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Word RAM transfer: finite TM compiler, checked logarithmic-width bridge and native kernels - #4538
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…program within 8NL+40N+8, phases, negation, metadata compiler (no new κ) Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
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This begins a bounded-word RAM migration of the complete multitape route, using the existing Problem 1.8 RAM implementation. It adds an actual finite multitape-to-RamStd compiler with genuine halt and output adaptation, an independently kernel-checked logarithmic-width/10k-step bridge for the existing IMP compiler, uniform packed-tape access kernels, and costed native affine/quadratic-phase/monomial algorithms with an explicit metadata compiler.
The generic IMP bridge preserves source operations; the new TM emitter and native kernels use neither word multiplication nor division. Five new Lean theorems pass fresh independent axiom checks (only propext, Classical.choice and Quot.sound). The remaining universal component proofs are informal, with exact portable optimized Python replays. The new TM emitter itself is not Lean-verified. All buffers, address bounds, input domains, finite precision and IO costs remain explicit.
Validation: registered research-package replay passes; an immutable Git-free export passes the same isolated checks; deliberate source corruption is rejected before child execution. Frozen Lean 4.33.0/Mathlib dependencies and reproducibility instructions are included. No isolated rebuild of all dependency sources, Linux-hosted execution or independent human review is claimed. No selected-frontier files are changed.
This is a semantic baseline plus native optimization building blocks, not a new kappa, a RAM complexity record, or a completed native multiplication rewrite. The next task is to replace one exact segment of a pinned multiplication caller and account for its full metadata, precision, buffering and serialization costs. See README and TASK.json for concrete next steps.
Credit: Dugongue and the retained Problem 1.8 formalization sources; Szymon Torunczyk and GPT's compositional-polytime lineage; the actual exact-RAM proofs from PRs #956/#647 and their #390, Sussman/P193, bridge, normalization and audit predecessors; retained native/controller, mixed-target, query/helper, physical, precision, prime, tape and outer-analysis suppliers. Detailed pinned overlap and attribution are in compiler/OVERLAP.md. Prepared with substantial OpenAI Codex assistance and three parallel agents; Apache-2.0.