The Spherical Model of the Universe 2.0: Standard Propagation, Spherical Inputs, and a Fourteen-Test Battery

We present the converged formulation of the Spherical Model of the Universe (SMU 2.0).The model adopts, without modification, the propagation laws of general relativity es-tablished as exactly equivalent to the c(Φ) representation in the companion Paper 0 andthe standard hot early universe, read in the SMU covariance dictionary. All heterodox con-tent is confined to inputs: (i) closed spatial topology (ΩK > 0); (ii) a single non-standardparameter of the primordial plasma, a large lepton asymmetry L; (iii) a keV-scale sterilefermion ocean resonantly produced in the QCD epoch; and (iv) a superhorizon isocurva-ture gradient reflecting the observer's off-centre position on the 3-sphere. From these inputsfollows the model's flagship mechanism: calibrated black-hole seeds degenerate fermioncores, ignited by dissipative baryonic concentration, collapsing at the Oppenheimer Volkoffmass MOV = 0.38m3 Pl/m2. For m ∼ 100 345 keV this yields seeds of 5×10^6 6×10^7M⊙at z ≳ 10, addressing the JWST early-quasar problem, and produces an over-constrainedobservational network: a redshift-independent floor in the early black-hole mass function,an X-ray decay line at E = m/2, birth ringdowns and a stochastic birth chorus in the LISAband, a low-spin early population, and a reionization budget all functions of the singleparameter m. Sixteen falsifiable tests, each with a named instrument and a decision horizonwithin one to two decades, are tabulated. Mechanisms of earlier SMU versions that failedquantitative scrutiny are retired explicitly, with their refutations. Foreword to SMU 2.0 This edition consolidates three rounds of revision. The structure of the model, its constitutional clause and its flagship mechanism are unchanged; what has been added is the outcome of a systematic audit — new verification computations, the extensions of testable content that follow from them, and, where an account does not close, an explicit statement to that effect. The test battery has grown from fourteen predictions to sixteen, and the paper now carries one figure. Pre-history and inputs. Phase I now carries a fourth messenger: the statistics of the primordial metric perturbations, which the laundry cannot erase and which the sky has already read out. Recorded as an independent hypothesis is the horizon mint — a possible origin of the lepton asymmetry L in the window after sphaleron freeze-out, with its costs stated. The nucleosynthesis corollary gains the neutron–proton diffusion hierarchy and the clarification that the sorting agent is charge, not mass. A new demonstration shows why active neutrinos cannot carry degenerate cores under any conditions, and why the sterile fermion emerges from that argument not as a choice but as the unique survivor. The abundance budget. The ocean's accounts are now opened separately. Three close: the required number density leaves four orders of margin against the permitted lepton asymmetry; the radiation contribution is negligible; and the free-streaming length places the ocean firmly in the cold dark matter regime, so that the entire structure-formation success of ΛCDM is inherited without modification. The fourth does not close, and is stated as the model's principal open problem: whether resonant production can deliver the observed abundance at 100–345 keV with a mixing angle beneath the hard X-ray bound. Both outcomes are spelled out, together with the fallback that gravitational and horizon production provide and the price it exacts on two predictions. New falsifiable content. The model now predicts that the Galactic 511 keV line is not dark-matter decay, with two independent locks. Prediction P9 acquires a lensing leg: subcritical cores lens as point masses and their population must terminate in a hard ceiling at the Oppenheimer–Volkoff mass — the bright floor and the dark ceiling being one number read from two sides. The dud billiard adds rare late births in dry mergers, with no electromagnetic counterpart of any kind. P15 establishes a magnetic threshold, B > B_CMB(z), governing whether seed energy escapes as radio synchrotron emission or is Compton-upscattered into X-rays — a partition that drives the 21 cm absorption trough in opposite directions and is therefore measured jointly with P10. P16 derives a Soltan deficit: because seeds are born electromagnetically silent, the local black-hole mass density must exceed the radiatively accreted budget by the seed fraction, which already places the lightest end of the flagship mass window under pressure. Corrections and honesty. The crossfire equation is stated dimensionally. A standing internal constraint is now made explicit: the closed sphere lives in a narrow corridor, since curvature large enough to be comfortable would destroy H₀ — and the model offers no resolution of the H₀ or S₈ tensions, inheriting them as the constitutional clause requires. Four kill conditions have been added. A figure now shows the crossfire directly: one mass, two instruments, and the excluded 7 keV reading marked on the same line. With this the model closes its ledger. Everything added is either computed, explicitly labelled as a hypothesis, or named as an unsolved problem. The remainder belongs no longer to the author, but to the instruments.