PREPRINT · v2.1 · REVIEW DRAFT ZERO FITTED PARAMETERS 7 July 2026

$\mathcal{A}$: A Thermally Gated Dark Medium on a Dynamical Time Vector

Galactic dynamics, the dark-sector abundance, and cosmology from one temperature — the Gated Frame Formalism (GFF). Draft for external review; criticism actively solicited.

Kavinda Weerachandra¹

¹ Independent Researcher · wk@iatrt.com

Abstract

We propose that the universe's regulatory variable is neither mass density nor geometric scale but acceleration. One dynamical unit timelike vector field $u^\mu$ — the bulk flow of a cold dark medium — supplies the preferred frame, the cosmic clock $(\theta = \nabla\!\cdot\!u = H)$, and the gate variable, its proper acceleration $a[u]$. One temperature, $\beta = 2\pi/H$, sets the acceleration floor $a_0(t) = cH(t)/2\pi$, the relaxation clock $\Gamma = \beta H$, and the thermofield split that produces the dark sector. Medium modes are awake (supported, non-clustering) where $|a[u]| > a_0(t)$ and condensed (the dark mass) below. From these postulates, with zero fitted parameters: MOND's constants and both its laws as isothermal identities; a derived transition function; the dark-sector abundance $\Omega_{\rm DM}/\Omega_b = 5.41$ from $x = 1-\cos\sqrt2$ (Planck: $5.36\pm0.10$); $w=-1$ exactly; the Milky Way's rotation-curve decline; and seventeen ways to die. Every number regenerates from standalone calculations on public data.

1 How to read this document

This is a request for adversarial review, not an announcement. This framework was built by one person; it has passed every test its author could construct, including a from-scratch recalibration audit, and that is precisely why it now needs hostile eyes. Every quantitative claim was produced by a standalone calculation from public data (SPARC rotation curves, Gaia-era Milky Way surveys, published cluster and cosmology anchors). The anchor registry records the verification status of every external input; the few remaining reconnaissance-grade values are tagged [RECON] where used. §10 lists what we most want attacked — blunt responses preferred.

2 The framework in four statements

One object

A dynamical unit timelike vector field $u^\mu$ — the bulk flow of a cold dark medium. It simultaneously provides the preferred frame, the cosmic clock $\theta = \nabla\!\cdot\!u = H$, the gate variable (its proper acceleration $a^\mu = u^\nu\nabla_\nu u^\mu$), and the relaxation congruence. Forced, not chosen: any frame-free (curvature-only) gate predicts a baryonic Tully–Fisher slope of 3 and a Milky Way halo boundary at 364 kpc; both are excluded by data (§4).

One temperature

$\beta = 2\pi/H$. It sets the acceleration floor $a_0(t) = cH(t)/2\pi$, the relaxation clock $\Gamma = \beta H$ (independently measured in dwarf-galaxy data), and the thermofield split that produces the dark sector.

One substance

The medium is the imaginary-branch (CPT/thermal double) fraction of matter: $x = 1-\cos\sqrt2 = 0.844$ from a massless spin-1 axial mediator, giving $\Omega_{\rm DM}/\Omega_b = x/(1-x) = 5.41$ — derived, versus Planck's $5.36\pm0.10$. The same identity yields a cosmic baryon fraction of 0.156 (Planck: $\simeq 0.157$).

One gate

Medium modes are awake (supported, non-clustering, structurally inert) where $|a[u]| > cH(t)/2\pi$ and condensed (the dark mass) below. All structure phenomenology follows: MOND-like galaxy dynamics, dwarf thermostats, cluster reservoirs, black-hole nulls, an exactly cold-and-dark early universe.

$$ \text{Gate}_{\mathcal{A}}:\quad \begin{cases} \text{Awake (draining)} & |a[u]| > a_0(t) \\[2pt] \text{Asleep (condensed)} & |a[u]| \le a_0(t) \end{cases} \qquad a_0(t) = \frac{cH(t)}{2\pi} $$ (1)

For an ambient settled flow rotating at $v_\phi$, the gate variable is the unsupported residual of the flow — supported rotation is asleep at any $g$:

$$ |a[u]| \;=\; g - \frac{v_\phi^{2}}{R}. $$ (2)

Inputs: $G, c, \hbar, k_B$, particle masses, $\omega_b$, and $H_0$ — the CMB-calibrated expansion rate (67.4). The framework predicts the local-ladder $H_0$ excess is a measurement systematic (falsifier D11). With $\omega_c = 5.41\,\omega_b$ derived and flatness, $\Omega_\Lambda = 0.684$ is derived, not input. No interpolation function, no free profile, no per-object freedom. Exactly one number in the Galactic chain is calibrated on data it helps predict: the LBK migration efficiency $q = 0.1$ (bounded a priori to [0.1, 0.5]) — the framework's single O(1) coefficient.

Acceleration floor $a_0 = cH_0/2\pi$

1.04×10⁻¹⁰ m s⁻²

CMB frame; ratio to measured g† = 0.98 after ladder rescaling

Dark abundance $x/(1-x)$, $x = 1-\cos\sqrt2$

5.41

Planck 2018: 5.36 ± 0.10 (0.7σ)

Fitted parameters

one bounded O(1) coefficient in the MW chain

Armed falsifiers

any one confirmed kills the framework

3 Postulates

P1 (medium). Space contains a cold, dark medium of cosmological abundance, collisionless on halo scales, with a macroscopic coherence length $10^2\,\mathrm{AU} \lesssim \ell_c \lesssim 0.3$ kpc — it misses stars and binaries and dresses galaxies.

P2 (gate, running floor). Modes are awake where the ambient-equilibrium congruence's proper acceleration exceeds the epoch's floor: $|a[u]| \gtrless a_0(t) = cH(t)/2\pi$ — a rate comparison (mode frequency against bath temperature), requiring no horizon and no Killing structure, but requiring the frame $u^\mu$.

P3 (relaxation and drain). Condensed medium follows collisionless dynamics; ambient accretion and phase mixing build envelopes at the bath-clocked rate $\Gamma = \beta H$; orbits entering awake zones are re-supported and lost — an absorbing drain. Gravity is Newtonian attraction of baryons + medium; GR enters as the measured weak-field lensing of real mass.

4 Derivations

4.1 The boundary construction and MOND's constants

The condensation boundary $r_b$ is the outermost radius with $g(r_b) = a_0$; for compact baryons $r_b \simeq r_M = \sqrt{GM_b/a_0}$. Velocity continuity onto the relaxed isothermal envelope forces

$$ \sigma^2 = \tfrac{1}{2}\sqrt{G M_b\, a_0} $$ (3)

with no freedom, from which $v_\infty^4 = G M_b a_0$ (the baryonic Tully–Fisher relation with MOND's normalization) and $g = \sqrt{a_0\, g_{\rm bar}}$ in the deep regime. MOND is recovered as the effective description of a relaxed gated medium — including why no single interpolation function fits all systems.

4.2 The clock

The dwarf-envelope relaxation scale is measured to be universal in $r/r_M$ across two decades of mass (slope $-0.086$, band $[-0.186, 0.000]$). Candidate clocks separate cleanly: constant-speed fronts give slope $-0.5$ (excluded), dynamical-time transport $-0.25$ (outside the band), a cosmic-bath clock $\Gamma \propto H$ gives $0$ (inside). The medium's relaxation is timed by the cosmic bath — the framework's load-bearing empirical selection, made before the mechanism was constructed.

4.3 The frame theorems

(i) Frame-free gates are excluded: gating on curvature puts the Milky Way boundary at 364 kpc (observed: 8.3) and gives Tully–Fisher slope 3 (observed: 4). (ii) The surviving gate variable — the proper acceleration of the medium's local-equilibrium congruence — passes five limits: settled halos, the smooth background (comoving = geodesic = asleep: cold dark behavior automatic), recombination wells ($1.5\times10^{-3}$ of the epoch floor: acoustic physics inherited), horizon approach (capture outruns clustering by $\ge 10^{11}$), and the drain itself. (iii) The sixth limit: for an ambient settled flow rotating at $v_\phi$, the gate variable is the unsupported residual, Eq. (2) — medium settled into rotation within the circularity tolerance $\sigma_{\rm tol} = a_0 r/2v_c$ is asleep at any $g$. Condensed interior mass is thereby permitted, the local dark density becomes a derived consistency, and the Galactic-centre null is protected by the tolerance itself (§5.2).

4.4 The drain operator, from the postulate

P3's absorbing drain, applied to orbit families: a family with pericenter inside the awake boundary drains at its pericenter-return rate — no capture constant. An isotropic-orbit Monte Carlo in the envelope potential yields captured fractions at $r = (1.5, 2, 3, 5)\,r_b$ of $(0.62, 0.45, 0.28, 0.14)$, against $(0.60, 0.46, 0.29, 0.15)$ measured in an independent orbit experiment months earlier — few-percent agreement with no adjustable input.

4.5 The hydrostatic identity and the derived transition function

Completing the anisotropic Jeans integration for the relaxed envelope ($\rho \propto r^{-2}$; tangential temperature pinned at the critical surface; radial sector carrying the seed bath) yields the exact identity

$$ v_c^2(r) = 2\sigma_t^2\left(1 + \frac{r_M}{2r}\right), $$ (4)

from which four verified consequences: the interior transit exponent $p = 1$ is derived; a drained core of radius $r_M/2$; the composite boundary at $r = 1.366\,r_M$; and a derived transition function with zero free functions:

$$ g_{\rm obs} = \tfrac12 g_{\rm bar} + \sqrt{a_0\,g_{\rm bar}}\;\;(g_{\rm bar}\le 4a_0), \qquad g_{\rm obs} = g_{\rm bar}\;\;(g_{\rm bar} > 4a_0), $$ (5)

continuous at $4a_0$ with a derivative kink — a falsifiable feature (D16). The anisotropy profile is likewise fixed: $\beta = (+0.5, 0, -1, -4)$ at $r = (0.5, 1, 2, 5)\,r_M$ — isotropic exactly at the gate (D8).

Figure 1 · The radial-acceleration relation. All 3320 SPARC points (164 galaxies, identical conventions for every model). The derived transition function, Eq. (5) — nothing fitted — against MOND-simple and the McGaugh exponential, both evaluated at their canonical fitted $g_\dagger$. Binned RMS: 0.033 dex (derived) vs 0.027 / 0.023 (fitted). The kink at $4a_0$ is falsifier D16. Hover for values; Data shows the binned medians.

5 Confrontation with data

Identical inputs, no per-galaxy freedom. One code, both regimes: 74 sub-floor dwarfs at 0.05–0.06 dex RMS across the full envelope profile (best previous mechanism class: factor ~70 off); 49 spirals at 0.091 dex median (MOND: 0.079; Newton: 0.271).

Figure 2 · The baryonic Tully–Fisher relation. The 55 flat-selected SPARC galaxies (repo selection: last-three $V_{\rm flat}$, slope < 0.10) against the derived identity $v_\infty^4 = G M_b a_0$ — slope 4 and normalization fixed by the gate, no fit. A frame-free gate predicts slope 3 (§4.3).

5.1 Galaxies — every curve, zero dials

show MOND

Figure 3 · Rotation-curve explorer. Any of 164 SPARC galaxies: observed points with errors, the baryonic curve ($\Upsilon_\star = 0.5$, bulge 0.7), and the zero-dial 𝒜 construction — boundary at $g = a_0$, $p=1$ transit interior, isothermal envelope, Eq. (3)–(4). The same two lines for every galaxy in the sample; nothing is tuned per object.

5.2 The Milky Way — the rotating interior and the derived decline

Under a proper axisymmetric McMillan mass model, the interior transition zone demands $\sim 8.7\times10^{10}\,M_\odot$ of dark mass inside 13.5 kpc — which the absorbing drain forbids as standing traffic. The resolution is the sixth frame limit, Eq. (2): medium settled into rotation within the circularity tolerance is asleep, and condensed interior mass is permitted. Its mass and profile follow from pre-existing pieces with nothing fitted — halo spin and angular-momentum profile, bath-clocked settling, the falling floor's exact trim, a streaming cut at 2.9 kpc, and measured churning. The result: $M_{\rm int}(<13.5\,{\rm kpc}) = 8.8\times10^{10}$ vs the $8.7\times10^{10}$ required — 2 percent. One directional term completes the profile: the Lynden-Bell–Kalnajs torque at $q = 0.1$, the chain's single bounded O(1) coefficient. All eighteen bins score $\chi^2/N = 1.31$ (decline zone 0.18), with the decline onset derived at $r_{\rm tr} = 20.7$ kpc and amplitude 24.4 km/s (observed: ~19–20 kpc, 24.9 km/s). MOND on identical baryons is flat forever; NFW at the abundance-matching mass scores 3.69. Immediately: the local dark density is a derived consistency (0.38 GeV cm⁻³, measured 0.2–0.5), and the local dark medium rotates — a slow lag of ~15–30 km/s with $\sigma \simeq 57$ km/s, not an isotropic 230 km/s halo (D17: direct-detection experiments adjudicate).

Figure 4 · The Milky Way rotation curve, zero fitted parameters. Three-survey median (Eilers 2019, Jiao 2023, Ou 2024) with honest errors, against the 𝒜 composite — baryons + settled rotating component + envelope + endowment ceiling, with the LBK term at $q=0.1$ (χ²/N = 1.31) and the $q=0$ baseline — MOND and NFW on identical baryons. The decline is derived, not fitted. Toggle components below the chart.

Figure 5 · The interior component: predicted vs required. The settled rotating component's enclosed mass (derived: spin + in-halo angular momentum + bath-clocked settling + streaming cut + churning + LBK) against the dark mass the data require inside each radius.

5.3 Clusters and groups

The dispersion scale $(\tfrac12\sqrt{GM_ba_0})^{1/2}$ gives ~700–1000 km/s at Coma (observed ~1000). The total budget is the cosmic ceiling $6.41\,M_b$: within 1 Mpc the sourced anchors give $M_{\rm tot}/M_b = 5.9$–7.7 — in band — while at 1.5–3 Mpc the budget runs ×1.5–2 above it. A deficit that grows outward is precisely the two-component signature of D7: the cold unrelaxed remainder dominating the outskirts. Real hydrostatic + lensing profiles decide; we ask for pointers to the best current data (§10).

5.4 Cosmology and the running floor

Wells at recombination sit at $1.5\times10^{-3}$ of the epoch's floor: the medium is exactly cold dark matter through recombination. At BBN the medium is $7\times10^{-6}$ of the energy budget — with a sharp prediction, $\Delta N_{\rm eff} = 0$ (D15). The floor evolves as $a_0(z) = E(z)\,a_0$; the one published high-$z$ measurement (MUSE-DARK III) finds the RAR's characteristic acceleration rising with redshift — the predicted direction, with their highest bin on the $E(z)$ curve exactly. Dark energy: $w = -1$ exactly (derived from the maximal symmetry of the imaginary-time branch), with a derived drain-conversion shadow $(w_0, w_a) \approx (-1.01, -0.02)$. The DESI evolving-$w$ preference is analyzed rather than absorbed: pivot-consistent with $w=-1$ at 0.7σ, the deviation concentrated at the $z\to0$ endpoint, reproducible by a +0.055 mag low-$z$ supernova calibration slip. Prediction (D13): as calibration tightens, the fitted $(w_0, w_a)$ collapses toward $(-1.01, -0.02)$; if the DESI point sharpens instead, this framework's dark-energy sector is wrong.

Figure 6 · The running floor. The predicted $a_0(z) = E(z)\,a_0$ (normalized at the local $g_\dagger$) against MUSE-DARK III (Ciocan et al. 2026): 79 galaxies at $0.33 < z < 1.44$. Their highest bin sits on the curve exactly (2.71 vs 2.70). Convention-entangled at the ~10% level — their own $z\to0$ intercept lies 35% below the local value; replication is falsifier D4.

5.5 Black holes — the null sector

Horizons sit $10^{13}$–$10^{22}$ above the floor: the medium there is maximally awake and inert. The Galactic-centre S-star field is predicted dark-medium-free at the $\sim M_\odot$ level ($10^{-7}$–$0.4\,M_\odot$ inside the S2 orbit vs the GRAVITY 2024 bound $\lesssim 1.2\times10^3\,M_\odot$ — a null safe by more than six orders). A confirmed dark spike kills the framework; a continued null kills CDM spike models. Naked holes dress at $v_\infty = (GM_{\rm BH}a_0)^{1/4}$, truncating at the endowment ceiling — for the Milky Way the flat curve ends near ~120 kpc with a Keplerian decline beyond (D12).

6 The gate, interactive

The entire galactic construction runs from two numbers you can set: a baryonic mass and a disc scale. Everything drawn below — boundary, envelope, asymptote — follows from Eqs. (1)–(5) with nothing else.

baryonic mass $M_b$ disc scale $R_d$ Newtonian comparison

Figure 7 · The 𝒜 construction, live. An exponential-disc toy galaxy: the gate marks the boundary $r_b$ (outermost $g_{\rm bar} = a_0$), the $p=1$ transit interior fills inside it, the isothermal envelope (Eq. 3) continues outside, and the curve approaches the derived asymptote $v_\infty = (G M_b a_0)^{1/4}$. The shaded strip shows the medium's state along the radius. Drag the sliders.

7 The ledger — predictions vs observed

The scoreboard, regenerated from one command against the repo. MATCH = inside the observed error bar. Misses are parked, never dismissed and never fitted away.

observable	predicted	observed	result
Ω_DM/Ω_b	5.41	5.36 ± 0.07 (Planck 2018)	MATCH (0.7σ)
a₀ vs RAR g†	1.13×10⁻¹⁰ (ladder frame)	(1.20 ± 0.02 ± 0.24 sys)×10⁻¹⁰	MATCH (0.3σ)
a₀ from BTFR (Υ = 0.5)	1.13×10⁻¹⁰	1.33×10⁻¹⁰ (N = 55)	BAND (+0.017 dex in V)
q₀	−0.528	−0.55 ± 0.05	MATCH (0.4σ)
z_accel	0.63	0.5–0.8	MATCH
recombination wells / floor	1.5×10⁻³	must be ≪ 1	PASS — CDM inherited
a₀(z=1)/a₀(0)	1.79	1.98 (MUSE-DARK III)	MATCH ~10% (convention-entangled)
Galactic-centre dark mass < 9 mpc	2.9×10⁻⁴ M☉	≲ 1.2×10³ M☉ (GRAVITY 2024)	NULL PASS (>6 orders)
Coma dispersion	703–1003 km/s	~1000 km/s	BAND (aperture-sensitive)
RAR shape	0.019–0.024 dex	floor 0.034	MATCH
MW local dark density	0.30–0.38 GeV/cm³ (derived)	0.2–0.5	MATCH
dwarf asymptote y_max	1.00 (derived)	0.99 (stack)	MATCH
relaxation-scale mass slope	0 (bath clock)	−0.086 [−0.186, 0.000]	MATCH
74 dwarfs + 49 spirals, one operator	both sectors from one code	—	0.067 / 0.091 dex
MW composite, 18 bins	χ²/N = 1.31 (q = 0.1)	MOND 1.55 · NFW 3.69	BEST-IN-CLASS + derived decline
cluster amount	6.41 M_b (ceiling)	5.9–7.7 within 1 Mpc	BAND — outward deficit = D7 signature
w₀ vs Planck	−1.00 (derived)	−1.00 ± 0.05	MATCH
w₀ vs DESI DR2	−1.00	evolving-w preferred (2.8–4.2σ)	MISS, DOWNGRADED — the make-or-break (D13)

8 Predictions and falsifiers

Seventeen armed kill conditions. External data can kill the framework at any time; that is a feature.

#	prediction	kills the framework if…
D1	size-residual pattern, mass-dependent	raw-curve correlation < 0.01 at all masses
D2	deep lensing on the MOND line; transition excess ≤ +0.04 dex	excess absent at 0.01-dex precision
D3	wide binaries Newtonian	any confirmed anomaly
D4	a₀(z) = E(z) a₀	replication flat or thermally flattened
D5	local dark density 0.30–0.45 GeV cm⁻³ (derived consistency)	precision value outside 0.2–0.5
D6	no smooth external-field effect	smooth EFE survives systematics
D7	cluster profile = relaxed share + cold remainder	profiles reject the two-component shape
D8	anisotropy β = (+0.5, 0, −1, −4) at r = (0.5, 1, 2, 5) r_M	a measured β(r) inconsistent with this curve
D9	nuclear EMRIs are vacuum-GR	confirmed dark-dress dephasing
D10	Galactic centre dark-free at ~M☉	confirmed non-remnant extended dark mass
D11	local-ladder H₀ excess (~8%) is a measurement systematic	ladder-independent local probes converge at ~73
D12	MW truncation derived: r_tr ≈ 20 kpc, Keplerian (γ = −0.50) beyond, decline 25 km/s	DR4-class data re-flattening beyond ~30 kpc
D13	(w₀, w_a) collapses to (−1.01, −0.02) with better SN calibration	the DESI point sharpens instead
D14	at most a small decaying cosmic dipole axis	a large confirmed common axis
D15	ΔN_eff = 0	significant extra radiation detected
D16	derivative kink in the RAR at g_bar = 4a₀	transition demonstrably smooth through 4a₀
D17	the local dark medium rotates: slow lag ~15–30 km/s, σ ≈ 50–57 km/s — not an isotropic 230 km/s halo	precision direct-detection fits confirming the isotropic halo

9 Open problems — the honest ledger

The Lagrangian is no longer absent but is not finished: the action ansatz exists (an Einstein–aether-class frame, a one-scale condensate, an SSB gate whose critical surface lands at $a_0 = cH/2\pi$ exactly via the rate-crossover criterion, and a Schwinger–Keldysh drain), and the central equilibrium target is closed — thermality is direction-blind, the tangential sector rides the pure cosmic bath as a theorem, and the geometric-mean law lives in the classical hydrostatic identity. Remaining: the kinetic closure ($\Gamma = \beta H$ with the fastcool asymmetry), the stability/PPN pass, and the mediator sector — the abundance derivation rests on the spin-1 mediator reading, whose fifth-force and radiation consistency checks are open, sharpened by our own D15. The production history of the imaginary-branch fraction is not derived. Cluster and group amounts are anchor-limited. The spiral sector retains a 0.03-dex gap to a hand-tuned variant. $H_0$ at the CMB value is a falsifiable stance. Particle masses and the why-now coincidence are untouched. A full assumptions confessional (twelve items) is maintained with the project records.

10 What we ask of the reader

In order of value to us:

Break the abundance chain ($\theta=\sqrt2 \to x \to 5.41$) — it is the most suspicious-looking derived number we have.
Attack the frame theorems — is there a frame-free gate we missed?
Point us to the best cluster hydrostatic + lensing profiles and group catalogs — our anchors disagree.
Check the DESI analysis against the real likelihoods.
Tell us which existing data already falsifies something in the table above that we have not noticed.

Blunt responses preferred: wk@iatrt.com

Appendix A Reproducibility

Every number herein regenerates from standalone calculations against public inputs — SPARC rotation curves and photometry, published cluster gas models, published halo assembly histories, survey acceleration measurements, Gaia-era Milky Way rotation-curve tables and the published McMillan mass model. The full simulation archive, blow-by-blow ledger (including failures and retractions), falsifier registry, and assumptions confessional are maintained as a private repository, available to any reviewer on request. The figures on this page are generated directly from that pipeline's outputs.

Appendix B The dark-sector derivation chain

Reproduced so it can be attacked directly (ask #1). The budget clock: one conserved currency defines a local clock $\kappa = \sqrt{1-2E}$; $g_{tt} = \kappa^2$ reproduces Schwarzschild statics and the classical tests. At $E = \tfrac12$ the clock stops; for $E > \tfrac12$, $\kappa \to i\kappa$: imaginary time — the Euclidean/thermofield continuation. The imaginary-time period reproduces the Hawking temperature; closing the budget on the flat shell yields $H^2 = 8\pi G\rho/3$ — Friedmann derived, with the expansion carried by the vector as $\theta = \nabla\!\cdot\!u = H$. The abundance: branch mixing through a massless spin-1 axial mediator; gauge marginality gives mixing angle 1 per channel; two transverse polarizations in quadrature, $\theta = \sqrt{2}$:

$$ x = 1-\cos\sqrt2 = 0.844, \qquad \frac{\Omega_{\rm DM}}{\Omega_b} = \frac{x}{1-x} = 5.41 \;[\text{Planck } 5.36\pm0.10], \qquad f_b = 0.156 \;[\simeq 0.157]. $$ (6)

Dark energy: the $E > \tfrac12$ branch is maximally symmetric, forcing $w = -1$ exactly; the drain conversion supplies the small predicted shadow $(w_0, w_a) \approx (-1.01, -0.02)$. The $a_0$ coefficient and the Hubble tension: extractions of $a_0$ from galaxy data are ladder-relative ($a_0^{\rm meas} \propto h^2$, $a_0^{\rm th} \propto h$); under coherent rescaling to the CMB-calibrated $h = 0.674$ the ratio is 0.98. The $h = 0.73$ branch is excluded within the framework (the acoustic angle shifts by 1.9%, measured to 0.03%), which is why D11 predicts the local ladder carries an ~8% systematic.

Appendix C The framework on one page

$$ a_0(t) = \frac{cH(t)}{2\pi}; \quad \text{awake iff } |a[u]| > a_0(t); \quad \Gamma = \beta H; \quad \frac{\Omega_{\rm DM}}{\Omega_b} = \frac{x}{1-x},\; x = 1-\cos\sqrt2. $$

$$ r_b:\ g(r_b) = a_0; \quad \sigma^2 = \tfrac12\sqrt{G M_b(<r)\,a_0}; \quad v_\infty^4 = G M_b a_0; \quad g_{\rm deep} = \sqrt{a_0 g_{\rm bar}}. $$

Families with pericenter inside the boundary drain at their return rate; supply is capped by assembled endowment; the temperature relaxes at the bath rate toward the epoch's floor. One code then yields: dwarf envelopes at 0.05–0.06 dex, spiral curves at 0.09 dex, the measured drain kernel to few percent, mass-flatness, CDM inheritance, BBN safety, black-hole nulls, $w=-1$ with a $-0.01$ shadow, and seventeen ways to die. One object, one temperature, one substance, one gate — and one unfinished Lagrangian.

References

Galactic and principal non-Galactic anchors, verified against primary sources July 2026.

McMillan P. J., 2017, MNRAS 465, 76 [arXiv:1608.00971] — Milky Way baryonic mass model; $v_c(R_0) = 232.8\pm3.0$ km/s; $\rho_{\rm DM,\odot} = 0.38\pm0.04$ GeV cm⁻³.
Eilers A.-C., Hogg D. W., Rix H.-W., Ness M. K., 2019, ApJ 871, 120 — MW circular velocity curve, $v_c = 229.0 - 1.7\,(R - 8.122)$.
Jiao Y., Hammer F., et al., 2023, A&A 678, A208 [arXiv:2309.00048] — detection of the Keplerian decline, 19.5–26.5 kpc.
Ou X., Eilers A.-C., Necib L., Frebel A., 2024, MNRAS 528, 693 — declining outer curve, red-giant sample.
Bullock J. S., et al., 2001, ApJ 555, 240 — halo spin $\bar\lambda' \simeq 0.035$; universal angular-momentum profile, typical $\mu = 1.25$.
Frankel N., et al., 2020, ApJ 896, 15 — radial migration (churning) ~3 kpc over 6 Gyr.
Portail M., Gerhard O., Wegg C., Ness M., 2017, MNRAS 465, 1621 — bar pattern speed $\Omega_p = 39.0\pm3.5$ km s⁻¹ kpc⁻¹; corotation at $6.1\pm0.5$ kpc.
Sellwood J. A., Binney J. J., 2002, MNRAS 336, 785 — churning at fixed circularity.
Lynden-Bell D., Kalnajs A. J., 1972, MNRAS 157, 1 — the directional torque.
Correa C. A., Wyithe J. S. B., Schaye J., Duffy A. R., 2015, MNRAS 450, 1514 [arXiv:1409.5228]; McBride J., Fakhouri O., Ma C.-P., 2009, MNRAS 398, 1858 [arXiv:0902.3659] — halo assembly histories.
Planck Collaboration VI, 2020, A&A 641, A6 — $\omega_c/\omega_b = 5.36\pm0.07$.
GRAVITY Collaboration (Abd El Dayem K., et al.), 2024, A&A 692, A242 [arXiv:2409.12261] — extended mass within the S2 apocenter $\lesssim 1.2\times10^3\,M_\odot$ (1σ).
Ciocan B. I., Bouché N. F., et al. (MUSE-DARK III), 2026, A&A 709, L16 [arXiv:2604.22613] — evolution of the RAR at $0.33 < z < 1.44$; $a_0(z\!\sim\!1) = (2.38\pm0.10)\times10^{-10}$ m s⁻².
DESI Collaboration, 2025, Phys. Rev. D 112, 083515 [arXiv:2503.14738] — DR2 BAO; evolving-$w$ preferred at 2.8–4.2σ across SN compilations.
Hughes J. P., 1997, in A New Vision of an Old Cluster: Untangling Coma Berenices [astro-ph/9709272] — Coma mass $(6.2\pm0.9)\times10^{14}\,M_\odot$ within 1 Mpc, luminous fraction 13–17%; Gonzalez A. H., Sivanandam S., Zabludoff A. I., Zaritsky D., 2013, ApJ 778, 14; Laganá T. F., et al., 2013, A&A 555, A66 — cluster baryon budgets.
McGaugh S. S., Lelli F., Schombert J. M., 2016, PRL 117, 201101 — the RAR; $g_\dagger = 1.20\times10^{-10}$ m s⁻²; Lelli F., McGaugh S. S., Schombert J. M., 2016, AJ 152, 157 — the SPARC database.
Schönrich R., Binney J., Dehnen W., 2010, MNRAS 403, 1829 — solar peculiar velocity.
Kuijken K., Gilmore G., 1991, ApJ 367, L9; Bovy J., Rix H.-W., 2013, ApJ 779, 115 — vertical surface density.
Deser S., Levin O., 1997, Class. Quantum Grav. 14, L163 — accelerated detectors in de Sitter (the temperature quadrature).
Read J. I., 2014, J. Phys. G 41, 063101 — the local dark-matter density.
Chae K.-H., 2024 [arXiv:2402.05720]; Banik I., et al., 2024, MNRAS 527, 4573; Cookson S., Banik I., El-Badry K., et al., 2026, MNRAS 547 [arXiv:2602.24035] — the wide-binary dispute (falsifier D3 watch).

\(\mathcal{A}\): A Thermally Gated Dark Medium on a Dynamical Time Vector