IndisputableMonolith.Foundation.ObserverFromRecognition
ObserverFromRecognition defines PrimitiveInterface as a map from carrier K to Fin n, the finite-resolution recognizer that turns configurations into distinguishable events. This supplies the pre-physical observer structure in the Recognition Science foundation. It is cited by modules that build recognition lattices from kernel classes and derive logic realizations. The module is definitional, establishing kernel equivalence and separation axioms via direct constructions.
claimA primitive interface on carrier $K$ is a function $r:K→Fin n$ for finite $n$, whose kernel equivalence $x∼y$ iff $r(x)=r(y)$ yields the initial distinction structure; associated axioms include reflexivity, symmetry, transitivity, nontriviality, and separation at reference points.
background
The module sits in the Foundation layer and imports PrimitiveDistinction to ground the carrier and basic distinction. It introduces PrimitiveInterface as the finite-valued recognizer, PrimitiveObserver as its concrete realization, and pointInterface variants that fix a reference point or enforce separation away from it. Kernel properties (refl, symm, trans, is_equivalence) are stated directly on the recognizer map, while NontrivialRecognition and Separates add the conditions that the image is not a singleton and that distinct points can be resolved.
proof idea
This is a definition module. It declares the interface type and then supplies one-line proofs that the induced kernel satisfies reflexivity, symmetry, and transitivity, hence is an equivalence; pointInterface lemmas handle the reference-point and separation cases by direct case analysis on the finite codomain.
why it matters in Recognition Science
The module feeds the master forcing-chain theorem in IndisputableMonolith and supplies the recognizer input required by RecognitionLatticeFromRecognizer to form the first recognition lattice as the quotient by kernel classes. It is also imported by RecognizerInducesLogic to realize the Law of Logic on the event space. It occupies the T0–T1 position in the forcing chain where finite recognition first produces distinguishable events before any spatial or dynamical structure appears.
scope and limits
- Does not introduce physical observers or mental states.
- Does not define spatial dimensions or dynamics.
- Does not derive constants such as phi or alpha.
- Does not prove uniqueness or forcing results beyond kernel equivalence.
used by (3)
depends on (1)
declarations in this module (17)
-
structure
PrimitiveInterface -
abbrev
PrimitiveObserver -
theorem
kernel_refl -
theorem
kernel_symm -
theorem
kernel_trans -
theorem
kernel_is_equivalence -
def
NontrivialRecognition -
def
Separates -
def
pointInterface -
theorem
pointInterface_at_ref -
theorem
pointInterface_away -
theorem
pointInterface_separates -
theorem
nontrivial_recognition_forces_interface -
theorem
nontrivial_recognition_forces_observer -
structure
ObserverFromRecognitionCert -
def
observerFromRecognitionCert -
theorem
observerFromRecognitionCert_inhabited