The Soliton Wake: Exploring RBH-1 as a Temporal Topology Candidate

1. Introduction: The RBH-1 Anomaly

Note: This paper does not calibrate TEP and is not part of the primary evidence chain. It applies existing TEP calibrations from terrestrial GNSS data (Smawfield 2025g) as a consistency check on an astrophysical candidate.

In December 2025, JWST spectroscopy confirmed the existence of the first candidate runaway supermassive black hole. Designated RBH-1, this object has an inferred mass of approximately $10^7 M_\odot$ and a proper motion of $v_{\bullet} = 954^{+110}_{-126}$ km/s, leaving behind a 62 kpc linear feature of active star formation. The discovery is consistent with theoretical predictions that supermassive black holes can be ejected from their host galaxies via gravitational wave recoil following a black hole merger (van Dokkum et al. 2025; Campanelli et al. 2007).

At $z \approx 0.96$, RBH-1 appears as a luminous streak extending from the galaxy RCP 28 in the constellation Sextans. A bow-shaped interaction region marks its leading edge, while the wake exhibits active star formation along its entire extent.

The Observational Puzzle

While the confirmation of RBH-1 as a runaway black hole is itself remarkable, the object presents a deeper observational anomaly. It appears as a linear streak of light extending 62 kpc ($\sim$200,000 light-years) from a distant galaxy ($z\approx 0.96$). At its tip lies a bright, bow-shaped interaction region where JWST spectroscopy reveals a sharp kinematic discontinuity: a line-of-sight velocity change of order $\sim 600$–$650$ km/s across $\sim$1 kpc (van Dokkum et al. 2023; van Dokkum et al. 2025).

In a purely hydrodynamic picture, a compact perturber moving at $v \sim 10^3$ km/s through circumgalactic gas would be expected to drive a strong bow shock and turbulent wake, producing post-shock temperatures of order $10^7$ K and associated hot-phase emission. RBH-1 instead exhibits a narrow, structurally coherent wake whose line diagnostics are consistent with gas cool enough to support ongoing star formation. This creates a fundamental quantitative tension.

Taken together, the kinematics and thermodynamic diagnostics suggest a large perturbation with limited thermalization. The following sections frame this tension through two related problems: the Temperature Paradox and the Geometry Problem.

The Cooling Bottleneck

A bow shock at $v_s \sim 10^3$ km/s corresponds to Mach numbers $\mathcal{M} \gg 1$ in typical circumgalactic conditions. Standard Rankine–Hugoniot jump conditions mandate substantial conversion of bulk kinetic energy into thermal energy. For $v_s \approx 1000$ km/s, the characteristic post-shock temperature is:

At this temperature, thermal pressure strongly suppresses gravitational collapse. Since the Jeans mass scales as $M_J \propto T^{3/2}$, raising the temperature from $100$ K to $10^7$ K increases the characteristic collapse mass scale by a factor of $10^{7.5}$ ($\sim 3\times 10^7$), making in-situ star formation in recently shocked gas difficult without highly efficient cooling.

The Cooling Bottleneck ($t_{\mathrm{cool}} \gg t_{\mathrm{dyn}}$)

The standard resolution invokes rapid radiative cooling, potentially aided by turbulent mixing or thermal instabilities (e.g., Gronke & Oh 2018). However, the viability of this mechanism is quantitatively constrained by the cooling physics. The following calculation demonstrates that under fiducial CGM conditions and standard optically thin cooling, the single-phase thermal shock model faces a severe radiative-cooling timescale tension.

Bremsstrahlung Cooling Time

The thermal energy density of a fully ionized plasma is $E = (3/2) n k_B T$, and the radiative cooling rate per volume is $\dot{E} = n^2 \Lambda(T)$, where $\Lambda(T)$ is the cooling function. At $T \sim 10^7$ K, cooling is dominated by free-free (Bremsstrahlung) emission with contributions from metal-line cooling, yielding $\Lambda(T) \approx 2.5 \times 10^{-23}$ erg cm$^3$ s$^{-1}$ for solar metallicity (Sutherland & Dopita 1993). The cooling time is:

Substituting the post-shock temperature $T = 1.4 \times 10^7$ K and a post-shock density $n = 0.1$ cm$^{-3}$ (this high value is adopted as a conservative upper bound for a compressed/clumpy phase, distinct from the ambient CGM mean $n_{\rm CGM} \sim 10^{-3}$ cm$^{-3}$; note that since $t_{\rm cool} \propto 1/n$, lower densities would yield even longer cooling times):

Dynamical Timescale

The relevant comparison timescale is the sound-crossing time of the wake. The post-shock sound speed for a fully ionized plasma ($\gamma = 5/3$, mean molecular weight $\mu = 0.6$) at $T = 1.4 \times 10^7$ K is:

For the observed wake radius $w \approx 0.7$ kpc (van Dokkum et al. 2025), the dynamical timescale is:

The Critical Inequality

Comparing these timescales yields the fundamental constraint:

This inequality is robust across the plausible parameter space. Sensitivity analysis shows that only at densities $n \gtrsim 1$ cm$^{-3}$ (an order of magnitude higher than typical circumgalactic values) does the ratio approach unity. While dust-gas collisional cooling can shorten timescales in some environments, high-velocity shocks ($v \sim 1000$ km/s) efficiently destroy dust grains via sputtering (Draine & Salpeter 1979), reducing the efficacy of this pathway in the immediate post-shock region. For fiducial parameters, shock-heated gas at $10^7$ K would expand and rarefy long before radiating sufficient energy to reach star-forming temperatures ($T \lesssim 10^4$ K).

The Observational Verdict

Yet the RBH-1 wake exhibits active star formation immediately behind the apex. The observed stellar continuum colors are "well-fit by a simple model that has a monotonically increasing age with distance from the tip" (van Dokkum et al. 2023)—the youngest stars are at the tip, not 35 kpc behind it where the cooling delay would place them. This creates a fundamental tension:

• If the gas was heated to $10^7$ K, it cannot cool fast enough to form stars ($t_{\rm cool}/t_{\rm dyn} \approx 30$).
• If the gas was never heated, the observed $\sim 650$ km/s velocity discontinuity cannot arise from a collisional shock.

Standard hydrodynamic resolutions require invoking multiple mechanisms simultaneously: magnetic draping to suppress turbulence (explaining the 50:1 aspect ratio), turbulent mixing to bypass the cooling bottleneck (explaining the cold wake), and non-equilibrium ionization to reconcile line ratios (explaining anomalous preshock temperatures). Critically, these mechanisms are dynamically antagonistic—magnetic draping creates the laminar sheath that suppresses the turbulent mixing required to solve the cooling problem.

This motivates considering a non-thermal driver. It is proposed that the observed velocity discontinuity ($\sim 650$ km/s) may reflect coherent acceleration by a proper-time gradient—a metric shock in the dynamical, rather than endpoint-redshift, sense. The resolved centroid span is then real bulk motion organized by Temporal Shear, while the much smaller local line dispersion measures random and unresolved differential motion. A conservative scalar body force can separate those first and second moments without identifying the full centroid span with thermal energy.

The Geometry Problem

The wake's geometry is also nontrivial. Hydrodynamic wakes generally broaden with distance: drag induces turbulence, and Kelvin–Helmholtz instabilities disrupt linear features, causing them to widen and disperse over time. Yet, the RBH-1 wake remains needle-thin and coherent over $\sim$200,000 light-years. It does not broaden as a typical turbulent wake; it remains exceptionally collimated.

This linearity has motivated alternative interpretations, including the possibility that the feature is a thin, edge-on galaxy (Sanchez Almeida et al. 2023). However, the extreme velocity gradient at the tip favors a localized interaction at the apex.

Implications

The coexistence of a large kinematic discontinuity and weak thermalization creates a cooling bottleneck ($t_{\mathrm{cool}} \gg t_{\mathrm{dyn}}$) that places simple single-phase hydrodynamic bow-shock interpretations under quantitative tension. Section 2 establishes the theoretical framework for the candidate soliton/wake interpretation. Section 3 develops the quantitative forward model for the metric shock. Section 4 confronts this model with the observational data (line widths, wake geometry, star formation). Section 5 outlines explicit falsification criteria for the soliton interpretation. Section 6 discusses implications for dark matter, and Section 7 concludes.

2. Theoretical Framework: The Soliton/Wake Interpretation

The driver of the RBH-1 wake may include a propagating structure in spacetime itself — explored here as a candidate Temporal Topology soliton/wake.^† This would be a coherent region of altered proper-time rate moving with the compact object (consistent with non-topological soliton solutions; see Kusenko 1997). Universal coupling makes the associated Temporal Shear dynamically active: as the structure traverses a gas cloud, matter experiences the conservative acceleration $\mathbf a_\phi=-c^2\boldsymbol\nabla\ln A$. The proposed distinction from a collisional shock is therefore coherent body-force acceleration rather than force-free refraction.

^† Terminology note: Here, "soliton" refers specifically to a non-topological defect in a scalar field (a Q-ball or oscillon analog) that saturates at a finite density $\rho_T$, distinct from the vacuum singularity solutions of pure General Relativity. While Schwarzschild and Kerr black holes are sometimes called "gravitational solitons" in the mathematical sense of stationary, localized solutions, the objects considered here have no event horizon and are characterized by a finite core density rather than a central singularity. Two distinct existence questions should not be conflated: the configuration invoked here is matter-sourced — bound to the compact object as its temporal well — so its existence reduces to a forced boundary-value problem, to which self-binding (Derrick-type) obstructions for free field lumps do not apply; the Q-ball/oscillon language is morphological analogy only. The forced problem is solved directly under the corpus's canonical scalar sector later in this section.

Phenomenology of the Time Lens

In this framework, RBH-1 acts as a moving proper-time potential. Inside the candidate profile, time flows more slowly relative to the ambient background ($d\tau < dt$). The spatial variation of that rate is physical: in the weak-field matter metric it accelerates gas according to $\mathbf a_\phi=-c^2\boldsymbol\nabla\ln A$. The observed position–velocity span is therefore assigned to coherent Doppler motion generated by Temporal Shear, not to a force-free apparent redshift.

The soliton is treated here as an effective phenomenological description—a macroscopic "texture" in spacetime. One theoretical realization arises from the bi-metric scalar-tensor structure of TEP (Smawfield 2025a, 2025g), where the gravitational metric $g_{\mu\nu}$ governs curvature while an effective matter metric $\tilde{g}_{\mu\nu}$ encodes the local proper-time rate. This implies a decoupling where kinematics (driven by $\tilde{g}_{\mu\nu}$) can be strong while lensing — sourced only by the scalar's distributed stress-energy in $g_{\mu\nu}$, suppressed by $\Delta\ln A/4$ relative to the apparent kinematic mass (§4) — remains weak. While this decoupling appears to violate the Equivalence Principle in its standard GR formulation, it is a known feature of bi-metric theories where matter and light couple to different effective metrics (e.g., Disformal Gravity models). This paper does not attempt to resolve this theoretical tension from first principles but instead tests whether the phenomenology matches the RBH-1 anomaly.

The characteristic density $\rho_T \approx 20$ g/cm³, which governs the temporal scale, is not a free parameter in this analysis. It is an external input derived from terrestrial constraints in the companion "Temporal Topology Saturation Scale" paper (Smawfield 2025g). This analysis tests whether this specific value, calibrated on Earth, correctly predicts the wake properties of a distant supermassive black hole.

The characteristic temporal scale $R_T$, while calibrated from terrestrial geodetics, operates here as the astrophysical geometric realization of the abstract environmental operator $\mathcal{S}_\Sigma(\mathcal{E})$. Modeling the RBH-1 wake as a candidate Temporal Topology soliton uses this geometric saturation profile to trace the continuous un-screening of the temporal shear field behind the metric shock, distinguishing it fundamentally from standard bulk thermalization models.

Forward Model: From Field Gradient to Coherent Velocity Flow

To move beyond qualitative description, the explicit mapping between the scalar field profile and the observed kinematic signatures is defined below. This "Forward Model" predicts how a metric soliton mimics a hydrodynamic shock.

Endpoint Transport and Matter Dynamics

In the TEP framework, the canonical causal matter metric $\tilde{g}_{\mu\nu}=-A_{\rm loc}^2(u_{\rm grav}(\mathbf x))U_\mu U_\nu+A_{\rm sp}^2(u_{\rm drift}(t,\mathbf x))\Pi_{\mu\nu}+B(\phi)\Pi_\mu^\alpha\Pi_\nu^\beta\nabla_\alpha\phi\nabla_\beta\phi$ ($U_\mu\equiv-\nabla_\mu\bar\phi/\sqrt{2\bar X}$, $\Pi_{\mu\nu}=g_{\mu\nu}+U_\mu U_\nu$; Paper 0, §2.2, Step 80) is related in the local clock projection to the gravitational metric $g_{\mu\nu}$ by the scalar function $A(\phi)$. The proper time interval $d\tau$ for a comoving observer is related to the coordinate time $dt$ by: \begin{equation} \label{eq:proper_time} d\tau = A(\phi) dt \end{equation}

An emitter resident on a different conformal plateau from the observer has the endpoint clock ratio \begin{equation} \label{eq:metric_redshift} 1 + z_{\text{metric}} = \frac{\nu_0}{\nu_{\text{obs}}} = \frac{1}{A(\phi)} \end{equation}

A conformal profile encountered only in the middle of the photon path contributes no additional open-path shift beyond this endpoint ratio. More importantly for a propagating soliton, the same spatial profile cannot leave universally coupled gas static. Expanding the matter geodesic in the nonrelativistic limit gives \begin{equation} \label{eq:matter_acceleration} \mathbf a_\phi=-c^2\boldsymbol\nabla\ln A, \qquad \Delta\!\left(\frac{u^2}{2}\right)=-c^2\Delta\ln A , \end{equation} where $u$ is the gas speed in the rest frame of a quasi-steady field profile. The endpoint and dynamical assignments are therefore not interchangeable. Assigning $\Delta v=650$ km s$^{-1}$ to $|\Delta\ln A|\simeq\Delta v/c$ predicts a traversing-matter speed $c\sqrt{2|\Delta\ln A|}\simeq1.97\times10^4$ km s$^{-1}$ and is excluded internally. The consistent branch assigns the measured span to coherent matter motion: \begin{equation} \label{eq:dynamical_depth} |\Delta\ln A|_{\rm dyn}=\frac{|u_{\rm out}^2-u_{\rm in}^2|}{2c^2}=\frac{\bar u\,|\Delta u|}{c^2}\equiv\eta\frac{\Delta v^2}{2c^2}. \end{equation} Here $\eta\equiv2\bar u/\Delta v$ records the explicitly chosen flow frame. The rest-entry normalization has $\eta=1$ and $|\Delta\ln A|=2.35\times10^{-6}$. As a translating-profile benchmark, ambient gas initially at rest in the host frame and accelerated collinearly with the published $v_\bullet=954$ km s$^{-1}$ pattern has profile-frame speeds 954 and 304 km s$^{-1}$, giving $\eta=1.94$ and $|\Delta\ln A|=4.55\times10^{-6}$. The measured two-dimensional velocity field will determine $\eta$ rather than leaving the frame implicit.

Predicting the Velocity Discontinuity

A critical distinction must be made between the core radius and the transition radius. The temporal scale $R_T \sim 7.8 \times 10^7$ km ($\approx 2.5\times10^{-9}$ kpc) is the fundamental geometric scale where the field saturates (derived from $\rho_T$). However, because the Temporal Topology is flattened in the deep density well of the compact object, the local Temporal Shear (field gradient) is strongly suppressed in the core region. The observable kinematic effects therefore manifest at the transition radius $R_{\rm trans} \sim 0.1$–$1$ kpc, where the Temporal Shear recovers continuously from its suppressed value.

The separation between these scales is parametrized explicitly as $R_{\rm trans} = \xi\,R_T$, and the data fix the prefactor: the observed $\sim 1$ kpc onset requires $\xi \approx 4\times10^{8}$ (range $4\times10^7$–$4\times10^8$ over the quoted 0.1–1 kpc interval). For comparison, the constant-density screening ansatz of Paper 6 — shear recovery where the enclosed mean density of the dynamically equivalent halo ($M_{\rm eff} \sim 4.9\times10^{10}\eta M_\odot$, Box 3.1) falls to $\rho_T$ — would place the transition at $\xi_\rho \approx 13.5\eta^{1/3}$, i.e. $\sim 7\eta^{1/3}$ AU. The measured onset therefore sits $\sim 3\times10^{7}\eta^{-1/3}$ times beyond the naive recovery radius: the shear-recovery profile is far broader than a constant-density reading, and the transfer function relating the saturation scale to the resolved onset is quantified rather than assumed. Equivalently, a recovery length $\ell \sim R_{\rm trans} \sim 1$ kpc corresponds to an effective field mass $m_{\rm eff}c^2 = \hbar c/\ell \approx 6.4\times10^{-27}$ eV — the scale the field solution must supply. In the TEP framework, the continuous spatial profile of the scalar field governs this transition. The observed position–velocity structure constrains the work integral of $A(\phi)$ across that boundary.

Existence of the required configuration under the canonical scalar sector is not a free-soliton question. The configuration is matter-sourced — the profile is bound to the compact object — so it is a forced boundary-value problem, and the Derrick-type obstructions that forbid static localized solutions of the source-free real-scalar equation do not apply. Solving the unit-term kinetic benchmark $P(X,\phi)=X-V+X|X|/\Lambda_X^{4}$ on the static spherical branch gives the flux-conserving profile $s\,[1+(s/\Sigma_{\rm bg})^{2}]=2\beta_A^{2}GM/(c^{2}r^{2})$ for the observable shear $s=|\nabla\ln A|$, with the shear floor $\Sigma_{\rm bg}=H_0/c$ and threshold $g_t=cH_0/(2|\beta_A|)$ fixed cosmologically rather than fitted (Paper 0, master-action closure), while on Paper 0's selected two-branch kinetic sector $P_{,X}=k\sqrt{\xi}+2\xi$ ($k=16.03$, zero free parameters; step_02_soliton_existence.json) the low-gradient tail transitions to a logarithmic potential $s_{\rm tb}(r)\propto r^{-1}$, enhancing the exterior shear at $r=1$ kpc by $3.28\times$ and at $r=10$ kpc by $32.8\times$ relative to the unit-term profile ($V_{\rm circ}(1\text{ kpc}) = 25.1\text{ km s}^{-1}$). For the baryonic mass alone this returns a localized, positive, monotonic halo with a stiff $r^{-2/3}$ interior branch and a shear-recovery radius $R_s=\sqrt{GM/g_t}\approx90$ pc — within an order unity factor of the resolved onset band, and moving into it ($R_s\propto\sqrt M$) for a sourcing strength above the baryonic mass. The interior amplitude sector independently saturates at the corpus quartic equilibrium, $\varphi_{\min}(\rho_T)\simeq6.9\times10^{-9}$ on the operative Cassini-compatible branch ($\lambda = 7.5\times10^{-66}$; the earlier $\lambda_{\rm ref} = 7.5\times10^{-71}$ point, giving $3.2\times10^{-7}$, fails the corrected Cassini evaluation, Paper 6 Appendix C). Because the halo relaxes on its light-crossing time $R_s/c\approx300$ yr — four orders of magnitude faster than the $\sim$Myr gas transit — the moving object adiabatically carries its well, and no metastability timescale is required of the configuration. The halo depth delivered by the bare baryonic charge, $7.9\times10^{-8}$ integrated across the $62$ kpc wake ($8.7\times10^{-8}$ with the swept CGM envelope), is supplemented at the observational level by the stellar-envelope/line-inference response scale $\rho_T/\langle\rho\rangle$ established in Paper 11 Step 62: the existence of the configuration class is thereby established under the selected action, while the full $650\text{ km s}^{-1}$ velocity span reflects the combined dynamical and response-depth normalization $\alpha_{\rm RBH,eff}$ (Box 2.2). (Existence audit: Reproducibility, step 02.)

For bookkeeping against the baryonic potential, define the operational response $\alpha_{\text{RBH,eff}}$ by $|\Delta\ln A|=\alpha_{\text{RBH,eff}}GM/(R_{\rm trans}c^2)$. In the rest-entry normalization the work integral gives

Predicting Line Widths (The Discriminator)

The key distinction lies in the second moment of the line distribution (line width).

• Thermal Shock: The velocity jump comes from chaotic thermalization. The line width $\sigma$ is dominated by thermal broadening: $\sigma_{\text{th}} \propto v_{\text{shock}}$. For $v \sim 1000$ km/s, $\sigma \sim 100$ km/s.
• Metric Shock: The velocity jump comes from a coherent potential gradient. The line width is dominated only by the gradient variation across the telescope beam width plus the intrinsic cold-gas thermal width: \begin{equation} \label{eq:line_width} \sigma_{\text{obs}}^2 = \sigma_{\text{th,cold}}^2 + \sigma_{\text{grad}}^2 + \sigma_{\text{inst}}^2 \end{equation} Since the gas can remain cold ($T \sim 10^4$ K, $\sigma_{\text{th}} \sim 10$ km/s) while sharing an ordered velocity field, the predicted local line width is narrow ($\sigma \ll \Delta v$). The published 31 km s$^{-1}$ dispersion and the 650 km s$^{-1}$ resolved span are distinct observables; their ratio constrains field non-uniformity only where the emitting components are shown to be co-spatial.

Prediction: the dynamical metric-shock model predicts a large resolved centroid gradient with small local dispersion where the Temporal Shear is coherent. If the 31 km s$^{-1}$ component samples the same flow, $\sigma/\Delta v=0.048$ and the corresponding rms depth non-uniformity is bounded at approximately $2\sigma/\Delta v\simeq0.095$.

Thermodynamics of a Metric Shock

The relevant distinction is not momentum transfer versus no momentum transfer, but ordered work versus microscopic thermalization. A standard collisional shock converts a substantial fraction of bulk kinetic energy into random motion. Temporal Shear supplies a conservative body force; it can generate a spatially resolved bulk flow while contributing little local dispersion when the profile is coherent. Heating then arises only from differential acceleration, collisions, or streamline crossing, and is independently tested by the line profile and ionization diagnostics.

1. Resolved kinematics: the gas acquires a real, coherent velocity field through the work integral of the scalar potential.
2. Local thermodynamics: the random component can remain small if the gradient is smooth across each emitting element; the same scalar sector lowers the threshold for gravitational collapse, as derived below.

The key point is that the Jeans-mass reduction is a derived consequence of the screened scalar-charge sector — the Einstein-frame anomalous attraction — not an ad hoc assumption. Its magnitude is set by the environment-dependent scalar charge $\alpha_{\rm eff}$, which is tied to the same field configuration constrained by the observed velocity discontinuity and the saturation scale.

The measured $\sim 600$–650 km s$^{-1}$ span is therefore retained as bulk flow, but its energy source is reassigned to the Temporal-Shear work integral rather than to an endpoint clock offset. The translational speed $v_{\bullet} = 954$ km s$^{-1}$ remains a measured boundary condition, not a field-theoretic output; it sets the wake age $t_{\rm wake} \sim L/v_{\bullet} \sim 70$ Myr and encounter geometry. The two velocities remain distinct: $v_{\bullet}$ describes the compact object's ballistic motion, while $\Delta v$ constrains the scalar profile's integrated dynamical depth.

The Discriminator: How can these models be distinguished? The primary discriminant is the line profile.
In a thermal shock where the emitting gas is predominantly hot, a large velocity change ($v$) implies a high temperature ($T \propto v^2$), which broadens spectral lines via thermal Doppler motion ($\sigma_v \propto \sqrt{T}$). Even in multiphase scenarios where [O III] arises from cooler zones, a substantial hot-phase contribution should produce detectable broad wings.
In a dynamical metric shock, the velocity change is an ordered bulk-flow gradient. The local centroid changes with position, while the line width remains narrow if differential acceleration inside each resolution element is small.

While the model is qualitatively attractive, it requires quantitative verification. If RBH-1 is a soliton, it must have a specific size. The next section tests this by applying a mass-radius scaling law derived from a completely independent source: terrestrial clocks.

3. Quantitative Predictions: Testing the Dynamical Metric Shock

The metric-shock hypothesis proposes that the observed resolved velocity span Δv ~ 650 km/s is coherent matter motion generated by a spatial gradient in the conformal factor A(φ), which relates the matter metric to the gravitational metric via $\tilde{g}_{\mu\nu} = A^2(\phi) g_{\mu\nu} + B(\phi)\nabla_\mu\phi\nabla_\nu\phi$ (conformal limit for this analysis). This section derives the required field parameters and checks for internal consistency.

A distinction is maintained throughout between geometry and amplitude. The temporal scale (and associated geometric scaling) is fixed a priori by $\rho_T$ (Paper 6), while the magnitude of the coherent kinematic discontinuity depends on screening/transition physics through the effective coupling at $R_{\text{trans}}$ and is therefore treated here as an empirical constraint rather than an independent free fit.

Table 2: Model Inputs vs. Predictions

Transport-Consistent Conformal Factor Gradient

The resolved position–velocity structure runs from approximately $-600$ to $+50$ km s$^{-1}$ across 1 kpc, giving $\Delta v=650$ km s$^{-1}$. The former endpoint assignment converted this linearly to $|\Delta\ln A|\simeq\Delta v/c$. That conversion applies to a stationary emitter and observer on different conformal plateaux; it cannot describe gas traversing the same profile. Universal matter coupling instead gives

The endpoint depth $\ln(1+\Delta v/c)=2.166\times10^{-3}$ would therefore accelerate matter from rest to $1.973\times10^4$ km s$^{-1}$, 30.4 times the observed span. In the rest frame of a quasi-steady profile, let $u$ denote the gas speed and define $\eta=2\bar u/\Delta v$. The dynamically consistent depth is then

Rest entry gives $\eta=1$. A collinear translating-profile benchmark using the published 954 km s$^{-1}$ pattern speed gives profile-frame entry and exit speeds 954 and 304 km s$^{-1}$, hence $\eta=1.94$ and $|\Delta\ln A|=4.55\times10^{-6}$. Across 1 kpc the rest-entry normalization gives $|\nabla\ln A|=7.62\times10^{-26}$ m$^{-1}$ and $|a_\phi|=6.85\times10^{-9}$ m s$^{-2}$. A Newtonian fit reads the same acceleration as $M_{\rm app}=4.91\times10^{10}\eta M_\odot$ at 1 kpc. On the canonical kinetic branch, the shell ledger gives $E_{\rm scalar}=(|\Delta\ln A|/4)M_{\rm app}=2.89\times10^4\eta^2M_\odot$ and $M_{\rm app}/E_{\rm scalar}=1.70\times10^6/\eta$. Relative to the discarded endpoint assignment, the rest-entry depth falls by a factor 921 and the canonical gradient energy by $8.49\times10^5$; the pattern-speed benchmark gives factors 476 and $2.27\times10^5$, respectively. These values are generated by the registered transport-consistency step.

Lensing and Kinematic Signatures

A critical prediction of the conformal scalar-tensor framework is the quantitative asymmetry between matter response and scalar stress-energy. The scalar field $A(\phi)$ generates coherent matter acceleration through the matter metric. Light follows the gravity metric $g_{\mu\nu}$, which is sourced by the total stress-energy — the baryonic mass plus the scalar contribution evaluated above. At the dynamical depth its projected canonical surface density is $\Sigma_{\rm scalar}=2.30\times10^{-3}\eta^2 M_\odot\,{\rm pc^{-2}}$ for the stated shell geometry, far below a cosmological strong-lensing critical density. The scalar-gradient contribution to lensing is therefore negligible on this branch, while the compact baryonic deflection remains.

For light passing through the wake boundary ($b \sim 1$ kpc), the compact deflection angle depends only on the baryonic mass $M \approx 2 \times 10^7 M_\odot$:

This value ($\sim 0.8$ milliarcseconds) is far below current observational limits (HST resolution $\sim 50$ mas).

Under the dynamical metric-shock interpretation the offset is real bulk motion. Universal coupling predicts the same local acceleration for gas and collisionless tracers at the same spacetime point, while hydrodynamic drag acts directly only on the gas. Newly formed stars should therefore inherit the local gas centroid at formation:

The decisive observable is the gas–star velocity relation along the wake: a universal metric force predicts a composition-independent acceleration law and a formation-epoch imprint in the stars, whereas ram pressure and turbulent entrainment permit systematic gas–star slip. Spatially resolved absorption and emission spectroscopy can test this relation directly.

Screening and Parameter Consistency

The above estimates assume the scalar field profile is governed by continuous Temporal Topology, where the local field gradient (Temporal Shear) is suppressed in deep density wells. The phenomenological scaling ansatz (detailed in Smawfield 2025e) is adopted:

Unlike traditional chameleon mechanisms that invoke discrete thin-shell boundaries with sharp density cutoffs, TEP screening operates through continuous field gradient flattening. The Temporal Shear is gradually suppressed in deep potential wells, avoiding the fine-tuning problems of thin-shell approximations while maintaining Temporal Shear suppression in steep ambient landscapes.

This $S$ is a coupling ratio—the bare coupling $\beta_0$ divided by the screened effective coupling $\alpha_{\text{RBH,eff}}$—and should not be conflated with the clock-amplitude response factor of Paper 6, $S_A = (\bar{\rho}/\rho_T)^{1/3}$, a radius ratio evaluated at a body's mean density. The two share the $(\rho/\rho_T)^{1/3}$ saturation scaling but are distinct quantities.

For RBH-1 at the crossover mass (M ~ 10⁷ M_☉, ρ ~ ρ_T ~ 20 g/cm³), the suppression factor is S ~ 1, meaning the Temporal Shear is near the transition between strongly flattened and asymptotically recovered profiles. This is consistent with the object being a "soliton" where the field saturates at the characteristic density. Two distinct uses of $\alpha_{\rm eff}$ must be kept separate: in the screening ansatz the effective charge is the response channel's screened coupling, and S ~ 1 at the crossover asserts that the shear profile transitions there — a statement about where the field flattens, not about its amplitude. In the velocity-discontinuity constraint (Box 2.2), $\alpha_{\rm RBH,eff} = 2.46\times 10^{3}\eta$ is the linear-response equivalent of the observed dynamical depth; read literally as a coupling ratio, S = $\beta_0/\alpha_{\rm eff}$ at S ~ 1 would require the bare response $\beta_0$ itself to carry the same $\sim 10^{3}$ amplification — the corpus's open response-normalization question (shared with $\kappa_{\rm Cep}$, $\kappa_{\rm MSP}$ and $\beta_{A,\rm eff}$), stated here explicitly rather than absorbed into the ansatz.

At higher densities (e.g., white dwarfs, neutron stars), S >> 1, and the Temporal Shear is suppressed below observational limits, explaining why precision GR tests show no deviation. At lower densities (e.g., galaxies), S < 1, and the scalar field produces the dynamical anomaly inferred as "phantom mass" under Newtonian bookkeeping (detailed in the companion paper, Smawfield 2025e).

5. Falsification Criteria

This paper treats the characteristic density $\rho_T \approx 20$ g/cm³ as a fixed input derived in Paper 6. This makes the RBH-1 analysis a consistency check: the model does not have the freedom to fit the temporal scale; it must match the geometric scale dictated by the $10^7 M_\odot$ mass and the universal density. Two bookkeeping facts delimit what the check establishes. First, $R_T \approx 2.5 \times 10^{-9}$ kpc lies $\sim 8.6$ orders of magnitude below the resolved scale at $z \approx 0.96$ ($\sim 1$ kpc per $0.1''$): the comparison $R_T \approx 1.3\,R_S$ is a theory-internal scale coincidence — the crossover mass at which the constant-density temporal-topology radius meets the horizon radius — not a match to a resolved feature. The observable kinematic onset lives at the transition radius $R_{\rm trans} \sim 0.1$–$1$ kpc, parametrized in Section 2 as $R_{\rm trans} = \xi\,R_T$ ($\xi \approx 4\times10^8$) and anchored physically by the two-branch exterior shear-recovery radius $R_s = \sqrt{GM/g_t} \approx 90$ pc. Second, the anchor itself carries product-level systematic scatter far larger than its formal uncertainty: propagating the measured calibration ensemble through the check (below) places the object's candidacy inside that systematic rather than cleanly past the falsification boundary.

The Soliton Size Prediction

Given $\rho_T \approx 20$ g/cm³ (from Paper 6), the consistency check for the temporal scale of RBH-1 ($M \approx 2 \times 10^7 M_\odot$) yields:

Uncertainty Propagation

The check uncertainty derives from two inputs: the mass estimate and the characteristic density. For the mass $M \sim 2 \times 10^7 M_\odot$ (van Dokkum et al. 2025), propagating through $R \propto M^{1/3}$ yields $\delta R/R = (1/3)(\delta M/M) \approx 10\%$. The density input is the larger term by far, and its uncertainty is not the $\pm 30\%$ formal figure quoted in earlier drafts: $\rho_T = 3M_\oplus/(4\pi\lambda_T^3)$ is set by the GNSS decoherence length, and the corpus's measured product-level ensemble spans $\lambda_T \approx 1{,}900$–$4{,}500$ km on the precise-product branch — pooled coherent-band estimates of 4,549 km (CODE), 3,764 km (IGS), and 3,328 km (ESA) from Paper 1, the Paper 33 value near 4,200 km, and the corrected Paper 14 multi-GNSS (MGEX) pooled estimate at 1,862 km. Propagating each calibration through $\rho_T$ and $R_T$:

Here $M_\times(\rho_T) = c^3\sqrt{3/(32\pi G^3\rho_T)}$ is the crossover mass at which $R_T = R_S$ — the falsification boundary of the mass test below. Across the raw unharmonized table, $R_T/R_S \in [0.59, 1.45]$ and $M_\times \in [9.1\times10^6, 3.5\times10^7]\,M_\odot$: the three primary full-day $[10, 500]\,\mu\text{Hz}$ calibrations and Paper 33 place RBH-1 ($2\times10^7\,M_\odot$) outside the horizon scale with margins of 6–45%, whereas the raw Paper 14 multi-GNSS (MGEX) number ($1{,}862$ km) appears lower by a factor of $2.25$. As established in Paper 0 (Step 08, step_08_empirical_tensions.json), this shift is an exact spectral-windowing consequence of MGEX's 8-hour Welch estimator (5-minute sampling with nperseg = 96, fundamental non-zero frequency bin $\Delta f = 1/28{,}800\text{ s} = 34.72\,\mu\text{Hz}$), which physically omits the $10\text{–}30\,\mu\text{Hz}$ diurnal and semidiurnal sub-bands ($\lambda = 5{,}912$ and $5{,}691$ km in Paper 1, Table 8a); evaluated on the identical $[34.72, 500]\,\mu\text{Hz}$ FFT grid, Paper 1's own CODE sub-band profile predicts $\lambda = 1{,}864.3$ km, agreeing with MGEX ($1{,}862 \pm 112$ km) to $0.02\sigma$. Mapped to the common $[10, 500]\,\mu\text{Hz}$ passband ($\lambda_{\rm MGEX,equiv} = 4{,}195$ km), the MGEX product yields $R_T/R_S = 1.34$, so every passband-matched calibration product satisfies $R_T/R_S \in [1.06, 1.45] > 1$. Under the nominal Paper 6 anchor alone, $R_T = 7.8\times10^7$ km with $\delta R/R \approx 14\%$ from the mass and nominal density terms in quadrature.

The correspondence $R_T \approx 1.3 R_S$ under the nominal anchor places the temporal topology scale just outside the Schwarzschild radius. This would predict a "naked halo" phenomenology if RBH-1 is a soliton: the object interacts with the environment via its metric gradient (the "hair") rather than through an absorbing horizon. The canonical TEP strong-field formulation, including the treatment of compact-object interiors and the soliton–horizon distinction, is developed in TEP-BH (Paper 28, Bahrain); the framing here is consistent with that treatment.

Explicit Falsification Criteria

The hypothesis that RBH-1 is a candidate Temporal Topology soliton makes specific, falsifiable predictions. It is important to distinguish between tests of this specific interpretation and tests of the underlying TEP theory. A failure in the object-specific tests below would rule out the soliton candidate model for RBH-1 (returning it to the status of an unexplained anomaly), but would not falsify the broader TEP framework.

1. Mass falsification (Object Specific): The crossover check $R_T \approx 1.3 R_S$ is sensitive to both mass and the density anchor. Under the nominal calibration, a dynamical revision of $M_{\text{RBH-1}}$ above $M_\times \approx 3 \times 10^7\,M_\odot$ (where $R_T < R_S$) would falsify the soliton interpretation for this object. The boundary itself moves with the anchor: across the measured calibration ensemble $M_\times$ spans $5.9\times10^6$–$3.5\times10^7\,M_\odot$, and the finest-scale products (Paper 14, MGEX) would place the present mass inside the horizon scale. The criterion is therefore conditional on the GNSS transfer-map resolution tracked in Papers 1, 14, and 33.
2. Discriminant falsification (Spectroscopy): If deep spectroscopy reveals:
   • Strong coronal-line emission ([Fe X], [Fe XIV]) or soft X-rays consistent with $T \sim 10^7$ K gas dominating the emission measure would exclude a predominantly cold Temporal-Shear flow.
   • Broad [O III] wings containing >50% of the flux, indicating thermal broadening from high-velocity shear, the narrow-line argument is falsified.
   • A gas–star velocity relation incompatible with universal acceleration: the dynamical metric-shock model predicts that stars inherit the local gas centroid at formation, whereas ram pressure and turbulent entrainment permit systematic gas–star slip. A resolved failure of the profile-frame work relation $\Delta(u^2/2)=-c^2\Delta\ln A$ for any admissible profile would exclude the candidate mechanism.
3. X-ray constraint: A search of the Chandra and XMM-Newton archives reveals no pointed observations covering the RBH-1 field. The ROSAT All-Sky Survey provides only shallow upper limits ($F_X \lesssim 10^{-13}$ erg/s/cm²) insufficient to constrain $T \sim 10^7$ K emission at $z \approx 0.96$. Dedicated X-ray follow-up (Chandra ACIS, ~50 ks) can test the full-wake thermal-shock emission measure ($L_X \sim 10^{41}$–$10^{42}$ erg/s expected if the bulk $\Delta v \sim 650$ km/s post-shock gas mass were predominantly thermalized at $T \sim 10^7$ K; detection at that bulk-shock threshold would falsify the predominantly cold body-force model, whereas a sub-dominant X-ray component from minor streamline crossing or apex boundary heating remains compatible with coherent acceleration of the star-forming wake).
4. Universal Calibration Failure (Theory Level): Unlike the object-specific tests above, if the external input $\rho_T \approx 20$ g/cm³ is invalidated by independent replication of the GNSS analysis (Paper 6), the basis for the specific quantitative consistency check collapses.

6. Discussion: Implications for Dark Matter

Observational Context

The confirmation of RBH-1 provides a rare observational laboratory for testing the interaction of a compact perturber with the circumgalactic medium. The primary analysis infers a supersonic motion, $v_{\bullet}=954^{+110}_{-126}$ km/s, and identifies a 62 kpc ($\sim$200,000 light-year) wake of rapid cooling and star formation (van Dokkum et al. 2025). Such velocities are physically plausible within gravitational-wave recoil scenarios (Campanelli et al. 2007; Colpi & Dotti 2011; Komossa 2012). However, the coexistence of a large kinematic discontinuity with a cold, star-forming wake remains difficult to reconcile with standard collisional shock expectations.

The central tension concerns the wake rather than the recoil. In standard gas dynamics, a $\sim 10^3$ km/s shock is expected to thermalize the flow, heating gas to $T\gtrsim 10^7$ K and providing pressure support against prompt collapse. The observation of shock-excited emission coincident with rapid cooling and star formation suggests that the dominant driver of the structure is non-thermal.

While recent hydrodynamic simulations (Ogiya & Nagai 2023) and ram-pressure stripping studies (Poggianti et al. 2019) have shown that star formation can occur in tails under specific conditions, they do not by themselves resolve the temperature paradox posed by the RBH-1 apex. The coexistence of a high-Mach kinematic discontinuity and cold, star-forming gas motivates consideration of non-thermal contributions to the observed discontinuity.

Resolution via Temporal Solitons

A metric-driven interpretation offers an alternative contribution to a purely hydrodynamic bow-shock model. If RBH-1 carries a propagating region of altered proper-time rate, its Temporal Shear supplies the conservative acceleration $\mathbf a_\phi=-c^2\boldsymbol\nabla\ln A$. The resolved 650 km s$^{-1}$ span then requires a dynamical depth of order $10^{-6}$—$2.35\times10^{-6}$ in the rest-entry normalization and $4.55\times10^{-6}$ in the stated collinear pattern-speed benchmark—rather than an endpoint redshift of order $10^{-3}$. This ordered body force can generate a large bulk-flow gradient without requiring the same energy to appear as local random motion, while the enhanced scalar attraction lowers the collapse threshold behind the front.

Theoretical analogies exist in the form of non-topological solitons in scalar field theories (e.g., Kusenko 1997; Heeck et al. 2021), which demonstrate how coherent field configurations can maintain stable cores. However, the argument presented here is primarily observational: a consistent density scale is observed emerging across vast differences in mass.

RBH-1 as a Naked Halo Candidate

This reinterpretation also offers a way to connect competing morphological interpretations: is RBH-1 a runaway compact object or a "bulgeless edge-on galaxy" (Sanchez Almeida et al. 2023)? In the soliton hypothesis, a temporal soliton corresponds to a "naked halo": a compact, self-contained packet of scalar-field energy whose passage could generate a narrow wake.

One possible formation channel is a major merger or strong interaction. In the TEP phenomenology, such events could excite non-linear dynamics in the underlying scalar sector and eject a compact field configuration from the parent halo. This framing makes the ambiguity observational: deep imaging and resolved kinematics can test whether the light traces a bound stellar disk or instead follows in-situ star formation triggered along a trajectory.

Signatures of Internal Dynamics

Two features of the RBH-1 data point to the internal physics of the soliton.

1. Wake Fragmentation (Empirical Scale Tension): A key empirical constraint comes from the scale of star formation itself. The wake contains "knots" or clumps of star formation with sizes $d \lesssim 1$ kpc. In a simple single-phase hydrodynamic shock picture ($v \approx 1000$ km/s), the post-shock temperature is $T \approx 1.4 \times 10^7$ K. At this temperature, the Jeans Length would be $L_J \approx 170$ kpc, far larger than the observed clumps. This places a strong constraint on models in which the dominant post-front phase remains very hot for an extended time.
2. Gravitational Echoes: A future test lies in gravitational waves. When two compact objects merge, the resulting "ringdown" signal decays exponentially. If the objects are horizonless solitons rather than true black holes, gravitational waves could be partially trapped between the photon sphere and the compactness scale of the soliton core, producing repeating pulses or "gravitational echoes" (Cardoso et al. 2016). The detailed strong-field prediction depends on the interior solution; the canonical TEP compact-object formulation is developed in TEP-BH (Paper 28, Bahrain).

Additional tests involving magnetar timing anomalies and their connection to the universal scaling law are discussed in Appendix A.

Broader Context

The characteristic density $\rho_T \approx 20$ g/cm³ used to check the RBH-1 wake geometry is not arbitrary. As detailed in the companion paper (Smawfield 2025g), this same parameter successfully organizes phenomena across 40 orders of magnitude in mass, from the atomic scale (Bohr radius) to galactic rotation curves (SPARC database) and the Milky Way's Keplerian decline.

The fact that a single calibration, derived from terrestrial GNSS clocks, yields a scale consistent with the wake properties of a distant $10^7 M_\odot$ black hole provides support for the hypothesis that RBH-1 may manifest universal scalar-field dynamics. The "dark sector" in this framework is not a particle fluid, but the shadow of temporal structure.

7. Conclusion

The data currently available show a resolved position–velocity span $\Delta v \sim 650$ km/s and an independently measured near-tip dispersion $\sigma \approx 31$ km/s. These are distinct observables, not the first and second moments of one unresolved line. Their coexistence places strong constraints on single-phase thermal-shock interpretations and is consistent with the dynamical Temporal-Shear prediction of a large ordered flow with small local dispersion. The work integral requires $|\Delta\ln A|=2.35\times10^{-6}\eta$, where the measured flow geometry fixes $\eta$; the rest-entry and collinear 954 km s$^{-1}$ pattern-speed normalizations give $\eta=1$ and 1.94, respectively. The former endpoint-redshift depth is excluded because it would accelerate matter to approximately $1.97\times10^4$ km s$^{-1}$.

If the broader TEP program is independently validated, the dark sector could be reinterpreted as temporal structure in the conformal metric sector rather than as an undetected particle species. In that interpretation, what is conventionally called dark matter is modeled as phantom mass, i.e., an apparent excess inferred when Temporal Shear is analyzed under an isochronous prior. The RBH-1 wake provides a concrete astrophysical case study in which this interpretation can be confronted with data.

A potential objection concerns the apparent "shadows" imaged for M87* and Sgr A* by the Event Horizon Telescope. These observations strongly support the existence of ultra-compact objects with photon-ring structure consistent with General Relativity, but they do not by themselves uniquely select a mathematical event horizon over all horizonless alternatives. In general, any sufficiently compact configuration that reproduces near-horizon light-bending and exhibits high optical depth can produce an apparent shadow-like depression. The RBH-1 hypothesis therefore does not require that all supermassive black holes be identical neutral soliton candidates; rather, it motivates a targeted comparison between RBH-1 and EHT-class objects, with particular emphasis on whether the central brightness depression behaves as a true absorbing horizon or as a saturating refractive core (Event Horizon Telescope Collaboration 2019; Event Horizon Telescope Collaboration 2022).

The key next step is falsification. Specific falsification criteria are outlined; decisive discrimination regarding the neutral soliton candidate interpretation awaits line-profile decomposition and X-ray flux limits.

• Resolved phase-space test: spatially resolved spectra should show an ordered centroid field whose local dispersion remains small where the inferred Temporal Shear is smooth.
• Gas–star universality: newly formed stars should inherit the local gas centroid at formation; systematic gas–star slip instead identifies hydrodynamic forcing.
• Wake Chronometry: Stellar population ages along the wake should be consistent with the transit time of the perturber across the observed wake length (distance/$v_{\bullet}$). Regions whose inferred stellar ages significantly exceed the local passage time would favor a pre-existing tidal feature; conversely, a tight age-distance correlation would support an in-situ instability front.
• Wake Collimation: The wake should remain narrow (high aspect ratio) over its full extent, consistent with a laminar metric disturbance rather than turbulent thermal mixing.

References

Appendix A: Prospective Observational Tests

This appendix outlines prospective observational tests in which the Temporal Topology and metric-shock phenomenology developed for RBH-1 yield distinct predictions across independent astrophysical systems.

A.1 EHT Polarimetry

Permeable horizonless temporal-well models predict detectable polarized flux inside the central brightness depression of Event Horizon Telescope (EHT) sources (M87* and Sgr A*) from rays transmitted through the regular core (developed quantitatively in Paper 28, TEP-BH).

• Observable discriminator: Non-zero interior polarized flux fraction and altered inner-ring Faraday rotation profile in full-Stokes VLBI reconstructions, tested via polarized radiative-transfer and GRMHD forward modeling.

A.2 Additional JWST Case Studies

Several late-2025 JWST/NIRSpec discoveries exhibit kinematic or stellar-population tensions where a refractive proper-time gradient provides a concrete, testable observable channel alongside standard baryonic models (analyzed at catalog scale in Paper 12, TEP-JWST, and Paper 19, TEP-LENS).

A.2.1 Little Red Dots (LRDs)

JWST has revealed a population of compact sources at $z \gtrsim 3$ with distinctive UV-optical continua and broad Balmer emission. Late-2025 population studies based on public NIRSpec/PRISM spectroscopy report samples of order $\sim 10^2$ objects and conclude that broad Balmer lines are widespread in LRD-selected sources (de Graaff et al. 2025; Barro et al. 2025). A large spectroscopic census further reports that a v-shaped UV-to-optical continuum, a rest-optical point-source component, and broad Balmer lines are strongly linked within a large $z>3$ NIRSpec sample (Hviding et al. 2025). Independent analyses of stacked multi-wavelength data report evidence for AGN-heated dust in median LRD SEDs, while also highlighting tensions in dust-based interpretations (e.g., hot-dust evidence and obscuration geometry; dust-budget constraints) (Delvecchio et al. 2025; Chen et al. 2025).

• Potential TEP connection. In a conservative TEP reinterpretation, part of the apparent broad-line width could include a gravitational-redshift component produced by a structured clock-rate field, in addition to virial motion and radiative-transfer effects.
• Discrimination. Separating kinematic broadening from redshift gradients using reverberation mapping, spatially resolved spectroscopy, and host-mass constraints.

A.2.2 Massive Quiescent Galaxies at High Redshift

PRIMER+JADES analyses report a mass-complete catalog of 225 quiescent candidates at $z>2$ with $M_{*} > 10^{10}\,M_{\odot}$ over $\sim 320$ arcmin$^2$, and infer number densities that exceed representative pre-JWST estimates by factors of order a few, while noting that simulations increasingly fall short at $z>3$ with discrepancies approaching $\sim 1$ dex (Stevenson et al. 2025).

• Potential TEP connection. In a time-field phenomenology, part of the tension could arise from inference systematics if clock-rate gradients contribute an additional refractive component to observables in dense environments. Under an isochronous GR prior, such contributions can be misinterpreted as excess mass or altered stellar-population parameters.
• Discrimination. Compare SED-based stellar masses to independent dynamical and lensing constraints (where available), and test whether residuals correlate with environment rather than with purely baryonic tracers alone.

A.2.3 Strong-Lensing Time-Delay Cosmography

The TDCOSMO 2025 analysis reports new JWST-NIRSpec stellar-kinematics spectra for multiple time-delay lenses (including spatially resolved kinematics for RX J1131−1231) and emphasizes that improved kinematics can break lensing degeneracies and sharpen cosmological inference (TDCOSMO Collaboration 2025).

• Potential TEP connection. This dataset is directly relevant to TEP because time delays are intrinsically chronometric observables. If an additional conformal contribution accumulates in the proper-time sector, the inferred time-delay distance could be biased in a way correlated with lens environment and with mass-profile degeneracies.
• Discrimination. Search for residual systematics that correlate with independent indicators of temporal structure, rather than with purely baryonic tracers alone.

A.3 Magnetar Timing Anomalies

Standard neutron stars experience "glitches" (sudden spin-ups). However, magnetars have exhibited rare "anti-glitches" (sudden spin-downs). In the TEP framework, these are interpreted as boundary interactions: as the star's light cylinder expands toward the soliton scale ($R \propto M^{1/3}$), the magnetosphere approaches a field transition, enabling a rapid change in torque.

The magnetar 1E 2259+586 provides a prospective test case—its spin period lies within 3% of the nominal TEP critical period ($P_{\rm crit} \approx 6.8$ s for a $1.4 M_{\odot}$ neutron star, using the same $\rho_T$ calibration as RBH-1), motivating a population-level test of whether the soliton boundary scale extends universally across compact-object mass scales.

• Potential TEP connection. The anti-glitch timing and magnitude could be correlated with the light-cylinder radius approaching the soliton boundary scale predicted by $\rho_T$.
• Discrimination. Statistical analysis of magnetar glitch/anti-glitch populations as a function of period; comparison with the critical period predicted by the universal scaling law.

A.4 Summary of Prospective Channels

These prospective channels are distinct from the primary RBH-1 wake analysis in the main text; each specifies a concrete observational signature—interior VLBI polarization, environment-correlated SED-versus-dynamical mass residuals, strong-lensing time-delay residuals, and the magnetar critical-period boundary—through which the universal $\rho_T$ scaling can be independently falsified.