preprintZenodo (CERN European Organization for Nuclear Research)May 1, 2026GREEN OA

PCF-2: A Program Statement for the Cubic Extension of the Δ-Discriminant Transcendence Predicate

PPpapanokechi papanokechi
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Abstract

This paper is a program statement, not a results paper. It frames PCF-2 (P13 in the SIARC stack), the cubic extension of PCF-1 (concept DOI 10.5281/zenodo.19931635; latest v1.3 = 10.5281/zenodo.19937196) from degree-two polynomial continued fractions to degree-three. PCF-1 established a sharp empirical dichotomy across 30 degree-two families: the sign of the balanced discriminant Δ₂ = β² − 4αγ predicts whether the limit of the PCF admits an elementary closed form (Δ₂ > 0, 24/24 Trans-stratum families) or fails PSLQ detection against an 18-element basis at 220 digits (Δ₂ 0.6 at Bonferroni p

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Topics & keywords

Topics
Keywords
  • Discriminant
  • Sign (mathematics)
  • Predicate (mathematical logic)
  • Invariant (physics)
  • Cubic function
  • Extension (predicate logic)
  • Sketch
UN Sustainable Development Goals
  • Reduced inequalities
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