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.
Jeremy Rodgers (Mon,) studied this question.