2006.06837
Stuttering Conway Sequences Are Still Conway Sequences
Éric Brier, Rémi Géraud-Stewart, David Naccache, Alessandro Pacco, Emanuele Troiani
correctmedium confidence
- Category
- Not specified
- Journal tier
- Note/Short/Other
- Processed
- Sep 28, 2025, 12:55 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper defines the look-and-say-again (LSA) sequence, proves the digit-set/property P statement and gives a commuting identity L∘η = η∘C on pieces, from which it asserts equivalence to classical look-and-say and convergence of length ratios to Conway’s constant λ . The model’s solution arrives at the same conclusions but makes the conjugacy explicit by constructing a left inverse U on the P-language and proving U∘L = C∘U globally, which addresses boundary/coalescence rigorously. A minor difference is that the paper’s Theorem 1 lists 3 among allowed digits, while the model states the tighter set {1,2,4,6,d} for all n≥1 (3 only occurs when d=3 and then solely as the trailing dd), but this does not contradict the paper’s claim.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} note/short/other
\textbf{Justification:}
This short note introduces a clean variant of the look-and-say process (LSA) and correctly identifies its structural relationship to the classical sequence. The core ideas are sound and well motivated, and the commuting identity neatly explains why Conway-style structure and growth carry over. Two small points could be improved: (i) make the global equivalence precise by formalizing the conjugacy/factor map beyond the piecewise identity, and (ii) tighten the digit-set statement (or clarify the role of the seed 3). These are minor clarifications and do not affect correctness.