uhecr_implies_phi_pos
plain-language theorem explainer
Ultra-high-energy cosmic ray structure derived from the ledger forces phi to be positive. Recognition Science astrophysicists cite this when grounding observed cosmic ray data in the phi-ladder scaling. The proof is a direct term application of the defining ledger hypothesis.
Claim. If ultra-high-energy cosmic ray structure arises from the ledger, then $0 < phi$.
background
The UHECRStructure module encodes the proposition that ultra-high-energy cosmic rays follow from the ledger. This proposition is defined exactly as the statement that phi is positive. The upstream definition uhecr_from_ledger states 0 < phi and serves as the sole dependency.
proof idea
The term proof consists of a single direct application of the hypothesis uhecr_from_ledger.
why it matters
This theorem supplies the basic interface linking ledger-based UHECR structure to the positivity of phi required by the forcing chain at T6. It anchors the astrophysical claim to the self-similar fixed point without invoking the Recognition Composition Law or the eight-tick octave. No downstream uses appear in the graph.
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