Research: audit already removed QQ16 centres and actual outer consumer boundaries

research/qq16-centre-lifetime-boundary-audit/PREDECESSORS.json

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+{
+  "schema_version": 1,
+  "canonical_source_base": "20ecf2891d80b5acf18d980b2164fb44ea7faa90",
+  "retained_pending_sources": [
+    {
+      "pr": 3952,
+      "head": "996ff698d3efd0bdce606e240f3b00e6ab91e7fc",
+      "source_path": "research/qq16-f17-demand-projection/WORD.json",
+      "local_path": "vendor/pr3952/WORD.json",
+      "sha256": "f513d235b8206211a4716d013a6dacf34aaebda6839da721b0231981cb8b905e",
+      "git_blob": "c23da2f205170b11f40299c5ec1dcab45b134861",
+      "purpose": "Exact owned output/temporary boundary of112-H1 projection. Only data is retained; no pending executable or Git object is needed during replay. Package-local invalidation covers this snapshot."
+    }
+  ],
+  "predecessors": [
+    {
+      "source": "research/joint-query/source_data.py and frozen certificate",
+      "credit": "Ali Romman / QQ16, centre-encoding campaign and portable clean-J reconstruction; retained lane/source notices",
+      "role": "Already removed all8H8 per orientation, with paid dirty-state correction. Reimplemented independently, not new retirement."
+    },
+    {
+      "pr": 2707,
+      "head": "efa51a6c7ffec6edd556a98deedfe9deeba65809",
+      "credit": "ywz65",
+      "role": "Literal full decoder/checkpoint and suffix. Source is a pinned canonical input; no executable imported."
+    },
+    {
+      "pr": 2681,
+      "head": "ea96706295631be10d92ae149b63c3e24acaeabc",
+      "credit": "Arham Tahir",
+      "role": "Complete logical inverse lineage."
+    },
+    {
+      "pr": 2512,
+      "head": "851dd3486a2d0549b51e85978a65ccb4eec619c0",
+      "credit": "ywz65",
+      "role": "Actual96-output F17 demand; inherited via3952."
+    },
+    {
+      "pr": 2346,
+      "head": "653520d7f18f686ea3a274b4963981f5be563477",
+      "credit": "alephnan",
+      "role": "Retained global ordinary bridge/terminal boundary; pinned canonical scope map."
+    },
+    {
+      "pr": 2470,
+      "head": "1b2eee3bf1ec67e68c0b0fa7f47c7b2a66febe56",
+      "credit": "thakrarsagar",
+      "role": "Retention census and constant-cover counterexample methodology; no executable imported."
+    },
+    {
+      "pr": 3908,
+      "head": "0d8880e38ed7c88d70eec6a48e5aa829d0fb22f3",
+      "credit": "1337isnot1337",
+      "role": "Scoped full-consumer fixed-profile obstruction."
+    },
+    {
+      "pr": 3946,
+      "head": "8dec5c663ace6285aeee49ec3f8eeae9a8bc9a58",
+      "credit": "Clear1nsight",
+      "role": "Independent quadrature and historical thresholds. New budget.py imports none of it and uses independent atanh arithmetic."
+    },
+    {
+      "pr": 3181,
+      "head": "80fc72d14546088e9fce3c06dc12bc67270da0af",
+      "credit": "dcharb78",
+      "role": "Historical retained-H8 profile premise; distinguished from literal QQ16 word."
+    }
+  ],
+  "additional_credit": [
+    "ywz65 PR2492/2468 native read lineage",
+    "starship-s and Ross Richardson decoder/record lineage",
+    "Douglas Colkitt and Sagar Thakrar supplier/coverage lineage",
+    "retained gauge44,T16 and source notices"
+  ],
+  "license": "New work Apache-2.0. Retained source notices unchanged; snapshot is prior Clear1nsight package data.",
+  "new_result": "Exact centre source-impact audit, lifetimes and corrected-word reconstruction; actual bridge and recovery readset counterexamples; independent budget-scope clarification."
+}

research/qq16-centre-lifetime-boundary-audit/PROOF.md

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+# Centre provenance and two actual continuation boundaries
+
+This is a source-impact and interface audit. The centre elimination is existing
+QQ16 work, not a new saving. The counterexamples exclude the specified
+substitutions; they do not exclude new consumers reading retained current state.
+All event indices below are zero-based JSON indices.
+
+## 1. Which eight rank-eight children actually exist?
+
+The frozen selected supplier's `slots/local/LOCAL-PROGRAMS.json.gz` has eight
+`center` events in each orientation. Forward copies the eight L registers
+`[92,57,81,224,11,240,9,256]` into C[0..7], transforms their frames 415..422 to
+identity with rank-eight children, and distributes them to L. Backward gathers
+L values into C in identity frame, applies the reverse frame change and adds
+each result to its corresponding centre L register.
+
+Each C lifetime is confined to this centre phase. For both orientations the
+last C clear is event 12758 and phase B begins at 12759; call exit is 24766.
+The complete read/write table, frame bases and every consumer L register are
+in RESULT.json. Forward private zeros exit in identity frame. Backward baseline
+private zeros exit in frames 415..422; zero content does not make those frame
+IDs identical. No nonzero C value survives into an outer call.
+
+That selected phase is already removed in canonical
+`research/joint-query/source_data.py:169` (`corrected_program`). The new prefix
+adds 580 dirty-correction ADDs and 16 CLEARs before phase A, and the whole old
+centre phase is deleted. Independently regenerating that construction from
+the selected scalar prefix gives exactly both frozen 25155-event QQ16 cores.
+
+| Core quantity | Selected forward | Selected backward | Existing clean QQ16 core |
+|---|---:|---:|---:|
+| Rank-eight centre children | 8 | 8 | 0 |
+| Child rank mass | 5586 | 5586 | 5522 |
+| Scalar primitive allowance | 198766 | 198814 | 202138 |
+| Scalar allowance inserted | — | — | 5532 |
+| Old centre-phase scalar allowance removed | 2160 | 2208 | — |
+| Net scalar increase | — | — | 3372 forward /3324 backward |
+
+The correction is paid already. Its 580 ADDs are not a standalone new saving.
+The checker independently verifies all 712 scalar input columns (704 persistent
+fields plus 8 arbitrary private inputs), 480 restored helper outputs, zero
+private outputs and the full canonical frame ledger. Persistent native events
+are literally unchanged. Deleting an H8 alone violates the old frame contract;
+deleting one correction ADD corrupts exact data/helper outputs. These are
+controls on this construction, not universal lower bounds.
+
+The actual packet F0 and B1_2 macros each invoke one clean core and respectively
+8 and 24 rank-one native lines. Every line recipe is checked to have rank one.
+Their profiles are
+
+    F0:   {1:2420,2:418,3:432,4:142,5:82}, mass 5530;
+    B1_2: {1:2436,2:418,3:432,4:142,5:82}, mass 5546.
+
+Both have zero H8. There is therefore no remaining literal set of eight H8
+centre children to retire from these QQ16 producer calls. PR3952's separate
+retained-eight profile was explicitly conditional and historical; its
+arithmetic did not establish that those operations occur in the QQ16 word.
+The audit closes the proposed second-retirement question at its source premise.
+
+## 2. A real outer continuation: the ordinary bridge before F2
+
+The actual selected replay archive contains
+`t16/global/hosted/GLOBAL-TEMPLATE.json.gz`. Its logical recipe starts F0,
+B1 on pair 0, bridge(+1,src1,dst0), F2 on pair 0. Its physical replica0 prefix
+also includes an idle sweep preparing pair 1 between B1 and the bridge:
+
+| Physical source_event | Operation |
+|---:|---|
+|0|local stage 0|
+|1|local stage 1|
+|2|idle pair 1, level−1 to1|
+|3|bridge src1 to dst0, coefficient+1|
+|4|local stage 2|
+
+The source bridge semantics are pinned in
+`docs/research/qq16-controller-scope-map.md`: on ordinary U ports,
+
+    X_dst += c X_src;       Y_src -= c Y_dst.               (1)
+
+These are real source instructions and typed demands. The template's selected
+provider is still gauge44; this audit does not claim the altered QQ16 locals
+have been admitted as a whole replacement supplier. We test this existing
+bridge as a proposed continuation of the new QQ16 local endpoint. The inserted
+idle sweep cannot be omitted from physical accounting; in the counterexample
+it acts on zero fields, which it preserves.
+
+PR3952 gives *earlier* y1_U in owned F17 outputs. The bridge reads *current*
+post-B1 Y2_U (and other current X/Y fields), with the source endpoint gauges.
+These values differ even if all frame conversions are granted free.
+
+Use the actual raw 8-by-112 R and K=R^T/4. For a chosen channel j put a=4e_j.
+Define original pair 0 inputs, constant in BOTH owner and payload, by
+
+    x0_U=K_U a,    x0_A=−11P_A a,    x0_T=0;
+    y0_U=0,        y0_A= 11P_A a,    y0_T=P_T a.
+
+All amplitudes are integers of absolute value at most 11. The real Gram
+identities on U,A,T are respectively48I,4I,4I. Applying the conserved F0
+formula gives x1=P_T a,y1=0. Applying B1 gives
+
+    Y2_U=K_U a,     Y2_A=0,     Y2_T=−11P_T a,
+    X2_U=0,        X2_A=0,     X2_T=12P_T a,
+    Q_1(Y2)=a.
+
+Consequently the projected output `Y2_U−K_U Q_1(Y2)` is 96 zeros, exactly as
+for the all-zero original execution. All other pairs are held zero. But (1)
+produces `Y_pair 1,U=−K_U a`, with48 nonzero integer coordinates for each j.
+The identity R_U R_U^T=48I proves eight independent separating directions.
+
+This is a genuine observation collision: no deterministic consumer of the
+96 projected outputs alone, with other-pair state fixed, can implement that
+bridge output on both cases. The counterexamples are valid for actual routes
+and native gauges: constant-owner fields are fixed by owner permutations,
+constant-payload fields are fixed by translations and normalized C_q lines,
+and tensor products preserve this constant sector. A nonzero witness on an
+invariant sector disproves an arbitrary-array equality.
+
+This does NOT say the bridge is impossible. PR3952 leaves current borrowed X/Y
+intact. Reading those fields still implements the original demand; the
+projection is then an added observer and does not replace the live state or
+justify a retirement credit. A changed composition must specify the additional
+query/access and physical invoice. The eight missing logical directions are
+not a theorem requiring eight new full-cover families.
+
+## 3. A genuine consumer of y1_U: the retained F0-inverse suffix
+
+PR2707's literal word has checkpoint2740, with Z=x1 and W=y1 in F17. Its
+continuation begins at2741:
+
+    W0 += Z0.
+
+A complete read-before-first-write audit finds all 112 Z and112 W fields are
+required at suffix entry. PR3952 provides W_U (96 fields); its 16 selected W temporaries
+are zero in identity frame and it provides no Z bank. Thus 128 required boundary
+values are absent. The first event fails its declared owned/frame input contract.
+The required private sweep also has16 fields rather than the projection's 8.
+
+A stronger information witness keeps the entire current Y bank identically
+zero and changes current X only at port 0 from 0 to 1. PR3952 returns the same 96
+zero outputs in both cases, but required checkpoint Z0 and the recovered
+original inputs differ. The checker verifies F0 inversion and F0/B1 forward
+composition for this pair, plus all 128 omitted checkpoint basis directions.
+These are constant-owner and constant-payload counterexamples; the separate
+universal identity/F17 frame mismatch is not inferred from constant values.
+
+The suffix's complete local invoice, *assuming its 224 inputs already exist*,
+is 584 unit ADDs, 448 quarter ADDs and 48 CLEARs, scalar allowance 10144, no native
+children or maps, and 16 private arrays. Adding 10144 to the projected allowance
+9376 would omit the cost of producing the missing boundary and is not a complete
+construction. Missing checkpoint values do not imply128 new physical families:
+a redesigned consumer could read existing borrowed inputs or use an encoding.
+
+One fully specified fallback is the retained full PR2707 decoder:
+
+    336 H1; 672 wrappers; 464 cover maps;
+    1808 unit ADDs; 896 quarter ADDs; 312 CLEARs;
+    scalar allowance 25840;224 owned outputs; peak private 16.
+
+This supplies the full required boundary by its original prefix. It is a
+source-priced fallback, not a lower bound on every possible completion.
+
+## 4. Budget applicability: fixed mass is not a retirement schedule
+
+The independent budget checker imports no predecessor arithmetic. It binds
+the reported source model m=73, W=896/9, centre=64,selected exponent
+`a=836330098538459/499163669901461541`, and average actual F0/B1 profile
+`{1:2428,2:418,3:432,4:142,5:82}`. Under the predecessor's *conditional* one
+consumer per two calls and fixed mass T=72W+64=7232, every idle rank is at most 51.
+Price per rank-mass unit decreases with rank, so fractional rank51 idle work
+is a favorable relaxation. Its moment is
+
+    G=[sum_r n_r(r/73)^(1−a)+(T−sum_r r n_r)/51*(51/73)^(1−a)]/W.
+
+Exact independent rational enclosures are:
+
+| Conditional consumer / retained H8 across pair | G |
+|---|---|
+|112 H1 /0 H8|[0.999995759878777677,0.999995759878777678]|
+|112 H1 /2 H8|[0.999999183632341047,0.999999183632341048]|
+|112 H1 /3 H8|[1.000000895509122732,1.000000895509122733]|
+|112 H1 /16 H8|[1.000023149907284635,1.000023149907284636]|
+|Full 336 H1 fallback /0 H8|[1.000097677880011248,1.000097677880011249]|
+
+The two/three threshold and older 61/62 and 121/122 brackets are correct within
+that fixed model. The full retained consumer still fails even with H8 absent;
+unknown physical costs cannot rescue that fixed-profile screen. This says
+nothing universal about a cheaper different completion or changed coverage.
+
+The phrase "retire fourteen of sixteen" describes fixed-T reallocation of H8
+mass into ideal idle work. It is not an actual task to remove fourteen still
+existing QQ16 children: none exist. Literal deletion also changes total mass;
+changing the family count or unpaid-coordinate allowance requires a new
+coverage argument. The selected W and centre 64 identity are checked on its
+896-family/nine-call/144-invocation assembly, not proved for a changed controller.
+Similarly, one consumer per pair does not supply a physical 9-call invocation
+schedule (4.5 demand invocations cannot simply be assumed).
+
+For the independent arithmetic, reduce logarithm arguments into [1,2], use
+40 positive atanh terms with tail at most `2z^81/[81(1−z²)]`, then a positive
+degree 14 exponential sum and geometric tail. Decimal endpoints round outward;
+all decisions compare exact Fractions. Deliberately labelled family-count,
+incidence and literal-deletion sensitivities in RESULT are hypothetical tests,
+not proposed admitted constructions.
+
+## 5. Decision and next bounded question
+
+The proposed centre-lifetime saving has no remaining literal target. A real
+outer bridge and a real recovery suffix have been pinned, and both require
+information outside the projected 96-output interface. Retaining current state
+avoids those information obstructions but supplies no source-retirement saving.
+The original full recovery fallback is priced and fails the fixed pair screen.
+No fully costed new retirement schedule follows.
+
+The next useful task is to bind a cheaper composition at one of these exact
+boundaries. For full recovery, choose a paid encoding or reconstruction of the
+128 missing x1/selected-y1 values from retained current X/Y and show actual
+eliminated work, legal frames, lifetimes and cleanup. For the ordinary bridge,
+state which current-bank reads can truly disappear and how the old T query is
+made available; simply decoding y1 and reconstituting current Y repays the
+projection. Establish productive-family and invocation counts before applying
+the numerical screen. Stop on an unspecified read/return boundary or failed
+complete allowance; do not pursue another centre-deletion or precision loop.
+
+Credit for the existing centre removal, clean-J correction, global recipes,
+QQ16 algebra, decoder, native and coverage proofs stays with the retained source
+lineage. This audit adds exact provenance/lifetimes, independently reconstructed
+source impact, actual continuation counterexamples and budget-scope clarification.
+Separate AI-agent checks and reviews are recorded in REVIEWS.json; no independent
+human or formal-kernel review, huge native payload execution or selected cold
+replay is claimed.