IndisputableMonolith.Potential
The Potential module defines the discrete potential function p on the recognition structure M together with DE and Kin, enforcing that p increases by a fixed increment δ along every edge of the relation M.R. Downstream work on ledger uniqueness imports these definitions and invariants. The module supplies the core definitions and edge-difference theorems that follow directly from the recognition axioms.
claimThe potential function satisfies $p(y) - p(x) = δ$ for every edge $(x,y) ∈ M.R$, where $δ$ is the fixed discrete increment; related objects include the discrete energy DE and kinetic term Kin.
background
The module sits inside the Recognition Science framework and imports IndisputableMonolith.Recognition (whose T1 states that nothing cannot recognize itself) together with IndisputableMonolith.Causality.Basic. It introduces the potential Pot as a real-valued function on M obeying the discrete edge rule, together with the auxiliary notions DE and Kin. The listed sibling theorems establish constancy of differences on ReachN, on connected components, and inside balls.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies the potential and edge-invariance results imported by IndisputableMonolith.LedgerUniqueness. It encodes the discrete edge rule that follows T1 in the Recognition chain and is required for any later uniqueness statements on the ledger.
scope and limits
- Does not derive explicit closed-form expressions for p.
- Does not relate δ to the phi-ladder or mass formula.
- Does not treat continuous or non-discrete limits.
- Does not address higher-dimensional or non-graph structures.