Published December 7, 2025 | Version v2
Publication Open

A Unified Collapse Geometry for Hardness: SPDP Rank, Observer Complexity, and an Unconditional P-Class Unprovability Theorem for the Riemann Hypothesis

  • 1. ROR icon Swansea University

Description

This preprint develops a unified SPDP–N-Frame framework in which the Riemann Hypothesis (RH) is recast as an explicit “RH interface” problem and then shows, unconditionally, that this interface lies beyond the polynomially bounded region accessible to P-class observers. Using the shifted partial derivative (SPDP) machinery from the author’s P≠NP work, it constructs a concrete SPDP polynomial family encoding critical-line behaviour and proves that it inherits exponential SPDP rank, so any complete NF–SPDP proof of RH in this encoding must leave the P-class region. Within this model, the main theorem is therefore an unprovability result: no finite-capacity, P-bounded observer can internally carry a full formal proof of RH-INT, and any Clay-style RH proof (if it exists) would appear hypercomputational relative to such observers, even though the paper does not claim that RH is unprovable in bare ZFC.

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