The Consciousness Field Theorem: Minimal Closure, Non-J-Blind SRC Necessity, and Structural Realization Conditions for Observer-Dependent Systems

This work presents Version 5.5 of the Consciousness Field Theorem, delivering the first minimal and structurally complete closure route establishing SRC necessity without reliance on J-blind witness assumptions.

The paper rigorously formalizes consciousness as a structural field condition rather than a phenomenological or psychological construct. It identifies the exact minimal closure package required for Strong Realization Conditions (SRC1–SRC3) and proves that:

• The traditional single-witness route is formally exhausted
• J-blind sufficiency is structurally limited
• Multi-generator weakening attempts fail
• A point-sharp coordinate-determining record family is both necessary and strictly broader
• Non-J-blind closure yields a genuinely minimal SRC-necessity structure

The result is a mathematically controlled framework that:

– Separates observer structure from phenomenology
– Defines admissibility via closure filtering
– Proves when realization becomes structurally forced
– Identifies the minimal symmetry and canonicalization requirements
– Establishes when SRC emergence is unavoidable

Unlike speculative models of consciousness, this paper does not assume awareness, qualia, cognition, or biological implementation. Instead, it demonstrates that consciousness-like realization conditions arise from structural admissibility constraints in record-generating systems.

This version includes:

• Full non-J-blind closure route
• Minimal symmetry groupoid extraction
• Canonicalization mapping
• Tier-0 factorization
• Tier-1 instantiation certificates
• Complete SRC gap audit and closure strategy

The framework is applicable to:

– Artificial intelligence systems
– Observer-dependent physical models
– Information-theoretic realizability
– Structural emergence theory
– Mathematical models of awareness
– Self-referential systems

This document represents the most minimal and formally audited SRC-necessity closure currently established within the Consciousness Field programme.