The STF Ultralight Condensate

Status note, 5 September 2026 — the scalar mass is an explicit, measurable input. Every calculation in this paper stands unchanged, evaluated at m_s = 3.94 × 10⁻²³ eV. What has changed is that value’s standing. From the Theory Edition (First Principles V9.7.2) the framework carries m_s as its one free scale: the theory states how each prediction depends on it, and specifies how it is to be measured — the knee at τ_c = ℏ/(m_sc²) in an activation-timing distribution, never a centroid (V9.7.2 §III.B). That is the same footing as the graviton mass in massive gravity or the coupling in scalar–tensor gravity — a scale the theory fixes the dependence on and hands to experiment. Study 21 established it by auditing every internal route for fixing the mass. Results below are accordingly conditional on the evaluation scale; where this paper calls the mass “derived”, read “evaluated at”, the figure being the historical association-implied value. Withdrawn is not deleted.

(formerly drafted as “Dark Matter as Geometry”; retitled at completion — see the revision note)

Version 2.0 — 22 August 2026

Z. Paz · Independent Researcher · zevpaz@gmail.com · ORCID 0009-0003-1690-3669

Revision note. This paper supersedes Dark Matter as Geometry (the “Full” paper, which retains its August 2026 status banner as a historical record). It is written against First Principles V8.1, the August 2026 galactic delegation record, and the completed B10 calculation (returned 22 August 2026 with its capacity audit; every checkable number independently reproduced before inclusion — 44/44). The retitling is a result, not a rebrand: B10 closed the all-dark-matter interpretation at the derived mass (§VI.B), so this is now a paper about an ultralight condensate sector carrying a stated exclusion, not a paper claiming the dark matter is explained. Claim taxonomy per V8.1 §I.E: theorem · derived · conditional · numerical · commitment · open.

Abstract

The Selective Transient Field (STF) framework contains an ultralight scalar, m_s = 3.94 × 10⁻²³ eV/c², whose oscillating condensate was the framework’s dark-matter candidate. This paper states what that candidacy now consists of, after the June–August 2026 audit cycle withdrew the framework’s former galactic mechanism and the B10 calculation decided the candidacy’s decisive constraint.

What stands, and is kept. At the cosmological background level the oscillation-averaged condensate is exactly pressureless: ⟨w⟩ = 0, ρ_φ ∝ a⁻³ (derived; WKB regime). In the non-relativistic regime it obeys Schrödinger–Poisson dynamics with de Broglie coherence λ_dB ≈ 1.4 kpc at Milky Way velocities and solitonic cores (derived). The same field’s residual potential supplies the dark-energy component, with w(z = 0) = −1 exactly from the T² nodal structure (derived within its own paper; the sourcing is conditional on the threshold normalization). The scalar mass is derived conditional on the selection of the 730 R_S separation — the threshold’s SI normalization bridge is open (V8.1 Appendix Q) — and the coupling ζ/Λ = 1.35 × 10¹¹ m² is conditional on its UV matching data.

What is withdrawn, once and here. The cross-disformal matter coupling — not generated by the framework’s own ten-dimensional reduction (B̂_KK = 0), its coefficient fixed by the withdrawn flyby amplitude match — and with it the entire former galactic mechanism: the B̂ ∝ r⁹ trigger, the nonperturbative Q-phase transition, the phonon–baryon vertex, the marginal-stability closure of γ_DM, and the cluster decoherence factor built on the same coupling. The claim that the field is “independently validated at planetary scales” through the flyby anomaly is withdrawn with the flyby force mechanism (four no-gos; the flyby is now a measurement-theory question — V8.1 Appendices F–M). MOND is not re-derived. The acceleration scale a₀ = cH₀/(2π) is demoted from result to conditional target: the candidate derivation (Clock-Gradient Marginality) leaves three named clauses undischarged, and the 2π itself currently has no derivation. None of these withdrawals touches the condensate sector.

What decided the candidacy. Lyman-α forest analyses exclude a free ultralight scalar below ≈ 2 × 10⁻²⁰ eV — a factor ~508 above m_s. The former escape route (a dressed perturbation mode screened through the cross-disformal coupling) was withdrawn with that coupling. The last named escape — the compactification’s φ²I₄ condensate self-interaction — has now been computed (B10, 22 August 2026, with a capacity audit of its own load-bearing step). The result is verdict (d): on the licensed branch the self-interaction’s fractional effect is ≲ 1.5 × 10⁻⁷⁵ at oscillation onset — too small to alter any transfer function at any epoch — and the one construction that would have made it large is unlicensed by the framework’s own capacity discipline and self-refuting where applied. The free-field mapping therefore holds, the Rogers–Peiris bound transfers intact, and the interpretation of the STF scalar as all of the dark matter at m_s = 3.94 × 10⁻²³ eV is closed (§VI.B). A subdominant fraction is not excluded, but the framework does not derive the fraction, so that reading currently has no computable content. This paper states the closure as a result, in the framework’s own discipline.

Two claims remain separable, as before. (A) Class-level: the convergent observational record — direct detection entering the neutrino fog, the wide-binary anomaly, the MOND Depth Index universality, tentative a₀ redshift evolution — has broken the explanatory monopoly of particle dark matter; non-particle alternatives are as responsible to investigate as continued particle searches. We hold this with high confidence and it does not require STF to be correct. (B) Mechanism-level: that the STF condensate is the realization. This claim rested on the condensate sector alone, was observationally in the fuzzy-dark-matter class at the same mass, and B10 has now decided it: at f = 1 it fails at the derived mass. What survives of (B) is the condensate as a physical sector of the framework — background-exact, Schrödinger–Poisson at small scales, partnered with dark energy — with its dark-matter role bounded above by an underived fraction. We hold the two claims to different epistemic standards and say so.

Keywords: dark matter, ultralight scalar, Schrödinger–Poisson condensate, MOND acceleration scale (conditional), Lyman-α constraint, dark energy, unified dark sector, two-clock theory, Calabi–Yau compactification

I. Introduction

I.A The problem and the observational shift

Forty years of direct searches have not produced a dark-matter particle. The LZ experiment’s 417-live-day null result with ten tonnes of xenon reaches into the irreducible neutrino fog — a floor that constrains WIMPs specifically, not ultralight scalars, axions or sterile neutrinos. Meanwhile the galactic phenomenology that any candidate must explain has sharpened: rotation curves organize on a single acceleration scale a₀ ≈ 1.2 × 10⁻¹⁰ m/s²; the radial-acceleration relation is tight across galaxy types; the MOND Depth Index classifies stellar systems from globular clusters to ultra-diffuse galaxies with one parameter; wide-binary analyses report a contested but persistent anomaly at accelerations below a₀ in systems that cannot host a dark halo; and both simulation extraction and first tentative direct kinematics suggest the acceleration scale grows with redshift.

This paper’s class-level claim (A) is that this record justifies treating non-particle dark-sector candidates as first-class research objects. Its mechanism-level claim (B) is the STF condensate. The two are argued separately throughout, because a reader can accept A and reject B.

I.B What changed since the previous version

The previous version of this paper derived MOND-like galactic dynamics from a cross-disformal matter coupling calibrated at the spacecraft flyby anomaly. The June–August 2026 audit cycle withdrew both the calibration and the coupling (§II.C states the withdrawals once, with reasons). This revision therefore makes a smaller mechanism claim than its predecessor, and says exactly which observations still discriminate for or against it. The framework’s own record of these corrections — including the errors found and fixed in its published locality proof and field normalization — is part of the evidence that its surviving claims have been checked rather than accumulated.

I.C Organization

§II gives the framework in its current (two-clock) form and states the withdrawals. §III presents the condensate dark sector — the surviving mechanism. §IV re-scopes the comparison with competing frameworks. §V compiles the observational landscape supporting claim A. §VI is the honest assessment: the Lyman-α constraint and the completed decision calculation that closed the f = 1 reading, the cluster question, and the falsifiers. §VII states the predictions with their statuses. §VIII concludes with the claim ledger.

II. The Framework in Its Current Form

II.A The field and the action

The STF scalar couples to the rate of change of spacetime curvature. In the current two-clock formulation (First Principles V8.1):

\[\mathcal{L}_{\rm STF} = \frac{M_{\rm Pl}^2}{2}R - \frac{1}{2}(\partial\phi)^2 - \frac{1}{2}m_s^2\phi^2 + \kappa\,\phi\,N^\mu\nabla_\mu\mathcal{R}_{\rm STF}(N)\]

with N^μ the universal clock vector (prescribed in the working theory; the dynamical carrier is the framework’s principal open construction), ℛ_STF(N) = √(R² + 8𝒲_N) the positive clock-relative curvature norm (𝒲_N the Bel–Robinson superenergy; reduces to √C² in Schwarzschild and |R| in FLRW), and κ = (ζ/Λ)/L*² ≈ 10⁷⁰ dimensionless. The response kernel is zero-mode-subtracted: static curvature produces no response. The earlier formulation’s clock vector n^μ = ∇^μφ/√(2X) is valid only where φ is monotone; in the oscillating regime this paper requires, a periodic scalar cannot carry a global ordering through its gradient (the gradient-clock obstruction — theorem), which is precisely why the two-clock formulation exists. For a comoving cosmological system u^μ = N^μ and the sampling and evolution derivatives coincide; nothing in the condensate sector depends on the open carrier choice.

II.B Parameters and their statuses

There is no parameter in this paper fitted to a galactic observation. There is also no longer a claim that any galactic observation validates these parameters.

II.C Withdrawn structure — stated once

Per the framework’s house practice, everything this revision no longer relies on is stated here, with reasons, and not re-argued elsewhere.

1. The flyby force mechanism and its validation of ζ/Λ. The mechanical derivation of K = 2ωR/c fails on four independent no-gos: F·v = 0 identically for the minimal velocity coupling; Killing-energy conservation on a stationary asymptotically flat effective metric; the spin-parity obstruction (every scalar curvature magnitude is even in source spin to O(a²), while Anderson’s K is linear in ω); and k^μ∇_μℛ = 0 on the stationary Earth background. The “98% independent validation at planetary scales” is withdrawn with it. The flyby is now treated as a measurement phenomenon (V8.1 Appendices F–M; The Flyby Anomaly as a Measurement), and nothing in the dark sector cites it.
2. The cross-disformal matter coupling ĝ_μν = g_μν + B̂(∂_μφ∂_νℛ + ∂_νφ∂_μℛ). Not generated by the framework’s own 10D reduction (block-diagonal ansatz ⇒ no vector ⇒ B̂_KK = 0); coefficient fixed by the withdrawn flyby match; one of its five selecting requirements (F·v ≠ 0) refuted by theorem.
3. The galactic mechanism built on it: the B̂ ∝ r⁹ trigger and h(r); the Q-phase transition; the phonon–baryon vertex and the X^{3/2} chain’s physical anchor; γ_DM and its marginal-stability closure; the temperature-decoherence factor D(T) for clusters. The fold-catastrophe mathematics and the field-normalization theorem survive as mathematics (recorded in the bannered Galactic Closure paper); their physical application does not.
4. a₀ = cH₀/(2π) as a result. Demoted to conditional target (§III.D).
5. Settled negatives (do not re-attempt): a static Yukawa force from φ at galactic scales (λ_C = 0.162 pc ⇒ suppression e^(−49 000) at 8 kpc); the linear 2ω_s self-response (⟨φ·K[R_{2ω_s}]⟩ = 0 identically — orthogonal harmonics); the “S_cos dressing” route to Lyman-α through the cross-disformal response (falls with item 2).
6. Two corrected framework-level claims this paper previously repeated: ghost-freedom is regime-limited (established on exterior-vacuum and Kerr backgrounds via the Gauss–Bonnet parent; open in general), and c_T = c is calculated on the scalar–Gauss–Bonnet route (|c_T/c − 1| ≲ 10⁻³⁰, fourteen orders inside GW170817), not “exact by construction.”

III. The Condensate Dark Sector

III.A Background cosmology (derived)

In the WKB regime (m_s ≫ H, satisfied for all z of interest), the oscillating field φ = A cos(m_st) has oscillation-averaged ⟨ρ_φ⟩ = ½m_s²A², ⟨p_φ⟩ = 0: ⟨w⟩ = 0 exactly, ρ_φ ∝ a⁻³ — indistinguishable from cold dark matter at the background level. The CMB acoustic structure, BAO imprint, equality redshift and damping tail constraining Ω_DM ≈ 0.27 are then measuring the gravitational effect of the oscillating condensate at recombination. Status: derived (background level). The perturbation level is where the candidacy was decided, and it is treated honestly in §VI.B, not assumed.

III.B Non-relativistic structure (derived)

The envelope decomposition yields Schrödinger–Poisson dynamics: quantum pressure below the de Broglie scale, cored profiles, solitonic ground states. Convention, declared (2π-Provenance Rule, case i): this paper quotes the full de Broglie wavelength λ_dB = h/(m_sv) = 2πħ/(m_sv); the reduced scale ħ/(m_sv) is 2π smaller (a factor 248 in volume). At v = 220 km/s: λ_dB ≈ 1.39 kpc (reduced: 221 pc); at dwarf-galaxy velocities ~20 km/s, λ_dB ~ 15 kpc (reduced: ~2.4 kpc). Comparisons with literature core radii must match conventions — soliton core radii in the simulation literature are defined dynamically (e.g. half-density radius of the ground-state solution), not as either bare wavelength, and quantitative core comparisons in this framework must use those definitions rather than λ_dB itself. These are the shared predictions of the ultralight-scalar class at this mass, and the framework claims them as such, without a distinctive STF signature unless and until B10 or the CGM programme supplies one.

III.C The dark-energy component (carried at its own status)

The residual potential at the stabilized modulus supplies the dark-energy density, with the T² nodal structure giving w(z = 0) = −1 exactly and effective (not fundamental) phantom behaviour at z > 0, and c_s²(z=0) = 1 (Dark Energy paper V0.1/V0.2). The unified-sector framing — one field, both components — is retained as an identificatory claim: the components share the field and its parameters, and the dark-energy sourcing is conditional on the threshold normalization (V8.1 §IV.E). It is not yet a dynamical demonstration that one field produces both regimes through its own equations of motion; the perturbation-level calculation of §VI.B is part of what that would require.

III.D The galactic sector, honestly

With the former mechanism withdrawn, the framework’s galactic-scale content is:

What it has. The condensate itself: cored dwarf profiles, soliton scaling, kpc-scale interference structure — the fuzzy-dark-matter phenomenology at m_s, with the mass supplied by the framework’s own (conditional) derivation rather than fitted to galactic data.

What it does not have. A derivation of MOND. Flat rotation curves, the baryonic Tully–Fisher relation and Faber–Jackson do not currently follow from the framework. The August 2026 delegation closed the direct routes: stationary curvature-rate sourcing vanishes for a galaxy-stationary carrier (and the cosmological-carrier alternative, Branch C, is kernel-suppressed by H/ω_s ≈ 4 × 10⁻¹¹); the Yukawa route is dead at galactic radii; the phonon route fell with the cross-disformal coupling.

The conditional target. The delegation’s permanent gain is the Spatial Clock-Gradient Invariance Theorem (proved, verified): the spatial logarithmic gradient of the universal-to-operational clock rate is invariant under all allowed relabellings of universal time, supplying an acceleration-dimensioned invariant 𝔞 = c²D^⊥ln J_C with the lapse↔︎potential normalization — no fitted conversion. Clock-Gradient Marginality would then give a₀ = cH/2π = 1.159 × 10⁻¹⁰ m/s² (−3.4% from the observed scale at H₀ = 2.43 × 10⁻¹⁸ s⁻¹). Three clauses remain undischarged: that one inverse-mass correlation length is the spatial write cell; that one complete internal phase is its temporal write interval; that universal strain transfers to the baryonic lapse with unit gain. And the 2π’s selection currently has no derivation. The arithmetic is exact — Hλ̄_C/T_s = cH/2π identically, the mass cancelling — but that identity pairs a reduced spatial correlation length with a full temporal recurrence, and why galactic dynamics compare exactly those two quantities is an underived constitutive choice (the Correlation–Cycle Write Principle), not an error and not a residual mystery: a declared selection awaiting a principle. The corpus’s only prior license for the pairing was the General Theory locality argument, which contained a corrected (2π)³ error. Additionally, the required clock completion must admit a nontrivial lapse, which the minimal completion provably does not. Status: conditional target — named, not claimed. The numerical proximity is real and is why the target is named; it is not evidence until the clauses close.

IV. Comparison with Competing Frameworks (re-scoped)

The systematic comparison of the previous version is retained in substance for ΛCDM, MOND, WDM, SIDM, emergent gravity and superfluid dark matter — their internal difficulties are unchanged by anything in §II.C. Two entries change.

Fuzzy dark matter. The previous version claimed three differentiators; one survives cleanly, one is conditional, one is withdrawn. (1) Mass provenance — survives with a conditional label: m_s comes from the framework’s threshold-and-timing structure, not from fitting galactic data (conditional on the separation selection). It is notable that an independent kinematic fit to the ultra-diffuse galaxy AGC 114905 (Bañares-Hernández et al. 2025) lands at m_a ≈ 2.3–3.2 × 10⁻²³ eV, within a factor ~1.5 of the STF value — an independent determination in the same narrow window, not a validation. (2) The a₀ connection — conditional (CGM, §III.D); fuzzy DM has no analogous target. (3) Planetary-scale validation — withdrawn (§II.C). The honest present position, now settled by B10: at the perturbation and halo level the STF condensate is in the fuzzy-DM class at m_s — the φ²I₄ self-interaction does not separate them (fractional effect ≲ 10⁻⁷⁵ on the licensed branch; §VI.B) — so the frameworks are observationally degenerate at this mass and the STF candidacy inherits the full force of the free-field bounds, which exclude the f = 1 reading.

MOND. The previous version presented STF as deriving MOND’s successes; it does not (§III.D). What STF retains against MOND is structural: MOND has no cosmology and treats a₀ as an unexplained constant; STF has a complete background cosmology and a named conditional route to a₀ with a testable z-dependence. What MOND retains against STF: at galactic scales MOND’s phenomenological successes are, at present, successes STF cannot claim.

V. The Observational Landscape (claim A)

This section supports the class-level claim and is deliberately mechanism-neutral. Direct detection: LZ’s 417-live-day null (Akerib et al. 2025) enters the neutrino fog — the WIMP-specific detection floor. Wide binaries: Chae (2024, 2025, 2026) and Hernandez & Kroupa (2025) report a >3σ anomaly at low accelerations in Gaia data (γ_g ≈ 1.3–1.6), contested by El-Badry (2024) on strict-cut grounds; the contamination and Galactic-tide caveats are real, and until Gaia DR4 resolves the cut methodology this is a Tier-2 (suggestive, contested) result. It bears emphasis that with the cross-disformal mechanism withdrawn, STF makes no specific wide-binary prediction at present; the anomaly’s role here is purely class-level. MOND Depth Index: Eappen & Kroupa (2026) — a one-parameter classification of stellar systems by the mass fraction beyond r(a₀), spanning six orders in mass with no exceptions; unexplained in ΛCDM. a₀ redshift evolution: Mayer et al. (2022) extract a₀ increasing ~3× to z = 2 from ΛCDM simulations; Vărăşteanu et al. (2025) provide first tentative direct kinematic evidence of the trend. This is the one observable where the STF’s conditional target is specific: CGM predicts a₀(z) = cH(z)/2π; standard MOND predicts a constant or, in the Milgrom–Sanders variant, a₀ ∝ H with unspecified coefficient. Scalar-field DM programme: growing mainstream interest (Matos & Ureña-López 2025) and the AGC 114905 mass coincidence noted in §IV.

VI. Honest Assessment

VI.A The epistemic structure

The candidacy had exactly one decisive near-term calculation (B10) — it has returned and decided against the f = 1 reading (§VI.B) — one conditional programme (CGM), and one class of shared-with-ULDM observables (soliton cores, dwarf kinematics). Everything else in this paper is either background cosmology (solid, but not discriminating against CDM) or class-level evidence (not discriminating for STF). With B10 closed, the sector’s open physics is the CGM programme and the underived fraction Ω_φ.

VI.B The Lyman-α constraint — the decisive test

The constraint. For a free ultralight scalar, the quantum-pressure cutoff in the matter power spectrum at m_s = 3.94 × 10⁻²³ eV lies inside the Lyman-α sensitivity window (k ~ 0.5–10 h Mpc⁻¹, z ≈ 2–5). Rogers & Peiris (2021) exclude m < 2 × 10⁻²⁰ eV — a factor ~508 above m_s; the Marsh–Niemeyer Eridanus II bound is a factor ~2500. These bounds transfer (shown below), and the dark-matter interpretation at the derived mass closes.

The withdrawn escape. The previous version proposed that the gravitating perturbation is a dressed mode screened by a factor S_cos ≳ 3 × 10⁵ through the cross-disformal response. That route is withdrawn with the coupling (§II.C item 5). No dressing of the perturbation variable is currently available to the framework.

The last escape — computed and closed (B10, 22 August 2026; verdict slot (d) of the pre-registered decision structure). The compactification’s φ²I₄ operator has a nonzero DC overlap with the condensate’s own 2ω_s curvature oscillation, ⟨φ²·K[R₂ cos 2ω_st]⟩ = A²R₂/5 = (6/5)ρ_φ²/(m_s²M_Pl²) (theorem; the linear response vanishes identically by half-period parity). The compactification fixes the parent coefficient and its sign: γ₂ = A″₀/96 = (√6/4M_Pl)(ζ/Λ)ω_s ≈ 3.44 × 10⁻²⁶ eV⁻² > 0, so the induced conservative self-interaction is attractive — the sign that could in principle have opposed quantum pressure. The calculation then forked on the response normalization, and the capacity audit that followed (B10 Addendum) settled which fork the framework licenses:

• The licensed, UV-faithful branch: the bare operator γ₂φ²K[I₄]. Its self-generated contribution begins at order ρ_φ³, with fractional size γ₂m_s²u² ≲ 1.5 × 10⁻⁷⁵ at the largest density where the oscillatory WKB treatment begins. Too small to alter a cosmological transfer function at any epoch. This is verdict (d) of the decision structure above.
• **The capacity-projected branch (β₂ = γ₂/L*² ≈ 1.0 × 10²⁰) is unlicensed. The audit proved a dimensional non-identity: the two “capacity” notions in the corpus — Appendix D’s curvature-response covector norm (units L⁻²) and the Closure–Capacity Correspondence’s Shannon/control rate (bits s⁻¹) — are different mathematical objects, and neither licenses the projection. Extending it anyway assumes unit quadratic utilization (η₂ = 1), contrary to the framework’s own stated discipline that capacity is not saturation (V8.1 App. L.3). The branch is retained only as a reductio**: automatic saturation would give δ⟨w⟩₀ = −0.147 and destroy the matter-like background by z ≈ 1, and would contradict the framework’s own present-day halo estimates by four orders — automatic quadratic saturation is self-refuting.
• No intermediate coefficient exists to fit. A quadratic utilization η₂ is a named missing datum, not an adjustable escape parameter: no compactification, kernel, saturation or topology result fixes it, and the bounded counterfactual is decisive anyway — any coefficient small enough to preserve the background (ℛ_bg ≤ 0.1 at oscillation onset) moves the equality Jeans scale by less than 0.1%, against the required factor √508 ≈ 22.5 in k. The two requirements exclude each other by five to six orders of magnitude in the coefficient (background safety allows β₂,eff ≤ 16–85; the required shift needs β₂,eff ≈ 1.16 × 10⁷).

(A record note: this paper’s earlier “settled” present-day estimates — self-interaction/gravity ≈ 6 × 10⁻¹⁰ in the Milky Way halo, 4 × 10⁻⁵ in a dwarf core — implicitly used the order-one normalization now identified as unlicensed; on the licensed branch the present-day self-interaction is smaller by a further factor γ₂m_s²u ≈ 2 × 10⁻⁸⁶ at halo density. The estimates are superseded, in the direction that strengthens the closure.)

The consequence. At leading order the perturbation equation reverts to the canonical free-ULDM form; the Rogers–Peiris exclusion m > 2 × 10⁻²⁰ eV transfers intact; and the interpretation of the STF scalar as all of the dark matter at m_s = 3.94 × 10⁻²³ eV is closed, by a factor of ~508 in mass. The verdict does not use the Eridanus II bound and is unchanged if that bound is discarded. Every checkable number in the B10 chain was independently reproduced before entering this paper (44/44, including the coefficient, the gate arithmetic, the WKB epochs, and the Jeans-shift bounds).

What this paper’s tension always was: the f = 1 tension. The previous versions of this paper asserted the condensate as all of the dark matter — implicitly: no statement of a fraction f appears anywhere in them — and the Lyman-α tension carried here has always been the f = 1 tension. That reading is now excluded. A subdominant reading (f < 1) is not excluded — the Lyman-α bound is derived for f = 1 and relaxes for small fractions — but the framework does not derive f: the condensate amplitude was always matched to the observed dark-matter density, and there is no misalignment or relic-abundance calculation in the corpus. So “the scalar is some of the dark matter” is presently a weaker match with an undetermined remainder, not a prediction, and this paper does not advance it as one. What would change this is a derived Ω_φ. A misalignment-style derivation is on hold by the author’s instruction; when it resumes, its outcome space is inverted relative to the usual hope — a derivation yielding Ω_φ ≈ Ω_DM would falsify the framework (Lyman-α excludes the scalar being all of the dark matter at this mass), so success for the sector is Ω_φ ≪ Ω_DM with the remainder owned by other physics.

The barred shortcut. The companion conjecture paper (Holographic Closure Capacity and Transactional Exhaust) contains, among its options for relating a hypothetical exhaust sector to this scalar, an “independence” option in which the exhaust is a second dark component. That option must not be used to rescue this sector. A subdominant f was always available by matching a smaller amplitude — no conjecture required — and what the exhaust would supply, the remaining dark density, has no derived abundance, equation of state or sound speed. Invoking it would replace one unexplained number with two while feeling like progress — the reasoning pattern that produced the withdrawn γ_DM closure and the r⁹ trigger — and would trip that paper’s own falsifier 6 (double counting without a derived partition). The connection stays on the record, usable if and only if a partition is ever derived.

VI.C Clusters and dark-matter-free dwarfs (open)

The cluster question — MOND-like frameworks underpredict cluster masses — was previously answered by the temperature-decoherence factor D(T), which fell with the cross-disformal coupling. The framework currently has no computed cluster story beyond the condensate’s CDM-like background behaviour, which may in fact suffice (a condensate with no MOND-like galactic force has no special cluster problem — it has whatever profile Schrödinger–Poisson dynamics gives it); this should be computed, not asserted. The apparently dark-matter-free dwarfs (DF2, DF4, FCC 224) pose the mirror question for any universal-field candidate; tidal-stripping of condensate is the plausible route and remains uncomputed.

VI.D What would falsify the STF dark sector

1. Reproducible laboratory detection of a dark-matter particle. (Fatal to the mechanism claim; the class claim dies with its motivation.)
2. B10 outcomes (b), (c) or (d) — the Lyman-α bound transfers. Realized: B10 returned (d), 22 August 2026. The dark-matter interpretation at m_s = 3.94 × 10⁻²³ eV (f = 1) is closed (§VI.B); this falsifier has fired and is retained as the record of a pre-registered test that was allowed to fail.
3. Soliton core sizes consistently inconsistent with r_c(m_s) across well-measured dwarfs. (Fatal to the mass, independent of Lyman-α.)
4. Direct high-z kinematics showing a₀(z) = const within ~5%. (Closes the CGM z-scaling; the z = 0 target survives as an unexplained match.)
5. ⟨w⟩ ≠ 0 or ρ ∝ a⁻³ violated at CMB precision. (Fatal to the background sector.)

The previous version’s falsifiers built on γ_DM universality and the Q-phase transition are removed with their mechanism, not because they were tested.

VII. Predictions

Predictions 1–2 do not distinguish STF from fuzzy dark matter; the paper says so. Prediction 5 would have, and its closure is itself the paper’s sharpest result; prediction 4 (CGM) is the remaining distinguishing target.

VIII. Conclusion and Claim Ledger

The STF condensate sector, stated at its current size: a UV-motivated ultralight scalar with a conditionally derived mass, exact CDM background behaviour, Schrödinger–Poisson structure at galactic scales, a dark-energy partner from the same field, no derived MOND, one conditional route to the acceleration scale — and a completed calculation that decided its most severe constraint against it: the scalar is not all of the dark matter at the derived mass (B10 verdict (d); the free-field Lyman-α bound transfers, factor ~508). A subdominant role is not excluded and not derived. That is less than any previous version claimed, the central negative is stated as a result rather than buried, and everything in the paper has been checked.

Claim ledger (current taxonomy).

Acknowledgements

The June–August 2026 audits and the galactic-sector delegation that produced the withdrawals and the Clock-Gradient results are recorded in the framework’s audit archive; every result carried here was independently reproduced before inclusion.

References

(Carried from the previous version where cited: Akerib et al. 2025 [LZ]; Anderson et al. 2008; Bañares-Hernández et al. 2025; Chae 2024, 2025, 2026; El-Badry 2024; Eappen & Kroupa 2026; Hernandez & Kroupa 2025 / Hernandez et al. 2024; Hu, Barkana & Gruzinov 2000; Iršič et al. 2017; Marsh & Niemeyer 2019; Matos & Ureña-López 2025; Mayer et al. 2022; Rogers & Peiris 2021; Schive, Chiueh & Broadhurst 2014; Vărăşteanu et al. 2025; Peters 1964. Project papers: First Principles V8.1; The Flyby Anomaly as a Measurement V1.0; Dark Energy V0.1/V0.2; Theory of Time V4.3; Topological Closure V6.3; B10 — STF Scalar Dark Matter Derivation* and B10 Addendum — Capacity, Saturation, and Quadratic Utilization (delegation records, August 2026); Holographic Closure Capacity and Transactional Exhaust V1.0 (conjecture program — cited only for the barred option of §VI.B); the bannered Dark Matter Full paper and Galactic Closure V0.1 as historical records.)*