IndisputableMonolith.Physics.QuantumDecoherenceFromJCost
Module packaging quantum decoherence as a forced consequence of the J-cost on the phi-ladder. It defines mechanisms, rung-wise coherence, a decay law, and a certificate bundle. Open-systems theorists in RS would cite it when linking phase diffusion to cost minimization. Content is mostly definitional structures plus a cert constructor, not a deep uniqueness proof.
claimThe module defines decoherence mechanisms (with a finite count), coherence $C(r)$ at rung $r$ of the $\varphi$-ladder, a coherence decay map, and a certificate asserting that environmental decoherence follows from the $J$-cost $J(x)=\cosh(\log x)-1$ under open-system coupling to the tick $\tau_0=1$.
background
Recognition Science forces the cost $J(x)=(x+x^{-1})/2-1$ (equivalently $\cosh(\log x)-1$) as the unique symmetric defect functional (T5). Coherence of a quantum amplitude is expected to degrade when the system couples to the discrete recognition tick $\tau_0=1$ and to the self-similar $\varphi$-ladder of rungs.
This Physics module imports only Mathlib and Constants (which fixes the RS time quantum $\tau_0=1$ tick). Sibling names introduce a mechanism type, a mechanism count, coherence evaluated at a rung, a decay operator, and a DecoherenceCert bundle with witness.
The local claim is that laboratory decoherence is not an extra postulate: it is the open-system shadow of minimizing $J$ against environmental degrees of freedom on the ladder.
proof idea
Definition-first module, not a deep proof development. It assembles named structures (mechanism, coherence-at-rung, decay, certificate) and a cert constructor. Any nontrivial lemmas reduce to algebraic identities on $J$ and the rung index, or to discharging side conditions inside the certificate. No multi-step tactic chain is indicated by the module skeleton.
why it matters in Recognition Science
No downstream used_by edges are recorded yet, so the module is a leaf definition layer for later open-system results. It ties the J-uniqueness step (T5) and the discrete tick/octave structure to phase diffusion and classical emergence. Work on measurement, the Berry threshold $\varphi^{-1}$, or the dream fraction $\varphi^{-3}$ would import these names when stating that decoherence rates sit on the same cost landscape as mass and coupling constants. Closes a scaffolding gap between pure cost calculus and laboratory open quantum systems.
scope and limits
- Does not derive a numerical SI decoherence rate from first principles.
- Does not prove uniqueness or completeness of the mechanism enumeration.
- Does not exhibit a concrete experimental Hamiltonian or Lindblad generators.
- Does not discharge a full master equation or completely-positive map theorem.
- Does not connect decoherence times to the alpha band or mass formula directly.