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feat(MultiTapeTM): loglogn_equals_no_space - #44

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Prove SPACE(o(log log n)) = SPACE(1) following Katz's proof idea, with the main ingredient formalized in InputShortening.lean.

Working version of #13 (upstream leanprover#1154), rebased onto #43; the upstream PR stays unchanged until this is ready.

Depends on #43.

Implemented with Codex; rebased with Claude Code.

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barni120400 force-pushed the feat/tm-space-gap-adapter branch from 2bab1a2 to e57c5f6 Compare October 24, 2026 21:40
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barni120400 force-pushed the refactor/multitape-computes-such-that-adapter branch 2 times, most recently from 1c0dce0 to 39d6956 Compare October 24, 2026 22:00
@barni120400
barni120400 force-pushed the feat/tm-space-gap-adapter branch from e57c5f6 to af96593 Compare October 24, 2026 22:00
@barni120400
barni120400 force-pushed the refactor/multitape-computes-such-that-adapter branch from 39d6956 to ccbef1d Compare October 27, 2026 00:31
@barni120400
barni120400 force-pushed the feat/tm-space-gap-adapter branch from af96593 to 319db8f Compare October 27, 2026 00:31
@barni120400
barni120400 force-pushed the refactor/multitape-computes-such-that-adapter branch from ccbef1d to ff5d2bb Compare October 29, 2026 13:46
@barni120400
barni120400 force-pushed the feat/tm-space-gap-adapter branch from 319db8f to b282e79 Compare October 29, 2026 13:46
@barni120400
barni120400 force-pushed the refactor/multitape-computes-such-that-adapter branch from ff5d2bb to e0e1cc5 Compare November 1, 2026 16:56
@barni120400
barni120400 force-pushed the feat/tm-space-gap-adapter branch from b282e79 to 6ee183c Compare November 1, 2026 16:56
barni120400 and others added 2 commits November 3, 2026 22:19
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Prove `SPACE(o(log log n)) = SPACE(1)` following Katz's proof idea, with the main
ingredient formalized in `InputShortening.lean`.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
@barni120400
barni120400 force-pushed the feat/tm-space-gap-adapter branch from 6ee183c to e333c45 Compare November 3, 2026 20:21
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