IndisputableMonolith.ClassicalBridge.CoarseGrain
The CoarseGrain module supplies definitions for mapping discrete ticks to continuum cells via explicit embeddings and cell volume weights. Workers deriving effective field equations from the Recognition Science phi-ladder cite it during discrete-to-continuum transitions. The module collects auxiliary objects such as Riemann sums and convergence statements but contains no proofs.
claimCoarse graining map from ticks to cells: embedding $e: Ticks → Cells$ equipped with volume weight $w(c)$ per cell.
background
The module resides in the ClassicalBridge domain and imports Mathlib for analysis primitives. It introduces coarse graining where ticks from the forcing chain receive an explicit embedding into spatial cells, each carrying a volume weight to support summation. This setup prepares Riemann sums and continuity statements for the sibling declarations.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module feeds the discrete-to-continuum continuity and H-convergence results that close the classical limit. It supplies the embedding and weighting tools required to recover the eight-tick octave and D=3 spatial structure from the T0-T8 chain.
scope and limits
- Does not prove any convergence statements.
- Does not specify the concrete embedding function.
- Does not address quantum or relativistic corrections.
- Does not fix the cell geometry beyond volume weights.