Bound QQ16 private d_A retention at the B1 cut

research/qq16-private-da-frame-floor-seed81b017/README.md

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+# QQ16 private-register retention frame floor
+
+This package tests one proposed way to realize the post-`B_1_2` observation
+`d_A = Y_A` used by the conditional two-query kernel in PR #2174: copy its eight
+A-port coordinates into the existing owned private fields `C0..C7` and expose
+them at that cut.
+
+The exact pinned `B_1_2` word ends with the retained backward stage-one core.
+That core returns all eight owned fields in frame I. At the same cut, the eight
+`Y_A` data fields have frames
+`f117, f124, f137, f144, f153, f163, f174, f228`. Each is the stage-one
+completed frame (the first 17 basis terms) minus its actual A-port label, so
+each differs from I in exactly 18 one-term Z4 entries. A matching-phase scalar
+ADD from `Y_A` into `C_i` is therefore not legal as written.
+
+The bounded normalization check enumerates all 3,650 registered cover maps
+for a one-map conversion of any of those eight frames to I. There are no such
+maps. In the deliberately favorable native line model, one rank-one line can
+change only one frame term. Aligning the eight private fields to their source
+frames therefore needs at least 8 × 18 = 144 line calls. The existing wrapper
+contract associates two full-cover maps with each added line call, giving 288
+cover-map operations. Eight coefficient-one scalar copies cost 32 real scalar
+primitives under the pinned scalar allowance. If the cut is terminal, eight
+private clears add another eight scalar primitives; if the existing next core
+is invoked, its clear events can perform that cleanup and the extra clear
+charge is zero.
+
+This is already over the generous budget comparison recorded in the active
+pre-F0 `B2 X_U` claim, Discussion #2074: its rank-eight output envelope leaves
+at most two additional rank-one-equivalent calls above the selected ceiling.
+The 144-call phase floor exceeds that slack before charging observation
+handling, any multi-map route, physical address/stream costs, global hosting,
+or recursive precision. This comparison is a planning screen against that
+live claim, not an independently reviewed frontier theorem. The local exact
+result does not rule out multi-map normalization, a different state layout,
+or another controller; it rules out the cheap one-map / one-term-line private
+bank relay tested here as a favorable repair.
+
+## Reproduction
+
+From the repository root:
+
+```sh
+python3 -I -B research/qq16-private-da-frame-floor-seed81b017/verify.py
+python3 -I -O -B research/qq16-private-da-frame-floor-seed81b017/test_package.py
+python3 -B scripts/research_package.py --package research/qq16-private-da-frame-floor-seed81b017 --check-only
+```
+
+Expected verifier output:
+
+```text
+PASS_QQ16_PRIVATE_DA_FRAME_FLOOR ports=8 frame_terms=18 single_map_hits=0 rank1_line_floor=144 cover_maps=288 scalar_add=32 no_kappa
+```
+
+The verifier pins the main-branch source certificate and checks the exact
+program endpoint, the final clear of every `C` field, all eight frame IDs,
+every registered single-map action, and the termwise line lower bound. Its
+positive controls include the identity map and a one-term line cancellation;
+its negative controls include wrong-stage and wrong-port frames and a mutated
+source certificate. Exact Z4 arithmetic is used throughout. The 144-line
+figure grants the new mechanism arbitrary legal one-term line operations on
+all private fields, even though the retained wrapper currently exposes a
+native-line path only for C0; it is therefore a favorable lower bound in this
+restricted model.
+
+The package does not implement a new full controller, prove that every
+multi-map route is expensive, or change the selected bound. PR #1969 supplies
+the retained QQ16 words and native wrapper conventions. PR #2174 supplies the
+conditional decoder whose `d_A` observation motivates this experiment. This
+work was produced with substantial OpenAI Codex assistance; it has no
+independent human review.
+
+The scoped claim is [Discussion #2192](https://github.com/CrocSwap/integer-mult-bounds/discussions/2192).
+Its entry overlap refresh at 2026-10-14 23:05 UTC completed pagination over
+435 open PRs and 877 Discussions with no warnings and no exact-scope match.
+The pre-submission refresh at 23:21 UTC completed pagination over 439 open PRs
+and 882 Discussions, also with no warnings or matches. At that check, PR #2174
+remained open at `f79470a7931f3943360c10d15b428e0e4e479c22`, and Discussion #2074
+remained open as the separate `B2 X_U` observation claim.
+
+## Open next questions
+
+- Can a bounded two-map or three-map route normalize the eight output frames
+  while preserving the selected values, and does its complete charged profile
+  stay within the same favorable envelope? A next attempt should search the
+  exact pinned map action graph to depth three and stop on first discovery or
+  exhaustive frontier completion. It is blocked here because the scoped
+  experiment only tested one-map normalization and one-term line conversion.
+- Can another state layout expose `d_A` without using a private field in frame
+  I? This would change the mechanism, so it needs a new exact interface and a
+  fresh full-cost screen.

research/qq16-private-da-frame-floor-seed81b017/RESULT.json

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+{
+  "a_ports": [
+    {
+      "frame": "f117",
+      "port": 0,
+      "single_map_hits": [],
+      "terms": 18,
+      "unit_line_distance": 18
+    },
+    {
+      "frame": "f124",
+      "port": 7,
+      "single_map_hits": [],
+      "terms": 18,
+      "unit_line_distance": 18
+    },
+    {
+      "frame": "f137",
+      "port": 20,
+      "single_map_hits": [],
+      "terms": 18,
+      "unit_line_distance": 18
+    },
+    {
+      "frame": "f144",
+      "port": 27,
+      "single_map_hits": [],
+      "terms": 18,
+      "unit_line_distance": 18
+    },
+    {
+      "frame": "f153",
+      "port": 36,
+      "single_map_hits": [],
+      "terms": 18,
+      "unit_line_distance": 18
+    },
+    {
+      "frame": "f163",
+      "port": 46,
+      "single_map_hits": [],
+      "terms": 18,
+      "unit_line_distance": 18
+    },
+    {
+      "frame": "f174",
+      "port": 57,
+      "single_map_hits": [],
+      "terms": 18,
+      "unit_line_distance": 18
+    },
+    {
+      "frame": "f228",
+      "port": 111,
+      "single_map_hits": [],
+      "terms": 18,
+      "unit_line_distance": 18
+    }
+  ],
+  "certificate_sha256_compressed": "a5ed85fac5ebf3c091482a113ab0d351eb5a7892fe2841a35e16017ec1ff49f7",
+  "comparison": "144 rank-one line calls exceed the two-call favorable slack before global hosting or address costs",
+  "controls": [
+    "identity map",
+    "single-term line cancellation",
+    "wrong stage rejected",
+    "wrong port rejected",
+    "mutated source certificate rejected"
+  ],
+  "copy_add_real_primitive_bound": 32,
+  "copy_adds": 8,
+  "cover_maps_at_two_per_line": 288,
+  "favorable_extra_rank_one_credit_from_discussion_2074": 2,
+  "next_core_cleanup_extra_charge": 0,
+  "no_kappa": true,
+  "observation_coordinates": 8,
+  "private_frame": "f0",
+  "rank_one_line_calls_lower_bound": 144,
+  "registered_maps_checked": 3650,
+  "scope": "Eight A ports at B_1_2; all registered one-map normalizers and the one-term native-line conversion model only.",
+  "single_map_hits": 0,
+  "source_base": "0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2",
+  "status": "PASS_QQ16_PRIVATE_DA_FRAME_FLOOR",
+  "terminal_cleanup_clear_macros": 8,
+  "terminal_cleanup_real_primitive_bound": 8,
+  "test_package_sha256": "e607bd03cf87101f5105b73bad1c2fc9a2ebe1de444e7e8aecce534e2d327e58",
+  "verify_py_sha256": "c041c1c46c5b007ec21061c605014265e175d9d42fea0d0d11dba5860355af90"
+}

research/qq16-private-da-frame-floor-seed81b017/SOURCES.json

@@ -0,0 +1,73 @@
+{
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+      "usage": "provenance"
+    },
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+  "predecessors": [
+    {
+      "author": "Ali Romman",
+      "integrated_commit": "a6e6ad3936f67b8f63b5b68c5e75d540610a65e7",
+      "pr": 1969,
+      "use": "Retained QQ16 local words, private field contract, and two-map wrapper convention."
+    },
+    {
+      "author": "@commdata2338",
+      "head": "f79470a7931f3943360c10d15b428e0e4e479c22",
+      "pr": 2174,
+      "use": "Conditional two-query decoder; its open question asks whether an actual controller realizes d_A at the B1 cut. Not imported as executable evidence."
+    },
+    {
+      "discussion": 2074,
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/2074",
+      "use": "Different pre-F0 B2 X_U query; its current favorable rank-eight envelope is used only as a planning comparator."
+    }
+  ],
+  "schema_version": 1
+}

research/qq16-private-da-frame-floor-seed81b017/TASK.json

@@ -0,0 +1,124 @@
+{
+  "actual_scope": "At the exact post-B_1_2 backward stage-one QQ16 cut, test whether existing owned C0..C7 fields in frame I can cheaply retain the eight Y_A coordinates used as d_A by a two-query decoder. Search all 3,650 registered single cover maps for one-step phase normalization, then derive the exact lower bound in the one-term native-line conversion model.",
+  "ai_assistance": "Substantial OpenAI Codex assistance in the mathematical reduction, exact checker, and writing. No independent human review is claimed.",
+  "author": "OpenAI Codex (GPT-6)",
+  "base_commit": "0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2",
+  "bottleneck_link": "The conditional QQ16 two-query kernel already uses d_A at the B1 cut, but an actual controller must realize that record. This tests whether the existing private bank can carry it without a new field or an unaffordable phase conversion.",
+  "budget_minutes": 60,
+  "catalogue_sha256": "d46eb6d5b3e279428753d770653663fbdf1063e55c255ea073d768f344927ef7",
+  "claim_discussion": 2192,
+  "evidence": "README.md, verify.py, test_package.py, and RESULT.json. Exact frame IDs, 3,650-map census, 144-line floor, 288 wrapper map operations, eight ADDs costing 32 real scalar primitives, and endpoint cleanup cases are recorded.",
+  "open_questions": [
+    {
+      "blocked_by": "This cycle stopped after the scoped one-map census and line-distance floor; no composed-map graph was explored.",
+      "first_step": "Search the exact pinned map action graph by depth 2, then depth 3 only if the fully charged rank-eight plus map budget remains favorable.",
+      "question": "Can a two-map or three-map normalization route carry d_A through this cut within the same favorable budget?",
+      "why_it_matters": "The present result only rejects a one-map shortcut and the single-term native-line fallback. A shorter multi-map route would change the paid interface cost."
+    }
+  ],
+  "original_card": {
+    "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.",
+    "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."
+    ],
+    "bottleneck_link": "The native local words exist; retained query information and its physical access are the missing link to a composed recursive interface.",
+    "first_experiment": "Apply the existing witness to one proposed extra observation or changed first pair. If it still loses the required record, stop. Otherwise derive one ordered two-call identity and charge the added read, chart maps and restoration before extending to more stages.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "scripts/research_baseline.py"
+      ],
+      "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+      "inspect": "Read the fixed-first-pair QQ16 witness before designing a controller. The checked #1969 local words do not evade that witness or supply global placement.",
+      "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."
+    },
+    "id": "joint-query-controller",
+    "methods": [
+      "Add one explicitly priced ordinary-to-selected observation and derive the ordered two-call map and inverse.",
+      "Change the first local pair or retained state, then test the existing lost-observation witness and price all new operations."
+    ],
+    "overlap_terms": [
+      "QQ16",
+      "joint-query",
+      "changing-chart controller",
+      "selected observation",
+      "1969"
+    ],
+    "question": "Can one explicitly changed QQ16 interface recover the missing chart query and close a two-call controller within a favorable full budget?",
+    "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."
+    ],
+    "starting_points": [
+      "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"
+    ]
+  },
+  "outcome": "negative-result",
+  "overlap_checks": [
+    {
+      "at": "2026-10-14T23:05:44Z",
+      "complete_pagination": true,
+      "discussions": 877,
+      "matches": 0,
+      "open_prs": 435,
+      "purpose": "Entry claim check.",
+      "warnings": []
+    },
+    {
+      "at": "2026-10-14T23:21:48Z",
+      "complete_pagination": true,
+      "discussions": 882,
+      "matches": 0,
+      "open_prs": 439,
+      "purpose": "Pre-submission refresh.",
+      "warnings": []
+    }
+  ],
+  "predecessor_refresh": {
+    "discussion2074": {
+      "checked_at": "2026-10-14T23:22:00Z",
+      "state": "open",
+      "title": "CLAIM: one paid pre-F0 B2 source observation (seed 3e62c004)"
+    },
+    "pr2174": {
+      "checked_at": "2026-10-14T23:22:00Z",
+      "head": "f79470a7931f3943360c10d15b428e0e4e479c22",
+      "state": "OPEN"
+    }
+  },
+  "predecessors": [
+    {
+      "author": "Ali Romman",
+      "integrated_commit": "a6e6ad3936f67b8f63b5b68c5e75d540610a65e7",
+      "pr": 1969,
+      "use": "Retained QQ16 local words, private field contract, and two-map wrapper convention."
+    },
+    {
+      "author": "@commdata2338",
+      "head": "f79470a7931f3943360c10d15b428e0e4e479c22",
+      "pr": 2174,
+      "use": "Conditional two-query decoder; its open question asks whether an actual controller realizes d_A at the B1 cut. Not imported as executable evidence."
+    },
+    {
+      "discussion": 2074,
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/2074",
+      "use": "Different pre-F0 B2 X_U query; its current favorable rank-eight envelope is used only as a planning comparator."
+    }
+  ],
+  "priority_revision": 4,
+  "refined_scope_key": "QQ16-B1-dA-C0-C7-frame-normalization-one-map-or-single-term-line",
+  "schema_version": 1,
+  "scope_change_reason": "Refines the card to the live PR #2174 missing interface: a concrete private-register relay for d_A at one fixed B1 cut. It changes no first pair or decoder identity and tests the native phase-conversion cost of using existing owned state, a distinct mechanism from the pre-F0 ordinary-to-selected B2 X_U observation in Discussion #2074.",
+  "scope_status": "refined",
+  "seed": "81b0173d58b26d95259d6f15464a5db3",
+  "selected_record_sha256": "10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32",
+  "selector_scope_key": "0e34adbc1dd119161c3a",
+  "stop_rule": "At the pinned B_1_2 cut, enumerate all 3,650 single-map normalizers for the eight A-port frames, then compute the exact one-term-line distance from each source frame to private frame I. Stop if the resulting 144 rank-one line calls exceed the two-call favorable rank-one slack after the rank-eight output charge. Do not search multi-map sequences, other cuts, or other first pairs.",
+  "task_id": "joint-query-controller",
+  "track": "recursive-interfaces"
+}