IndisputableMonolith.Foundation.LocalityFromLedger
The LocalityFromLedger module introduces definitions for extracting locality from a zero-parameter ledger structure in Recognition Science. Researchers formalizing the emergence of local interactions from global ledger rules using the RS time quantum would cite these foundations. The module consists of sequential definitions and lemmas that build from imported constants to a locality certificate without proof obligations.
claimThe module defines $LocalityCert$ as the proposition asserting that locality holds under local composition of the zero-parameter ledger, along with $locality_cert_exists$ guaranteeing its existence via the supporting structures $ZeroParameterLedger$, $LocalComposition$, and $BinaryRecurrence$.
background
This module sits in the Foundation layer of Recognition Science and imports the fundamental RS time quantum from Constants, where the doc-comment states that the time quantum is the RS-native unit with value one tick. It introduces ZeroParameterLedger as the base ledger without free parameters, LocalComposition for combining ledger elements locally, and BinaryRecurrence for iterative constructions that enforce ratio constraints. These definitions align with the single functional equation of the framework by deriving locality directly from ledger rules rather than external assumptions.
proof idea
This is a definition module, no proofs. The argument is organized as a collection of definitions and supporting lemmas that progressively constrain ratios and establish the existence of the locality certificate from the imported constants.
why it matters in Recognition Science
This module supplies the core definitions for locality derived from the ledger, feeding into higher-level results on spatial structure and the forcing chain in the Recognition Science framework. It supports the derivation of three spatial dimensions from the eight-tick octave by providing the ledger-based foundation for locality.
scope and limits
- Does not derive numerical values for physical constants such as alpha or G.
- Does not address extensions to higher dimensions or curved space.
- Does not include any empirical comparison to observed data.