Clag_eq_phi_neg5
plain-language theorem explainer
The equality sets the ILG coherence energy parameter equal to phi to the negative fifth power in RS-native units. Workers deriving recognition bandwidth from the holographic bound and per-bit cost ln(phi) cite this when fixing the energy quantum per recognition event. The proof is a one-line wrapper that unfolds the definition of Clag and reduces via the ring tactic.
Claim. $C_{lag} = phi^{-5}$, where $C_{lag}$ denotes the ILG coherence energy (energy quantum per recognition event).
background
The RecognitionBandwidth module connects five Recognition Science elements: the holographic bound on information, recognition cost per bit k_R = ln(phi), ILG parameters including C_lag = phi^{-5}, the eight-tick cadence, and consciousness boundary cost. Recognition bandwidth is introduced as R_max = S_holo / (k_R · 8 tau_0), a hard ceiling on ledger throughput. The upstream definition states Clag : R := 1 / (phi ^ (5 : Nat)), with the theorem confirming this matches the coherence exponent E_coh.
proof idea
The proof unfolds Clag and applies the ring tactic to confirm the algebraic identity.
why it matters
This anchors the ILG coherence energy inside the Recognition framework, fixing the parameter that enters bandwidth formulas and the phi-ladder mass scaling. It directly supports the module's unification of holographic capacity with the eight-tick octave and RCL. No downstream uses are recorded yet; the result closes the parameter specification for later bandwidth monotonicity and positivity claims.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.