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Exact compiler theorem

FPRD-T126

Simultaneous record batches compile into one scaffold node

Exact statement

Every bounded simultaneous record transducer with s roots, at most A fresh q-field records per letter, and old-address bound r compiles exactly and letter-synchronously into a native scaffolding automaton of degree max{1,s+Aq} and observation/update distance at most r+1, provided its initial data is one fixed finite immutable pointer-closed record graph, its plans factor through finite control, the input letter and bounded labelled rooted unfoldings, and its roots and fields target missing, bounded old addresses, or current fresh slots. Physical pointer identity is not an observable test. Initial records are virtual finite decoder data; dynamic fresh targets use SELF plus a finite slot tag, including self-loops, forward references and mutual cycles.

StatusCorrected compiler proof; broader application audit remains
External reviewNo documented external or specialist review of this FPRD result is recorded.

Context

One physical node tuple-packs every logical record created at one input time. A decoded pointer is a physical node together with a finite slot tag.

Hypotheses and scope

  • The source has fixed finite control, tags, payloads, roots, fresh slots, field arity, and old observation radius.
  • Its initial record graph is fixed, finite, immutable, and pointer-closed; transitions inspect bounded labelled rooted unfoldings and do not branch on pointer identity.
  • The target is the Loff–Moreira–Reis scaffold model, including SELF.

Proof or evidence

Root ports and field ports encode dynamic old addresses as bounded raw paths. Fixed initial records use virtual tags and a permanent finite decoder table. Every fresh target uses SELF, while the source node's finite label records the target slot. The initialization state handles the empty prefix; equality of finite labelled adjacency tables gives the one-step decoder square; induction gives run and language equivalence.

Tuple-packed compiler →

Verification notes

A 9 September 2026 separate same-model review confirmed the dynamic tuple-packing mechanism and found the fixed-initial-heap parameter gap. On 10 September, two separate same-model passes attacked a virtual-initial-record repair and its direct-palindrome application. The corrected proof and application are integrated in Draft 3. These passes share model dependencies; no complete palindrome audit or original checker rerun occurred. The earlier public checker exercises deterministic self, forward, and mutual cycles, 250,000 randomized commuting squares, and more than five million typed-address translations.

Limitations

  • The finite checker is regression evidence, not proof of the universal theorem.
  • The theorem does not establish that an arbitrary program satisfies the bounded transducer hypotheses. The corrected virtual encoding preserves the degree bound, but it has no external expert review or proof-assistant formalization.
  • This correction does not revalidate the receipt recurrence, Kaplan–Tarjan bridge, allocation inventory, or complete palindrome theorem.

Open work

Audit the remaining palindrome dependency chain and seek an external specialist check of the corrected compiler; compare it with existing graph-machine encodings.

Notes

This corrects the stale root statement's omitted initialization and positive-degree clauses, following the written compiler-interface proof in the 23 September Site checkpoint. Labelled unfoldings do not reveal physical alias identity; a fixed copied-address plan still preserves existing aliases. The virtual base case and commuting square prove the whole-run construction. Finite compiler checks corroborate it. The causal manuscript's two boundary clauses await a coordinated edition; its generic compiler is independent of the sequence implementation gap. See docs/integration/reconciliation/T125-T128.md.