Second-Order Science and the Ledger Structure for Evaluating Universality Claims: A Necessity Result for Coherence Restoration Under Unbounded Novelty

Abstract

First-order science lacks enforced closure on the objects it manipulates (hypotheses, methods, results, interpretations). This produces predictable failure modes: bounded message one-shot evaluation cannot reliably accept framework-extending claims; operational coherence degrades as unresolved constraints accumulate; and distributed evidence for universality claims is repeatedly reset by demands for single decisive tests. These failures are structural, not contingent, and cannot be repaired by incremental reforms internal to first-order process norms.[T] Necessity result (reverse approach): We prove that any process that restores coherence under unbounded novelty must implement an adaptive functional core isomorphic (up to representation) to a canonical operator algebra. Consequently, any cross-domain coherence solution must factor as domain-relative external operators plus a domain-invariant internal core of the FMA form. The Functional Model of Adaptation (FMA) is treated as a canonical representative of this necessity class, not as a speculative content model to be “proven true” under first-order standards.[E] Second-order instantiation: We define a strongly typed evidence ledger with explicit accumulation operators, persistence rules, and threshold conditions. The paper is not an argument for second-order science; it instantiates second-order science. Evaluate it by the ledger and its admissible moves.