characteristic_tier_scaffold
plain-language theorem explainer
The definition fixes the integer tier at 1 so that the stellar mass-to-light ratio evaluates to phi to the first power. Astrophysicists working with recognition-cost models of stellar collapse would cite this constant when placing M/L on the phi-ladder. It is a direct constant assignment with no lemmas or reduction steps.
Claim. The characteristic tier level for the stellar mass-to-light ratio is the integer $1$, obtained from the 5:3 partition of the eight-tick cycle.
background
The Recognition Science cost function is $J(x) = ½(x + 1/x) - 1$. During stellar collapse the module compares the recognition cost of photon emission events against the cost of bound-mass storage events; the difference fixes an integer exponent on the phi-ladder. The eight-tick cycle supplies the partition that selects the exponent 1 for typical stellar populations, yielding M/L in the interval {phi^n : n in [0,3]} and the representative value phi^1 in solar units.
proof idea
Direct constant definition that assigns the literal integer 1. No upstream lemmas are invoked; the value is supplied as input to the exponentiation appearing in the downstream stellar M/L definitions.
why it matters
This constant supplies the exponent required by ml_stellar_value, which proves the stellar M/L ratio equals phi. It implements the eight-tick octave (T7) by selecting the tier from the 5:3 partition of the cycle and thereby places the result on the phi-ladder demanded by the Recognition Composition Law. The choice also aligns the predicted M/L interval with the observed range [0.5,5] solar units.
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