The Natarajan Dichotomy as One D-Sector Readout in Two Regimes

Anchor paper: Natarajan, P., Chiang, B. T., Dutra, I., 2026, ApJL 1001, L12, 'New Cold Dark Matter Crisis Revealed by Multiscale Cluster Lensing' (doi:10.3847/2041-8213/ae53ea)

Review status: Five-referee internal peer-review panel completed (cluster-lensing observational, theoretical cosmologist, SIDM microphysics, statistical/methodological, editor + recipient-perspective). All five converged on MINOR REVISIONS / SEND-AFTER-MINOR-FIXES; revisions applied prior to deposit. External peer review not yet completed.

Abstract

Natarajan, Chiang & Dutra (2026, ApJL 1001, L12) report a new cold-dark-matter crisis from multiscale gravitational lensing of three massive clusters (MACS J0416, J1206, J1149) compared to TNG-Cluster ΛCDM analogs. Four substructure diagnostics yield a dichotomy: the same member-galaxy subhalos must carry steep inner density slopes (core-collapsed SIDM-like) and collisionless-CDM-like outer tidal extents. We pre-register a Category-τ reading as one D-sector readout in two regimes, with three τ-distinctive positive readings (outer Newtonian-limit r_t; inner M∂(R) number-promotion; transition r_trans ≈ 3.4–10.8 kpc), and an 11-row N16 falsification surface. Headline pre-registered falsifier: host-mass independence of r_trans at fixed SHMF, testable with Euclid + Rubin LSST + JWST/Roman by ~2029. Three derivational gaps are flagged honestly; the inner-density-slope-direction tension is reframed as a count-axis-vs-slope-axis discriminator in GGSL+kinematics joint inference.

New Cold Dark Matter Crisis Revealed by Multiscale Cluster Lensing

Natarajan, Chiang & Dutra report a multiscale strong+weak gravitational lensing analysis of three relaxed massive clusters; four substructure diagnostics yield a dichotomy that no single particle-DM microphysics satisfies.

Relation to this note: Engaged as the anchor paper. The τ-program offers a non-particle Category-τ reading as a pre-registration, not as an adjudication.

Core Claim

The Natarajan dichotomy is a regime-projection of one D-sector readout — inner M∂(R) number-promotion at the host nodal-capacity maximum, outer Newtonian-limit truncation via V.D261 cluster-screening — governed by a single transition scale ℓ_cl,sub(M_sub) = √(GM_sub/a₀).

What This Note Does Not Claim

• It does not derive the γ ≳ 2.5 inner density slope from existing primitives.
• It does not derive the SHMF amplitude (slope only).
• It does not derive the 5σ–40σ inner-excess amplitude (sign-correctly produced; amplitude deferred).
• It does not supersede the V.T203 conjectural status in the KSZ-categorical note.
• It does not claim τ-physics is Lean-verified as external physics.
• It does not engage Natarajan, Chiang, or Dutra adversarially; the note is offered as pre-registration, not adjudication.

Falsification and Challenge Surface

• Host-mass independence of r_trans at fixed SHMF: a τ-prediction r_trans ∝ M_sub^{1/2} vs SIDM r_trans ∝ (σ/m)^α at fixed cross-section; CDM has no transition; MOND wrong scale.
• Joint ι_τ universality across LRD + cluster samples: a single ι_τ = 2/(π+e) ≈ 0.341 pre-factor generates both LRD aperture-saturation (Signature 3) and cluster M∂(R) inner-promotion.
• M∂(R) radial-shape discriminator between 1/R and 1/R³ inside R_200.
• Concentration-dependent saturation radius R_*(c) = 1.25 R_200 / c² from V.D352 + V.T348 Chern–Weil derivation.

Reading Note

The PDF contains the full argument. This web page records the public metadata, claim boundary, anchor-paper context, verification posture, and related public surfaces for the citable v1.0 Research Note artifact.

How to Read This Note

Read this as a categorical pre-registration response to a flagship cluster-lensing CDM-crisis paper. The Natarajan et al. (2026) dichotomy presents at face value as a microphysical paradox: the same subhalo must be collisional in cores and collisionless in outskirts. The Category-τ reading is different — there is one D-sector readout that produces two regime-separated nonlinearities at the cluster-substructure scale, organized by a single length scale ℓ_cl,sub that depends on subhalo mass, not on a particle parameter.

Three τ-distinctive readings

1. Outer regime — Newtonian-limit on tidally-pruned capacity wells. At r ~ 10–100 kpc the V.D261 cluster screening factor (1 + r/ℓ_τ) ≈ 1 to one part in ~10⁵, and the Roche-like tidal expression reduces to the standard Newtonian form by construction. The Natarajan Figure 3 r_t distribution and the Chiang+2026a five-sigma rejection of strongly collisional SIDM are matched as a consistency check.

2. Inner regime — M∂(R) inner-promotion. At R/R_200 ≲ 0.2 the boundary-holonomy mass M∂(R) is enhanced at the host nodal-capacity maximum (V.D272), preferentially promoting sub-threshold capacity peaks above the spectroscopic luminosity threshold. The Natarajan Figure 2 5σ–40σ inner excess is sign-correctly produced; amplitude is deferred as gap G3.

3. Transition scale ℓ_cl,sub. For M_sub ∈ [10¹⁰, 10¹¹] M☉, ℓ_cl,sub = √(GM_sub/a₀) ∈ [3.4, 10.8] kpc, in order-of-unity agreement with the empirical break at r ~ 10 kpc across all three MACS clusters. a₀ = c H₀ ι_τ / 2 is the τ-derived MOND-equivalent acceleration scale, with ι_τ kernel-fixed by I.T05/I.D34 — not a free parameter.

Eleven-row N16 falsification surface

Headline pre-registered falsifier: host-mass independence of r_trans at fixed SHMF (N16.3), testable with Euclid + Rubin LSST + JWST/Roman cluster-lensing data by ~2029. SIDM core-collapse predicts r_trans ∝ (σ/m)^α with no M_sub scaling; Category τ predicts r_trans ∝ M_sub^{1/2}; CDM predicts no transition; MOND fails the cluster-mass scale (per Famaey, Pizzuti & Saltas 2025).

Key Caveat

This note does not derive the γ ≳ 2.5 inner density slope, the SHMF amplitude, or the 5σ–40σ inner-excess amplitude from existing primitives. The τ-saturation family (V.P16) is structurally anti-cusp: τ predicts flatter, not steeper, inner slopes at r ≲ kpc. This direction-tension is reframed as a count-axis-vs-slope-axis discriminator in joint GGSL+kinematics inference, building on the Tokayer+2024 result that count-axis-only baryonic rearrangement is insufficient.

External Source Routes

• Natarajan, Chiang & Dutra 2026, “New Cold Dark Matter Crisis Revealed by Multiscale Cluster Lensing”
• OSF deposit v1.0 (10.17605/OSF.IO/BFRX3)
• Companion KSZ-categorical note