[Dugongue]

The constant-overhead backend in #4538 can transfer correctness without changing the time scale. This package instead constructs and pays for short TM-window transition tables, packed two-word window updates and binary IO codec tables. For a fixed finite TM with a known polynomial execution/address envelope, it proves the informal uniform bounded-word RAM bound

O((T(n)+n+m)/log(n+2) + (n+2)^(1/16) log(n+2)).

With packed binary operands and output cap 2n, a supplied conditional TM multiplication bound T(n)=O(n(log n)^(1-kappa)) therefore yields O(n/(log n)^kappa) RAM operations, including each input's preprocessing and IO. The target uses no word multiplication/division or exact complex-cell primitives. The program/hidden constants depend on the fixed machine and envelope; this is an asymptotic result, not a practical-speed claim.

No improved TM kappa, new best-known unconditional RAM record, or worldwide priority is claimed. Kappa is inherited: selected #4359 gives 0.0023; pending #4535 gives 0.003020165 only with its complete antecedent and assumptions. #4536's arithmetic check does not validate those full assumptions. No selected-frontier files change.

The package contains a complete informal construction proof and exact finite operational models, not a fully emitted RamStd program or new Lean formalization. The generic run_packed interface computes its epoch/origin and generates every table afresh, without supplied runtime fuel. All 16 pairs of 2-bit integers pass a fixed 144-state TM fixture through the whole packed codec/window/table/output chain; one extra fresh generic run checks complete composition. That fixture is not an all-length multiplier. Local tables/reference TM replay, codec reversal/cap/termination controls and short-product carry controls also pass.

Validation: registered research-package replay, immutable Git-free export/replay and source-corruption rejection passed. Source/commit/staging hashes and shielded author/committer passed. All Python is standard-library and portable; Linux-hosted execution and hosted CI are not asserted. Independent agent reviews checked the proof's state-bit cutoff, numeric span, setup costs, packed ABI and genuine halting. No human peer review is claimed.

We also searched actual paid-profile changes: whole-prefix helper retiming, full-Clifford contact labels and 7,140 physically valid X/Y shared-axis assignments (plus 54,672 relaxed assignments). No valid cheaper profile was established; these failures are retained as local checkpoints rather than misreported as a kappa gain. Open next questions cover complete emitted/refined code, binding an exact complete TM supplier, and a genuinely changed paid native graph.

Credit Hopcroft, Paul and Valiant (1975), Section 4, for classical logarithmic simulation; the original theorem's T>=n log n input-floor condition is addressed here by explicit packed IO rather than silently dropped. Credit Fuerer's log-RAM model/comparison, #4538 and retained Problem 1.8 RAM/compiler sources, Szymon Torunczyk/GPT, the original OpenAI manuscript, Dillon #4532, hexapode #4535, Cinna Davis #4470, zxv, Jacob Alan Sussman, Ryanson Jonathan, Dugongue and all inherited physical/precision/prime/analytic/recovery suppliers. Existing #647/#956 exact-scalar RAM providers retain their separate model and credit. Detailed primary-source and PR overlap is included. Prepared with substantial OpenAI Codex assistance and three parallel agents; Apache-2.0.