Firecrown likelihood for the tomographic ξ± layout + CAMB↔CCL cross-check

[cailmdaley]

Closes #248. PR 5 of the PRD #241 series (row 5 of §7); stacked on #245 (sacc_io).

What

A minimal firecrown Gaussian ξ± likelihood (sp_validation.blinding_likelihood) — the theory engine PR 6's Smokescreen will call — plus a CAMB↔CCL cross-check test validating that the two theory stacks agree on our binning. No blinding wiring in this PR (that's PR 6).

Why

Smokescreen shifts the data by t(hidden) − t(fiducial), computed through firecrown + CCL, while inference runs CosmoSIS + CAMB. The shift only means what we intend if the stacks agree at fixed cosmology (PRD #241 §5). The likelihood is the only code that knows the data vector's exact layout (bin pairs, θ grid), so its compute_theory_vector is how theory gets aligned element-wise with the data.

How it works

• Consumes the analysis SACC ({version}.sacc), extracting the coarse ξ± subset (past COSEBIs/pseudo-Cℓ/ρ/τ) with its aligned covariance — required, since firecrown models every point it reads and Smokescreen enforces sacc.mean == likelihood data vector.
• Generic over N tomographic bins (today's single-bin data = n=1); theory vectors realign to SACC insertion order via each statistic's sacc_indices, independent of statistic listing order.
• TheoryConfig is the single config surface: fiducial cosmology + model choices, defaults mirroring the CosmoSIS v1.4.6.3 _A_cell fiducial — S8=0.80, Ωm=0.30 (converted to CCL-native σ8/Ωc with the neutrino density correctly subtracted), Ωb=0.0469, h=0.70, nₛ=0.96, mν=0.06 eV, HMCode2020+feedback (logT_AGN=7.5) via CAMB, NLA wired but off by default (the shift nearly cancels IA; flipping to the inference stack's A=1.0 is one config value), normal-hierarchy neutrinos. The PRD's open fiducial choice changes config values, not code.
• Fine-grid ξ± shift is out of scope here — PR 6 computes it as a direct CCL theory difference.

Validated

19 tests. Likelihood: construction from a sacc_io file, theory-vector shape/determinism/SACC-alignment (order-independence pinned against a genuinely reversed statistic order), 2-bin N-generality, config fail-fast. Cross-check: firecrown+CCL vs an independent CAMB-P(k)→CCL path agree to 0.21% (ξ+) / 0.10% (ξ−) at fiducial and 0.25%/0.12% at a blind-sized offset (tolerances 0.5%/1.0%). The σ8-vs-A_s convention is settled inside the test — CAMB's A_s is iterated to share CCL's σ8 (a nominal A_s leaves σ8 ~3% off, which would blow the comparison to ~9–10%; the reconciliation is load-bearing and tested). The cross-check validates P(k)-recipe + amplitude consistency, not CCL's Limber+Hankel independently (both paths use it; documented in the module).

An independent adversarial review before opening drove the full attack list empirically and found no correctness bugs (verdict: open as-is). Highlights: the Ωm↔(σ8, Ωc, Ων) conversion verified to 5 decimals through firecrown's own CCLFactory path; Smokescreen 1.5.6's actual loader driven end-to-end — ConcealDataVector construction, _verify_sacc_consistency, concealing-factor calculation and application all succeed against this module, with the applied shift exactly matching the theory difference; extract-covariance alignment stress-tested on a 3-pair file with non-contiguous insertion order. One review note for PR 6: Smokescreen's loader never passes theory_config overrides — the module's defaults ARE the fiducial in the blinding path (overrides are reachable only from direct callers), and Smokescreen's shifts_dict values replace parameters rather than add (its documented-vs-actual gotcha).

Fast tests run in the default suite (~8 s); CCL/CAMB theory tests are slow with a fast smoke variant. Full fast suite green up to the two known pre-existing environmental failures (candide data paths from a worktree; snakemake absent from the local venv), both confirmed present at the base commit with this PR's files absent.

— Claude (Fable, with Opus implementation agents) on behalf of Cail.

🤖 Generated with Claude Code

https://claude.ai/code/session_016Ko89uZF84ez6HEDcTWbJe

[cailmdaley]

Retiring this PR under the amended plan (see the plan-amendment comment on #241): the SACC/blinding stream now runs on the UNIONS-WL/Smokescreen fork, whose theory entry point is a plain theory_fn callable with a built-in CCL backend — the standalone firecrown likelihood this PR built is no longer a deliverable, and there is no successor PR. The CAMB↔CCL cross-check developed here survives: it moves into the blinding PR (#253) as a theory-consistency test on the same CCL backend that PR introduces (σ8-matched amplitude convention, matched halofit_version strings, 0.5%/1.0% ξ± tolerances).

This PR is to be closed without merging (close left to Cail).

— Fable on behalf of Cail.