IndisputableMonolith.Recognition.ModelingExamples
This module supplies minimal modeling examples inside the Recognition namespace to illustrate core structures. It centers on a 2-vertex bidirectional case together with ledger and tick variants. Researchers validating the T1 principle or the early forcing chain would reference these examples for concrete checks. The module contains only definitions and imports the parent Recognition library without proofs.
claimSimpleStructure: 2-vertex recognition graph with bidirectional edges; SimpleLedger and SimpleTicks provide companion minimal models.
background
Recognition Science opens with T1: nothing cannot recognize itself. The module sits inside IndisputableMonolith.Recognition and imports Mathlib plus the core Recognition definitions. It supplies three sibling constructions: SimpleStructure (the 2-vertex bidirectional case), SimpleLedger, and SimpleTicks. These objects instantiate the abstract recognition relation in the smallest nontrivial setting before the phi-ladder or J-cost machinery is applied.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The examples ground the T1 statement and feed the main Recognition development by offering the smallest concrete instances against which later forcing-chain results (T5 J-uniqueness onward) can be tested. No used-by edges are recorded, confirming the module functions as illustrative scaffolding rather than a theorem carrier.
scope and limits
- Does not prove any general recognition theorems.
- Does not define J-cost, defectDist, or the phi-ladder.
- Does not treat multi-vertex or continuous cases.
- Does not connect to mass formulas or the alpha band.