M44 inverse response jets v1
This tranche runs the corpus architecture backwards over the frozen M44 evidence:
It is an inversion of the existing evidence ledger, not a new raw-data fit.
Minimal response algebra
| Jet | Meaning | Current state |
|---|---|---|
| \(J_0\) | location or intercept | quotiented by spectral zero and cluster-wide normalization |
| \(J_1\) | first spatial derivative | survives the current quotient |
| \(J_2\) | curvature or Hessian | unresolved; nonlinear fits collapse toward broad linear limits |
| \(D\) | discontinuity or crease | not selected |
| \(W\) | intrinsic residual width | observed only as an undeconvolved mixture |
| \(C\) | cross-line coherence | not observed |
Only \(J_1\) survives as a presently usable response coordinate. The three-dimensional gradient has magnitude 0.04432 km/s/pc, and its held-out mean-absolute-error gain beyond the single tail coordinate is 0.02239 km/s with the frozen paired interval excluding zero. This identifies an affine residual field—not its generator.
Observable equivalence classes
The location kernel contains the ordinary constant model, constant displacement and constant tilt. All three are observationally equivalent under the present reader. Constant displacement and constant tilt also cannot explain the surviving spatial derivative without an additional evolution or coupling law.
The affine-gradient class contains ordinary tail or perspective dynamics, calibration or population drift, a generic unnamed latent gradient, and a possible smooth geometric bend. The ordinary affine model is the preferred empirical surrogate because it improves held-out prediction and requires no missing transfer law. This preference does not prove its detailed physical cause.
The width class contains measurement and fit uncertainty, binaries, atmosphere and rotation, ordinary dynamical dispersion, and possible geometric thickness. The current 1.43 km/s robust scatter does not distinguish them.
Backwards result
Working backwards succeeds in recovering the smallest observational algebra and the exact places where semantics are lost. It does not reconstruct a unique geometry. The next separator is the same one independently selected by the calibration contract: a frozen ordinary phase-space prediction followed by multi-epoch, line-resolved spectroscopy on two independently calibrated instruments, retaining star, line, epoch, instrument and covariance identity.
The termination condition is explicit: do not infer a geometric forward law from these response points alone.