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def definition def or abbrev high

PrimitiveObserver

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PrimitiveObserver aliases the recognitionInterface stage in the Stage inductive of the pre-temporal forcing order. Researchers tracing Recognition Science foundations cite it when showing non-trivial recognition forces an observer interface before time or spacetime. The definition is a direct one-line assignment to the Stage constructor.

claimLet $Stage$ be the inductive type enumerating pre-temporal dependency stages. Define the primitive observer as the recognition interface stage: $PrimitiveObserver := Stage.recognitionInterface$.

background

The PreTemporalForcingOrder module records a forcing order on stages prior to physical time, where $A$ precedes $B$ when $B$ requires $A$ as prior structure. The Stage inductive enumerates: distinction, recognitionInterface, singleValuedPredicate, symmetricComparison, compositionConsistency, rcl, jCost, arithmeticObject, timeTick. Recognition-light (the primitive revealing act) is distinguished from physical light (null-cone carrier downstream of J-cost and spacetime). Upstream, ObserverFromRecognition defines PrimitiveObserver K as an abbreviation for PrimitiveInterface K, noting that the observer is the interface structure recognition forces rather than an external entity.

proof idea

One-line definition that directly assigns PrimitiveObserver to the recognitionInterface constructor of Stage.

why it matters in Recognition Science

This supplies the PrimitiveObserver stage used in PreTemporalOrderCert to certify precedence over timeTick and physical light, and in theorems such as primitive_observer_before_time and nontrivial_recognition_forces_observer. It fills the recognitionInterface slot in the forcing chain, supporting the claim that the observer is internal to recognition. The placement aligns with the pre-temporal segment of the T0-T8 chain before timeTick emerges.

scope and limits

formal statement (Lean)

 153def PrimitiveObserver : Stage := Stage.recognitionInterface

proof body

Definition body.

 154
 155/-- Embodied observer: a physical subsystem with finite resolution, downstream
 156of spacetime and physical light. -/

used by (9)

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

depends on (8)

Lean names referenced from this declaration's body.