IndisputableMonolith.Gravity.GravitationalWaveMemory3FromJCost
Module packaging a certificate that three-dimensional gravitational-wave memory follows from the Recognition J-cost. It defines a domain cost, a positive canonical threshold, and an inhabited GWMemory3Cert record. Gravity and RS auditors cite it when linking permanent strain memory to the unique cost functional rather than to a free GR ansatz. The argument is definitional plus elementary nonnegativity and positivity lemmas over the Cost import.
claimOn the Recognition cost $J$, a domain cost $C$ and a canonical threshold $\theta>0$ are fixed so that a certificate $\mathrm{GWMemory3Cert}$ records that three-dimensional gravitational-wave memory is realized whenever the cost data meet $\theta$. The certificate type is inhabited.
background
Recognition Science forces a unique dimensionless cost $J(x)=(x+x^{-1})/2-1$ (T5) and three spatial dimensions (T8). Gravitational-wave memory is the permanent metric offset left after a wave train; here the claim is that the three-dimensional memory signature is not an extra GR postulate but a threshold phenomenon read off $J$.
The module sits in the Gravity domain and imports only Constants (RS time quantum $\tau_0$) and Cost (the $J$ infrastructure). Sibling definitions introduce a domain-restricted cost, its evaluation identity, nonnegativity, a canonical positive threshold, and the certificate bundle GWMemory3Cert together with an explicit inhabitant.
proof idea
Definition module with light supporting lemmas, not a deep derivation. domainCost and canonicalThreshold are introduced as defs; domainCost_at_eq and domainCost_nonneg discharge algebraic identities and $J\ge 0$ style facts from the Cost import; canonicalThreshold_pos is a positivity check. GWMemory3Cert packages the data; cert and cert_inhabited supply a concrete witness so downstream code can assume the certificate without constructing it.
why it matters in Recognition Science
Closes a Gravity-side interface: permanent three-mode strain memory is tied to the same $J$ that forces $\phi$, the eight-tick octave, and $D=3$. No downstream consumers are wired in the graph yet (used_by empty), so the module is a leaf certificate ready for waveform or ILG hooks. It does not replace the full GR memory calculation; it asserts that the RS cost already supplies the threshold structure those calculations need.
scope and limits
- Does not derive the GR memory tensor or quadrupole formula from Einstein equations.
- Does not numerically predict strain amplitudes or detector SNR.
- Does not prove uniqueness of the threshold beyond the Cost lemmas used.
- Does not connect yet to ILG rotation curves or other Gravity modules (no used_by edges).
- Does not address polarization content beyond the named three-dimensional memory certificate.