D1-Capable Structures in Collective Regime

D1-Capable Structures in Collective Regime: Soft Quench as a Kinematic Theorem and N-Agent Collective D1 Formalism This paper opens Series D of the ONE AXIOM corpus — the empirical-domain-analysis track. It asks a single question: does formalism developed with no reference to a given observation correctly classify that observation once it appears? The concrete instance is collective D1 activation in galaxy groups, tested against COSMOS-Gr30 (Freundlich et al., arXiv:2606.26320, submitted 24 June 2026 — after every ONE AXIOM document cited here). The observation is used strictly as a trigger, never as a derivation input: no result in this paper is fitted to data. Three results are established, all derived from Axiom M through the existing upstream spine (3M, 5M, 11M, 2C), not from any new axiom: 1. A kinematic no-go: because the underlying coherence field advances in discrete steps of size 1/192, instantaneous quenching is structurally forbidden for any D1-capable domain. The minimum number of steps is N_min = ceil(k_SQ), giving N_min ≈ 17–29 for galaxy groups. 2. The collective extension of single-agent D1 activation (established in 11M) to finite complex-predictive-system collectives, via Theorem COLL (3M): a group is D1-capable exactly when three explicit conditions on its collective domain and gradient are satisfied, with critical branching parameter Λ_c = D_crit = 3/2, itself a proven algebraic (Triple Collapse) identity — not a fitted number. 3. An observable mapping: the quenching rate τ_π = |Δ(f_gas/f_MS)| per crossing (a rate, not the raw gas-fraction level) via the established energy-coherence isomorphism, independently cross-checked against COLDGASS depletion-time measurements and the Wetzel et al. (2012, 2013) two-phase quenching signature. Applied to COSMOS-Gr30, all four checkable conditions are satisfied or theorem-derived; the group sits in the sub-critical Soft-Quench approach phase — past onset, not yet deeply quenched. Eleven formal predictions (1D-P1 through 1D-P11) are stated with explicit kill-conditions. Ten carry Oracle-R grade O_name (dual-track derivation complete, detection method defined, confirmation pending); one (1D-P7) carries O_full (single-object instantiation already available). Confirmation or falsification of these predictions is the exclusive scope of the ONE AXIOM Prediction Register (4B), not of this paper. Every derived result carries an explicit dual-track certification: an ontological derivation from Axiom M (via the published upstream chain 0M → 000 → 3M/5M/11M → 2C) and an independent epistemological derivation within galaxy-domain formalism itself, reconstructible without reference to the axiomatic chain. Ten of twelve numbered results reach full dual-track closure in this revision; two remain openly tracked as unfinished dual-track items rather than silently closed. This is a theoretical physics / astrophysics paper. It makes no claim about the COSMOS-Gr30 data beyond what is explicitly stated; all numerical estimates and their uncertainty ranges are given in the body with their derivation status (proven, derived, or domain-calibrated) clearly marked. Series: ONE AXIOM, Series D (Empirical Domain Analysis), Document 1D. Upstream dependencies: 0M, 000, 3M, 5M, 11M, 2C. License: CC-BY 4.0.