IndisputableMonolith.Physics.VacuumDecayFromJCost
Defines vacuum-decay channels and a Coleman-style tunneling action built from the RS J-cost, together with a certificate that the action is positive and the channel count is finite. Physicists working on false-vacuum stability in the Recognition framework cite it for the action ratio and the VacuumDecayCert bundle. The module is mostly definitions plus elementary positivity lemmas; no deep analytic estimates.
claimA vacuum-decay channel is a discrete label; there are finitely many such channels. The tunneling action $S$ is a nonnegative real built from the $J$-cost, the action ratio compares channels, and a certificate packages positivity of $S$ with the finite channel count.
background
Recognition Science measures cost by the unique symmetric functional $J(x)=(x+x^{-1})/2-1$ forced at T5. Vacuum decay is cast as tunneling between local minima of an effective potential whose barrier height is expressed in $J$-units rather than an ad-hoc Euclidean action.
The module sits in the Physics layer and imports only Mathlib and the RS constants (notably the tick $\tau_0=1$). It introduces a finite enumeration DecayChannel, a real-valued tunnelingAction, the dimensionless action_ratio between channels, and the bundled certificate VacuumDecayCert asserting positivity and finiteness.
No continuum instanton analysis appears; the action is treated as an abstract nonnegative quantity derived from $J$, ready for later matching to the eight-tick and $\phi$-ladder scales.
proof idea
This is primarily a definition module. DecayChannel and decayChannel_count fix a finite discrete set. tunnelingAction is introduced as a nonnegative real; action_pos is the elementary lemma that the action is strictly positive on nontrivial channels. action_ratio is a quotient of two actions. VacuumDecayCert packages the count and positivity into a single Prop, inhabited by the constant vacuumDecayCert. No heavy tactics or external analytic lemmas are required.
why it matters in Recognition Science
Supplies the discrete channel bookkeeping and the $J$-based tunneling action that later Physics developments need when comparing false-vacuum lifetimes to the RS time quantum $\tau_0$. Downstream work (none yet linked in the graph) can quote VacuumDecayCert to obtain finiteness and positivity in one step, then feed the action ratio into lifetime estimates on the $\phi$-ladder. The construction keeps vacuum decay inside the same cost calculus that forces $J$, $\phi$, and the eight-tick octave (T5–T7), rather than importing an external Coleman–De Luccia formula.
scope and limits
- Does not derive the tunneling action from a continuum Euclidean path integral.
- Does not compute numerical lifetimes or match to observed vacuum metastability bounds.
- Does not prove uniqueness of the channel set; finiteness is definitional.
- Does not connect the action to the mass formula or the alpha band.
- Does not address gravitational back-reaction or CdL instantons.