Cookie Consent by Free Privacy Policy Generator Program synthesis — geometry of the cosmic web (E0–E2) | Igor Moiseev

Program synthesis — geometry of the cosmic web (E0–E2)

Program synthesis — geometry of the cosmic web (E0–E2)

One-line summary: under correctly length-matched evaluation the simple Hessian baseline matches or beats the orientation lift essentially everywhere as a filament finder; the lift survives as an anisotropy descriptor, a hybrid ingredient, and the program’s physics probes produced clean refutations of the geometric transport thesis.

Correction (2026-07-04). The first E0 verdict (“lift wins sparse-regime completeness +0.07, p≈10⁻¹⁴”) was an evaluation artifact. Length matching was enforced on a proxy (hysteresis-mask volume); realized skeleton lengths differed systematically (lift ~19% longer at sparse levels), and length buys completeness. The corrected extractor (iterative correction until the skeleton itself hits the target) flips the sign. Detected when an instrument change made for E1 retroactively shifted E0 parent scores; the archived n_est fields confirmed the mismatch. All numbers below are from the corrected reruns.

All experiments: 128³ boxes (256³ resolution check), matched spine length, calibrate/held-out discipline, paired Wilcoxon statistics. Chain of hypotheses, in the order they were tested and what each result forced next:

H1 — the lift is a better filament finder

H2 — physics-informed (tidal) coefficients help

Dead. Multiplicative tidal-alignment weighting hurts mass coverage even with the clean-field tidal frame (E1b: b1_clean < b0), so this is not a noise-in-the-estimate problem — the weighting itself is wrong. (E1’s sparse-frame version was already null-to-negative.)

H4 — transport follows sub-Riemannian geodesics of the lifted metric

Refuted in the bulk; a weak, sign-correct residual survives inside filaments (E2, 4 PM N-body runs, 200k tracked particles). Deviations of true trajectories from ballistic chords are perpendicular to the filament axis in the bulk (⟨(d̂ev·e3)²⟩ = 0.21–0.23 vs isotropic 1/3): transverse pancake infall is what builds filaments, the opposite of “cheap along the axis”. Only within ~4 vox of spines does the deviation turn weakly parallel (0.364 ± 0.010). Velocity–axis alignment is a flat ~0.56 (null 0.5). Geodesic-shooting machinery (Tier B) is therefore unmotivated as a formation model; at best it describes streaming within formed filaments.

Sub-findings that survive

  1. E1-M3: unweighted lift spines align with the tidal eigenframe at 0.73–0.76 vs Hessian 0.67 (null 0.5) — the lifted geometry is a better static descriptor of web anisotropy even where it loses on mass.
  2. E0b (corrected rerun): strong hypoelliptic diffusion (splitting scheme) is harmful at every curvature × sparsity tested including the most-curved tercile; weak diffusion is neutral-to-harmful except a small positive (+0.01, p=0.03) at the ultra-sparse level. (Caveat: crude numerical scheme, not the exact SE(3) kernel.)
  3. E0c hybrid: the sum of normalised scores improves purity and junction F1 over the Hessian at moderate sparsity — a practical recipe.
  4. E2’s instrument recovered known Zel’dovich pancake physics from scratch — the perpendicular-infall signature — which validates the PM + tracking pipeline.
  5. The length-matching lesson: matched comparisons must enforce the match on the score-buying quantity itself (realized skeleton length), not a proxy (mask volume). The proxy manufactured a p≈10⁻¹⁴ phantom win.

Status of the program’s claims

What would continue the program (not executable locally)

E0d addendum (post-correction follow-ups, 2026-07-04)

  1. Splitting convergence: 8-step Trotter splitting at equal total diffusion reproduces the coarse-splitting result at both sparsity levels (fine −0.017 vs coarse −0.020 at n_gal=2500; both ≈ +0.01 at 1200). The diffusion verdict is operator-level, not numerical. Caveat closed.
  2. Sparsity limit: no honest lift-win regime exists anywhere: at n_gal=400–600 the Hessian wins again (−0.017/−0.021, p ≈ 0.003); the 800–1200 tie is a narrow band, not a trend. The pooling advantage never exceeds the positional-accuracy cost at any tested density.
  3. Hybrid on gravity: hyb_sum halves the lift’s band-coverage deficit but still trails the Hessian (−0.009, p = 0.04 at 5k; −0.016 at 20k). The hybrid’s niche remains toy purity/junctions.

With these, every locally executable hypothesis and caveat of the program has a replicated verdict. Remaining: E3/H3 on real survey data (blocked on data download approval).

E3 addendum (real data, 2026-07-04)

BOSS CMASS-North (z 0.45–0.55, 274k galaxies in 18 tiles) × Planck: H3 supported — spine networks carry a ~4–5σ Compton-y excess over footprint-matched controls (lensing null, noise-dominated); the Hessian’s spines carry slightly more signal than the lift’s at matched length (4.8σ vs 4.1σ), consistent with the corrected H1/E1b. M3-real: the lift’s anisotropy-descriptor advantage replicates on the real Universe (0.677 ± 0.016 vs 0.617 ± 0.016 over tiles, null 0.5). Caveats: control placement does not preserve galactic latitude; tracer-halo gas not masked; single shell, no systematics weights. With E3 executed, every hypothesis of the program — H1–H4 — now has an empirical verdict.

E3b addendum (second pass, 2026-07-04)

Latitude-matched nulls STRENGTHEN the y-detection (9.0σ Hessian / 6.9σ lift) — H3a supported. Tracer-halo masking leaves 1.95σ / 0.07σ — the signal is dominantly halo gas; a between-halos (WHIM) component is a hint, not a result (H3b). The radial profile is extended to ≥60′ but cannot discriminate filament gas from clustered halo gas at Planck resolution (H3c). Program closed: pushing H3b further needs deeper tSZ data (e.g., ACT/SPT), not more analysis of this set.

E3c addendum (ACT DR6, 2026-07-04) — program close

The decisive WHIM test at ACT depth returns a null: masked residual 1.77σ (3′) / 1.11σ (7′) — the halo-only model survives; between-halo gas along CMASS spines is bounded, not detected. Diagnosis: shell-projection places the signal at degree scales that ACT’s map filters (unmasked stack 2.95σ vs Planck’s 9σ on the overlap); ACT-depth WHIM work needs a small-scale analysis design. With the pre-registered gate failed, the program is now closed end to end: every hypothesis (H1–H4, H3a–c) carries a replicated verdict, and the two guaranteed outputs stand — the methods/benchmark contribution and a measured 9σ web-gas detection with an honest halo-vs-filament decomposition.

E3d addendum (2026-07-04) — terminal result: bridge gas detected

E3c’s null carried the diagnosis (wrong angular scales for ACT), and the design it prescribed delivered: the galaxy-pair bridge stack (876k CMASS pairs, disc-averaged sampling, six-angle ring controls that null any circularly-symmetric halo by construction) detects inter-halo gas at 5.24σ on ACT DR6 (2.28×10⁻⁸) with Planck concurring at 19σ (2.97×10⁻⁸). Model A (halo-only baryons) is rejected; Model B (gas along the bridges between halos) is established at both instruments. The program therefore closes on a positive terminal measurement, reached by following its own negative result’s diagnosis.

E3e addendum (validity battery) — final calibration of the claim

Jackknife errors and unconnected-pair nulls trim the E3d-v2 headline: on-axis excess stands at 3.3σ (ACT, honest errors), but the null pairs reveal Planck’s 4.7σ fake bridge (beam leakage, as diagnosed) and the null-subtracted bridge is ~1.2–1.4×10⁻⁸ at ≈2σ per instrument — reproducing the published amplitude, short of an independent detection. The program’s recurring moral holds to the last experiment: every strong claim, put under its own strictest control, shrinks to its honest core — and the honest core here still says the bridges are real (two instruments, right amplitude), just not yet ours to claim at 5σ.

T1 addendum (2026-07-04) — the theory box closes the table

T1 executed (docs/T1-note.md): the Jacobi-type variational principle is refuted constructively. In growth-factor time the Zel’dovich flow is free motion (straight lines; the potential is absorbed into initial velocities, leaving no force to conformalize), and the adhesion model’s exact variational principle is Hopf–Lax — quadratic-cost optimal transport on a FLAT metric. Filaments are singularities (shocks/caustics) of the transport map, not geodesics of a lifted metric; the derivation predicts both E2 signatures (transverse arrival, weak in-tube streaming) and explains why the lift works as a descriptor (M3) but not as a transport model. With T1 closed, every item of the original program — T1, E0–E3, H1–H4 — carries an executed verdict. The program is complete.

E4 addendum (H4’, 2026-07-04) — the adjustment-term reframing, tested

Reframed hypothesis (the program owner’s original intent): the lifted geometry is not the mechanism but an adjustment term on top of standard models. E4 measured that term directly — the residual between true PM transport and each particle’s own Zel’dovich prediction. Result: the adjustment is real and tidal-frame-anisotropic, but TRANSVERSE (⟨(R̂·e₃)²⟩ = 0.21–0.30 < 1/3; R∥/R⊥ = 0.63–0.89 everywhere): the correction current models need is anisotropic damping of motion across walls/filaments (adhesion-like), not enhanced transport along them. H4’ refuted as stated; the constructive product is the measured form and amplitude of the true adjustment term. Consistent with T1 and E2.

E5 addendum (H-T2, 2026-07-04) — the adjustment term becomes a model

The E4-corrected form of the adjustment conjecture was built into an effective transport model: ZA rays + transverse-only momentum damping in the local tidal frame at shell-crossing. Against PM truth from identical initial conditions (competitor-favouring calibration, 5 held-out seeds): best model overall (4.91 vs ZA 5.00 vs isotropic stick 5.34 median voxel error), with the clearest win exactly at the web (−7% vs ZA, −14% vs stick at 0–2 vox) and a small deficit vs ZA in the 2–4 vox outskirts. The program therefore ends constructively: from conjecture → refutation of the strong form → measurement of the true correction → a working anisotropic-adhesion term that improves the classical proxy.

E5c/E5d addendum (2026-07-05) — refinement converged at the frame bound

The declared optimization campaign froze the model: ZA rays + 60% transverse damping in self-density tidal frames (2 h⁻¹Mpc smoothing) at first crossing (ρ_c = 5). Held-out: 4.52 vs ZA 4.98 (−9%), 0.05 vox from the oracle frame-information bound (4.47) — 89% of the recoverable gap closed. Structural findings: partial damping is required for self-density frames to pay (full damping self-amplifies crossings); pancake-ordered sequential damping underperforms at this resolution. Full specification, capabilities, limitations and failure modes: docs/MODEL-CARD.md. The refinement scope is complete; remaining error at the web is post-crossing (multi-stream) physics, out of scope by design.

E6 addendum (2026-07-05) — transfer verified, trend physical

The frozen model transfers without re-calibration to coarser voxels and to weaker/stronger clustering, with the advantage growing monotonically with sigma8 (−3% → −13% overall; up to −22% at the web at sigma8 = 1) — the behaviour of a physical correction term. Model-card scope widened accordingly. With this, every locally testable hypothesis — including the card’s own declared limitations — carries a verdict.

E7 addendum (2026-07-05) — scope table complete

The last two unverified rows close: under flat ΛCDM (Ωm = 0.31) the frozen model keeps −10%/−17% (overall/web), and at 0.5 Mpc/h voxels −10%/−15% (one seed), with physical-unit errors nearly identical across all regimes — the signature of a geometric, growth-parametrized correction. Every scope row of the model card testable on this machine is now verified. The program has no remaining executable hypothesis of any kind.

E9/E10 addendum (2026-07-05) — referee battery: the framing settles

Literature baselines implemented and run on identical ICs: 2LPT degrades transport at these scales (8.07; known shell-crossing overshoot); MUSCLE ties the frozen model (4.49 vs 4.52) and wins small-scale phases, while the damping model wins mid-scale amplitudes. The paper’s contribution is therefore the mechanism, not the engine: E4’s measurement (the beyond-ZA correction is transverse in the tidal frame) plus the demonstration that this single directional ingredient reproduces MUSCLE-level accuracy — explaining WHY shell-crossing corrections of the MUSCLE class work. E10: truth converged in time (0.008 vox under step doubling); comparison invariant. Referee points 1–3 are now executed; the optional external cross-check (Quijote) awaits download approval.

E11/E12 addendum (2026-07-05) — hybrid refuted; truth externally validated

E11: the naive hybrid (MUSCLE’s Lagrangian collapse trigger + directional damping) underperforms both parents (4.67 vs 4.49/4.52) — the evolving Eulerian trigger carries real information; field-level combination is the remaining (unpursued) hybrid route. E12: our PM truth, evolved from CAMELS CV_0’s own ICs, matches Arepo to 0.41 Mpc/h median per particle (r ≥ 0.94 for k ≤ 1.3 h/Mpc) — the referee’s external-validation item is closed; at a 10× resolution extrapolation the frozen model still does not harm (1.127 vs ZA 1.140). The three referee must-fix points (baselines, truth validation, field-level metrics) are all executed; the paper draft (docs/PAPER-DRAFT.md) carries the results.

E12-astrid addendum (2026-07-05) — two-code truth validation closed

The second external code (MP-Gadget, Astrid_DM CV_0; shared ICs verified by per-ID prediction at z=15 to 0.068 vox) reproduces the Arepo verdict identically, and the codes agree with each other to 0.029 Mpc/h median per particle. Hierarchy: code consensus 0.03 « our PM offset 0.41 « measured effects 4-5 Mpc/h. The referee’s truth item is closed at two independent production codes. All three follow-up points (two-code external check, paper audit, posts publication-ready) are complete.