Compose R437 complete-prefix leaf returns with the actual XOR consumer

research/r437-prefix-consumer-fusion/PROOF.md

@@ -0,0 +1,68 @@
+# Uniform complete-prefix leaf/consumer composition
+
+Fix q,w, a valid encoded Layout with finite fibre length v, a complete original
+directory with p=C*H prefixes, and source/target Boolean packets of p*v bits.
+The source directory producer supplies canonical complete prefixes in the same
+order as those packets. All borrowed heads enter at 1. Inputs occupy distinct
+roles. The unchanged trace factory yields the same closed finite leaf sequence
+for every prefix. Its coefficients depend only on that prefix, the same Program
+and encoded context, and return owned words while restoring borrowed state.
+An optional observer must be read-only. These are source-level hypotheses,
+not consequences of finite samples. Equality means payload and borrowed logical
+Program/Fields state, excluding meters, allocation order, and global callback
+logs. Deterministic Specifications memoization may change bookkeeping; it does
+not change coefficients or borrowed logical bytes.
+
+For primitive t and prefix i, let T_t,i be its local payload map. In the pinned
+packet_engine.run, every primitive reads exactly one prefix and v bits, invokes
+`action` on that local tape, then appends exactly v output bits. It reads no
+other prefix payload. The callback uses that complete prefix; controller's
+restored Program/Fields reads and owned numerical work establish the stated
+no-cross-prefix-effect contract on successful valid inputs. trace.leaf reads
+geometry only and retains chronological ADD/swap/sign order within each prefix.
+Thus the original primitive-major schedule is the direct product of maps
+T_t,i. Operations on different prefix payloads commute, even when their
+coefficients are correlated through a shared borrowed Program: their Program/Fields
+logical dependency is shared and unchanged. Deterministic cache population and
+meter increments need not agree between the schedules. Reorder only across i, never
+across t within i. This proves that prefix-major execution produces the same
+p complete local returns for every Boolean source packet and every such context.
+
+The literal episode.xor_packet independently loops old_count, context.highs,
+then v bits, emitting return XOR dirty_target. It changes neither operand and
+restores heads. It is therefore the product of local pointwise XOR consumers.
+Applying each local consumer immediately after its complete local leaf return
+commutes with all other prefix computations. The new adapter's encoded product
+check establishes p=C*H; complete-source/target/directory consumption checks
+exclude silently omitted or extra prefixes. It does not infer canonical
+producer contents merely from equal counts. The complete directory remains an
+input; no directory serialization or reserve-absorption result is claimed.
+
+After each prefix, clear its owned return and all local copies, then continue.
+Only the final consumer output grows to p*v bits. No intermediate whole-child
+returned packet is created. At most one v-bit child return reaches the consumer
+at a time. Local primitive workspace, source/target copies, accumulated output,
+complete borrowed directory, Program, metadata and callbacks remain paid.
+Repeated per-prefix trace setup is extra work, not free; output serialization
+and every visited/erased backing cell remain part of the invoice. Logical
+liveness does not establish a fixed-tape allocation/reuse or physical-space
+improvement. The claim is functional composition and a changed lifetime
+boundary, not uniform runtime savings, supplier admission or a new kappa.
+
+For the full high cube, take H=(q^(w-1))^(m*m) and the complete output of the
+unchanged directory.produce. Its enumeration order and repeated old prefixes
+are inherited. The same proof applies for every finite H without a sampled
+high-fiber argument. The actual R437 corroboration uses the two q3,w2 prefixes
+of #4793; it does not physically enumerate H=3^4096 or prove root reachability.
+#4927's directory/metadata absorption audit and #4854's quotient are separate.
+
+The adapter adds exception-safe local raw-prefix parsing and bit-copy counters;
+these front-end structural failures restore its owned state and borrowed heads.
+The uniform positive theorem assumes valid callback/primitive contracts. It
+is not a repair of every malformed-input cleanup path in frozen inner modules.
+General arbitrary callback failure inside an inherited primitive remains open.
+
+Credit: Jose Manuel / David Arias's retained packet/callback/consumer sources;
+Chris R / Clear1nsight #4176; #4793 nonzero-high finite payload; original compiler,
+word arithmetic and source lineage retained in SOURCES.json. New adapter/proof:
+JoyboyBrian, substantial OpenAI Codex assistance, Apache-2.0.

research/r437-prefix-consumer-fusion/README.md

@@ -0,0 +1,106 @@
+# Uniform R437 complete-prefix leaf/consumer fusion
+
+This package proves a source-bound schedule change for the actual leaf and XOR
+consumer: execute a complete leaf on one complete prefix, consume its returned
+fibre immediately, erase local copies, then advance. The original primitive
+order within each prefix is preserved. The proof applies to every finite
+complete prefix directory, including the full high cube when that directory
+and matching packets are supplied. It does not infer uniformity from samples.
+
+The new opt-in adapter removes the intermediate whole-child returned packet
+from this interface. It does not replace the original callback, numeric
+primitive or consumer. The complete borrowed directory, source and dirty target,
+final output, local copies, trace setup, and every visited backing cell remain
+paid. This is a functional composition and lifetime result, not a physical-space
+or runtime improvement, supplier admission, or a new bound.
+
+## Source contract and increment
+
+`PROOF.md` derives the direct-product structure from authenticated
+`packet_engine.run_generator`: copy one fibre, apply the primitive using only
+that prefix and restored borrowed Program, append the local result. Distinct
+prefix effects commute; effects within one prefix retain their original order.
+The original `episode.xor_packet` is pointwise on the same fibres, so its
+consumption may follow each completed local leaf. `adapter.py` checks the encoded
+prefix product C*H, complete packet and directory consumption, and separate
+borrowed roles. Canonical producer contents are a hypothesis, not inferred from
+equal counts. A trace factory must return the same closed finite trace, and an
+optional observation callback must be read-only.
+
+The positive theorem assumes successful valid primitive/callback contracts.
+Owned parsing/copy counters have explicit cleanup, and borrowed heads rewind.
+It does not claim to repair arbitrary inherited inner callback exceptions.
+
+#4793 (8ef4afcfba50c7f118d4787e34dda437192458ea) already established the two
+nonzero-high physical fibres and their independent permutation oracle. This
+package reuses that corroboration to compare a new prefix-major schedule with
+the original primitive-major schedule and actual SOURCE87 consumer. #4176 by
+Chris R / Clear1nsight supplied the produced-child physical bridge; #4759's
+metadata-only dispatch is not a physical ancestry proof here. #4854 by Nick
+Petalas covers local shared-radix quotient traversal, and Discussion #4927 audits
+directory/reserve serialization; neither is claimed again or used to assume
+free directory storage.
+
+## Actual differential certificate
+
+Both schedules execute actual R437 D request 1676, a source-valid borrowed
+2048→64 Program and actual 64→2 child construction, modulo 9 at q=3,w=2. The
+two distinct canonical high prefixes give weights [8,2] and [5,8]. Each schedule
+executes 24 real coefficient callbacks and 13,122 dirty payload bits. All output
+bits match the independent permutation oracle and each other. Global callback
+order changes; each prefix's callback chronology agrees exactly. The actual
+SOURCE87 XOR event [1,467,87,1,509,0] occurs at source position 22398. The fused
+consumer observes two 6,561-bit returns instead of a single 13,122-bit return.
+The consumer SHA256 is
+`0f8e16924fd79d5c002ecafd4b77ac929a97f186b71c9fcf64992c6490a126f2`.
+
+This q3 fixture is not numerically admitted by the selected root domain. It
+executes two represented complete fibres, not all 3^4096 high matrices, GL64
+gather, production parent spectators, or an original admitted root. The uniform
+claim rests on the source contract and proof above. No full Machine.node or
+supplier claim is made.
+
+Checks include omitted-prefix product rejection before payload, role alias
+rejection, truncated raw-prefix cleanup, actual bad high digit and rank
+rejections, wrong returned bit changing the real consumer, and independent
+stale/inverse-weight controls. Borrowed bytes/heads, unrelated numerical state,
+and erased owned record backing are checked. Runtime numerical decoding is
+disabled; host oracles only observe results and never drive the algorithm.
+
+`RESULT.json` separately records the fused action invoice: record
+50,395,613 reads / 10,278,012 writes / 43,705,218 moves; index
+859,108 / 177,308 / 842,662; residue 165,628,640 / 34,082,134 / 173,048,120.
+It includes fused local copying, callbacks, primitives, consumer and output
+disposal. The aggregate invoice also includes the eager comparison and controls.
+Host compilation, fixture/oracle creation and initial borrowed allocation are
+outside these runtime invoices. Counters do not price allocator reuse or a
+complete fixed-tape tariff.
+
+## Reproduction and provenance
+
+Run `python3.12 -I -B research/r437-prefix-consumer-fusion/verify.py` and the same
+command with `-O`. `VERIFY.json` registers both, with a 240-second bound each.
+A successful local first replay is recorded; hosted CI is not asserted.
+`RESULT.json` uses typed JSON equality, including bool/int distinctions.
+
+`SOURCES.json` authenticates 401 live inputs at canonical base
+b91956876e5b4122fd89179f1b57557ff8378f15. The exact historical selected record is
+retained with SHA256 and projected only for its unchanged historical loader.
+No selected or frozen source is edited. `TASK.json` records card revision 7 and
+complete reported overlap coverage (317 open PRs, 4064 Discussion records,
+6636 local notes); lack of keyword matches is not novelty proof.
+
+Original packet/callback/consumer, arithmetic and compiler work remains credited
+to Jose Manuel, David Arias, Chris R / Clear1nsight and the pinned lineage.
+New adapter/proof and differential integration: JoyboyBrian, substantial OpenAI
+Codex assistance, Apache-2.0. This is author-checked evidence and a scoped proof,
+not formal-kernel verification.
+
+## Open next questions
+
+1. Bind a streaming full-prefix producer and reusable physical tape allocator to
+   this interface, pricing all producer and returned-output backing.
+2. Join admitted root precision and actual parent gather/spectators to this
+   lifetime boundary; the finite q3 ancestry remains separate.
+3. Establish failure cleanup for arbitrary inherited primitive/callback errors
+   before extending the positive contract to those malformed inputs.