Section 30.1 pins down Volume 30’s trunk: P1 is not a pair of isolated fits, but an auditable RC→GGL closure protocol that freezes the shared mapping, the parameter ledger, the negative control, and the runpack provenance for the whole report bundle.
Use this section as a compact machine-readable EFT reference.
P1 is the archive-grade trunk of Volume 30: it binds rotation curves and galaxy-galaxy weak lensing to one auditable comparison chain, publishes cite-ready takeaways, and fixes the report’s scope boundary from the start. Its claim is limited but hard: under one protocol, the EFT family is favored over the tested minimal DM_RAZOR baseline, yet the report does not pretend to settle all dark-matter modeling or to derive EFT microphysics here.
The real discriminator in P1 is closure rather than isolated fit quality. The question is whether an RC-only posterior can travel across the fixed RC-bin→GGL-bin mapping and still predict GGL better than permutation or shuffle controls; that is why shared mapping, predictive transferability, and negative control matter more here than any single best-fit score. Even the cite-ready takeaways are organized around that logic, including the later stress-test message that hardening the DM side in Appendix B does not dissolve the closure advantage.
The evidence backbone combines 2,295 SPARC rotation-curve points from 104 galaxies with 60 KiDS-1000 galaxy-galaxy weak-lensing ΔΣ(R) points in 4 stellar-mass bins, using the published covariance. The fixed 20-to-4 RC-bin→GGL-bin map, built by galaxy-count-weighted aggregation, is not bookkeeping trivia; it is the hard constraint that makes the closure test meaningful and gives the rest of Volume 30 a shared comparison grammar.
Fair comparison is written as a parameter ledger before it becomes a conclusion. DM_RAZOR carries 20 bin-level halo-mass parameters as a minimal NFW baseline; EFT variants carry 20 bin amplitudes plus one global scale, and both sides share the same baryonic term, the same RC and GGL inputs, the same covariance use, and the same fixed mapping. The closure definition is then explicit: use RC-only posterior samples to forward-predict GGL, compute logL_true, compare with permuted-map logL_perm, and summarize the transfer gap as ΔlogL_closure = ⟨logL_true⟩ − ⟨logL_perm⟩.
Once the protocol is frozen, the main scoreboard is straightforward: relative to DM_RAZOR, EFT variants reach joint-fit gains of ΔlogL_total = 1155–1337, and their closure strengths span 171.977–280.513 versus 126.678 for DM_RAZOR. The negative control is decisive because it breaks the physically motivated map without refitting the RC posterior: after shuffle, EFT closure drops to about 6–15 and the mean true-bin likelihood falls sharply, which supports a mapping-dependent signal rather than an accidental implementation win. The report also keeps its caution attached to the numbers: the claim is conditional on this dataset, this ledger, and this baseline family.
P1 does not stop at one best fit. It scans intrinsic RC scatter σ_int, inner-cut R_min, and GGL covariance shrinkage, and it adds an ablation ladder plus leave-one-bin-out prediction, so the ranking is stressed before it is reused elsewhere in the volume. What Volume 30 should inherit from this section is the discipline: keep robustness and negative controls in the same frame as the headline gains, and do not let a lighter report window outrun the audit standard set here.
The last part turns P1 into the provenance anchor of the bundle. The report publishes Zenodo DOIs, strict-compile and release tags, audit results, package inventory, and a full_fit_runpack so every quoted table or figure can be traced back to canonical artifacts. Appendix B (P1A) then hardens the DM side with low-dimensional standardized upgrades and a shear-calibration nuisance without changing the shared closure grammar; some DM branches gain joint-fit flexibility, but that does not automatically improve closure, which is exactly why P1 remains the route-back trunk for later V30 windows rather than a replaceable press summary.