NucleosynthesisFalsifier
This structure collects the explicit conditions under which the Recognition Science derivation of light-element abundances would fail. Cosmologists testing predicted helium and deuterium yields against observations would reference it when checking consistency with the phi-derived baryon-to-photon ratio. The declaration is a plain structure definition that bundles three propositions with an implication asserting that two of them cannot hold together.
claimA structure whose fields are the propositions that the baryon-to-photon ratio is unrelated to the golden ratio, that the helium-4 mass fraction differs substantially from 25 percent, that Big Bang nucleosynthesis predictions fail to match observations except for lithium, and that the conjunction of the second and third propositions yields a contradiction.
background
Big Bang nucleosynthesis occurs in the first minutes after the Big Bang and produces deuterium, helium-3, helium-4, and lithium-7. Observed values include a helium-4 mass fraction near 24-25 percent, D/H approximately 2.5 times 10 to the minus 5, and a lithium-7 abundance of roughly 1.6 times 10 to the minus 10 that remains discrepant. In Recognition Science the baryon-to-photon ratio is obtained from the golden ratio, nuclear magic numbers follow from the eight-tick structure, and abundances are fixed by these constrained parameters.
proof idea
The declaration is a structure definition with an empty body. It simply assembles the four fields listed in the signature without invoking any lemmas or tactics.
why it matters in Recognition Science
The structure supplies the concrete falsification criteria for the nucleosynthesis module COS-012 and thereby anchors the claim that eta is phi-related and that the eight-tick octave controls reaction rates. It feeds the broader test of Recognition Science against early-universe data while leaving the lithium discrepancy noted in the module documentation as an open question.
scope and limits
- Does not compute numerical abundance values from first principles.
- Does not resolve the lithium discrepancy.
- Does not incorporate neutrino species count or explicit reaction rates.
- Does not reference specific observational datasets or error bars.
formal statement (Lean)
221structure NucleosynthesisFalsifier where
222 eta_not_phi : Prop
223 helium_wrong : Prop
224 bbn_fails : Prop
225 falsified : helium_wrong ∧ bbn_fails → False
226
227end Nucleosynthesis
228end Cosmology
229end IndisputableMonolith