Information Tension: Geometric Projection Explains Galactic Rotation Without Dark Matter Halos — SPARC Validation, Pre-Registered Falsifiers, and FAIR Data Package

Abstract Spiral galaxies rotate too fast at their edges for visible matter alone. For fifty years, cosmologists have explained flat rotation curves by invoking dark matter halos tuned independently for each galaxy—a flexible but difficult-to-falsify paradigm. Modified Newtonian Dynamics (MOND) compresses the phenomenology into a single universal acceleration scale a0 ≈ 1. 2 × 10−10 m s−2, yet its interpolation function is inserted by hand rather than derived from the Einstein field equations. Meanwhile, the Hubble tension between early-universe and local expansion measurements is typically treated as unrelated to galactic dynamics. We propose that both anomalies trace to a projection mismatch: observers measure gravity in four dimensions while the vacuum carries richer geometric structure than our measurements capture. This deposit packages the flagship preprint synthesizing Information Tension (IT) —an effective stress–energy in the modified Einstein equations sourced by that geometric deficit—together with open analysis code, SPARC galaxy results, timestamped pre-registrations, supplementary derivations, and reproducibility artifacts forming a FAIR (Findable, Accessible, Interoperable, Reusable) research record for independent replication and citation. In the slow-motion, weak-field regime of disk galaxies, IT reduces to a self-consistent acceleration law with no per-galaxy parameters: atot = abary × ½ + √ (¼ + a0/abary). The universal scale a0 = (χ2 c H0) / (2π κ) × √5 ≈ 1. 22 × 10−10 m s−2 is fixed from geometric invariants (χ ≈ 1/√2, κ ≈ 0. 954) before any galaxy data are consulted, matching the empirical MOND value within measurement uncertainty. Environmental coupling χ (r), modulated by local baryonic surface density with three universal constants shared across all galaxies, captures the transition from Newtonian inner disks to boosted outer rotation without fitted halo profiles. We validate IT against the public SPARC database (175 spiral and irregular galaxies; 135-object quality cohort with Vflat, obs > 0). Baryons-only Newtonian gravity yields 70. 5% RMS residual across the full sample. IT environmental coupling with canonical normalization achieves 22. 5% RMS (median 20. 0%) with 37 of 135 galaxies passing a strict 2σ outer-disk test—roughly a threefold improvement with zero per-galaxy knobs. We state plainly: ΛCDM with tuned halos can fit individual galaxies better; the SPARC test establishes that visible matter plus one global geometric law decisively outperforms visible matter alone, and the derived acceleration scale matches MOND without fitting a0. The Radial Acceleration Relation—the tight correlation between observed and baryonic acceleration across five decades of galaxy data—emerges without invoking invisible mass. Low-surface-brightness galaxies, historically the hardest cases for dark matter models, benefit most from environmental coupling, exactly as the geometric picture predicts. These three properties—parameter economy, pre-registered falsifiability, and cross-scale coherence—distinguish IT from another phenomenological curve fit. The framework extends beyond disks. Horizon-scale holonomy predicts CMB acoustic peak shifts (Δℓ1 = −0. 16) and distance corrections relevant to the Hubble tension. Five independent falsifiers—JWST JADES DR3 photometry, Simons Observatory CMB, SPARC dwarf extensions, turbulence thresholds, and quantum spectral gaps—were archived before data release. Formal proof artifacts and the reproducible Python pipeline godₜheoryₑvidenceₛprint. py accompany this deposit. Keywords: modified gravity, MOND, dark matter alternative, cosmology, SPARC, rotation curves, radial acceleration relation, Hubble tension, geometrically ordered dynamics, information tension, Stiefel manifold, pre-registration, open science, formal verification, galactic dynamics, CMB, JWST falsifiers, zero-parameter theory. Package contents InformationTensionFlagshipManuscript. md — main preprint (~2, 400 words) InformationTensionSupplementaryInformation. md — derivations, holonomy, Lean proofs, SPARC protocol godₜheoryₑvidenceₛprint. py — reproducible evidence sprint pipeline godₜheoryₒutput/ — task JSON outputs, SPARC CSV, pre-registration record CoverLetterScienceEIC. md — journal submission cover letter (reference) License and access CC-BY-4. 0 · Open Access. Author ORCID: 0009-0001-1303-7190.