IndisputableMonolith.Physics.EffectiveFieldTheory2FromJCost
Packages second-order effective field theory (EFT2) as a certificate built from the Recognition Science J-cost. Defines a domain cost, a positive canonical threshold, and an inhabited certificate recording nonnegativity and threshold bounds. Physicists tracing how continuum EFT structure is read off the discrete cost would cite this module. Content is definitional assembly plus elementary positivity lemmas from Cost.
claimThe module introduces a domain cost $C$ built from the J-cost $J(x)=(x+x^{-1})/2-1$, a canonical threshold $\theta>0$, and an EFT2 certificate asserting $C\geq 0$ together with the threshold bound on the working domain, with an inhabited witness.
background
Recognition Science derives physics from a unique cost $J$ fixed by the Recognition Composition Law (T5 in the forcing chain). The Cost import supplies $J$ and its elementary identities; Constants supplies the RS-native time quantum $\tau_0=1$ tick.
This Physics-layer module packages a second-order effective-field-theory reading of that cost: a domain-restricted cost functional, its nonnegativity, and a positive canonical threshold used as a certification boundary. Sibling names mark the pieces: domain cost and evaluation/nonnegativity facts, the threshold and its positivity, and an EFT2 certificate type with an inhabited instance.
The certificate is the handoff object. Downstream continuum or effective-action arguments can assume one inhabited witness instead of re-proving basic cost inequalities at each use site.
proof idea
Definition-and-certificate module, not a deep forcing argument. The domain cost is defined from $J$; short lemmas record nonnegativity and on-shell evaluation. The canonical threshold is a positive constant. The EFT2 certificate type bundles those facts; a concrete certificate term and an inhabitedness proof supply the witness. Structure is assembly of Cost facts into a physics-facing package, with Mathlib only for ambient arithmetic.
why it matters in Recognition Science
Bridges the pure Cost layer to Physics by exposing an EFT2 certificate that continuum or effective-action developments can import. No used_by edges are recorded yet, so this is a leaf packaging step: the inhabited certificate is the intended hypothesis for any later claim of the form "J-cost implies EFT2 bounds."
In the broader framework it aligns with reading continuum structure off the unique $J$ forced at T5, rather than postulating an action by hand. It does not itself run the T0--T8 chain (phi, eight-tick octave, $D=3$); those remain upstream foundation results this module presupposes when used in a full RS physics stack.
scope and limits
- Does not derive a full Standard Model Lagrangian or numerical couplings.
- Does not prove uniqueness of the EFT2 certificate beyond the given inhabited instance.
- Does not treat higher-order EFT operators or renormalization-group flow.
- Does not force spacetime dimension, phi, or the eight-tick octave (T-chain lives elsewhere).
- Does not connect yet to recorded downstream theorems (used_by is empty).