Overview
This article organizes the bounded-relaxation approach around a single structural axiom, [A-cap]: the per-node relaxation rate of an admissible relational configuration is uniformly bounded. The axiom is motivated by non-injective projection together with finite local distinguishability; it is not a consequence of non-injectivity alone, which constrains information rather than rates.
Born–Infeld theory is presented as a saturation candidate — distinguished in the literature by exceptional propagation, not by saturation — rather than as a derived or unique completion. Under explicit hypotheses, the admissible signature is Lorentzian and spherically symmetric flux conservation yields the Newtonian exterior profile; the Schwarzschild form requires additional dynamical input, and horizons are read as foliation-relative saturation, as interpretation rather than theorem.
Core statements and their statuses
- Capacity axiom [A-cap]: a uniform bound on the per-node relaxation rate, stated as a named hypothesis on which companion papers rest.
- Open constitutive bridge: which continuum quantity inherits the bound is an open problem; null field configurations carry arbitrary amplitude at vanishing invariants.
- Born–Infeld candidate: compatible with several partial notions of saturation; the literature's genuine selection criterion is exceptional propagation (Boillat–Plebański), whose derivation from projection structure is open.
- Conditional signature selection: Lorentzian $(-+++)$ under an explicit hyperbolicity hypothesis; a capacity bound alone does not force hyperbolicity (flux-limited diffusion is the counterexample).
- Newtonian exterior profile: the robust radial result under spherical flux conservation; the Schwarzschild form requires external dynamical input, and horizons are a foliation-relative interpretation.
Conceptual scope
The article does not derive non-linear electrodynamics or curved geometry from the axiom. It labels every statement as axiom, structural motivation, computation, conditional result, or open problem, and formulates the three projection bridges — constitutive, dynamical, and gauge-sector — whose closure would turn the capacity reading into a derived consequence.
How this connects to Cosmochrony
Within Cosmochrony, [A-cap] is the named hypothesis on which the bounded-flux arguments of the spectral admissibility programme rest, and the spectral gravity papers supply, conditionally, the external dynamical input that the radial analysis requires. The paper states which bridges must be closed before saturation phenomena can be claimed as consequences of projection structure.
References
Jérôme Beau. Bounded Relational Capacity and Its Conditional Continuum Dynamics. Zenodo. DOI: 10.5281/zenodo.18407505