Bind pooled R437 replica-indexed native requests and charge widened source codes

research/r437-pooled-native-interface/.gitattributes

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research/r437-pooled-native-interface/PROOF.md

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+# Replica-indexed native request boundary for pooled R437
+
+## Result and exact dependency
+
+PR3995 at ae29394a128ba2016919446a7377c7d75ff9c18e binds Rohan Arun's
+63 PR3959 moves to the actual retained emitter, and proves the old catalogue's
+replica symmetry guard fails. Its emitted-IR and slot-packing results are reused,
+not rediscovered. We construct the next interface: a complete replica-indexed
+request vocabulary, actual owner charts, source templates and explicit IDLE
+selection. This is a source/compiler interface, not a physical caller execution
+or supplier admission. PR3980 supplies the dyadic determinant and separation
+checker; all actual pooled calls are checked here without replica symmetry.
+The local-only follow-up on PR3959 already proves the first helper's permutation
+transport and common-plan equality. We do not claim that as new work.
+
+## Physical objects and request keys
+
+There are 288 local calls, indexed by (stage, replica), with 659 roles each.
+The absolute owner of a role is exactly the pooled template's family and route.
+Requests are keyed by (kind, stage, caller replica, position), except IDLE uses
+its local copy/role instead of position. The catalogue enumerates all paid
+physical request sites, not one replica followed by a multiplicity factor.
+Its local order is stage, replica, positive literal MOVE/COPY position; IDLE
+order is the retained compiler's child, replica, local-copy order. The lazy
+sequence merely constructs that finite table on demand. It does not identify
+requests across replicas. In particular, different replicas can own distinct
+slots of the same absolute family.
+
+Local bases, frames, chronology and COPY/ERASE matching come from the authenticated
+current unpooled R437 word; the pooled compiler changes only the declared owner
+records. The existing canonical adapter verifies that literal word and local
+program. For MOVE, the request family and chart come from the actual call role.
+For COPY, the target is the existing private common family 28416, while its source
+chart comes from the actual role. The canonical Template method retains the
+rank/base/preparation construction and appends the native/common tag to a record
+that now starts with schema and caller replica. All2592 ERASE guards expand to
+(stage,replica,erase-position,capture-position,role,base-key).
+
+For IDLE,  the retained compiler establishes that occupied cells form a compact
+prefix of the actual pending-axis list in each (child,absolute-family). The
+request base is precisely the remaining suffix, not a suffix inferred from
+replica 0. The family is already absolute. `idle_identifiers(child,replica)`
+selects that replica's entries exactly once; `idle_family(id,replica)` checks the
+request's replica and returns its family with no extra stride. The old `idles`
+interface is deliberately unavailable. An existing consumer must replace its
+IDLE lookup by this explicit API before it can consume this topology.
+
+Every request's key is checked back to its exact ordinal and every local ordinal
+back to the actual caller's request vector. IDLE enumeration is checked for
+coverage and uniqueness. This gives a finite constructive bijection between
+paid literal sites and catalogue entries. The cardinality is 903456, consisting
+of 836928 MOVE, 2592 COPY and 63936 IDLE requests, with rank mass 1808352.
+The profile contains 400877 rank 2 requests and exactly one rank 14 request, so it
+cannot be represented by multiplying a canonical profile by 32.
+
+## Uniform owner separation and right action
+
+Let D=Z[1/2]. Every actual pooled chart sigma is a 64 by64 matrix over D.
+The independent reconstruction agrees with the canonical chart constructor for
+all 1235 labels. Exact elimination gives determinant +1 for 236 labels and -1 for 999.
+Consequently every chart is invertible modulo every odd prime and every odd
+prime power. This is a finite certificate of a uniform algebraic premise, not
+enumeration of all primes or GL64 classes.
+
+For each of the 179802 unordered pairs of different roles sharing a family in
+one actual call, the checker exhibits an entry of sigma_a-sigma_b that is a
+unit of D. Thus the charts remain different modulo every odd prime. For any
+invertible common low d0, the native packet lows are ell_a=d0 sigma_a^-1 and
+ell_b=d0 sigma_b^-1; equality would imply sigma_a=sigma_b modulo q, a contradiction.
+Different families are separate physical registers; same-family owners use
+different low packets. All 288 actual calls are checked; no 32-fold symmetry
+extension is used for this pooled source. Sequential calls may reuse these
+packets and must observe the latest family state.
+
+The address action is on the right: rho_sigma(g)=g sigma. Given native low
+ell=d0 sigma^-1 modulo q and a high-digit matrix X, let g=ell+qX modulo q^w.
+Canonical reduction of g sigma has low d0 and unique high matrix Y. Right
+multiplication by the invertible sigma is a bijection of these complete fibres.
+Its inverse uses sigma^-1. No invertibility of the high-digit matrix X is
+required. Canonical quotient extraction includes carries; a permutation-only
+formula cannot replace this for general rational charts. Equality of these
+address maps gives equality of their pullbacks pointwise for every Boolean
+function, including arbitrary dirty dependence. Correct routing therefore
+transports arbitrary complete packets, conditional on the physical route
+primitive realizing this specified permutation. This algebra does not execute
+or price that primitive.
+
+In groupoid terms, the objects are the typed family/low fibres and the arrows
+are these invertible chart transports. The caller replica is part of the
+request object even when arrows happen to use the same family. Collapsing the
+objects before selecting their charts is precisely the old interface error.
+
+## Codebook identity and complete incremental bill
+
+For fixed q let L=|GL64(F_q)|. The old vocabulary had 28233 requests and source
+code limit 2*28233*L. The new one has 903456=32*28233 requests and limit 32 times
+larger. Since ceil(log2(32x))=5+ceil(log2 x), the exact fixed source-code width
+increases by five bits for every fixed odd prime q. At q=3 this is 6507→6512.
+This is code-field width, not a claim that all physical descriptor layouts grow
+by only five cells: any layout depending on that width must be recompiled and
+charged. The lazy host-side representation gives no free run-time compression.
+
+A source handle contains schema, source-codebook identity and integer code.
+The identity binds q, dimension, request cardinality, code width, the exact retained
+low-code codec, the authenticated unpooled request digest and exact pooled move
+bytes. Cross-prime handles are rejected as well. The supplied Specifications must be bound to the same catalogue object.
+A stale/untyped handle or mismatched Specifications context is rejected before the canonical source
+compiler. The new Template record also includes replica and schema; successful
+compilation of one integer under a different context cannot be mistaken for
+historical source compatibility. Fixed-context integer codes remain internal
+to the retained Specifications implementation. Handles are an interface check,
+not a new authenticated physical serialization protocol. The fixed codebook
+identity can be a static compilation parameter; if serialized dynamically,
+its scan/storage cost remains additional and must be charged.
+
+The exact event multiplicities remain, per low class, 189792 local gathers and
+189792 local scatters,63936 IDLE gathers and 63936 IDLE scatters, and 379584 local
+routes. With N low classes and completed tariffs G,S,R, the complete owner
+transport term is 253728N(G+S)+379584NR. Neither the new table nor the separation
+proof removes any route/scan. The request rank profile changes exactly as in
+PR3995; COPY reads, paid child transforms, native preparation, private lifetime,
+ERASE, dirty restoration, bridges, exchange, parking and full source consumers
+remain separately charged. A complete caller bound must also replace each old
+source-code width by width+5 in every descriptor, header, history checkpoint,
+serialization and scanner where that field is present, re-evaluate alignment,
+and sum the actual read/write/rewind rates. In the retained records.py grammar, STEP length is c=Q+2I+90 and
+Program length P_h=2I+L+6+h*c; the exact increment is therefore 5h symbols
+per Program. Each raw field has length Q+2+4096(L+1), increasing by 5.
+With n_f raw fields and a Program with h steps, this contributes exactly
+5(n_f+h) extra source-code symbols before checkpoint encoding and repeated
+consumption. In the fixed four-symbol parking codec credited to PR3983, a
+chronological depth-d Program stack starting at h_0 incurs 20[d*h_0+d(d-1)/2]
+extra parked body symbols. Root record lengths are unchanged when I,L are
+fixed. Alignment and any changed I,L require separate recomputation.
+The count of those occurrences,
+primitive tariffs and whole-run visited-cell reserve are unknown here. This is
+an exact incremental interface invoice with explicit unknowns, not a complete
+numerical physical cost bound.
+
+## Evidence and limits
+
+The verifier compiles representative actual q=3 specifications: the relocated
+MOVE in common and native form, the unique pooled rank 14 IDLE,  and actual COPY.
+Their typed records, ranks and replica identities are checked. This is finite
+source compilation, not execution on a shortened or production-volume packet.
+The all-q statement concerns the chart and owner-separation algebra; the complete
+supplier and all its source/child/physical obligations remain conditional.
+Negative controls reject omitted replica, wrong IDLE replica, legacy enumeration,
+replica-factorized profile, duplicate chart, stale/cross-prime codebook, untyped source and
+native COPY. No kappa/frontier change is asserted.

research/r437-pooled-native-interface/README.md

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+# Pooled R437 replica-indexed native request interface
+
+This package fills the next source boundary exposed by PR3995: all actual pooled
+requests now include the caller replica, actual owner charts and absolute IDLE
+families. The new topology has an explicit replica-indexed IDLE API. It does not
+execute a physical CALL/RETURN or admit the pooled supplier.
+
+The complete source audit checks:
+
+- 903,456 paid request sites: 836,928 MOVE, 2,592 COPY and 63,936 IDLE; exact
+  pooled rank profile and rank mass 1,808,352.
+- Every request key and actual caller identifier, plus exactly-once IDLE coverage.
+- All 1,235 actual charts, with dyadic entries and determinant ±1, and all 179,802
+  same-family owner pairs in all 288 calls, each with a dyadic-unit separation
+  witness. This certifies owner separation for every odd prime without assuming
+  replica symmetry.
+- Actual retained q=3 source compilation for the first relocated MOVE in both
+  native/common forms, the unique rank-14 IDLE, and a COPY. The committed result
+  reports good/fallback classification; compilation is not fallback execution.
+- Exactly five additional source-code bits at every fixed q: q=3 grows from
+  6,507 to 6,512. Program histories and raw fields must pay for that expansion.
+- Wrong replica, legacy IDLE lookup, stale or cross-prime source-code context,
+  mismatched Specifications, untyped source, duplicate chart, replica-scaled
+  profile and invalid native COPY are rejected.
+
+The ordered request digest is
+`29ad864c2a6a31ad15162b0165b4f047cf580d9f2c147aebcfccfd564ccbbc60`.
+The first moved helper's MOVE is request 563291; the same literal position in
+replica 0 is request 560376. Both use family 209, with distinct charts. This is
+why absolute family alone cannot identify the caller's request.
+
+Run the registered, standard-library replay:
+
+```
+python3 -B scripts/research_package.py --package research/r437-pooled-native-interface
+```
+
+No Git, network or predecessor worktree is used by verification. `SOURCES.json`
+authenticates retained bytes and the canonical source closure. Pending source
+files are retained locally; source-provenance metadata identifies their original
+commits. The inherited full compiler file is retained unchanged, but only its
+source overlay/slot validator is executed here, not its unused emitter helpers.
+The new catalogue intentionally requires an IDLE consumer change; it is not a
+silent replacement accepted by the old physical compiler.
+
+`PROOF.md` states the complete changed contract and uniform algebra, exact
+transport multiplicities, code-width invoice and remaining unknowns. Physical
+routing, complete residual/source access, prior dirty-state observation, native
+preparation, CALL/RETURN, all consumers, source acceptance, chronological history,
+parking and global visited-cell/resource coupling remain obligations. There is
+no shortened-volume execution passed off as a production result, no new kappa,
+and no frontier change.
+
+Credit Rohan Arun's PR3959/3958/3939 for pooling and its conditional endpoint;
+ai-nanachi's PR3647, Ali Romman's PR1043 and Sagar Thakrar's PR3700/2423 for the
+R437 word/hosting lineage; PR3995 for absolute-owner emission and the catalogue
+counterexample; PR3980 for the dyadic owner checker; PR3983 for complete
+chronological parking accounting; Nick Petalas's PR2989 for earlier owner
+separation/compiler correspondence. The prior PR3959 local follow-up already
+established the first helper's permutation transport and common plan identity.
+Canonical physical/source/compiler credit includes zxv, David Arias, Jose Manuel
+(jmbarrancoml), ywz65, alephnan, Adam Gall, Ross Richardson and the retained
+notices, together with mightyOil, DaysSky, chafreaky, DreamingOfClouds and eumemic.
+
+New interface, audit and writing: Chris R / Clear1nsight with substantial OpenAI
+Codex assistance. Same-session AI cross-review is distinct from human or formal
+kernel acceptance. Apache-2.0; inherited notices and byte-exact retained sources
+are preserved.
+
+## Open next questions
+
+1. Adapt the full physical compiler's IDLE enumeration and bind the first actual
+   pooled gather/native source/return with its preceding dirty read and every
+   consumer. Source compilation and owner separation are ready premises;
+   physical primitive and complete source acceptance are still required.
+2. Substitute the widened source-code field into the actual chronological
+   history, raw fields, checkpoint codec, scans and returns. Count all occurrences
+   and whole-run reserve before claiming a complete numerical physical bill.
+3. Join the actual pooled caller to an admitted child supplier and all-size,
+   stock, precision and analytic bounds. A successful finite replay alone does
+   not discharge these remaining supplier obligations.

research/r437-pooled-native-interface/RESULT.json

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+{
+  "ERASE_guards": 2592,
+  "chart_count": 1235,
+  "chart_sha256": "8d8d44ca739b1c87902a19af89c961c76c9081c2a821cee8dcc64cae68153426",
+  "code_bits_delta": 5,
+  "compiled_actual_sources": [
+    {
+      "common": true,
+      "good": true,
+      "kind": "MOVE",
+      "rank": 2,
+      "replica": 1,
+      "request": 563291
+    },
+    {
+      "common": false,
+      "good": false,
+      "kind": "MOVE",
+      "rank": 2,
+      "replica": 1,
+      "request": 563291
+    },
+    {
+      "common": false,
+      "good": false,
+      "kind": "IDLE",
+      "rank": 14,
+      "replica": 0,
+      "request": 896352
+    },
+    {
+      "common": true,
+      "good": false,
+      "kind": "COPY",
+      "rank": 7,
+      "replica": 0,
+      "request": 1598
+    }
+  ],
+  "controls": [
+    "replica omitted",
+    "wrong idle replica",
+    "legacy idle consumer",
+    "replica factorized profile",
+    "same-family duplicate chart",
+    "stale source codebook",
+    "different prime source codebook",
+    "mismatched Specifications context",
+    "untagged integer source",
+    "native COPY request"
+  ],
+  "determinants": {
+    "-1": 999,
+    "1": 236
+  },
+  "family_scans_per_low": 507456,
+  "first_moved_request": 563291,
+  "full_physical_caller_executed": false,
+  "idle_owner_gathers_per_low": 63936,
+  "local_owner_gathers_per_low": 189792,
+  "new_q3_code_bits": 6512,
+  "old_q3_code_bits": 6507,
+  "per_stage_pairs": {
+    "0": 6848,
+    "1": 13920,
+    "2": 27392,
+    "3": 27872,
+    "4": 27872,
+    "5": 27808,
+    "6": 27322,
+    "7": 13920,
+    "8": 6848
+  },
+  "profile": {
+    "1": 380160,
+    "2": 400877,
+    "3": 22176,
+    "4": 26592,
+    "5": 29376,
+    "6": 17375,
+    "7": 26496,
+    "14": 1,
+    "42": 403
+  },
+  "rank_mass": 1808352,
+  "replica_zero_request": 560376,
+  "request_count": 903456,
+  "request_kinds": {
+    "COPY": 2592,
+    "IDLE": 63936,
+    "MOVE": 836928
+  },
+  "request_sha256": "29ad864c2a6a31ad15162b0165b4f047cf580d9f2c147aebcfccfd564ccbbc60",
+  "routes_per_low": 379584,
+  "same_family_pairs": 179802,
+  "source_identity": "84cc5d15252e334b9bed24c50d6826fd3d765710857e5db04889fc76d62aed1e",
+  "status": "PASS_POOLED_REPLICA_NATIVE_REQUEST_INTERFACE",
+  "supplier_admitted": false,
+  "unique_chart_pair_witnesses": 463,
+  "witness_sha256": "1818977337134cdda43778d82d79ca4a061a4fc271ad5cb0ec2966659abf2185"
+}