Covariance-Limited Identifiability of Cosmic Number-Count Dipoles: A CMB-Grounded Multicarrier Study

Covariance-Limited Identifiability of Cosmic Number-Count Dipoles: A CMB-Grounded Multicarrier Study CatWISE inference, low-multipole covariance, and prospective survey capacity. OVERVIEW Large-angle number-count dipoles are routinely compared with the kinematic expectation inferred from the cosmic microwave background (CMB). This release shows that the resulting scientific category can be governed more by low-multipole covariance and operator identifiability than by the fitted dipole itself. A CMB-grounded multicarrier framework is constructed and applied to a declared local sectoral connection in Return Theory (RT). The connection maps beta_CMB = 0.0012335867 and its measured Galactic direction (l, b) = (264.021, 48.253) degrees into the expected carrier response, with no catalogue-specific free dipole amplitude. CatWISE2020 was the only directional target opened, once. MAIN RESULTS Fitted amplitudes: beta_hat / beta_CMB = 2.128 to 2.239, displaced by 21.9 to 27.9 degrees from the CMB direction, stable across three masks and across a 250-source extreme-red spectral-tail branch. Adjudication: the Poisson covariance layer classified every mask as incompatible with the connected CMB vector (p = 1.99996e-5), while the frozen lognormal stress layer classified every mask as compatible but nonconfirmatory (p = 0.9943 to 0.9956). The mandatory cross-layer consensus rule therefore returned not_identifiable. Covariance anatomy: the two layers differ by a factor 49.8 in amplitude uncertainty and a factor 2481 in variance. 92.6 per cent of the covariance-trace increment is carried by the masked-sky ell = 3 sector. The frozen lognormal layer retains only 1.2 per cent power to distinguish beta_CMB from 2.2 beta_CMB, which is why the test was blind rather than the data uninformative. Prospective capacity: target-independent screens using public Quaia mocks and published radio-survey products did not meet the preactivation power or identifiability requirements. A LoTSS DR3 screen was not_evaluable because the power envelope straddles the threshold and no auditable target-independent sensitivity reduction is available through the documented public interface. The study neither confirms nor refutes RT. Its durable outputs are a frozen CatWISE directional estimate, a quantitative diagnosis of covariance-limited non-identifiability, and release-driven capacity requirements for a future genuinely multicarrier test. REPRODUCIBILITY FINDINGS ON PUBLIC UPSTREAM PRODUCTS Two documentation discrepancies were encountered while reconstructing published inputs and are reported in section 3.1 as provenance diagnostics only. Neither changed the frozen target selection, and neither used target directional information. 1. A complete rescan of all 141,698,603 prefiltered CatWISE2020 rows returns 8,535,013 objects for the stated W1 - W2 >= 0.8, 9 < W1 < 17 stage, whereas the deposited generation README associates 3,082,140 objects with that stage. The 9 < W1 < 16.4 interval instead returns 3,082,141, leaving a one-row residual for which no cause is asserted. 2. The public notebook and README mask constructions use Galactic and equatorial/ICRS HEALPix grids respectively, so pixel indices are not directly comparable across them. Evaluated on a common Galactic Nside = 64 grid, the included-pixel counts are 23,298 and 22,284, with 1,021 pixels included only by the notebook construction and 7 only by the README construction. CONTENTS AND DATA POLICY The archive contains the paper source, bibliography, PDF, tables and figures; portable analysis code and tests; compact masks, response tables, calibration arrays and derived summaries; execution records, validation reports and decision contracts; a machine-readable external-product register; a complete attempt ledger; and a SHA-256 manifest covering every embedded file. It deliberately contains no source catalogue, no large public mock ensemble and no raw sky image. Every external product is identified by DOI or authoritative URL, version, access date, query or filename, byte count and checksum wherever that information is available. One upstream file identity (RACS-low2) is explicitly marked unresolved; no missing identity has been replaced by an inferred value. PROVENANCE LEDGER Appendix B and metadata/COMPLETE_ATTEMPT_LEDGER.json record all 29 archived attempts with their registered status and full archive SHA-256, including 5 explicit hard-gate failures, 4 pre-result implementation errata, 0 seed reruns performed to obtain a pass, and 1 directional target opened in total. CLAIM BOUNDARIES The CMB temperature dipole is an anisotropy; its kinematic interpretation is not identical to measuring a geometric coordinate without a declared connection. The frozen carrier law is standard Doppler and aberration kinematics, so compatibility could not have uniquely confirmed RT. Incompatibility would reject only the declared sectoral connection and analysis domain. A not_identifiable result must not be relabelled as support, tension or ambiguity. The source-count dipole is mapped to beta through the frozen carrier response and is not directly identified with beta. Quaia, RACS-low2 and LoTSS directional targets were never opened and furnish no evidence for or against RT. LICENSING Text, figures and data records: CC BY 4.0. Code: MIT. Bundled font: SIL Open Font License 1.1. Third-party adapter components retain their original BSD-2-Clause terms. RELATED WORKS Return Theory (RT): Foundations, https://doi.org/10.5281/zenodo.21195693Return Theory (RT): Empirical Late-Time Cosmology, https://doi.org/10.5281/zenodo.21209098 KEYWORDS cosmic dipole; CMB dipole; number counts; covariance; identifiability; CatWISE2020; Quaia; RACS; NVSS; LoTSS; survey capacity; preregistration; reproducibility; Return Theory