Bind first selected gauge44 provider and rule out fixed QQ16 role conjugacy

research/qq16-provider-binding/README.md

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+# First selected gauge44 provider versus corrected QQ16 F0
+
+The literal first selected provider is not corrected QQ16 F0. At the
+constant-character, common-cover specialization its data map is
+`G(x,y)=(x,y+x)`. The corrected QQ16 map Q has trace 120, whereas G has
+trace 224. Including all 480 arbitrary persistent helpers gives traces
+600 and 704. Thus **no fixed invertible role change conjugates these two
+maps**, even if that role change mixes the data and all borrowed helpers.
+The first direct output mismatch is already X_0, before any B1 decoder cut.
+
+This is a scoped negative result and exact local invoice, not a new supplier,
+an unrestricted impossibility theorem, or a selected-frontier change.
+
+## Actual source and boundary
+
+The base is `20ecf2891d80b5acf18d980b2164fb44ea7faa90`. The verifier binds
+`calls[0]` in the pinned selected archive's
+`t16/global/hosted/GLOBAL-TEMPLATE.json.gz`: time 0, replica 0, stage 0,
+provider gauge44, orientation forward. Its forward program hash is
+`071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8`.
+The embedded provider program equals the separate selected gauge44 program.
+This selects actual source coefficients, not a similarly named abstract shear.
+
+There are 704 distinct physical owner IDs: L_0,...,L_111 are X, L_112,...,
+L_223 are Y, and L_224,...,L_703 are borrowed helpers. The first 224 IDs are
+0,...,223 and their owner descriptors are `[1,0,p mod 112]`. Each remaining
+helper retains its literal owner descriptor. The eight C registers are
+separate owned private values. The source `CANONICAL-WORD.json.gz` supplies
+all 704 input and output frame IDs; the receipt pins both full frame arrays
+and the full owner list by canonical JSON SHA256. Frame IDs are not treated
+as equal merely because their contents agree at the specialization.
+
+The inherited [bridge convention](../joint-query/evidence/BRIDGE-REVIEW.md)
+fixes the constant Fourier character: each native line is
+`C_a=((1+i)I+(1-i)T_a)/2`, hence C_a(1)=1; translations and signed products
+also fix it. Cover permutations fix arrays constant over covers. The
+common-chart scalar specialization therefore supplies a necessary test for
+role-only correspondences that preserve this subspace. The verifier executes
+all scalar instructions in their actual order and specializes the declared
+native events to identity. This does not reverify native child kernels or
+the global hosting theorem.
+
+All 712 independent formal inputs are retained during replay. Both outputs
+have identity rows on all 480 helpers and zero rows on all eight private
+values. Data outputs are independent of initial helper and private values.
+Native helper frames can change; identity here means their specialized
+logical content. The full 712-dimensional maps discard private inputs and
+are not asserted invertible.
+
+## Exact first mismatch and mapping class
+
+Let A and T be the eight selected sets in the QQ16 packet, U their
+96-port complement, R its actual 8-by-112 centre matrix, and K=R^T/4.
+The independent formula check gives
+
+```
+f = R x
+X'_U = x_U - K_U f
+X'_A = K_A R_T x_T
+X'_T = K_T f
+Y'_U = y_U + X'_U
+Y'_S = y_S + x_S - X'_S       (S = A union T)
+```
+
+In particular, selected gauge44 returns `X'_0=x_0`, whereas QQ16 returns
+`X'_0=(x_76-x_81+x_87+x_92)/2`. Input x_0=1 with every other data and helper
+symbol zero is already decisive.
+
+The excluded class consists of a **single fixed invertible matrix P on the
+704 persistent specialized roles**, used at both entrance and exit. It
+would require `P^-1 G P=Q`; trace invariance contradicts 704 != 600.
+This includes permutations, signed/diagonal role gauges, and arbitrary
+invertible constant mixing of those roles. A physical correspondence whose
+restriction is such an invertible P also fails this necessary test.
+Different entrance and exit encodings, a noninvertible relation, a change
+of native representation that does not preserve the tested subspace, and
+paid adapters are outside this class. No claim of a complete program
+bisimulation or all-purpose representation obstruction is made.
+
+## Paid repair obligation and local invoice
+
+The exact rank of Q-G on the 224 data roles is 24. A proof of its kernel is
+short: equality requires x_S=0 from the selected Y equations, then
+R_U x_U=0 from the U equations. Since R_U K_U=12I, that kernel has dimension
+96-8=88 in x and all 112 dimensions in y. Thus its dimension is 200.
+The verifier also establishes rank 24 directly by rational elimination and
+checks that Q is invertible. Any post-adapter E with E Q=G must consequently
+have `rank(E-I)=24`. A product of rank-one elementary updates requires at
+least 24 such factors, by rank subadditivity. This is an algebraic lower
+bound, not a full physical invoice or an adapter implementation.
+
+| Exact local item | Selected gauge44 | Corrected QQ16 F0 |
+| --- | ---: | ---: |
+| Real scalar primitive allowance | 198766 | 211210 |
+| Extra scalar allowance before any repair | 0 | 12444 |
+| Source centre children | eight H8 | zero |
+| Added selected native lines | zero | eight H1 |
+| Borrowed helper outputs | 480 returned | 480 returned |
+| Owned private outputs | eight zero | eight zero |
+
+Persistent climb/adapter/residual-adapter event lists are compared exactly
+and are unchanged. The scalar allowances count the full literal words,
+including private clearing and dirty-helper correction. The native difference
+`-8 H8 + 8 H1` is conditional on a valid replacement: the missing boundary
+repair cannot be omitted from a construction budget. No native saving,
+physical repair cost, or global advantage is certified here.
+
+The requested matched boundary through B1 therefore stops at F0. Carrying
+an unmatched source state into a B1 decoder would assume the correspondence
+this check disproves. A new round needs either paid distinct boundary maps
+or an explicitly broader correspondence and its physical price.
+
+## Reproduction and validation
+
+```
+python3 -I -O -Werror -B research/qq16-provider-binding/verify.py --controls
+python3 -B scripts/research_package.py --package research/qq16-provider-binding
+```
+
+Every live input is hashed before parsing; no predecessor Python module is
+imported. Exact source and output hashes are in SOURCES.json and RESULT.json.
+The normal replay is read-only; `--write` creates only this
+package's receipt when absent and refuses to overwrite an existing receipt. The controls independently mutate a selected-source
+coefficient and a QQ16 wrapper coefficient and require both to fail.
+The registered test also verifies a Git-free source export and rejects a
+changed source hash and a changed receipt, including a Boolean/integer type
+substitution. No complete selected cold replay or formal theorem proof is
+claimed or needed for this isolated obstruction package.
+
+## Attribution and overlap
+
+The selected physical archive, original corrected joint-query construction,
+and its scalar/native/bridge reviews are retained unchanged and credited to
+their original contributors. This extends the selected-caller missing-binding
+audit (#3976) by evaluating the actual first provider and supplying a precise
+mapping-class obstruction. It does not repeat the query decoder optimization
+in #4003 or the zero-extra-owned-register decoder of #4015
+(`0fff81d8997cef646538bcd4f60d7d455cf93b8e`). The fixed-104-owner,
+one-common-query-frame formal-moment obstruction in tekuuu's #4030
+(`12df564caa8918453de658fe49601de6a9227017`) concerns a different consumer
+class; no result from that pending package is assumed here.
+
+Chris R / Clear1nsight with substantial OpenAI Codex assistance supplied this package.
+New code and prose are Apache-2.0. No independent human review is claimed.
+
+## Open next questions
+
+1. Can distinct, paid entrance and exit maps bind QQ16 F0 to this exact
+   selected call? Start by constructing E=GQ^-1 in the specialized algebra,
+   then bind its native frames, owner routes, scratch returns and full cost.
+   The rank-24 obligation and +12444 scalar delta prevent treating it as free;
+   no affordable physical lift is yet available.
+2. Can an end-to-end source substitution change the first provider and its
+   caller contract instead? Start from this literal F0 mismatch and name the
+   exact downstream selected work replaced. A first B1 consumer match and
+   complete family budget are prerequisites for another decoder round.

research/qq16-provider-binding/RESULT.json

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+{
+  "QQ16_added_native_lines": 8,
+  "QQ16_scalar_real_primitives": 211210,
+  "arbitrary_helpers_returned": 480,
+  "archive_member_sha256": {
+    "t16/global/base/providers/gauge44/CANONICAL-WORD.json.gz": "16bc0ebb04b4be6c0ade74badc6a0c0cdba4215eda86e4ff9f13abf8ecebd219",
+    "t16/global/base/providers/gauge44/LOCAL-PROGRAMS.json.gz": "241fde27d4e43f5a9cb6b128f9f76c5131a53d09f0371676163f914d0b0fef3a",
+    "t16/global/hosted/GLOBAL-TEMPLATE.json.gz": "73f47a1e60b1e4ea66dbca9a497c411c8e6adc7984e276a437a10a9a7a13b47a"
+  },
+  "data_difference_rank": 24,
+  "data_traces": [
+    224,
+    120
+  ],
+  "first_mismatch": {
+    "QQ16": "(X_76-X_81+X_87+X_92)/2",
+    "output": "X_0",
+    "selected": "X_0"
+  },
+  "independent_input_symbols": 712,
+  "minimum_rank_one_factors_for_post_adapter": 24,
+  "persistent_traces": [
+    704,
+    600
+  ],
+  "post_adapter_rank_minus_identity": 24,
+  "private_outputs_zero": 8,
+  "scalar_delta": 12444,
+  "schema_version": 1,
+  "scope": "Exact first source call and constant-character common-cover specialization; fixed invertible role conjugacy only. No physical adapter, B1 match, or supplier is constructed.",
+  "source_call": {
+    "local_program_sha256": "071ecdacc0bb3ac16046aad4119ed551a945cb0ed6c57002a548a3e2232503d8",
+    "orientation": "forward",
+    "pair": 0,
+    "provider_id": "gauge44",
+    "replica": 0,
+    "stage": 0,
+    "time": 0,
+    "window": {
+      "local_axes": [
+        0,
+        1,
+        2,
+        3,
+        4,
+        5,
+        6,
+        7,
+        8
+      ],
+      "prefix_axes": []
+    }
+  },
+  "source_center_ranks": [
+    8,
+    8,
+    8,
+    8,
+    8,
+    8,
+    8,
+    8
+  ],
+  "source_final_frames_sha256": "feef65df95af9ae193a9988edb5a7e9d3c607c8e4b7ffab3f3ef610dc184f1be",
+  "source_owner_list_sha256": "b0a39b7a3e5f5f4b7ab8c38d87de9ab66ec1499b3c0f3e50090d08c3dcfe62b3",
+  "source_scalar_real_primitives": 198766,
+  "source_start_frames_sha256": "bf49fb9bd01d22ae305cd0909e13409c6ffe0290fc1c2a35928e2c6162758f54",
+  "status": "scoped obstruction; no frontier change"
+}

research/qq16-provider-binding/SOURCES.json

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+{
+  "schema_version": 1,
+  "base_commit": "20ecf2891d80b5acf18d980b2164fb44ea7faa90",
+  "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"
+    },
+    {
+      "path": "research/joint-query/evidence/BRIDGE-REVIEW.md",
+      "usage": "input",
+      "git_blob": "86139908c418235588045324f0873de6ac9f9707",
+      "sha256": "d01b5f4959f7c91f835496d050dfae3eeab9dee2f581571c316a42571eaa1cd3"
+    },
+    {
+      "path": "research/joint-query/evidence/JOINT-QUERY-TRANSFER.md",
+      "usage": "input",
+      "git_blob": "a6805c58f23132f9420efebf90f5b7e863c2e179",
+      "sha256": "9e13e73ebf3192a6548798c2f1d13bd4d83957e8db0dc34de12b1a5311a52a75"
+    },
+    {
+      "path": "research/joint-query/evidence/SCALAR-REVIEW.md",
+      "usage": "input",
+      "git_blob": "e060789dfa3deafc49002b9f127de89800578bd1",
+      "sha256": "aa7b9f74430b56c42e1099029a501a9b6be9ab56b81bfdc681e4c2e6ff5bc97d"
+    }
+  ]
+}

research/qq16-provider-binding/TASK.json

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+{
+  "schema_version": 1,
+  "task_id": "joint-query-controller",
+  "priority_revision": 6,
+  "base_commit": "20ecf2891d80b5acf18d980b2164fb44ea7faa90",
+  "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": "Bind the literal first selected gauge44 forward provider to corrected QQ16 F0 and test fixed invertible persistent-role conjugacy.",
+  "scope_change_reason": "The actual source-provider match is required before importing a B1 decoder cut; this tests that prerequisite directly.",
+  "bottleneck_link": "A decoder budget cannot replace source work until the actual F0 boundary and its repair price are bound.",
+  "budget_minutes": 60,
+  "stop_rule": "Stop at the first exact mismatch or scoped correspondence obstruction; do not optimize an unbound decoder.",
+  "outcome": "negative-result",
+  "evidence": "RESULT.json; verify.py; exact 712-symbol replay and rank/trace proof in README.md",
+  "author": "Chris R / Clear1nsight with OpenAI Codex assistance",
+  "ai_assistance": "Substantial OpenAI Codex assistance for analysis, code, and prose; no independent human review claimed.",
+  "open_questions": [
+    {
+      "question": "Can distinct paid boundary maps bind this literal source provider?",
+      "why_it_matters": "A valid source substitution needs matching boundaries.",
+      "first_step": "Construct GQ^-1 at the specialization and price a native lift.",
+      "blocked_by": "No native frame/owner/cleanup implementation or favorable full invoice."
+    },
+    {
+      "question": "Can an end-to-end caller change replace selected first-provider work?",
+      "why_it_matters": "A different caller may permit a broader correspondence.",
+      "first_step": "Name the exact downstream work replaced and bind the first B1 input.",
+      "blocked_by": "No matched B1 boundary or family-level budget."
+    }
+  ]
+}