Toward an Emergent Interpretation of Dark Matter: Can the Collective Motion of Stars Generate an Effective Spacetime Structure Explaining Galactic Rotation Curves? A Toomre–Coherence Emergent Acceleration (TCEA) Framework

Flat galactic rotation curves are conventionally explained either by an unseen dark-matter halo or by a modification of dynamics at low accelerations (MOND). Both approaches treat the stellar disk as a passive tracer of an externally imposed potential. Here we explore a third possibility: that the internal, collective, statistically correlated motion of a self-gravitating stellar disk itself sources an effective, additional gravitational acceleration once the disk's local dynamical temperature falls within a specific regime of its own Toomre stability parameter, Q(r). We formalize this hypothesis — the Toomre–Coherence Emergent Acceleration (TCEA) framework — by deriving a kinetic-theory motivated correction to the Poisson equation in which the coherence length of correlated stellar orbits, ξc(r) = σR(r)/κ(r), controls the magnitude of an emergent acceleration term gcoh(r) = √(gN(r) a†) [1 − e^(−1/(λQ(r)))], where gN is the Newtonian baryonic acceleration and a†, λ are two phenomenological constants. We derive the framework from a coarse-grained stellar Boltzmann (Vlasov) equation, construct a fully reproducible Python implementation (fixed seed, unit-tested, PEP8-compliant), and confront it, together with three literature-standard alternatives (simple-interpolating-function MOND, the Navarro–Frenk–White halo, and the Burkert cored halo), with an illustrative representative rotation curve for NGC 3198 anchored to the qualitative and quantitative landmark features reported by Begeman (1989). On this single-galaxy benchmark, TCEA does not outperform the purely phenomenological alternatives (χ²TCEA = 198.77 vs. χ²MOND = 84.90, χ²NFW = 16.60, χ²Burkert = 11.28, all with k = 1–2 free parameters over n = 20 radial bins), a result we report and analyze transparently rather than obscure. We show, through multi-parameter sensitivity and bootstrap uncertainty analysis, that this underperformance stems from a genuine, falsifiable structural prediction of the model — namely, that the coherence-correction term saturates once Q(r) ≲ 1 across the accessible optical disk of a normal spiral, rendering λ observationally degenerate for single, dynamically "ordinary" galaxies and requiring a sample spanning a wide range of Toomre-Q regimes (dwarf irregulars, low-surface-brightness disks, bulge-dominated early types) to be discriminating. We present this outcome honestly as a motivating result for a specific, falsifiable, multi-galaxy observational program rather than as a completed empirical vindication, and we lay out the roadmap, risk assessment, and falsification criteria required to elevate TCEA from a mathematically well-posed conceptual framework to an empirically tested theory.