yardstick
plain-language theorem explainer
The yardstick supplies the sector base scale for masses on the phi ladder as two to the B power times coherence energy times phi to the r zero power. Mass prediction code in AnchorPolicy and SpectralEmergence applies it to compute species masses via rung offsets. The definition directly encodes the cube geometry table without further computation.
Claim. For each sector $s$, define the yardstick $A_s := 2^{B(s)} E_coh phi^{r_0(s)}$, where $B(s)$ is the sector power of two and $r_0(s)$ the phi exponent offset, both fixed by cube edge counting.
background
This module centralizes parameter-free constants derived from first principles. The local setting starts from D equals 3 cube geometry, yielding E total equals 12 edges, E passive equals 11, W equals 17 wallpaper groups, and A equals 1 active edge per tick. E coh is the coherence energy unit phi to the minus five. B pow and r zero are sibling definitions that tabulate the exponents per sector from these counts. Upstream results include the Generation type as a finite type of size three.
proof idea
The definition is a direct one-line expression using the pre-derived B pow and r zero values for the input sector. It multiplies the power of two, the coherence energy, and the phi power without any tactics or lemmas beyond the sibling definitions.
why it matters
The yardstick serves as the base for all mass predictions, feeding directly into mass rung and predict mass routines. It realizes the mass formula yardstick times phi to the rung minus eight plus gap in the phi ladder. This closes the derivation from the eight tick octave and D equals three in the forcing chain, enabling downstream theorems on mass scaling by phi.
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