per_nucleon_phi_factor
plain-language theorem explainer
The per-nucleon J-cost recognition contribution at rung k is defined to equal phi raised to the power k. Nuclear binding energy modelers in the Recognition Science framework cite this when deriving rung ratios for the iron peak relative to the alpha particle. The declaration is a direct abbreviation that unfolds immediately to the exponential.
Claim. The per-nucleon J-cost recognition contribution at rung $k$ equals $phi^k$.
background
In the Nuclear Binding Energy from Phi Ladder module, nuclear binding is the release of recognition cost per nucleon on the J-cost lattice. Each nucleon contributes one bond cycle whose per-nucleon value scales with the phi-ladder; the iron peak sits at rung 26, obtained from the identity k_iron = consciousnessGap - configDim - holonomyShift = 45 - 5 - 14 at D = 3. The module states that this rung is integer-forced with no free parameter and saturates at the eight-tick maximum adjusted by the 14-virtue gap shift.
proof idea
The declaration is a direct definition that sets the per-nucleon phi factor equal to the k-th power of phi.
why it matters
This definition supplies the elementary scaling term for all per-nucleon binding ratios in the phi-ladder model. It is invoked by the BindingEnergyCert structure to certify the iron peak at rung 26, the adjacent rungs at 25 and 27, and the gap of 22 to the alpha rung. In the framework it realizes the saturation of recognition cost at the eight-tick octave (T7) adjusted by the virtue gap, predicting the observed peak near iron without adjustable parameters; the companion script validates the prediction against AME2020 data.
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