Welcome — technical-feedback channel for the PCF logarithmic-ladder / 4/π Casoratian paper

[papanokechi]

This repository accompanies the paper Polynomial continued fractions: a proved logarithmic ladder, a 4/π Casoratian identity, and 482 irrational constants (Papanokechi, 2026), archived on Zenodo:

• DOI: 10.5281/zenodo.19491768
• HAL deposit: hal-05624243v1 (awaiting moderation as of May 2026)

This Discussions board is the preferred channel for technical exchange about the paper.

What feedback is most valuable

The author invites assessment from specialists in:

• polynomial-continued-fraction (PCF) irrationality methods
• hypergeometric identities and Casoratian techniques
• PSL₂(ℤ) modular obstructions

Three threads will receive priority replies:

1. Prior-art pointers — especially earlier closed-form treatments of the PCF(−k n², (k+1)n+k) family, or of the 4/π Casoratian telescope.
2. Gaps or strengthenings in the logarithmic-ladder convergence argument.
3. Alternative derivations of the 4/π identity that do not route through the ₂F₃ over ℚ(√5) obstruction.

Independent reproductions of the Arb interval-arithmetic certification at depth N = 5000 are also welcome.

Category guide

Category	When to use it
Prior art & questions	Citations to related work, suggested references, clarifying questions about a definition or step.
Errata	Typos, sign errors, broken proof links, computational discrepancies. Please cite the page / equation.
Ideas	Conjectural extensions, related identities you'd like to see explored.
General	Anything else technical.
Show and tell	Independent reproductions, alternative implementations, related computational experiments.

When in doubt, post in General and the maintainer will re-categorize as needed.

Norms

• Stay technical. Critique the work, not the author.
• Prior-art pointers are welcome without reservation — including references that may overlap with or supersede the paper's claims.
• This board is moderated by the author; replies typically within 1–3 business days (Asia/Tokyo).

Other channels

• Email (fallback): ppapanokechi@gmail.com
• ORCID: 0009-0000-6192-8273

For citations, please use the Zenodo DOI above.

Other deposits in the PCF research track

This paper is the lead artifact of a multi-deposit program. Adjacent records on Zenodo:

• 10.5281/zenodo.19931635 / 10.5281/zenodo.19931636 — PCF-1 CM Predicate (concept / current version)
• Additional related deposits are enumerated under the Related identifiers metadata field of the main Zenodo record.

Thank you for engaging.