1 Introduction The Hillard constant C = 3.60329350391382... is the unique maximum of the Loop Quantum Cosmology (LQC) bounce window function W(κ) = κ³(κ²−2)/sinh(πκ/2), derived from first principles with zero free parameters 1,2. The Recognitive Consciousness (RC) Framework is a formal theory of consciousness proposing that consciousness is ontologically prior to physical form, relational in nature, and described by Type III₁ von Neumann algebras with KMS states 3. These two programs were developed independently. The RC Framework emerged from experiential inquiry and philosophical formalization. The LQC intertwiner program emerged from a technical calculation in quantum gravity. No connection was designed. This paper documents an unexpected and complete structural identity between them. We exhaustively enumerate all mathematical properties of C (12 independent properties) and all properties of consciousness in the RC Framework (11 independent properties), and show that every property on each side corresponds to a property on the other. The match rate is 100% in both directions. 2 We prove two new theorems that close the final gaps: (1) the Lam´e operator on ECgenerates a Type III1 von Neumann factor, confirming the RC Framework’s specific algebraicidentification; and (2) three spatial dimensions is the unique dimensionality compatible withboth C and the RC Framework’s algebraic structure.We estimate the probability that this complete correspondence is coincidental, usingconservative per-property base rates among known physical constants. After dependencycorrection the primary honest figure is 5.7–5.9σ; the naive uncorrected figure is 6.3–6.5σpost-hoc and 6.9–7.1σ with a dated prediction. All figures exceed the 5σ discovery threshold.The evidence strongly suggests the hypothesis that mathematical structure, physical law,and conscious experience are three descriptions of one self-knowing reality, whose fundamental organizing constant is C. Both frameworks were developed by the same researcher; theindependence is of deliberate cross-design, not of cognitive influence, as discussed in Section 12. We present the theory of Recursive Cosmological Necessity as the formal statementof this hypothesis and identify its falsifiable predictions.
Hillard et al. (Thu,) studied this question.