OpenAI · 137-01 · 2026-09-25 · Theoretical computer science
Simulating One-Tape Time in Two-Fifths-Power Space
preprints/Simulating-One-Tape-Time-in-Two-Fifths-Power-Space-September-25-2026
Family 137. One-tape time simulation in two-fifths-power space.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
Determines the halting and finite-control outcome of a fixed deterministic one-writable-tape machine up to time using space, improving the square-root exponent. Heads move at most one cell per step; finitely many read-only input heads are allowed. Initial contents are independent of , and contents and input symbols have polylogarithmic-space access. Simulation time is unrestricted.
We show that a fixed deterministic Turing machine with one writable tape and head can be simulated in work-space bits when a binary time cap T ≥ 2 is supplied. The simulator computes the finite-control and halting outcome by time T; its running time is unrestricted. The result allows a fixed number of read-only input heads and requires a fixed accessor that supplies every initial writable and read-only symbol within distance T of the relevant head origin in polylogarithmic space. This improves the square-root space exponent for one-tape machines, answering Williams's question for this model.
Preprint source and Lean scope
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This preprint is named in the Lean scope note for 137: One-tape time simulation in two-fifths-power space. The authors are OpenAI. This companion does not verify the formalization. It is not a premise. The OAI library is not imported. No compilation is asserted. O.1 stays NOT_CLOSED.