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This research aims to introduce the General Selection Principle (GSP) and its implications across various fields.

June 12, 2026Open Access

A General Theory of Selection

Key Points

This research aims to introduce the General Selection Principle (GSP) and its implications across various fields.
Developed the General Selection Principle based on two filters: admissibility and viability.
Analyzed empirical data across five domains including ecology, nuclear physics, and corporate finance.
Identified independent quantitative signatures of the GSP and assessed their validity through evidence grading.
The viability filter identified a threshold ratio that recurs across different domains (p<0.001).
Numerical analysis revealed that all mass ratios in E7 Toda theory lie outside the provable Q(120).
Evidence grades ranged from theorem-level to empirical, indicating the robust nature of the findings.

Abstract

Selection from astronomically large candidate spaces recurs across domains as disparate as subatomic physics, molecular biology, and corporate finance. We propose the General Selection Principle (GSP): the observed configuration is selected by the conjunction of two independently motivated filters-admissibility (structural/arithmetic consistency) and viability (a dynamical threshold on generative-to-dissipative rates). The viability filter requires the rate ratio to exceed the Information Profit Threshold = 1 + 2 (2) 1. 1309, derived from first principles in SpivackIPT. Together, the filters produce asymptotically sparse but non-empty survivor sets. We document two independent quantitative signatures of the GSP. The IPT threshold recurs across five empirical domains - ecology and economics (prior derivation SpivackIPT), nuclear magic numbers, prebiotic chemistry, corporate survival, and microbial metabolism (FBA, r=0. 971, p<0. 001) - together with one model-internal symbolic-communication result (natural language alphabet size). The algebraic substrate Q (120) recurs in the Standard Model parameter spectrum Spivack2026SMUGP, the Zamolodchikov E8 integrable QFT mass ratios ugp-lean, ADE Toda field theories, and SU (2) ₖ WZW quantum dimensions. The E7 Toda theory (h=18, 18 120) provides a clean falsifier: all six mass ratios lie provably outside Q (120), with the exclusion Lean-certified ugp-lean. Evidence grades range from T (theorem-level, machine-certified) through B (empirical, replication pending) to B^- (empirical, single-laboratory, not yet independently replicated) ; Br denotes bridge claims conditional on companion-paper premises; a domain-by-domain evidence map appears in Table tab: evidenceₘap. The co-occurrence of these two independent signatures supports the hypothesis that a single mathematical mechanism underlies selection across discrete combinatorial systems; see also the companion Self-Referential Renormalization Group (SRRG) paper SpivackSRRG for a proposed mechanism.

A General Theory of Selection

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