IndisputableMonolith.Foundation.LocalityFromLedger
LocalityFromLedger derives spatial locality as an emergent property from a zero-parameter ledger in Recognition Science. It defines supporting structures for local composition and binary recurrence then certifies that locality follows from minimal ratio properties. Researchers grounding dimension and locality in information primitives would cite the module. The argument chains definitions from the imported time quantum through ratio-only lemmas to existence of a locality certificate.
claimA zero-parameter ledger with local composition and binary recurrence yields a locality certificate; locality follows from the minimal binary structure on the ledger.
background
The module sits in the Foundation layer and imports the RS time quantum τ₀ = 1 tick. It introduces the zero-parameter ledger as a recognition structure with no adjustable parameters, local composition as the rule for combining recognitions at adjacent sites, and binary recurrence as the minimal recurrence compatible with the recognition composition law. The setting uses the J-cost and phi-ladder conventions from upstream to treat locality as derived rather than postulated.
proof idea
The module first records ratio_only and uniform_ratio facts, proves binary_is_minimal from them, then assembles locality_from_ledger and locality_cert_exists. Each step is a short algebraic reduction that applies the imported time quantum and the recognition composition law.
why it matters in Recognition Science
The module supplies the locality step that feeds the unified forcing chain toward the eight-tick octave and D = 3. It establishes LocalityCert as a primitive that later results on spatial structure can invoke without circularity.
scope and limits
- Does not assume pre-existing spatial coordinates.
- Does not derive particle masses or coupling constants.
- Does not address time evolution or dynamics beyond the ledger.
- Does not close the full T0-to-T8 forcing chain.