J_bit
plain-language theorem explainer
J_bit supplies the logarithmic unit for recognition cost as the natural logarithm of the golden ratio. Researchers deriving stellar mass-to-light ratios from ledger principles cite this to anchor phi-ladder scalings without external calibration. The declaration is a direct constant assignment in the mass-to-light module.
Claim. The recognition cost bit is defined by $J_{bit} := ln φ$, where $φ$ is the golden ratio.
background
Recognition Science assigns the cost of any recognition event to its J-cost via the multiplicative recognizer on positive ratios. J_bit sets the base unit so that cost differentials produce exact powers of phi. The module derives the stellar mass-to-light ratio from three strategies: J-cost weighting in stellar assembly, phi-tier structure of nuclear and photon fluxes, and geometric constraints from wavelength, time, and coherence scales. Upstream results include the non-negative J-cost assignment for events and the structure of J-cost itself.
proof idea
The declaration is a direct definition that assigns the natural logarithm of the golden ratio to J_bit. No lemmas or tactics are invoked beyond the imported constant phi.
why it matters
This definition anchors the three-strategy derivation of the mass-to-light ratio that completes zero-parameter status for Recognition Science. It supplies the scaling unit required for the claim that all astrophysical calibrations follow from the ledger. The step aligns with J-uniqueness and the phi fixed-point in the forcing chain.
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