photonProductionFunctional
plain-language theorem explainer
Structural photon-production functional for a time-dependent boundary modulation: the product of squared amplitude and squared rate. Dynamic-Casimir and parametric-drive modelers cite it as the minimal bookkeeping term that converts boundary work into real photons. The body is a direct algebraic definition, quadratic as expected for a parametric boundary drive.
Claim. For a time-dependent boundary modulation with amplitude $A$ and rate $r$, the structural photon-production functional is $A^{2} r^{2}$.
background
The module treats the dynamic Casimir effect as the time-dependent boundary case: changing the admissible mode inventory can convert boundary work into real photons. Only structural statements are proved here; device-level φ-locked schedules stay hypotheses until connected to circuit data.
A boundary modulation is a triple of reals (amplitude, rate, carrier frequency). The functional reads only amplitude and rate, forming the scalar cost of the parametric drive. Carrier frequency is recorded on the structure but does not enter this expression.
In the local QFT scaffolding, this is the term that must vanish for a static wall and become strictly positive when both amplitude and rate are nonzero.
proof idea
Definition, not a theorem. The body is the product of the square of the modulation amplitude with the square of the modulation rate. No lemmas or tactics; the expression is the structural model of parametric photon production.
why it matters
Supplies the scalar used by the static-boundary vanishing theorem (zero amplitude forces the functional to zero) and the nonzero-modulation positivity theorem (nonzero amplitude and rate force a positive value). Both properties are packaged in the DynamicCasimirCert structure as the certificate for theorem-level dynamic Casimir structure.
Within Recognition Science QFT, this is the bookkeeping term for boundary work turning into real photons under a changing mode inventory. The module explicitly leaves φ-locked device schedules open until circuit data is attached; the functional itself is only the structural quadratic skeleton of a parametric drive.
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