Structural Stabilization and Spectral Screening in Nonlinear Wave Substrates: Proof of Concept for a Spectral Emergence Programme
Abstract
We establish that structural stabilization via nonlinear self-trapping (Structural Stabilization Requirement, SSR) is a necessary condition for the existence of robust localized structures in dispersive substrates (Theorem 1), that a soliton's self-generated potential well supports exactly the eigenmode that generates it — perfect self-consistency (Theorem 2) — and that the linearity of the Hilbert space formalism axiomatically screens any such nonlinearity from the descriptive level (Theorem 3). We demonstrate the complete chain — self-trapping, emergent eigenmodes, heat kernel spectral decomposition, and structural screening — in an exactly solvable model (the one-dimensional cubic Soler equation [3]), extracting the spectral mass gap from K(τ) = Tr(e−τ D2) with four-digit precision and proving that the screening is exact (eigenvalue difference = 0.00). A formal classification theorem (the Dynamical Ledger, Theorem 4) eliminates twenty-one candidate field theories by systematic application of four independently motivated predicates — topological localization, emergent spinorial structure, descriptive linearity, and CPT conjugation — leaving exactly three surviving classes: nonlinear Dirac (Soler), chiral sigma (Skyrme), and their self-consistent coupling, the Chiral Quark Soliton Model (CQSM). This provides the mathematical foundations for a programme of ten companion papers (Emergence Papers I–X [13–22]) in which the self-consistent mean-field limit of these dynamics — the chiral quark-soliton model (CQSM) of Diakonov and Petrov — is recovered as a benchmark and tested against hadronic observables spanning five orders of magnitude in energy, with no adjustable parameters beyond ΛQCD.
Related
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BibTeX
@misc{dechery2026structural,
title = {{Structural Stabilization and Spectral Screening in Nonlinear Wave Substrates: Proof of Concept for a Spectral Emergence Programme}},
author = {Fabien Déchery},
howpublished = {HAL},
year = {2026},
month = oct,
url = {https://hal.science/hal-05787457v3},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Structural Stabilization and Spectral Screening in Nonlinear Wave Substrates: Proof of Concept for a Spectral Emergence Programme
AU - Fabien Déchery
PY - 2026
DA - 2026/10/08
PB - HAL
UR - https://hal.science/hal-05787457v3
AB - We establish that structural stabilization via nonlinear self-trapping (Structural Stabilization Requirement, SSR) is a necessary condition for the existence of robust localized structures in dispersive substrates (Theorem 1), that a soliton's self-generated potential well supports exactly the eigenmode that generates it — perfect self-consistency (Theorem 2) — and that the linearity of the Hilbert space formalism axiomatically screens any such nonlinearity from the descriptive level (Theorem 3). We demonstrate the complete chain — self-trapping, emergent eigenmodes, heat kernel spectral decomposition, and structural screening — in an exactly solvable model (the one-dimensional cubic Soler equation [3]), extracting the spectral mass gap from K(τ) = Tr(e^−τ D^2) with four-digit precision and proving that the screening is exact (eigenvalue difference = 0.00). A formal classification theorem (the Dynamical Ledger, Theorem 4) eliminates twenty-one candidate field theories by systematic application of four independently motivated predicates — topological localization, emergent spinorial structure, descriptive linearity, and CPT conjugation — leaving exactly three surviving classes: nonlinear Dirac (Soler), chiral sigma (Skyrme), and their self-consistent coupling, the Chiral Quark Soliton Model (CQSM). This provides the mathematical foundations for a programme of ten companion papers (Emergence Papers I–X [13–22]) in which the self-consistent mean-field limit of these dynamics — the chiral quark-soliton model (CQSM) of Diakonov and Petrov — is recovered as a benchmark and tested against hadronic observables spanning five orders of magnitude in energy, with no adjustable parameters beyond Λ_QCD.
ER -