Measured and Observed: A Two-Clock Account of Anderson’s Coefficient
Anderson’s empirical relation for the Earth-flyby anomaly, ΔV∞ = (2ωR/c)V∞(cos δ_in − cos δ_out), emerged unexpectedly when the Selective Transient Field — a framework built from ultra-high-energy cosmic-ray and gamma-ray-burst timing — was applied to spacecraft trajectories. This paper establishes what that emergence was and was not. Three theorems close the reading of ΔV∞ as a real transfer of kinetic energy: the minimal velocity-dependent STF coupling produces an antisymmetric, Coriolis-type force with F·v = 0 identically; a stationary asymptotically flat effective metric conserves Killing energy, so V∞,out = V∞,in; and every scalar curvature magnitude — Weyl-squared, Kretschmann, the Bel–Robinson norm — is even in the source spin to O(a²), so no scalar channel can produce a term linear in ω, which Anderson’s coefficient is. To these we add a fourth: for a stationary axisymmetric source, k^μ∇_μℛ = 0 for any invariant scalar along a rigidly corotating clock, so the repaired universal-rate interaction vanishes identically on the Earth background.
What survives is stronger than what was withdrawn. Pulled back to a worldline the original interaction is a connection one-form, 𝒜_μ = γφ∇_μℛ, whose curvature ℱ = γ dφ∧dℛ is antisymmetric — and an antisymmetric connection does exactly two things: its mechanical action does no work, and its closed-loop integral ∮𝒜 = ∫ℱ need not vanish. The No-Work Holonomy Correspondence: zero mechanical work and a potentially nonzero observable phase holonomy are not opposites but the same property. What was read as the framework’s failure at the flyby is the structure the observation requires. The bridge from that holonomy to the measured Doppler residual is stated here as the open target, not claimed as derived.
We then derive the coefficient’s structure — conditional on such a bridge existing at all — without inserting it. Anderson’s factor of two is the vorticity of the Earth-fixed internal-clock congruence relative to universal time, ∇×(ω×r) = 2ω — not uplink-plus-downlink counting, which the standard two-way Doppler conversion removes. Its equatorial radius and declination-only angular dependence are the operator norm of the rotational clock channel over the closed carrier, sup_{∂C}|ℓ_s| = (ΩR/c)cos δ, attained at the equator; a station-local effect would carry cos λ and right ascension, which Anderson’s formula does not. Its independence of G and M is the signature of an observer-clock parameter: a source-local rotational gravitational effect carries the compactness factor GM/(c²R) ≈ 7×10⁻¹⁰, nine orders below the observed coefficient, while the rotational rapidity ΩR/c carries none.
Two structural results follow. The Source–Observer Degeneracy Theorem: in every original event Earth was simultaneously the rotating source and the rotating observational clock carrier, so K_source and K_observer coincide identically and Earth-only data cannot locate the coefficient’s causal origin. And the Clock-Carrier Capacity–Observability Theorem: the maximum apparent first-order velocity fraction available to a transaction closed by a rotating carrier is the operator norm 2|Ω|R cos δ/c, while the realized fraction is its projection through the actual observation operator — ΔV̂/V∞ = (2Ω_OR_O/c)[η_in cos δ_in − η_out cos δ_out], with the utilization η_a computed from each arc’s orbit-determination design matrix and never fitted. Anderson is the saturated case η = 1. This single equation accommodates the early detections, the later Earth nulls (Rosetta II/III, Juno — all published null, and the Juno row in the framework’s own flyby paper is arithmetically wrong), the failure of planet-local scaling, and the absence of any physical energy change.
We state honestly what is not derived: the constitutive law coupling operational clocks or radio phase to the STF connection with unit normalization is new physics, not implied by clock separation alone, and a Local Reciprocal-EFT No-Go shows that no local, gauge-invariant, real-quadratic, polarization-independent photon operator supplies it on a stationary background with an ideal coherent transponder. The surviving routes are named. The paper closes with the decisive experiment — one encounter measured through two differently closed clock architectures — and with the calculation that can be done today from archived tracking metadata: compute η_a for every historical detection and null, before consulting the reported anomaly. If detections cluster at high utilization and nulls near zero, the two-clock measurement theory becomes quantitative. If they do not, this route is closed and the paper says so.
The Deep Space Network does not measure a spacecraft’s kinetic energy. It measures accumulated radio phase against a station clock, and a round-trip light time. The two-way Doppler observable is y = −dρ/dt_3, a rate of change of round-trip light time; range is a light-time observable; and the asymptotic velocity V∞ is a parameter of an orbit fit obtained by adjusting a trajectory model until computed observables match measured phase counts. Anderson et al. characterized the anomaly from incoming and outgoing asymptotic declinations after fitting separate arcs; they did not supply a physical derivation, and they did not measure an energy.
One thing should be said before anything else. The flyby anomaly may have no exotic content at all: unmodelled solar radiation pressure, thermal recoil, attitude and antenna-phase-centre effects, atmospheric drag at low perigee, or artefacts of how separate inbound and outbound arcs were fitted remain live explanations, and a published reanalysis found that radiation-pressure uncertainties could account for some events. This paper does not argue that those explanations fail. It argues that if the residual is real, the Selective Transient Field predicts a measurement effect rather than a force — and it proposes a computation, on archived data, designed to discriminate the two-clock account from conventional systematics and from each other. The result of that computation may be that this route is closed.
This distinction is not pedantry. It is the whole content of the paper. A framework that predicts a phase effect and a framework that predicts an energy effect make the same first-order Doppler residual and different everything else — different range behaviour, different angular residuals, different link-mode dependence, different response to how the tracking arcs were closed. The Selective Transient Field, we will show, predicts the first and forbids the second.
Status of the emergence. The STF Lagrangian was constructed from UHECR/GRB/GW timing, in ignorance of spacecraft tracking (discovery record held separately; dependency graph: First Principles V8.1 Appendix E′). That the Anderson structure appeared when the framework was applied to a completely different observational regime is an out-of-sample structural coincidence, not something engineered. What was engineered — and is withdrawn here — is the later mechanical interpretation of that structure.
2.1 No work. For a nonrelativistic generalized potential linear in velocity, L_int = A_i(x,t)v^i − A₀, the Euler–Lagrange force is F_i = −∂_iA₀ − ∂_tA_i + v^jF_ij with F_ij = ∂_iA_j − ∂_jA_i antisymmetric. For the stationary pure-vector part used in the original derivation, F_i = v^jF_ij and therefore F_iv^i = vivjF_ij = 0. The force is Coriolis/Lorentz-like: it rotates the velocity and perturbs a trajectory or a light time; it cannot change the speed by mechanical work. Open or closed trajectory, no difference. Status: derived. (Appendix A.)
This invalidates the endpoint-difference step: the earlier derivation applied the fundamental theorem of line integrals to a non-gradient force and read ΔV = (ζ/Λ)[ℛ̇_out − ℛ̇_in] with “the contributions add” as the origin of the factor of two. A first-principles note of April 2026 conceded F·v = 0 while fencing off “the geometric derivation of K = 2ωR/c is correct and stands.” The fence does not hold: the geometric derivation is the endpoint difference. Both are withdrawn.
2.2 Stationarity. Let a spacecraft follow geodesics of an effective metric g̃_μν with ∂_tg̃_μν = 0, approaching the same asymptotically flat form on both legs. The Killing vector ξ = ∂_t gives conserved E = −g̃_μνξμuν, and the asymptotic relation between E and geocentric hyperbolic excess speed is the same at both ends. Hence V∞,out = V∞,in. A local interval with F·v ≠ 0 does not evade this; nonzero instantaneous work is insufficient, because stationarity forces the total asymptotic work to vanish. An open hyperbola does not help. Status: theorem under the stated hypotheses.
A permanent change therefore requires explicit nonstationarity, dissipation, different asymptotic structures, or a non-mechanical inference from the tracking observable. The one nonstationary route is a co-rotating nonaxisymmetric pattern φ₀(r,θ,φ − ωt), whose helical Killing vector k = ∂_t + ω∂_φ conserves E − ωL_z and gives ΔE = ωΔL_z; Anderson would then require ΔL_z/m = (2RV∞²/c)(cos δ_in − cos δ_out), a concrete torque target. An axisymmetric Kerr or Lense–Thirring field cannot supply it, since E and L_z are separately conserved.
2.3 Spin parity. For slow Kerr rotation, E_ij = E⁽⁰⁾_ij + O(a²) while B_ij = O(a), with a = J/(Mc) ∝ ω. Therefore C² = 8(E² − B²) = C₀² + O(a²), and equally √(8(E² + B²)) = √(8E₀²) + O(a²): both the Lorentzian scalar magnitude and the positive Bel–Robinson magnitude are even under ω → −ω. No scalar curvature magnitude possesses a term linear in the spin, and none can reverse sign for retrograde Venus. Anderson’s K is linear in ω. Status: theorem. (Appendix B.)
The same parity argument closes the scalar-source route at its origin: the breathing mode is sourced by the parity-even C², so σ(a) = σ(−a) and ∇σ = ∇σ⁽⁰⁾ + O(a²). The claim that ∇φ₀ carries one power of ω is unsupported by the reduced scalar equation. The parity-odd information lives in the Pontryagin density P = C·*C ∝ a cos θ/r⁷, or in the frame-dragging metric component g_tφ = O(a).
2.4 Stationary axisymmetry. For a stationary axisymmetric source with Killing vectors t^μ and ψ^μ, every invariant scalar satisfies ℒ_tℛ = ℒ_ψℛ = 0, so a rigidly corotating clock direction k = t + Ωψ gives k^μ∇_μℛ = 0 exactly. Rotating a perfect sphere changes nothing. Under any universal slicing adapted to the stationary symmetry, **N^μ∇_μℛ = 0: the repaired universal-rate interaction vanishes on the Earth background at the background level, and Earth’s rotation does not alter this. Status: derived.**
2.5 What the four theorems leave. The universal field does not evolve at Earth; the field’s own force does no work; no scalar magnitude carries the spin sign; and a stationary effective metric cannot change V∞. If the flyby signal is STF’s at all, it must live in (i) curvature orientation, which is spin-odd, and (ii) the relation between the clocks that read the universal history — that is, in the measurement, not in the mechanics.
Here is the paper’s central result, and it costs nothing new: it is the original interaction, read correctly.
Pull the curvature-rate interaction back to a worldline:
\[L_{\rm int} = \gamma\,\phi\,u^\mu\nabla_\mu\mathcal R = \mathcal A_\mu u^\mu, \qquad \mathcal A_\mu \equiv \gamma\,\phi\,\nabla_\mu\mathcal R .\]
𝒜 is a connection one-form. Its curvature is
\[\mathcal F_{\mu\nu} = 2\nabla_{[\mu}\mathcal A_{\nu]} = \gamma\big(\nabla_\mu\phi\nabla_\nu\mathcal R - \nabla_\nu\phi\nabla_\mu\mathcal R\big) = \gamma\,(d\phi\wedge d\mathcal R)_{\mu\nu},\]
manifestly antisymmetric. The Euler–Lagrange force is a^μ = ℱμ_νuν, so u_μa^μ = ℱ_μνuμuν = 0 — the no-work result of §2.1, now seen as an identity of the connection rather than an accident of the coupling. But the same object has a closed-loop integral
\[\oint_\Gamma \mathcal A = \int_\Sigma \mathcal F = \gamma\int_\Sigma d\phi\wedge d\mathcal R ,\]
which vanishes only if ∇φ and ∇ℛ are everywhere parallel. Therefore:
No-Work Holonomy Correspondence. An antisymmetric STF connection does zero mechanical work and may carry nonzero phase holonomy. The two properties are not opposites; they are the same property seen locally and globally.
Status: derived. The consequence for the framework’s history is worth stating plainly. Version 7.9 obtained the first half — the Coriolis-type, no-work force — and treated it as a failure requiring repair, adding a cross-disformal matter metric so that a spacecraft could gain energy. On the reading given here, no work was never the failure. It was the prediction, and the repair was a response to the wrong criterion. The correct question is not whether the interaction can change a speed. It is whether its connection produces the measured radio-phase holonomy.
The Doppler-space target. For two-way tracking at low speed y ≃ −2V_LOS/c, so an apparent velocity discontinuity corresponds to δy = −2ΔV∞/c. With Anderson’s form the required raw residual is
\[\delta y_{\rm Anderson} = -\frac{4\Omega R V_\infty}{c^2}\big(\cos\delta_{\rm in} - \cos\delta_{\rm out}\big),\]
and the derivation to be completed is
\[\frac{1}{2\pi\nu_0}\frac{d}{d\tau_E}\oint_\Gamma \mathcal A = \delta y_{\rm Anderson}.\]
This is a more fundamental target than ΔV∞, because Doppler phase is what was measured and ΔV∞ was inferred.
Not every effect that exists locally survives a coherent round trip. Two theorems select what can.
4.1 Reciprocity selection. Decompose a small optical-metric perturbation relative to the universal clock: h^(γ)μν = 2ΦN_μN_ν + 2N(μA_ν) + H_μν, with A and H spatial. For a ray of spatial direction ℓ, c δt = ∫(Φ − A_μℓ^μ + ½H_μνℓμℓν)dℓ. Under exact retrace ℓ → −ℓ, the scalar Φ adds, the vector contraction A·ℓ cancels, and the tensor contraction H_ℓℓ adds. Any clock-shift coupling of the form N_(μΞ_ν) is in the cancelling sector: on an exactly retraced link its two-way contribution is zero, and for moving endpoints only the loop holonomy ∮Ξ = ∫dΞ survives — a Sagnac-like area observable, not twice an endpoint value. Status: derived. (Appendix C.)
This demotes a tempting intermediate result. Evaluating the Kerr curvature-phase gradient at the surface gives a natural two-way scale K_phase = 6a/R = 6k_I ωR/c, and with Earth’s measured moment factor k_I = 0.3307 this is 0.992 times Anderson’s coefficient — a 99.2% agreement obtained without inserting the coefficient, and predicting a genuinely different value for Jupiter (3k_I ≈ 0.79). It is a striking number. But the legs cancel, so 6a/R is a local geometric scale, not a derived DSN coefficient, and we record it as such.
4.2 Coherent-link cancellation. Let J_A = dT_U/dτ_A be the rate of an operational clock against universal time. For a coherent two-way link Earth → spacecraft → Earth with turnaround ratio q, the spacecraft clock factor cancels identically: ν₃ = qν₀[J_E(3)/J_E(1)]P_↑P_↓. For the same station with a stationary clock map, J_E(3) = J_E(1) and the ordinary internal/universal rate difference disappears entirely; a slowly varying map leaves only J_E(3)/J_E(1) ≃ 1 + Δ_RT d ln J_E/dT_U, a derivative over one round-trip light time — not the difference of inbound and outbound declinations.
Coherent-Link Cancellation Theorem. In an ideal coherent two-way radio link the spacecraft’s internal clock rate cancels identically, and a constant station clock-rate conversion cancels between transmission and reception.
Status: derived. So a two-clock effect cannot be an ordinary local clock drift. What survives turnaround is a direction-odd conversion, ν_I(k) = [1 + ε(x,u,ℓ)]ν_U(k) with ε(−ℓ) = −ε(ℓ), for which the coherent ratio gives (1+ε)/(1−ε) ≃ 1 + 2ε. Equivalently — the Clock-Holonomy Requirement — a two-clock effect survives a closed coherent link only if the universal-to-internal clock relation has nonzero connection curvature, or if the observational protocol fails to close the phase contour.
4.3 The link-mode hierarchy. Three-way (transmit at A, receive at B) retains ln[J_B(T₃)/J_A(T₁)]; a one-way downlink from an onboard oscillator retains ln[J_A/J_S]. Two-way, three-way and one-way tracking of the same encounter therefore constitute a clock-separation experiment: 𝒟_AB − 𝒟_AA = ln[J_B/J_A] + ΔΠ_BA exposes differences a same-station coherent link hides. A source force is blind to link mode. (Appendix D.)
Anderson’s K has five properties that a mechanism must supply: linearity in Ω; sign reversal under Ω → −Ω; independence of G and M; the scale ΩR/c; and the angular factor cos δ with no right ascension. This section derives all five. It does not derive the existence of the channel that carries them: the conditional form of the result is if a clock-to-observable bridge exists, its coefficient is forced to be 2ΩR cos δ/c — and §7.4 shows precisely where that bridge cannot live. The reader should hold the conditional in view throughout; it is the paper’s principal open item, not a footnote to it.
5.1 The factor of two is vorticity. Let U^μ_E = Γ_E(N^μ + β^μ_E) be the Earth-fixed internal-clock congruence relative to the universal clock, with β_E = (ω×r)/c in the weak rigid-rotation limit. The spatial curl relative to N is fixed by the exact identity
\[\nabla\times(\boldsymbol\omega\times\mathbf r) = 2\boldsymbol\omega \quad\Longrightarrow\quad \boldsymbol{\mathscr H}_C = \frac{2\boldsymbol\omega}{c},\]
so that with the curvature-defined radius r_𝒞 = R at Earth’s clock-carrying boundary, 𝒦_C = r_𝒞|𝓗_C| = 2ωR/c. This is Anderson’s K, and its two is the curl of rigid internal-clock motion — the same factor that appears in congruence-adapted gravitoelectromagnetic decompositions. It is not uplink-plus-downlink counting: the raw round trip does contain twice the one-leg contribution, but the conventional DSN conversion to range or velocity divides by two and removes it. There are three distinct “twos” and only this one survives into the reported coefficient. (Appendix E.)
5.2 The equatorial radius and cos δ are an operator norm. A single antenna at latitude λ has rotational radius R cos λ and its rotational projection onto an asymptotic direction ŝ(α,δ) is ℓ_s(θ,λ) = (ΩR cos λ/c) cos δ sin(α − θ) — carrying station latitude, right ascension and rotational phase, none of which appear in Anderson’s formula. But the closed carrier’s operator norm is
\[\|\ell_s\|_{\infty,C} = \sup_{x\in\partial C}|\ell_s(x)| = \frac{|\Omega| R}{c}\cos\delta ,\]
attained at the equator, where the cylindrical radius is greatest, and at the rotational phase where the carrier velocity aligns with the equatorial projection of ŝ, whose magnitude is cos δ. Status: theorem. The global norm of a closed axisymmetric rotating carrier’s clock channel therefore contains equatorial R rather than station R cos λ, declination rather than right ascension, linear sign-sensitive rotation, and no G or M — the whole list, from one supremum. (Appendix F.)
Note also that the correct angular object is a norm: v_⊥ = √(v·v − (v·ŝ)²) = V∞ cos δ. A linear contraction ŝ·v would give V∞ sin δ, which is why earlier attempts produced the wrong function.
5.3 Why the absence of G and M is the decisive clue. A source-local rotational gravitational effect scales as ε ~ GJ/(c³R²) = (GM/c²R)(ΩR/c) — the rotational rapidity multiplied by the body’s compactness. For Earth the compactness is 7×10⁻¹⁰, so ε ~ 10⁻¹⁵ against Anderson’s 3×10⁻⁶: nine orders. A curvature-sourced force must therefore forget G and M by nine orders, which the earlier construction achieved only by fixing its coupling to reproduce Anderson. The observer-clock parameter is the bare ΩR/c and carries no compactness at all. Together with the spin-parity obstruction, this is why the symmetry audit selects the measurement branch rather than merely permitting it.
5.4 The transponder and the arcs. With a direction-odd conversion ε_σ = σ_γ𝒦_C v_⊥/c, the coherent ratio gives y_STF = 2𝒦_C(V∞/c)cos δ; the conventional two-way relation y ≃ −2δV_LOS/c then returns δV_arc = −𝒦_C V∞ cos δ per arc, and separately closed inbound and outbound fits differ by
\[\frac{\Delta V_\infty}{V_\infty} = \frac{2\omega R}{c}\big(\cos\delta_{\rm in} - \cos\delta_{\rm out}\big),\]
which is Anderson’s formula, with no physical energy change anywhere in the derivation. Status: derived, conditional on the direction-odd conversion existing with unit normalization. That conversion is new constitutive physics; §7.4 states a no-go bounding where it can come from and names the surviving routes. The conditional is load-bearing and is not discharged anywhere in this paper.
Every event in the original set was a flyby of the rotating Earth observed through the rotating Earth’s tracking and clock infrastructure. Consider the two candidate origins of the coefficient: K_source = 2Ω_sR_s/c belonging to a field generated by the central body, and K_observer = 2Ω_oR_o/c belonging to the rotating clock congruence used to reconstruct the trajectory. For an Earth flyby tracked from Earth, source = observer = ⊕ and the two are identically equal.
Source–Observer Degeneracy Theorem. When the rotating gravitational source and the rotating observational clock carrier are the same body, a source-local dynamical correction and an observer-local temporal correction possess the same first-order rotational coefficient. Earth-only flyby observations cannot identify the causal location of that coefficient.
Status: theorem. The consequence reframes the empirical record. A non-Earth flyby separates the roles: the dynamical branch predicts the encountered planet’s 2Ω_BR_B/c with projections on its spin axis, while the observer branch predicts Earth’s 2Ω_⊕R_⊕/c with projections on the terrestrial network. Failure of planet-local scaling does not falsify the STF curvature-rate operator. It falsifies the claim that the Anderson coefficient is a universal source-local spacecraft force — and it leaves, and may favor, the observer-clock reading.
This is what “observational relativity” means in a rigorous inverse-problem sense: the inferred parameter belongs not to the trajectory alone but to the relation among trajectory, universal clock, internal clock, observer congruence and link closure. It is also a caution: the non-Earth evidence is not yet clean, because planetary gravity-field knowledge, bound-orbit reconstruction and conventional residual sources complicate those comparisons.
7.1 Capacity is not saturation. The operator norm of §5.2 is a maximum: the largest rotational clock transfer available to the closed carrier. Possessing capacity does not imply using it — the framework’s own Closure–Capacity Correspondence is explicit that capacity gates whether a loop can close, not what a closed loop outputs. Treating the norm as the observed anomaly would require the claim that every completed measurement transaction saturates its carrier’s directional clock capacity, which is too strong: fully closed later flybys would then show the same effect, contrary to the nulls.
7.2 Two branches, and which law belongs to which. The paper contains two physically distinct routes and they must not be merged. B1 — no-work projection (§7.3): the original antisymmetric force produces a real transverse deflection with δ|V| = 0, and a Doppler-dominated estimator represents it as a scalar speed change; linear end to end, no new coupling. B2 — clock holonomy (§3, §5.4): the connection’s phase holonomy enters the observable through a direction-odd conversion; requires the constitutive bridge of §7.4. The capacity–utilization law below is a B2 prediction: the operator norm 2ΩR cos δ/c bounds how much apparent velocity a rotating clock carrier can inject into a transaction, which is not what sets the amplitude under B1 — there the scale is the deflection integral δv = ∫a_STF dT. The η_a machinery applies to both, with a branch-dependent template s_STF,a, and that is itself the discriminator: the two branches predict different templates through the same estimator, so computing η_a with each template is the experiment.
Introduce a utilization coefficient η_a ∈ [−1,1] per tracking arc (B2 form):
\[\frac{\widehat{\Delta V}}{V_\infty} = \frac{2\Omega_O R_O}{c}\Big[\eta_{\rm in}\cos\delta^{(O)}_{\rm in} - \eta_{\rm out}\cos\delta^{(O)}_{\rm out}\Big].\]
Anderson is the saturated case η_in = η_out = 1; a null occurs when η ≈ 0 or when the two weighted terms coincide. The law is predictive only if η_a is computed rather than fitted, and it can be: orbit determination is a linear estimator, so
\[\eta_a = \frac{\mathbf h_V^{T}WP_\perp\,\mathbf s_{{\rm STF},a}}{C_a\,\mathbf h_V^{T}WP_\perp\mathbf h_V}, \qquad C_a = V_\infty\frac{2\Omega_OR_O}{c}\cos\delta_a ,\]
with h_V the velocity-step template, W the weight matrix, P_⊥ the projector removing fitted clock, station, trajectory and media parameters, and s_STF,a the predicted STF signature. Three structural checks make the definition well-posed rather than a free function. (i) Dimensions: numerator and denominator both carry the units of s and h contracted through W, so η is dimensionless. (ii) Bound: |η| ≤ 1 is not automatic from the ratio — it follows only when ‖P_⊥s_STF,a‖ ≤ C_a‖P_⊥h_V‖ in the W-metric, i.e. when the predicted signature does not exceed the carrier capacity in the estimator’s own geometry; we impose it as part of the capacity claim and note that a computed |η| > 1 falsifies the capacity bound directly. (iii) Degenerate case: for a single-arc, Doppler-only fit with s_STF,a ∝ C_ah_V — the saturated, fully degenerate configuration — the ratio gives η = 1 exactly, recovering Anderson. That check is what distinguishes a computed η from a fitted one. η_a is then a property of the measurement architecture — station identities, tracking windows, link mode, phase continuity, range and VLBI coverage, clock resets, solve-for parameters — not a new physical constant.
Clock-Carrier Capacity–Observability Theorem. For a measurement transaction embedded in universal time and closed by a rotating internal clock carrier, the maximum apparent first-order velocity fraction is the operator norm 2|Ω|R cos δ/c; the realized fraction is its projection through the transaction’s actual observation operator.
Status: stated (branch B2). Its components are derived — the operator norm (§5.2, Appendix F) and the linear-estimator projection (§7.2) — while the step from capacity to realized observable rests on the utilization definition and is what the empirical program tests.
The law carries a falsifiable bound: |ΔV̂/V∞| ≤ (2|Ω_O|R_O/c)(cos δ_in + cos δ_out). Any reliable anomaly exceeding the carrier capacity rules out the mechanism.
7.3 The No-Work Projection Theorem. There is a second, entirely linear route to an apparent ΔV that requires no new coupling at all. Since F·u = 0, a small STF perturbation satisfies V·δV = 0, so δ|V| = 0 to first order while the direction changes, δv̂ = δV/V∞ ≠ 0. Two-way Doppler is sensitive to the line-of-sight projection, δy = −(2/c)n̂·δV, which does not vanish. If Doppler dominates and angular information is weak, the velocity template is partially degenerate with direction templates and the estimator represents a transverse deflection as a scalar speed change:
No-Work Projection Theorem. A force orthogonal to the spacecraft four-velocity produces no physical energy change while generating a nonzero fitted asymptotic speed change whenever the tracking design matrix does not independently resolve the induced directional perturbation.
Status: derived. As tracking rank increases — continuous multi-station coverage, range, angular data — the degeneracy breaks and the same signal is reconstructed as a tiny deflection, absorbed into a trajectory correction, or rejected as inconsistent across observables: ΔV̂ → 0 without the field switching off. Later nulls become evidence of greater observational closure, not of an effect that vanished. This branch uses only the original Lagrangian and should be evaluated first.
7.4 What is not derived. The direction-odd clock conversion of §5.4 is new constitutive physics, not a consequence of clock separation. Standard frequency measurement is ν = −k_μu^μ/2π and its direction dependence is ordinary Doppler; an additional ε(k) represents a new law in the receiver, transponder or matter sector, and it is nonanalytic (a norm and a sign function), observer- and ray-dependent, and not generated by the scalar STF action. Nor can the framework’s topology normalize it: the closure certificate is invariant under λ_C → λ_C + δλ as long as the threshold is still crossed, so closure can gate the bridge on or off but cannot fix its amplitude — the one-bit lemma applied to the framework’s own flyby claim. And a continuous coefficient like ωR/c cannot be carried by a one-bit advanced channel at all.
A no-go bounds the search. Assume a local action, gauge invariance, a real action quadratic in F_μν, a stationary clock background, polarization-independent propagation, and an ideal coherent transponder. Then the photon constitutive tensor reduces to effective metric + dilaton + axion; the dilaton is direction-even, the axion acts on polarization, and the effective metric’s direction-odd part is a reciprocal one-form delay that cancels on retrace and cannot alter the frequency ratio of a stationary passive transponder. No operator in this class produces the required bridge. The escapes are exactly the assumptions one must abandon: birefringence; dissipation or nonreciprocity (a skewon response, which would depend on hardware, temperature and power); nonlocality; active matter or transponder physics; or a return to a real force — which §2 has closed. (Appendix G.)
8.1 The decisive experiment. During a single encounter, measure simultaneously: coherent two-way Doppler from one station; three-way Doppler using a second station; a one-way downlink from a stable onboard oscillator; range; and independent angular or optical tracking. Then a common reconstructed energy change supports a work-producing force; a common directional deflection with δE∞ = 0 supports the original no-work interaction (§7.3); a station- or link-dependent residual with no optical trajectory change supports the carrier/holonomy branch; disappearance under full joint estimation supports observational projection; and disappearance with no structured dependence weakens the STF–flyby identification altogether.
8.2 The calculation available today. For Galileo I/II, NEAR, Cassini, Rosetta I/II/III, Messenger and Juno, assemble the archived tracking metadata and compute η_a from the design matrices — before consulting the reported anomaly. The prediction is that detections cluster at high utilization and nulls near zero. This is the single step that converts the theory from an interpretation into a quantitative claim, and it uses data that already exists.
8.3 Falsifiers. (i) A reliable anomaly exceeding the capacity bound. (ii) Anomalies scaling with the encountered planet’s 2Ω_BR_B/c under Earth tracking. (iii) An onboard accelerometer or independent angular reconstruction showing a real energy change with δE∞ ≠ 0. (iv) Computed η_a uncorrelated with the detection/null pattern — operationally: compute η for all nine arcs under both branch templates, then test rank correlation against reported |ΔV| at a significance criterion fixed before the anomalies are consulted; failure at that pre-registered level closes this route. (v) A Doppler residual with no corresponding range residual under an optical-delay reading, or a carrier-frequency dependence (δV ∝ 1/ν) indicating an additive field phase rather than a metric delay. (vi) For the framework generally: any demonstration that the STF connection’s holonomy vanishes identically on the relevant link geometries.
8.4 The empirical record, corrected. The framework’s own flyby paper requires correction and this paper supplies it: Juno’s null reconstruction was published in 2014, not “pending”; its listed geometric factor 0.476 should be cos 18.4° − cos 39.2° = 0.174, whence the paper’s own formula predicts 5.60 mm/s rather than the tabulated 4.8 — and either conflicts with the observed null; Rosetta II and III were labelled symmetric with zero predicted, whereas the Anderson evaluation gives 0.523 and 1.099 mm/s against nulls; and the original set’s agreement is not “within measurement uncertainty” under the paper’s own error bars (Galileo I 2.75σ, Rosetta I 5.4σ, Cassini 9.3σ). The quoted R² = 0.997 excludes the one genuinely predictive test. (Appendix H.)
The Selective Transient Field does not push spacecraft. Its curvature-rate interaction is an antisymmetric connection: it cannot change an asymptotic speed, and it can carry a phase holonomy that a coherent radio transaction reads. The coefficient that made the flyby famous is, on this reading, the vorticity and operator norm of the observer’s own rotating clock carrier — factor of two from ∇×(ω×r) = 2ω, equatorial radius and cos δ from a supremum over the closed carrier, absence of G and M because an observer’s rotational rapidity carries no compactness. Earth flybys could never have told this apart from a source field, because Earth was both. The later nulls, which looked like refutation, are what a capacity–utilization law predicts when the tracking architecture closes the phase contour.
None of this is yet a completed theory. The constitutive law that couples clocks or radio phase to the STF connection with unit normalization is not derived, and a no-go tells us where it cannot live. But the framework now makes a quantitative, falsifiable, archival-data claim where it previously made a mechanical assertion — and it makes that claim with the interaction it started from, not with a repair. That the original Lagrangian forbids the energy transfer everyone assumed, while carrying exactly the structure — zero work, nonzero holonomy — that the observation requires, is the strongest structural evidence yet that it was describing something real. Whether that structure reaches the measured Doppler residual with the measured coefficient is the open question, and the η_a computation is how it gets answered. ***
Convention: claims in the body carry Status: labels (theorem / derived / conditional / stated); steps in these appendices carry verification tags instead. Tags as in the First Principles record: [reproduced] — recomputed symbolically or numerically from the framework’s own definitions; [standard] — textbook result; [stated] — named target, not proved. Signature (−,+,+,+).
A.1 Euler–Lagrange force. L_int = A_i(x,t)v^i − A₀(x,t) ⇒ F_i = −∂_iA₀ − ∂_tA_i + v^j(∂_iA_j − ∂_jA_i). For the stationary pure-vector part, F_i = v^jF_ij with F_ij = −F_ji, hence F_iv^i = vivjF_ij = 0 by antisymmetry. Independent of trajectory topology. [reproduced]
A.2 Why the earlier derivation failed. The superseded chain was: L_int = (ζ/Λ)φ(n^μ∇_μℛ) → a = (ζ/Λ)φ₀∇ℛ̇ → ΔV = (ζ/Λ)[ℛ̇_out − ℛ̇_in] → “ℛ̇_out = −ℛ̇_in ⇒ contributions add” → factor of 2 → K = 2ωR/c. Steps 2–4 apply the fundamental theorem of line integrals to a force that is not a gradient, and treat a velocity-dependent potential as static. The April-2026 note conceded F·v = 0 while asserting that the geometric derivation of K “is correct and stands”; but the geometric derivation is the endpoint difference, so the concession and the assertion are inconsistent. Both are withdrawn. [reproduced against the source]
A.3 Cascade. Every result calibrated from the flyby amplitude falls with it: the “98%” validation of ζ/Λ; the Earth/Jupiter/Venus reconstruction after fixing the cross-disformal coefficient by the Anderson match (an identity); the Ulysses ephemeris discrepancy read as a direct velocity detection; the balance of spacecraft energy gain against planetary rotational energy loss; and the binary-dephasing bounds 10⁻²⁰–10⁻¹⁴ rad. The numerical coincidences survive as coincidences; their logical status changes. [record]
B.1 Slow-Kerr expansion. E_ij = E⁽⁰⁾_ij + O(a²), B_ij = O(a). Writing schematic magnitudes E = E₀ + e₂a², B = b₁a: C² = 8(E² − B²) has a¹ coefficient zero; 𝒲_N = E² + B² has a¹ coefficient zero; E·B has a¹ coefficient E₀b₁ ≠ 0. Both the Lorentzian scalar magnitude and the positive superenergy norm are even in the spin to O(a²). [reproduced]
B.2 Consequence. D√C² and D√(8𝒲_N) contain no term linear in ω and cannot reverse sign for retrograde rotation; Anderson’s K is linear in ω. Any scalar-magnitude channel is excluded at first order. [reproduced]
B.3 Where the odd information lives. The Pontryagin density P = C·*C = 288m²a cos θ/r⁷ + O(a³) is odd; equivalently the complex Weyl invariant 𝔍 = C² + iP = q²e^{2iϑ_C} with q = 4√3 m/ρ³ (even) and ϑ_C = 3 arctan(a cos θ/r) ≃ 3a cos θ/r (odd), ρ = √(r² + a²cos²θ). Verified exactly: |𝔍| = q², arg 𝔍 = 2ϑ_C. The curvature-phase connection 𝒜_C = q dϑ_C has ℱ_C = dq∧dϑ_C = 36√3 ma sin θ/ρ⁵ dr∧dθ — linear in a, sign-reversing, equatorial maximum, zero on the axis, and ∝ cos δ since sin θ = cos δ. [reproduced, exact]
B.4 The scalar source is spin-even. The reduced parent sources the breathing mode through A(σ)C², and C²(a) = C²(−a), so with spin-independent boundary conditions σ(a) = σ(−a) and ∇σ = ∇σ⁽⁰⁾ + O(a²). Hence the cross-disformal tensor H^XD_μν = B̂(∇_μσ∇_νq + ∇_νσ∇_μq) has no intrinsic O(a) carrier: the claim that “one factor from ∇φ₀ carries ω¹” is unsupported by the reduced scalar equation. Any O(a) contribution would have to come from the background Kerr connection (g_tφ = O(a)) — i.e. from standard frame dragging, a different derivation, and still subject to §2.2. [reproduced]
B.5 Numerical correction. The Kerr parameter of Earth is a = k_I R²ω/c = 3.27 m with k_I = 0.3307, so a/R = 5.1×10⁻⁷ — not the ≈ 0.009 m and 10⁻⁹ quoted in the framework’s First Principles record. Note 3a/R = 1.54×10⁻⁶ ≃ ωR/c precisely because 3k_I ≃ 1 for Earth. [reproduced]
C.1 Selection. h^(γ)μν = 2ΦN_μN_ν + 2N(μA_ν) + H_μν; c δt[ℓ] = ∫(Φ − A_μℓ^μ + ½H_μνℓμℓν)dℓ. Ray reversal ℓ → −ℓ: Φ even (adds), A·ℓ odd (cancels), H_ℓℓ even (adds). [reproduced]
C.2 The vector sector cancels. For the two-clock optical shift g̃ = g + 2λ_ΞN_(μΞ_ν) with N·Ξ = 0, the one-way correction is δt = −(λ_Ξ/c)∫Ξ_i dx^i and an exact retrace gives δρ = 0. For moving endpoints the legs close with the station worldline to ∮Ξ = ∫_Σ dΞ, and δV_eq = −(λ_Ξ/2)(d/dt)∫_Σ dΞ. A toy rectangular loop r ∈ [r₁,r₂], θ ∈ [θ₁,θ₂] gives ∮Ξ = −3a ln(r₂/r₁)(cos θ₁ − cos θ₂) ∝ (sin δ₁ − sin δ₂) — not Anderson’s cos δ_in − cos δ_out — and carries ln(r₂/r₁), i.e. tracking-distance, station and arc dependence that Anderson’s expression lacks. [reproduced]
C.3 Status of 6a/R. At r = R, −∂ϑ_C/∂θ ≃ (3a/R)cos δ per leg; assuming equal unit-gain legs gives K_phase = 6a/R = 6k_I ωR/c, so K_phase/K_Anderson = 3k_I: Earth 0.992, Venus ≈ 1.01 (sign-reversed), Jupiter ≈ 0.79. A derived 99.2% Earth agreement and a genuine multi-planet discriminator — but the assumption of additive legs is exactly what C.2 refutes. Status: local geometric scale, not a derived DSN coefficient. [reproduced; demoted in-session]
C.4 The tensor candidate. g̃ = g + λ_Bχ𝒢(W)B_μν/√W with W = E² + B² is quadratic in ℓ and therefore adds. Weak Kerr: B̂_ℓℓ = −√(3/2)(1/r)[2(a·ℓ)(n·ℓ) + (a·n)(1 − 5(n·ℓ)²)] + O(a²) — the mass cancels (normalization), O(a/r). Straight-ray integral ∫B̂_ℓℓ ds = (3π/2)√(3/2) a·b̂ = 5.771 a·b̂ (verified numerically for a ∥ b̂; zero for a ⊥ (b̂,ℓ) and a ∥ ℓ), against Anderson’s 2ωR/c = (2/k_I)(a/R) = 6.046 a/R — a 4.5% contact from a rank-2 Kerr angular integral, not an inserted coefficient. Not a prediction: the integral has units of length, a real ray is finite, endpoints bring range/impact-parameter/station terms, λ_B is underived, and B̂_ℓℓ is even in ℓ and in v, so it cannot produce cos δ_in − cos δ_out by itself. The closure gate 𝒢(W) is essential, else M → 0 leaves a finite normalized effect. [reproduced]
D.1 Two-way. J_A ≡ dT_U/dτ_A; ν_A = J_A(1/2π)dΦ/dT_U. Earth emits ν₀ ⇒ ν^(U)↑ = ν₀/J_E(1); spacecraft receives J_S(2)P↑ν₀/J_E(1) and emits q times that; converting back divides by J_S(2), so ν^(U)↓ = qP↑ν₀/J_E(1) — the spacecraft clock cancels identically — and Earth receives ν₃ = qν₀[J_E(3)/J_E(1)]P_↑P_↓. Same station, stationary map: J_E(3) = J_E(1). Slowly varying: J_E(3)/J_E(1) ≃ 1 + Δ_RT d ln J_E/dT_U. [reproduced]
D.2 Three-way and one-way. ν_B/(qν_A) = [J_B(3)/J_A(1)]P_↑P_↓; ν_E/ν_S = (J_E/J_S)P_↓. Differencing: 𝒟_AB − 𝒟_AA = ln[J_B(T₃)/J_A(T₃)] + ΔΠ_BA. [reproduced]
D.3 Direction-odd survival. ν_I(k) = [1 + ε(ℓ)]ν_U(k) with ε(−ℓ) = −ε(ℓ) and ℓ_↓ ≃ −ℓ_↑ gives ν_U,↓/(qν_U,↑) = (1+ε)/(1−ε) ≃ 1 + 2ε. y_STF = 2ε; with y ≃ −2δV_LOS/c the conversion returns δV_arc = −𝒦_C V∞ cos δ. [reproduced]
D.4 Holonomy requirement. The measurement contour is Γ = γ_↑ + γ_↓ − γ_E; δΦ = ∮_Γ𝒜 = ∫_Σℱ. If 𝒜 = dχ (a pure scalar clock rescaling) then ∮dχ = 0. Survival requires ℱ ≠ 0 or an unclosed observational contour. [reproduced]
D.5 Sagnac is not the anomaly. With the synchronization one-form 𝒜_μ = h^(N)_μνβ^ν_E and Wilson-line transport W_γ = exp(iq_C∫γ𝒜), an exact retrace gives W{γ⁻¹}W_γ = 1. Non-retraced legs closed with the station and spacecraft worldlines give ∮𝒜 = ∫ℱ — the ordinary Sagnac holonomy, already modelled in relativistic time transfer and in JPL’s separate uplink/downlink light-time solutions. Clock connection plus ordinary parallel transport reproduces standard Sagnac physics, not a new effect. [reproduced]
E.1 The identity. ∇×(ω×r) = 2ω, verified componentwise. For the Earth-fixed congruence U_E = Γ_E(N + β_E) with β_E = (ω×r)/c, the spatial curl relative to N is 𝓗_C = 2ω/c; with r_𝒞 = R at the clock boundary, 𝒦_C = 2ωR/c. [reproduced]
E.2 Why not the Kerr normalization. The Kerr route uses a = J/(Mc) = k_I R²ω/c and therefore carries the moment-of-inertia factor; the clock-flow route uses ω directly, has no GM/(c²R) suppression, and requires no cancellation of the source mass. [reproduced]
E.3 Three factors of two. (i) Uplink + downlink: real in raw phase, removed by the standard round-trip-to-one-way conversion δρ = (c/2)δT₂. (ii) Inbound vs outbound branches: could survive, needs a derived sign reversal. (iii) K = 2ωR/c: the vorticity identity of E.1 — the only one that reaches the reported coefficient. [reproduced]
E.4 Frobenius. N_μ = −∇_μT_U/√(−∇T_U·∇T_U) is hypersurface-orthogonal, so its own vorticity vanishes: the universal clock supplies ordering, not rotation. All rotational structure lives in the relation between U_E and N. [standard]
F.1 Setup. Closed rotating carrier C with universal normal N^μ, internal phase θ ∈ S¹, axial generator ψ^μ, rate Ω_C; spatial metric h_μν = g_μν + N_μN_ν; cylindrical radius ρ(x) = √(h_μνψμψν); boundary radius R_C = sup_{∂C}ρ (the equator for Earth); carrier velocity v^μ_C = Ω_Cψ^μ.
F.2 The channel and its norm. ℓ_s(x) = v_{Cμ}s^μ/c; for a rotating sphere ℓ_s(θ,λ) = (ΩR cos λ/c)cos δ sin(α − θ). Then ‖ℓ_s‖{∞,C} = sup{∂C}|ℓ_s| = (|Ω|R/c)cos δ, attained at λ = 0 and α − θ = π/2. Verified on a 2001×2001 (λ,θ) grid: numerical supremum agrees with (ΩR/c)cos δ to machine precision. Restoring orientation, κ_C(s) = sgn(Ω)‖ℓ_s‖. [reproduced]
F.3 What the supremum explains. Equatorial R rather than station R cos λ (the sup selects the largest cylindrical radius); declination and not right ascension (the sup over rotational phase removes α); linearity and sign-sensitivity in Ω; and no G or M anywhere. [reproduced]
F.4 Two-way capacity. C_2w = 2κ_C = (2ΩR/c)cos δ; saturated inbound and outbound records give exactly Anderson. [reproduced]
F.5 The angular norm. v_⊥ = √(v_μP^{μν}⊥v_ν) with P⊥ = h_N − Ω̂_CΩ̂_C equals V∞ cos δ; a linear contraction ŝ·v gives V∞ sin δ. [reproduced]
G.1 Constitutive decomposition. S_γ = −⅛∫√−g χ^{μνρσ}F_μνF_ρσ with χ antisymmetric in each pair; a real action forces pair-exchange symmetry χ^{μνρσ} = χ^{ρσμν} (reciprocity). Premetric decomposition: principal (20 components; generically birefringent), axion (1), skewon (15; nonreciprocity, gain/loss — absent from a real quadratic action). [standard]
G.2 The naive couplings vanish. ℱC_μνF{μρ}F^ν{}_ρ = 0 because F{μρ}Fν{}_ρ is symmetric while ℱ^C is antisymmetric; the dual version vanishes by F{μρ}F̃ν{}_ρ = ¼g{μν}F_αβF̃{αβ}. Clock vorticity cannot couple linearly to a quadratic photon stress through these contractions. [reproduced]
G.3 Class by class. Dilaton −¼Z_CF²: reciprocal, direction-even, changes normalization/impedance only. Axion −¼ϑ_CFF̃: boundary term if constant; polarization rotation or helicity splitting if varying — wrong observable. Kinetic mixing −(ε_C/2)ℱC_μνF{μν}: source/diagonalization term, no direction-odd vacuum cone. Principal metric-like ½K{μν}(F_μρF_ν{}ρ − ¼g_μνF²): equivalent to Maxwell in g^{μν} + K^{μν} — the only polarization-independent option. Generic Weyl-type W^{μνρσ}F F: multiple optical cones (birefringent). [standard]
G.4 The surviving operator fails. The required K^{μν}req ∝ N{(μ}R{ν)} is direction-odd, gauge-invariant and polarization-independent — but it is precisely an optical shift one-form, so δt↑ + δt_↓ = 0 on retrace (Appendix C.2). And a stationary passive medium in the transponder conserves frequency by time-translation symmetry: it changes wavelength, phase velocity, group delay and impedance, but the exiting carrier frequency is fixed by the entry frequency and the turnaround ratio; slowly varying parameters give δν ~ ν d(L_dev ε/c)/dt, suppressed by L_dev/c ~ ns–μs against flyby timescales of minutes to hours. [reproduced]
G.5 The theorem. Under (i) a local action, (ii) gauge invariance, (iii) a real action quadratic in F, (iv) a stationary clock background, (v) polarization-independent propagation, (vi) an ideal coherent transponder with fixed turnaround ratio — the constitutive tensor reduces to effective metric + dilaton + axion, and none produces the required Anderson clock bridge. Escapes: birefringence; dissipation/nonreciprocity (skewon — hardware, temperature and power dependent); nonlocality; active matter/transponder physics (e.g. M⁻²Bμ_Cψ̄γνψF_μν — composition- and design-dependent, and lacking a universality theorem); or a real force. [reproduced]
G.6 Closure cannot normalize. Under λ_C → λ_C + δλ the winding number and binary closure certificate are unchanged as long as the threshold is crossed, so topological data cannot distinguish λ_C = 1 from 0.9. Closure gates the bridge; it cannot set its amplitude. A unit coefficient must come from canonical normalization of a clock connection, a quantized minimal clock charge, a 10D reduction of an explicit matter/photon operator, or an independently derived constitutive principle — and note that q_C𝒜_μ is invariant under 𝒜 → a𝒜, q_C → q_C/a until the kinetic normalization is fixed. Separately: a one-bit closure channel cannot carry the continuous, planet-dependent ωR/c at all. [reproduced]
H.1 The 2008 set cannot self-validate. Anderson’s relation was extracted from the six then-available flybys; those events cannot independently test it. Under the framework’s own quoted uncertainties the agreement is not “within measurement uncertainty”: Galileo I 0.22/0.08 = 2.75σ; Rosetta I 0.27/0.05 = 5.4σ; Cassini 0.93/0.10 = 9.3σ. The quoted R² = 0.997 excludes the one predictive test and is dominated by NEAR. [reproduced]
H.2 Out-of-sample. Rosetta II: Anderson predicts +0.523 mm/s — reconstruction null. Rosetta III: +1.099 mm/s — null. Juno: +6.34 mm/s from published asymptotes — null, published 2014, with metre-scale reconstruction accuracy reported despite the post-perigee safe-mode event. [reproduced]
H.3 Errors in the framework’s flyby paper. Juno is listed as “not published / pending”; its geometric factor is given as G = 0.476 whereas the listed declinations give cos 18.4° − cos 39.2° = 0.174; the paper’s own formula then yields (3.099×10⁻⁶)(10389 m/s)(0.174) = 5.60 mm/s, not the tabulated 4.8 — and either value conflicts with the null. Rosetta II and III are labelled “symmetric, zero predicted” whereas the Anderson evaluation gives 0.523 and 1.099 mm/s. These are arithmetic and currency errors independent of any theoretical position and are corrected here. [reproduced; deployed page checked]
H.4 What the record supports. The ungated source-only relation is rejected by the later nulls. A fixed-hardware explanation is also constrained: Rosetta showed an anomaly in 2005 and nulls later on the same radio system; Juno’s coherent X-band transponder produced a null; reported anomalies span S and X bands. What the record correlates with more plausibly is tracking coverage, attitude and solar-radiation-pressure modelling, and how separate inbound and outbound arcs were fitted — a published reanalysis found reflectivity and direct solar-pressure uncertainties could account for some cases while stressing that missing tracking and attitude data prevent a firm conclusion. Juno’s encounter had unusually extensive tracking: a plausible zero-utilization case, to be demonstrated from metadata rather than asserted. [record]
H.5 The η_a program. For each of Galileo I/II, NEAR, Cassini, Rosetta I/II/III, Messenger, Juno: assemble station identities, transmit/receive time tags, link mode, count intervals, ramp records, range coverage, angular/VLBI data, clock resets and solve-for parameter lists; construct H and W; form P_⊥ = I − A(AᵀWA)⁻¹AᵀW; compute η_a against the STF template s_STF,a from the no-work deflection (§7.3) and, separately, from the connection holonomy (§3); compare with the detection/null pattern after the computation is fixed. [stated]
Project papers (existshappens.com): STF from First Principles V8.1 — The Two-Clock Theory; The Clock-Separation Theorem V1.1; The Universal Embedding Principle V1.1; The Closure–Capacity Correspondence V1.0; One Bit of Destiny V1.0; Theory of Time V4.3 (§10.3, universal and local time); The Structure of What Happens V3.1; Topological Closure on the Complexified Null Cone V6.3; observational discovery record (held separately).
External: Anderson, J.D. et al. (2008), Phys. Rev. Lett. 100, 091102. Acedo, L. (2017), arXiv:1701.05735. Costa, L.F.O. & Herdeiro, C. (2008), gr-qc/0612140; Costa & Natário (2014), arXiv:1207.0465. Hehl, F.W. & Obukhov, Y.N. (2003), Foundations of Classical Electrodynamics; Hehl (2016), arXiv:1601.00320. Henry, R.C. (2000), astro-ph/9912320; Cherubini et al. (2003), gr-qc/0302095. JPL DESCANSO Monograph 2 §13 (DSN observables); Monograph 14 ch. 5 (transponders); Descanso 16 (Juno telecommunications); JPL deep-space navigation history, AAS 20-447; NASA NTRS 20160008163 (Juno reconstruction). Margot, J.-L. et al. (2018), NTRS 20190002330 (Earth moment factor); Jupiter interior, arXiv:1109.1627; Venus rotation and interior, arXiv:2103.01504. Mbelek, J.P. (2008), arXiv:0809.1888. Minguzzi, E. (2002), gr-qc/0204063 (clock synchronization connection). Nichols, D.A. et al. (2011), Phys. Rev. D 84, 124014. Semerák, O. (2016), arXiv:1608.05948. Senovilla, J.M.M. (2000), gr-qc/9906087 (superenergy). Turyshev, S.G. & Toth, V.T. (2010), arXiv:0907.4184. TU Delft flyby reanalysis, repository uuid:a537388f-c526-45ee-b762-514a8d0ed14f. Wald, R.M. (1984), General Relativity. Yunes, N. & Pretorius, F. (2009), Phys. Rev. D 79, 084043.