[Dugongue]

The actual inverse owner recoding has eight mode numerators but 448 quotient uses. This adds a literal Word RAM program that rounds each mode once, preserves the exact nearest-even output, and charges setup, constants, scratch, branches and halting. At the documented k = 4 instance, the in-place static count is 1,329 versus 18,929 for the stated duplicate-quotient control. The proof gives the exact general saving and local error ≤ 2h, with source-bound norms 26 and 38/13.

The same focused package supplies three supporting interfaces: a literal native-unit serialization with all source events, owned dirty-entry/cleared-exit handling and 19 explicit axis embeddings; a completion-free three-query terminal decoder preserving every independent output; and sufficient width-uniform recovery bounds. Each component has a written proof, source pins and meaningful rejection controls. The native verifier checks the committed exports, all 12,544 code entries and actual address-map frame spans.

No new complete multiplication κ is claimed. The p19 gauge/compiler remains incomplete; a one-column four-term expansion is not a uniform ordinary compiler. The selected #5413 provider is not the /52 recoding consumer. The helper interface changes no recursive profile. These facts prevent substituting the local instruction saving into an outer exponent.

Validation: fresh Git-free normal and optimized package replays pass on CPython 3.12; the retained assertion-dependent decoder always runs in a non-optimized child. Independent agent review and maximum-word recoding tests passed. No Lean kernel audit or hosted Linux CI is claimed. Windows and Linux use only Python's standard library. Canonical package metadata and historical Git source provenance validation also pass. No shared tooling or selected record is changed.

Reproduce:

python -I -B research/native-wordram-interfaces/verify.py
python -I -O -B research/native-wordram-interfaces/verify.py

Frozen main: 32890bc5de034ab8fc93ac88ead7279a6a416d04, priority revision 7. Entry review covered 200 recently updated all-state PRs; a second 100-PR refresh and rendered handoff/mechanism pages informed scope. The final refresh also compared #5464’s joint odd-E8 cross-cube primitive and its explicit unpaid acquisition/caller obligations; it is complementary, not consumed source. This is not an exhaustive historical/unpublished overlap claim. #5462's numerical-headroom-only step is acknowledged without republishing it.

Credit Dugongue #4929 and the previous counted Word RAM kernel; Cao Yifan #4610; Cinna Davis #4694/#4698; Ali Romman #5388/#5457/#5451/#5421; DaysSky #5440/#5270; Matarener #5433/#5438; Dillon Amburgey #5402; Chris R/Clear1nsight #5413 and companion reviews; GamingPuzzled #5462; zxv, Jacob Alan Sussman and the retained native/compiler/Clifford/analytic lineage. Full notices and exact public content hashes are included. Substantial OpenAI Codex assistance by one coordinator and three agents; Apache-2.0/source-specific terms retained.

Open next questions specify how to attach the recoding to a complete caller, finish an all-width native gauge compiler, use an observation to remove a named paid request, and bind recovery to actual residuals. Each has a concrete first step and explicit blockers.