverse identities alone do not close the global controller. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "scripts/research_baseline.py"
+      ],
+      "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+      "inspect": "Read the revision-6 family record and #2965 producer-defect transfer after the local QQ16 decoder contract. Its author-checked output-error estimate does not implement producer interiors, bound dirty helpers, or pay for the consumer; independently check the implication used.",
+      "scope": "Source-bound orientation only. Read the named package and review before relying on its local evidence; this command is not its replay or supplier admission."
+    },
+    "first_experiment": "Pin one literal F0/B1 producer and its native-child contracts; derive the actual intermediate magnitude ledger and completed-output defects, including dirty helpers and correlations. Compare with #2965 budgets and price storage, movement, cleanup and F17 consumption. Stop with a precise missing bound if no producer contract supplies it; do not optimize another decoder precision constant in isolation.",
+    "bottleneck_link": "The native local words exist; retained query information and its physical access are the missing link to a composed recursive interface.",
+    "allowed_variations": [
+      "One paid query, one changed first pair, or one precisely specified affine helper state.",
+      "A counterexample or lower bound for that exact proposed repair.",
+      "One unresolved obligation of a newer local decoder, with exact source heads and a distinct claim/domain."
+    ],
+    "scope_change_triggers": [
+      "Retaining the fixed first pair and ordinary schedule while allowing only homogeneous selected-only control, already excluded by the witness.",
+      "Treating cover-map counts as zero-cost physical address operations.",
+      "Recreating the pending complete local decoder or early-record/output-bank coalescing already under investigation without a distinct audit or changed premise.",
+      "Treating a completed-output defect inequality as a producer-interior, dirty-range or physical-cost certificate."
+    ],
+    "overlap_terms": [
+      "QQ16",
+      "joint-query",
+      "changing-chart controller",
+      "selected observation",
+      "1969",
+      "2540",
+      "early record",
+      "output-bank retention",
+      "complete native decoder",
+      "2965",
+      "producer defect",
+      "dirty-helper range",
+      "F17 consumer"
+    ]
+  },
+  "scope_status": "refined",
+  "actual_scope": "Price the one adjacent scalar ADD after the first rank-positive F0 climb: event 9895 is L546 -= L561 in frame 4, with no extra frame change.",
+  "scope_change_reason": "The card's first experiment asks for one literal F0 producer's intermediate bill. PR #3932 already binds climb event 9894 and leaves the next ADD unpriced. PR #4114 ledgers rays L359 and L112. This package prices only that named adjacent pair under the retained nested-frame contract.",
+  "bottleneck_link": "The native local words exist; a same-frame ADD is the first continuation after the unpaid rank-1 climb. Its frame bill says whether that continuation asks for another relocation before any consumer is priced.",
+  "budget_minutes": 60,
+  "stop_rule": "Stop after this one pair. Do not assign physical tape origins, replay the six-tape kernel, or price later adds that read L561.",
+  "outcome": "partial",
+  "evidence": "Source-bound frame replay of the pinned forward word: the ADD is legal with both operands already in frame 4, the climb is the only rank-1 child, and the coefficient -1/1 costs 4 retained scalar work steps. No recipe climbs from frame 4 back to frame 0.",
+  "author": "unpaidmoon",
+  "ai_assistance": "Cursor Grok 4.7 wrote the verifier and the note. No independent human or formal-kernel review.",
+  "open_questions": [
+    {
+      "question": "What physical head moves does this ADD cost once L546 and L561 are placed on real six-tape windows?",
+      "why_it_matters": "Same-frame legality does not meter layout, encoding, or the climb's kernel. Unknown physical cost is not zero.",
+      "first_step": "Bind both registers to the two data windows named by PR #3932 and count head motion for one coordinatewise subtraction.",
+      "blocked_by": "PR #3932 leaves physical intervals, origins, and head positions unbound."
+    },
+    {
+      "question": "Which cleanup child, if any, returns L546 from frame 4 to its entrance frame 0?",
+      "why_it_matters": "The in-frame inverse ADD restores only the post-climb value. Entrance restoration is a separate rank-decreasing step, and the pinned recipe table has no child (4, 0).",
+      "first_step": "Search the forward cleanup phase for a rank-decreasing return of register 546, or prove none exists.",
+      "blocked_by": "The forward contract only admits strict rank increases, so the return is not a forward climb."
+    }
+  ]
+}

research/qq16-adjacent-add-bill/VERIFY.json

@@ -0,0 +1,17 @@
+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [
+    "research/community-frontier1042-audit/selected-replay.tar.gz",
+    "research/joint-query/certificate.json.gz"
+  ],
+  "commands": [
+    {
+      "argv": ["{python}", "-B", "{package}/verify.py"],
+      "timeout_seconds": 120,
+      "checks": "Literal events 9894 and 9895, nested-frame legality of that ADD, scalar work 4, absent reverse child (4, 0), and controls that drop the climb, move L561, or change the coefficient."
+    }
+  ]
+}