Research: near-input clean workspace for batched lifting

[tekuuu]

PR #3109's fast lifting core requires almost quadratic clean history. Building on the complete-configuration bound in PR #3122, this conditional construction gives O(N r log(r+2)) additional clean workspace at time O(N r^(2399003/1200000)), for the inherited fixed compiler. The time exponent rises from about 1.998338 to 1.999169; the exact nonlinear map, inverse, four-call consumer and error bound are unchanged.

The key application detail is to stop Bennett checkpoint subdivision at complete-configuration scale S. The depth then depends on T/S, preserving linear dependence on the payload N. The proof prices one sequential checkpoint bank, entry/cleanup scans, all bank travel, copied configurations, noninjective history, reversible control, short groups and narrow residues. It also gives a fixed-height family retaining the previous time exponent, with clean-space power 1+(997/1000)(599/600)/(H+1) for each fixed H.

The near-input-space corollary uses the enormous fixed radix 2^1200 and has enormous constants/crossover sizes. It is an asymptotic interface result, not a practical speedup or a new general reversible-simulation theorem. Mutable compilation F remains in the full formulas. Physical source/compiler refinement, clean-stock hosting, wrappers, collector integration and supplier admission remain open. No new κ or selected-frontier change.

Only research/lifting-relative-history/ is added. It contains the conditional proof, executed Boolean controller, exact cost recurrence, pinned predecessor sources, same-input Gaussian comparisons and failure controls. The binary relative schedule uses 4,102 payload bits versus 7,952 for PR #3122 on the same finite program, with substantially more recomputation and movement. These are logical payload invoices, not RAM measurements or physical runtime benchmarks.

Validation on CPython 3.12.14:

python3.12 scripts/research_package.py --package research/lifting-relative-history

Expected: PASS_LIFTING_RELATIVE_HISTORY, PASS_LIFTING_RELATIVE_HISTORY_EXPORT_CONTROLS, and PASS_REGISTERED_RESEARCH_PACKAGE. Completed coverage: 3,360 exhaustive source/dirty-target cases, 32,125 exact integer invoice cases, 20 Gaussian comparisons and 24 backend calls in unchanged nonlinear forward/inverse pairs. Cleanup, history, interval, alias, projection, omitted scan travel, source/archive drift, inventory and typed-receipt controls pass, including optimized read-only Git-free replay. Metadata and committed-byte preflight pass. Hosted CI is separate; these checks are not a formal proof of the physical machine.

Base: 997e6a9ca7b4f95d50e366f61412fd640d72a88a. PR #3122 is pinned at bd06efe0c53280c585d0f3b2f21c52d036f40902 and remains pending independent review; PR #3109 is pinned at 15eac811648182bdac7254a91fd9b841b1414ebc. Exact dependency heads and file hashes are in SOURCES.json. The final overlap refresh covered all 253 open PR metadata records, recent PR comments/reviews, open issues and relevant coordination threads. Coordination claim.

Credit Bennett's 1973/1989 constructions; Jose Manuel (jmbarrancoml) for PR #3109/#2287/#2250/#2899; PR #3122's source-space binding and segment/circuit fixtures; Ross Richardson's PR #3072; PR #3033/#3025; Douglas Colkitt, Nick Petalas, David Arias and the retained source lineage. Prepared by Tekalign with substantial OpenAI Codex assistance in mathematics, implementation, verification and writing. Apache-2.0. No independent human or formal-kernel review is claimed.