module module high

`IndisputableMonolith.RRF.Models.Trivial`

The Trivial module supplies the singleton state space as the base RRF consistency model. Researchers verifying internal consistency of the Recognition Rate Function axioms cite it as the degenerate case that satisfies all core conditions. The module consists of definitions for the point, zero strain, closed ledger, and well-posed octave together with direct verification lemmas.

claimLet $S = {*}$ be the singleton state space. The strain map satisfies $s(*) = 0$, the ledger is closed, the configuration is a J-cost minimizer, and the octave structure is well-posed.

background

RRF.Core is the umbrella module that re-exports only definitional content for the Recognition Rate Function axioms with no physical constants or hypotheses. The Trivial module specializes those definitions to the case of a single-point state space. Sibling declarations introduce TrivialState, trivialStrain, trivialLedger, trivialChannel, and trivialOctave along with the associated balance and validity statements.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

The module feeds the RRF.Models umbrella, which collects concrete examples proving that the RRF axioms are internally consistent. It supplies the simplest such example before non-trivial models are considered.

scope and limits

Does not introduce physical constants or units.
Does not contain any hypotheses beyond the RRF core axioms.
Does not treat non-singleton state spaces.
Does not reference the forcing chain T0-T8 or the phi-ladder.

used by (1)

From the project-wide theorem graph. These declarations reference this one in their body.

IndisputableMonolith.RRF.Models module_import

depends on (1)

Lean names referenced from this declaration's body.

IndisputableMonolith.RRF.Core module_import

declarations in this module (15)

abbrev TrivialState L24
def trivialStrain L27
theorem trivial_balanced L34
theorem trivial_is_minimizer L37
def trivialLedger L41
theorem trivial_ledger_closed L46
def trivialStrainLedger L49
theorem trivial_is_valid L54
def trivialChannel L58
def trivialChannelBundle L63
def trivialOctave L69
theorem trivialOctave_wellPosed L76
theorem trivialModel_consistent L80
def trivialVantageTriple L85
theorem trivialVantageTriple_unified L88