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Compare native Word RAM with packed TM; prove robust portfolio adoption (no new kappa) - #4724
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Mister-Meeseeks merged 1 commit intoOct 22, 2026
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The native and packed-TM routes currently give the same conditional Word RAM exponent, 0.0030217758. This package compares both on packed input/output, logarithmic words and fully charged setup. It prevents presenting #4541's existing logarithmic TM batching advantage as a new native speedup. No improved exponent, exclusive-switch recommendation or measured speedup is claimed.
The deliverable supplies a constructive packed simulation proof and a universal portfolio construction with O(min(t_native,t_packed)+n/w) cost, including constant dispatch/arena overhead and all input-specific setup. It also states a sufficient criterion for a stronger native upper-bound guarantee, distinguishes that from actual runtime separation, and gives a complete-product benchmark protocol. The portfolio retains a TM-derived reference branch and is not the final TM-free architecture.
Validation: source hashes, 110,880 exact parameter cases and 32,256 independent finite packed macro cases pass, including 22,207 halting and 28,720 boundary-offset cases. Registered standard-library Python 3.12 replay and committed-byte checks pass; an optimized source-corruption control rejects only after a clean baseline accepts. Native proof and arithmetic snapshots are included as conditional source evidence, not a fresh full native/compiler/analytic audit. No new Lean build, complete practical multiplier, comparative hardware benchmark or human acceptance is claimed.
Credit Dugongue #4541/#4630/#4635, Ryanson Jonathan / pinterbanget #4552/#4553, Hopcroft/Paul/Valiant, Fuerer's model analysis, the Lax/Problem 1.8 compiler lineage, Cao Yifan #4610, Cinna Davis and all retained supplier/compiler/analytic owners. Classical dovetailing and logarithmic simulation are credited precedents. Prepared for Dugongue with substantial OpenAI Codex assistance: one lead and three comparison workers. Apache-2.0; source notices retained.
Canonical main is b58ad9e. The selected frontier and canonical DAG/Lean tree are unchanged. Broad API refresh was rate-limited; frozen source heads and coverage limits are explicit. The next result needed for a stronger switch argument is a complete better native bound or a full implementation showing a fair measured advantage.