Panta-Rhei-Research · AnSoFuchs · May 17, 2026 · May 17, 2026 · May 17, 2026
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+# The Natarajan Dichotomy as One D-Sector Readout in Two Regimes
+
+A τ-Categorical Pre-Registration against the Natarajan, Chiang & Dutra (2026, ApJL 1001, L12) Multiscale Cluster-Lensing CDM Crisis.
+
+This Research Note pre-registers a Category-τ reading of the cluster-substructure dichotomy reported in Natarajan, Chiang & Dutra (2026) — the apparent need for the *same* member-galaxy subhalo to behave collisionally in inner cores (γ ≳ 2.5–3) and collisionlessly in outer tidal extents (r ~ 10–100 kpc). The note commits three τ-distinctive readings, one numerical anchor (r_trans ≈ 3.4–10.8 kpc), and an 11-row N16 falsification surface (headline falsifier: host-mass independence of r_trans at fixed SHMF, testable with Euclid + Rubin LSST + JWST/Roman by ~2029). It is honest about three derivational gaps and reframes the inner-density-slope-direction tension as a count-axis-vs-slope-axis discriminator in GGSL+kinematics joint inference.
+
+Release date: 2026-05-17
+Type: Research Note
+Publication code: RN-032
+Version: v1.0
+Zenodo DOI: [10.5281/zenodo.20251191](https://doi.org/10.5281/zenodo.20251191)
+
+## Public Routes
+
+- Website: https://panta-rhei.site/publications/research-notes/natarajan-cluster-dichotomy-categorical/
+- PDF: https://panta-rhei.site/assets/pdfs/research-notes/research-note-2026-05-17-natarajan-cluster-dichotomy-categorical.pdf
+- Zenodo: https://doi.org/10.5281/zenodo.20251191
+
+## Files
+
+- `research-note-2026-05-17-natarajan-cluster-dichotomy-categorical.pdf` — citable v1.0 PDF artifact.
+- `natarajan-cluster-dichotomy-categorical.tex` — release source snapshot.
+- `metadata.yml` — publication metadata.
+- `manifest.json` — artifact checksum and release metadata.
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+  "id": "2026-05-17-natarajan-cluster-dichotomy-categorical",
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+  "publication": {
+    "title": "The Natarajan Dichotomy as One D-Sector Readout in Two Regimes",
+    "subtitle": "A τ-Categorical Pre-Registration against the Natarajan, Chiang & Dutra (2026) Multiscale Cluster-Lensing CDM Crisis",
+    "authors": "Thorsten Fuchs and Anna-Sophie Fuchs",
+    "publication_type": "Research Note",
+    "date": "2026-05-17",
+    "version": "v1.0",
+    "status": "v1.0 public release",
+    "license": "CC-BY-4.0",
+    "doi": "10.5281/zenodo.20251191",
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+    "pdf_filename": "research-note-2026-05-17-natarajan-cluster-dichotomy-categorical.pdf",
+    "source_website_page": "_research_notes/2026-05-17-natarajan-cluster-dichotomy-categorical.md",
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+    "artifact_availability": "local_pdf",
+    "route_status": "released",
+    "abstract": "Natarajan, Chiang & Dutra (2026, ApJL 1001, L12) report a new cold-dark-matter crisis from multiscale gravitational lensing of three massive clusters compared to TNG-Cluster 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, one numerical anchor (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.",
+    "claim_boundary": {
+      "claim": "Under the τ-framework's capacity-gradient gravity sector and boundary-holonomy mass closure (V.D272), the Natarajan dichotomy is a regime-projection of one D-sector readout — inner M∂(R) number-promotion + outer Newtonian-limit truncation — governed by a single transition scale ℓ_cl,sub(M_sub).",
+      "non_claim": "It does not derive the γ ≳ 2.5 inner density slope, the SHMF amplitude, or the 5σ–40σ inner-excess amplitude from existing primitives; it does not supersede the V.T203 conjectural status; it does not claim τ-physics is Lean-verified as external physics; it is not a substitute for direct dialogue with the source-paper authors."
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+      "/corpus/registry/",
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+      "/verify/taulib/",
+      "/verify/release-manifest/"
+    ]
+  },
+  "integrity_note": "Hashes attest to the PDF bytes and release source snapshot only; they do not certify correctness, peer review, legal status, or content validity. The Zenodo DOI 10.5281/zenodo.20251191 provides the citation-grade resolvable identifier for this artifact."
+}
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+publication_id: RN-032
+publication_key: research_notes.natarajan_cluster_dichotomy_categorical
+title: "The Natarajan Dichotomy as One D-Sector Readout in Two Regimes"
+subtitle: "A τ-Categorical Pre-Registration against the Natarajan, Chiang & Dutra (2026) Multiscale Cluster-Lensing CDM Crisis"
+authors:
+  - Thorsten Fuchs
+  - Anna-Sophie Fuchs
+type: Research Note
+status: v1.0 public release
+version: v1.0
+date: 2026-05-17
+program: Panta Rhei Research Program
+license: CC-BY-4.0
+website: https://panta-rhei.site/publications/research-notes/natarajan-cluster-dichotomy-categorical/
+pdf: https://panta-rhei.site/assets/pdfs/research-notes/research-note-2026-05-17-natarajan-cluster-dichotomy-categorical.pdf
+source: natarajan-cluster-dichotomy-categorical.tex
+doi: 10.5281/zenodo.20251191
+doi_url: https://doi.org/10.5281/zenodo.20251191
+zenodo_url: https://zenodo.org/records/20251191
+anchor_paper:
+  citation: "Natarajan, P., Chiang, B. T., Dutra, I., 2026, ApJL 1001, L12"
+  doi: 10.3847/2041-8213/ae53ea
+  title: "New Cold Dark Matter Crisis Revealed by Multiscale Cluster Lensing"
+tags:
+  - tau-framework
+  - cluster-lensing
+  - dark-matter
+  - cluster-substructure
+  - capacity-gradient-gravity
+  - boundary-holonomy-mass
+  - non-particle-dark-matter
+  - mond
+  - sidm
+  - natarajan-dichotomy
+  - categorical-pre-registration
+summary: >
+  This Research Note pre-registers a Category-τ reading of the cluster-substructure
+  dichotomy reported in Natarajan, Chiang & Dutra (2026, ApJL 1001, L12) as one
+  D-sector readout in two regimes, not two DM components. Three τ-distinctive
+  positive readings are committed (outer Newtonian-limit r_t; inner M∂(R)
+  number-promotion; transition r_trans = ℓ_cl,sub(M_sub)) plus one numerical anchor
+  (r_trans ≈ 3.4–10.8 kpc) and an 11-row N16 falsification surface with one
+  headline pre-registered falsifier (host-mass independence of r_trans at fixed
+  SHMF). 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.
+claim_boundary:
+  core: >
+    Under the τ-framework's capacity-gradient gravity sector and its boundary-
+    holonomy mass closure (V.D272), the Natarajan dichotomy is a regime-projection
+    of one D-sector readout — collisional-like inner core via M∂(R) number-
+    promotion at the host nodal-capacity maximum, collisionless-like outer
+    tidal extent via the V.D261 cluster-screening factor (1 + r/ℓ_τ ≈ 1) — with
+    a single transition scale ℓ_cl,sub(M_sub) = √(G M_sub / a₀) governed by
+    subhalo mass, not by a particle-DM cross-section.
+  non_claims:
+    - 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 via the M∂(R) mechanism; amplitude deferred).
+    - It does not claim τ-physics is Lean-verified as external physics.
+    - It does not supersede the conjectural status of V.T203 in the KSZ-categorical note.
+    - It does not engage Natarajan, Chiang, or Dutra adversarially; the note is offered in the spirit of pre-registration, not adjudication.