PCF Research

Computational research on polynomial continued fractions, partition asymptotics, and irrational constant identification.

Preprints

Paper 14 — Ratio universality for Meinardus-class partition functions and the G-01 law
https://doi.org/10.5281/zenodo.19491667

Polynomial continued fractions: a proved logarithmic ladder, a 4/π Casoratian identity, and 482 irrational constants Concept DOI: https://doi.org/10.5281/zenodo.19491767 (v1: 19491768). Dedicated reproducibility repo (verification scripts + 482-constant catalogue): https://github.com/papanokechi/pcf-casoratian-identities (see also casoratian/ here for a pointer.)

Subdirectories

• casoratian/ — pointer to the dedicated April-10 paper companion repo
• area2/ — self-adjoint structure of PCF recurrences
• channel/ — Channel Theory (asymptotic channels, ξ₀ universality)
• pcf2/ — PCF-2 cubic-extension transcendence predicate
• vquad/ — V_quad family and Painlevé III(D₆) reduction

Key scripts (top level)

• g01_lemma_k_diagnosis.py — Lemma K verification
• dichotomy_d34_scan.py — Generalized Dichotomy scan
• vquad_heun_connection_check.py — V_quad Heun analysis
• generalized_dichotomy_scan.py — Parameter space scan

Requirements

Python 3.10+, mpmath

``` pip install mpmath ```

Citation

If you use this work, please cite the Zenodo records above.