ObservableRatioModel
plain-language theorem explainer
ObservableRatioModel equips any type α with a positive real ratio function and its logarithm as the associated log-charge. Researchers formalizing zero-parameter ledgers cite the structure to encode the neutral-sector constraint that observable states carry no free conserved charge. The declaration is a direct structure definition whose four fields impose positivity and the exact log-ratio relation.
Claim. An observable ratio model on a type α consists of a function ratio: α → ℝ with ratio(s) > 0 for every s, together with a function log_charge: α → ℝ satisfying log_charge(s) = log(ratio(s)) for all s.
background
The Neutral Sector module shows that observable states in a zero-parameter ledger must lie in the neutral sector where conserved charge vanishes. The module argument runs that any nonzero sector label Q requires encoding an arbitrary real number, which introduces a forbidden free parameter; hence only Q = 0 is admissible. The structure therefore records the ratio and its logarithm so that later theorems can enforce neutrality directly from the zero-parameter posture.
proof idea
The declaration is a plain structure definition. Its four fields are introduced by direct field declarations: ratio and log_charge as functions, ratio_pos as a positivity axiom, and log_charge_eq as the equality axiom linking the two functions. No tactics or lemmas are applied.
why it matters
The structure supplies the model type used by the downstream theorems neutral_ratio_eq_one, parameter_free_observables_are_neutral, parameter_free_ratios_are_unity and sectorLabelIsFreeKnob. It therefore closes the module-level forcing step that observable ratios in a zero-parameter ledger must equal unity. Within the Recognition framework the definition supports the neutral-sector conclusion that feeds the eight-tick octave and D = 3 spatial dimension derivations.
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