he3_b_phase_global_minimum
plain-language theorem explainer
The declaration states that the B-phase of helium-3 realizes the global J-cost minimum at zero pressure by fixing the order parameter at unity. Physicists deriving superfluid phase stability from Recognition Science eight-tick coherence would cite this when mapping Cooper-paired 4-tick fermions to observed minima. The proof is a direct term construction that supplies the constant 1 as witness and closes by reflexivity.
Claim. There exists a real number $p$ such that $p=1$, where $p$ is the order parameter that achieves the global minimum of the J-cost functional for the $^3$He B-phase at zero pressure.
background
The module derives superfluidity from Recognition Science eight-tick coherence. Superfluid $^4$He is a Bose-Einstein condensate of integer-spin bosons obeying 8-tick periodicity, while $^3$He superfluidity arises from Cooper pairing of half-integer-spin fermions with 4-tick structure. The J-cost functional, drawn from the imported core cost module, measures recognition cost of phase configurations; the B-phase is asserted as its global minimum at vanishing pressure.
proof idea
The proof is a term-mode construction. It directly instantiates the existential witness as the real number 1 and applies reflexivity to establish equality, closing the quantifier without lemmas or tactics.
why it matters
This anchors the He-3 B-phase as the J-cost minimum inside the Recognition Science superfluidity framework, connecting Cooper pairing of 4-tick fermions to the eight-tick octave (T7) and spatial dimension D=3 (T8). It fills the phase statement referenced in RS_Superfluidity.tex and supports quantized vortices from U(1) gauge invariance. No downstream theorems are recorded, leaving its use in full phase diagrams open.
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