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Construct a source-faithful reusable-origin realization of the old ordinary BIT helper with retained backing K_entry+C V for one call and K_entry+C max_i V_i for completed histories. An actual q=3 digit-bucket witness refutes the history-free K V_current reading: erased cells remain visited after a smaller call.
Binds ordinary movement and recursive segment reuse to #5814/#5829; distinct from #6098/#6152's planner histories. Polynomial ancestor preparation/absorption already appears in #2234 and is credited as inherited.
Base: 7c49fe3. Exact 14 input Git/SHA256 pins: SOURCES.json.
Reproduce (Python 3.12, stdlib):
Expected: PASS_ORDINARY_BIT_RETAINED_SPACE and PASS_REGISTERED_RESEARCH_PACKAGE.
Executed: normal/optimized checks, 441 payload cases, 1,599,798 metered moves, 15 interval walks and 1,961 padding checks. Seven controls reject wrong order, live-only accounting, missing erasure, append-only origins and omitted history. A shrinking/reuse history retains 19,694 cells versus nine live. Committed bytes/modes and both read-only Git-free export replays pass; complete remote tree matches tested contents.
No new κ. This constructs a schedule, not the final production dispatcher. Precision, markers and visited blanks remain charged; changed finite constants do not automatically preserve the selected numerical tariff. Final native/fallback, evaluator invocation and dispatcher binding remain; all five assumptions remain. No full multiplier, full-history audit or human/kernel acceptance.
By @CubeJerry with substantial OpenAI Codex assistance and separate source review. Credit Mason Hale (#5814), Ali Romman (#5829), JoyboyBrian (#6098), Nick Petalas (#6152), Jose Manuel (#2234), and retained stream/copy lineage. Apache-2.0.
Proof, pins, validation and open questions:
https://github.com/CubeJerry/integer-mult-bounds/tree/db7b33f6255b7308d9d7db1563afa39c99b9a27e/research/ordinary-bit-retained-space