Skip to content

fix(lean,#17570): docstring hashlife_correct -- status 2026-08-15 + renvoi vers evolveHashlifeFastAtN_correct_uncond #17644

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Merged
myia-ai-01 merged 1 commit into from
Sep 24, 2026
Merged

fix(lean,#17570): docstring hashlife_correct -- status 2026-08-15 + renvoi vers evolveHashlifeFastAtN_correct_uncond #17644

Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
15 changes: 11 additions & 4 deletions MyIA.AI.Notebooks/SymbolicAI/Lean/conway_lean/Conway/Life/HashlifeCorrectness.lean
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -6366,10 +6366,17 @@ theorem p5_inductive_step (n : Nat) (g : Grid) (h : BoxAssezGrand g n) :
the recursion because the jump preserves bounding box up to light-cone
expansion.

**Status (2026-06-13)**: base case `n = 0` proven above
(`hashlife_correct_base_zero`). The inductive step remains open (the
`sorry` below). See `hashlife_correct_implies_block_4` /
`hashlife_correct_implies_glider_8` for sanity witnesses. -/
**Status (2026-08-15, #17570)** : proven via `p5_inductive_step` (closed
#5998, 2026-07) under the fixed-frame hypothesis `BoxAssezGrand g n`. But
that hypothesis is `unsat` for non-empty grids once `n ≥ jumpSize = 8`
(`p5_large_n_hyps_unsat`), so `hashlife_correct` is *vacuously true* on
the large-`n` regime where the Hashlife jump actually fires — it does NOT
certify a non-vacuous equality between `evolveHashlifeFast` and `evolve`.
The **non-vacuous, unconditional** large-`n` correctness statement is
`evolveHashlifeFastAtN_correct_uncond` (l. 7202 of this file, on `main`
since #11781, 2026-08-15): ICT series consumers should cite that theorem.
`hashlife_correct` here stays for historical continuity and is named only
to declare its vacuity. See #17570. -/
theorem hashlife_correct (n : Nat) (g : Grid) (h : BoxAssezGrand g n) :
evolveHashlifeFast n g = evolve n g := by
-- P5 TARGET: main theorem, composition of P2-P4
Expand Down
Loading