IndisputableMonolith.Physics.WavePacketSpreadingFromJCost
Module linking free-particle wave-packet spreading to the Recognition Science J-cost. It defines a domain cost, a positive canonical threshold, and a WavePacketCert bundle asserting that spreading is controlled by J. Physicists deriving decoherence or packet width bounds from the cost functional would cite it. The file is mostly definitions plus elementary nonnegativity and inhabitation facts.
claimIntroduce a domain cost $C$ built from the J-cost $J(x)=(x+x^{-1})/2-1$, a canonical positive threshold $\theta>0$, and a certificate type asserting that free wave-packet spreading is governed by $C$ relative to $\theta$ (with inhabitation of a default certificate).
background
Recognition Science takes the unique symmetric cost $J(x)=(x+x^{-1})/2-1$ (equivalently $\cosh(\log x)-1$) as the generator of dynamics; the Recognition Composition Law constrains how $J$ multiplies under products and ratios. The Cost import supplies that functional; Constants supplies the RS tick $\tau_0=1$.
This physics module sits downstream of those foundations. It packages a domain-level cost (evaluated on a spatial or momentum domain), proves the cost is nonnegative, and fixes a canonical positive threshold against which spreading is measured. The WavePacketCert structure is the interface object: a proof-carrying record that the packet's width growth is controlled by the domain cost relative to that threshold.
No forcing-chain step (T5–T8) is re-proved here; the module assumes $J$ and works in the RS-native units already fixed by Constants.
proof idea
Definition-heavy module. domainCost is introduced from J; domainCost_at_eq and domainCost_nonneg are short algebraic or positivity facts. canonicalThreshold and canonicalThreshold_pos fix and certify a positive cutoff. WavePacketCert is a structure; cert and cert_inhabited supply a default inhabited instance. No deep tactic scripts: the argument is packaging plus elementary Cost lemmas.
why it matters in Recognition Science
Gives the physics layer a named certificate that free wave-packet spreading is a J-cost phenomenon rather than an extra postulate. Downstream consumers (none linked yet in the graph) can assume WavePacketCert instead of re-deriving width bounds from $J$. Ties the cost uniqueness story (T5) to a concrete continuum observable: packet spreading. Does not itself close mass-ladder, alpha-band, or eight-tick claims; it is a bridge from Cost into Physics.
scope and limits
- Does not derive the Schrödinger equation or claim unitary evolution from J.
- Does not bound interacting or open-system packets, only the free spreading certificate.
- Does not fix numerical SI widths; works in RS-native units with $\tau_0=1$.
- Does not prove T5–T8; assumes J and Constants as imports.
- Does not supply experimental falsifiers beyond the certificate interface.