A
plain-language theorem explainer
Defines the active-edge count per tick as the integer constant 1. In the gap-balance identity this exponent makes η_B · Θ_crit = φ^A = φ, tying matter and coherence scales. Anyone citing the B-22 gap derivation or the φ-ladder anchor will use it. The body is a one-line constant definition.
Claim. The active edge count per tick is the integer $A = 1$. Equivalently, the product of the Berry factor $\eta_B = \varphi^{A-\mathrm{gap}}$ and the critical coherence scale $\Theta_{\mathrm{crit}} = \varphi^{\mathrm{gap}}$ equals $\varphi^A = \varphi$.
background
Module Foundation.GapDerivation closes boundary item B-22: a recognition event has $D+2$ independent degrees of freedom (D spatial from T8, one temporal tick from T2, one ledger-balance from T3), so the coherence energy is $E_{\mathrm{coh}} = \varphi^{-(D+2)}$. At $D=3$ this is $\varphi^{-5}$.
The integer $A$ is the active-edge count per tick. Sibling material in the same module builds the configuration dimension, parity count, and the gap $D^2(D+2)=45$ at $D=3$. Upstream anchors fix the same convention: Masses.Anchor sets active edges per tick to 1, and the gap-balance identity is $\varphi^{1-\mathrm{gap}}\times\varphi^{\mathrm{gap}}=\varphi$.
Related gap objects appear in Gap45.Derivation (product of closure and Fibonacci factors) and in RSBridge.Anchor (the display residue $\mathcal{F}(Z)$). Here $A$ is only the unit exponent on the matter side of that balance.
proof idea
Pure definition: the constant is introduced as the integer literal 1. No lemmas, tactics, or reduction steps. Downstream proofs simply unfold or rewrite with this value when they need the active-edge exponent.
why it matters
Fixes the unit active-edge count that makes the matter-coherence link read $\eta_B\cdot\Theta_{\mathrm{crit}}=\varphi$. That identity is listed among the module's main results as gap_balance and is part of closing B-22: once $D=3$ forces gap 45, the exponent $A=1$ keeps the product on the golden ratio itself.
The constant is referenced widely across Action (Noether shifts, J-action convexity, Christoffel data for the Hessian metric) and CostAlgebra (uniqueness of the cost via Aczél, continuous J-automorphisms). In the forcing chain it sits next to T5 (J-uniqueness), T6 ($\varphi$ as self-similar fixed point), and the eight-tick/D=3 landmarks (T7, T8), because the coherence yardstick $E_{\mathrm{coh}}=\varphi^{-5}$ is exactly $\varphi^{-(D+2)}$ at three dimensions.
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