IndisputableMonolith.CrossDomain.WorkingMemoryFromCube
The module defines canonical span structures and related span functions for working memory models derived from cubic geometries in the Recognition Science framework. Its central object is the canonical span equal to 7, expressed as 2 cubed minus 1. Cross-domain researchers modeling discrete memory or lattice systems would cite these when extending the eight-tick octave. The module proceeds via a chain of definitions and equalities on span positions and brackets.
claimThe canonical span satisfies $7 = 2^3 - 1$.
background
This module sits in the CrossDomain section and imports only Mathlib. It introduces definitions for canonicalSpan (the fixed span of 7), spanAt (position-specific spans), span_strict_mono (monotonicity), super_normal_jump, and miller_bracket, all built around the cubic structure. These objects formalize discrete spans tied to the eight-tick octave of period 2^3. The module doc-comment states directly: Canonical span: 7 = 2³ − 1.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies the discrete geometric primitives that feed parent results on working memory and cross-domain extensions in the Recognition framework. It directly supports WorkingMemoryFromCubeCert and links to the T7 eight-tick octave step in the unified forcing chain, where the 2^3 period produces the canonical span of 7. Downstream theorems use these spans to model memory thresholds on the phi-ladder.
scope and limits
- Does not derive the span value 7 from the forcing chain axioms.
- Does not address continuous or field-theoretic limits.
- Does not include numerical evaluation or simulation code.
- Does not connect spans to mass formulas or alpha-band constants.