Testing UDEL Against
the Observable Sky

H₀ Model tab: σ(t) grows quadratically as the football manifold's counter-rotating arms separate. This narrows phase-alignment windows and reallocates the finite update budget from internal equilibration (B_int) toward separation hops (B_exp). The effective Hubble rate is H_eff(t) = H_early × (1 + α_H × σ(t)). With α_H = 0.1746, calibrated to the present-epoch late-time H₀ target, the model recovers 73.50 km/s/Mpc at t_now = 0.72 and can then explore the phase structure and directional consequences of the strain picture.

Strain Evolution tab: σ(t) accumulates until σ_max is reached, triggering the recoil phase. The current epoch sits at σ ≈ 0.518 — mid-expansion, approaching but not yet at the threshold. The recoil epoch at t≈1.00 is a model-dependent future marker, not a confirmed prediction.

Axis Test tab: The CMB kinematic dipole, quadrupole, and octupole axes cluster within 20–30° — the known "axis of evil." This clustering is consistent with a preferred spine axis in UDEL. The Tully-Fisher H₀ dipole sits ~41° from the predicted axis — outside the ±30° TF error cone, though the TF measurement itself carries significant directional uncertainty. Phase 4 explains this offset as a two-component signal rather than a simple miss.

Calibration note: α_H is explicitly fitted so the model recovers the observed late H₀ value. The calibrated recovery demonstrates that the strain-clock mechanism is numerically capable of producing the observed split — it does not constitute an independent prediction of that value.

What Phase 1 does establish: The strain-clock picture can recover the H₀ split within a self-consistent geometric framework, and several CMB low-multipole anomalies are consistent with a preferred spine axis. Phase 4 provides the genuinely non-calibrated directional result.

Void/Wall H₀ tab: A signal through a cosmic void (M̄ ≈ 0.14) encounters higher hop cost than one through a filament wall (M̄ ≈ 0.37). This inflates the inferred distance and therefore H₀ along void-dominated sightlines. ΔH₀ ≈ +2.83 km/s/Mpc — consistent in sign and rough magnitude with the KBC supervoid outflow hypothesis. The mechanism agrees; the amplitude remains model-dependent.

JWST Clock tab: The JWST "early galaxy paradox" has two distinct layers. The first — and more fundamental — is a kinematic clarification: once the distinction that lookback time is not the same as emission distance is made explicit (see the short kinematic note: Lookback Time Is Not Emission Distance ↗, Kaplan Healion 2025), much of the perceived JWST early-galaxy paradox dissolves without any new physics. A galaxy at high redshift may have been far away and already evolving for a long time before that light was emitted. The second layer is UDEL's specific geometric contribution: early-universe low σ(t) means wider phase-alignment windows and more internal update budget available for structure formation. In this UDEL implementation, galaxies at z≥10 receive roughly 25% additional effective development time relative to a standard ΛCDM reading — a model-generated clock effect, not an observationally established correction. UDEL's contribution is real but secondary — the kinematic argument does most of the work.

Environment → Directionality link: The void/wall H₀ split modeled here (+2.83 km/s/Mpc) is one of two physical contributions that Phase 4 shows combine into the observed H₀ dipole. The environment-driven component (Dipole A) points toward the local void structure; the spine-flow component (Dipole B) points along l=295°. See Phase 4 for the full two-dipole decomposition.

BAO vs Redshift tab: Δδφ decreases with z as the lattice becomes less differentiated at earlier epochs. This is a qualitative analog of DESI's evolving dark energy residual, produced without adding a dark energy fluid. It remains a proxy, not a direct data fit.

Phase 2 establishes: The propagation picture generates environment-sensitive H₀ shifts, a high-z clock contribution, and a qualitative BAO trend — all as structural outputs from the model geometry. The JWST claim is deliberately modest: UDEL adds a geometric layer on top of the prior kinematic clarification that the apparent paradox is partly a framing error. Both arguments are independently valid; neither overclaims.

LSS Anchors tab: For the first time, the maturity grid M(x,y,z) is anchored to real structures. The Great Attractor complex (M=0.95) forms a high-M wall at l≈325°. The KBC void (M=0.03) creates a deep low-M region at l=190°. Our observer sits at (0.35, 0.15, −0.10) — inside the transition zone between them.

H₀ Dipole tab: The all-sky H₀ map now shows a physically asymmetric field driven by the GA wall and KBC void contrast. The dipole amplitude is physically realistic but the direction still needs CF4 precision anchoring.

BAO vs Redshift tab: Δδφ decreases with z — void paths show lower phase residuals at higher redshift as the lattice becomes less differentiated. This is the UDEL prediction for DESI's evolving dark energy signal: not a fluid, but a clock drift that weakens in the early universe.

What is imposed vs. what emerges: The attractor positions and void locations are imposed from observations. The maturity values at those positions are phenomenological choices. The BAO z-trend and spine signal strength emerge from the model geometry. Keeping these categories distinct is essential for evaluating which results are genuine outputs.

Phase 3 establishes: An anchored large-scale environment sharpens the directional anisotropy and produces a qualitative BAO trend consistent with DESI's signal. The dipole direction problem is precisely identified: it requires CF4 precision anchoring, which Phase 4 addresses.

CF4 Anchors tab: The CF4 bulk flow (428 km/s toward l=297°,b=5°) and the CF4 multipole spine axis (l=295°,b=5°) are separated by 2.0°. This near-perfect alignment is a non-calibrated UDEL result: bulk matter flow should be driven by the spine's torsional asymmetry. In ΛCDM, a 428 km/s coherent bulk flow out to 266 Mpc has a <0.015% probability. In UDEL it emerges naturally from the spine-flow picture.

Two Dipoles tab: The key Phase 4 insight. UDEL predicts two physically distinct dipoles in the H₀ field:

• Dipole A (hop-cost): Points toward voids (l≈40°,b≈−20°), environment-driven, roughly redshift-independent at low z.
• Dipole B (spine flow): Points along the spine (l=295°,b=5°), velocity-driven, decreases with redshift.

The observed CF4 TF "H₀ dipole" at (142°,52°) is likely their vector convolution as seen from our position. Euclid and Rubin should be able to separate these two components by their different redshift scaling — this is a specific, falsifiable UDEL prediction.

BAO vs z tab: The spine-aligned BAO residual (Δδφ_spine) is 3× stronger than the void/wall residual — a clean signature distinguishing UDEL from generic environment models.

Handedness tab: The full LoS torsion integral produces a handedness boundary exactly perpendicular to the spine axis. Surveys should find the L/R transition at the great circle ⊥ (l=295°,b=5°).

Phase 4's strongest contribution: The two-component interpretation of the H₀ anisotropy field. Instead of treating the directional mismatch as a failure, the model suggests current surveys may be blending environment-driven and spine-flow-driven contributions with different redshift scaling. Separating them is a specific, falsifiable prediction that Euclid and Rubin can test.

Log-scale transparency: Phase 4 switched from 1/M to −log(M+ε) hop cost. This was done explicitly because the 1/M function over-amplified void contrast and produced unrealistic ΔH₀ amplitudes. The log-scale brings the modeled amplitude into the observed range — this is a calibration adjustment, not a free parameter, and it is noted here transparently.