Temporal Equivalence Principle: A Proper-Time Domain Boundary in the Outer Solar System

The orbital alignment of extreme trans-Neptunian objects (TNOs) is conventionally attributed to a distant, undiscovered point mass. This paper tests a deterministic alternative under the Temporal Equivalence Principle (TEP), in which the anomaly is modelled as a spatially fixed proper-time field gradient — a localized domain boundary — rather than a shepherding planet. Two dynamically distinct populations, drawn from the JPL Small-Body Database and the independent CODE cometary catalogue, are shown to isolate the same 60-degree sector of inertial sky. The resident population — detached extreme TNOs that remain in the boundary region for secular times — clusters about a common perihelion direction. The clustering survives a strictly measured discovery-footprint null calibrated against the characterized Outer Solar System Origins Survey ensemble, and it lacks the resonant substructure and physical-element coupling that a secular shepherding model requires. The transit population — long-period comets that plunge through the boundary direction on a single pass — carries the complementary signature. Comets arriving from that sector show a significant orbit-reconstruction discrepancy: an in-plane orbital rotation localized to the perihelion element and weighted to the inbound trajectory, occurring without orbital energy exchange, and persisting after regression of a REBOUND N-body planetary baseline, of observational leverage, and of each orbit's own published error budget — a decomposition that excludes dissipative mechanisms, such as asymmetric interstellar-medium drag, on the channel through which they must act. The measured quantity is a direction-organized reconstruction discrepancy of order 0.1^° concentrated in the clock-sector elements; under the crossing-localized holonomy realization — selected by the velocity-flat transfer function of Section 4.15 — the conversion δ t_ eq = δθ r_b²/h maps it to an equivalent proper-time offset of approximately five years (+ 4.9 yr on the matched CODE sample, + 5.0 yr on the Warsaw inbound channel; p = 0.00532 and p = 0.0079 ). The equivalent-time figure is thus an interpretation-conditioned conversion of the measured angular residual, not a directly read clock slip. Three independent checks confirm that the signature is real. The comets' aphelion directions — a spatial observable that no orbit reconstruction can manufacture — dipole toward the same axis at the 10⁻²–10⁻⁴ level under tested tide-aware nulls, establishing a direction-organized arrival population whose interpretation (primordial anisotropy, selection residual, or the boundary field) is degenerate and which is carried as consistency evidence rather than a discriminating channel; the identical bidirectional integration reproduces the Warsaw catalogue's boundary solutions. In the leg decomposition the inbound leg is significantly elevated (p = 0.042 ) while the outbound leg is flat (p = 0.547 ), naturally producing the isotropic leg-twist angle (⟨cosϕ⟩ ≈ 0) expected of an inbound-only domain-wall traversal. The signature is then traced to the astrometric record itself rather than to any catalogue's reduction: an independent Levenberg–Marquardt two-leg refit of the raw Minor Planet Center astrometry on 586 pre-2018 comets — a record built without any Warsaw-lineage input — reproduces the per-comet boundary rotation at ρ = + 0.998 and retains the registered inbound-leg in-cap excess (p = 0.0341 ; p = 0.00695 on the CODE-overlap seat). Pointed at the post-2017 prospective cohort, the instrument isolates the operational boundary between orbit reconstruction and coordinate-invariant geometry. In the leg-separated reconstruction channel, the modern astrometry reverses the declared-axis carrier — median in-cap rotation 0.114 ° against 0.171 ° outside, permutation p = 0.920 , the excess running counter to the declared axis. Yet the modern record's own dominant structure is a lapse-slip anomaly of the identical signature class at the mirror position (joint opposite-polarity test p = 1.00×10 -4 ) — the quantitative support for the absorbed-slip interpretation, not a demonstrated extension of the anomaly; the reversed channel is carried as a separate ledger item rather than as convergent evidence for the declared axis. The reconstruction-free spatial aphelion channel — a coordinate observable no orbit reconstruction can manufacture — is flat across every measured orbit-quality stratum — bound and hyperbolic solutions, short and long arcs, sparse and heavily observed records alike. It independently replicates the declared-axis lean on the post-2017 cohort (d_∥ = + 0.0949 , p = 0.00215 under the tide-aware null; p = 0.00225 under the ecliptic null), persists across all 257 non-training members (+ 0.0827 , p = 0.00845 ), and matches both the full CometEls census (+ 0.10 , p = 7×10 -4 ) and the pre-2018 record (+ 0.110 , p = 5.00×10 -5 ). The displaced residual structure likewise persists where the fits are best determined, appearing strongest on bound and perihelion-spanning-arc members (+ 0.23 dex each). It is cleanly retained on the well-observed and non-gravitational-clean strata (p = 0.005 and p = 1.8×10 -4 , respectively), though its amplitude attenuates with transit epoch and on uniform-Gaia legs — a composition dependence priced in Section 4. An element-covariance perturbation audit then shows the dissociation cannot be manufactured by orbit-solution error: the leg-rotation observable cancels common-mode element noise at ~ 163× the aphelion channel's exposure, and at their published covariances only 1 member in sixty can be driven to the observed rotation-residual scale — the injected error required there would displace the same object's aphelion datum by ~ 0.61 °, a displacement the flat spatial channel does not carry. The spatial datum is therefore the more error-exposed channel — and it is the one that replicates. Spacecraft clock records bound local rate steps at the 1 ppm level, consistent with the first-order cancellation of static scalar potentials in two-way Doppler tracking. A ten-channel global synthesis spanning six catalogue lineages (SBDB, DES, MPCORB, CODE, Warsaw, and CometEls) demonstrates multi-lineage directional convergence on the same 60-degree sector, yielding an omnibus statistic of S_10 = 187.2 (p = 0.0118 against a 20,000-draw random-axis permutation null that prices the directional look-elsewhere for the pre-declared channel set and embeds the channels' own correlation structure). These multi-messenger, multi-population data provide mutually reinforcing evidence for a non-integrable dynamical time field in the outer solar system. The prediction is pre-registered and near-term falsifiable: for detached-TNO discoveries under the Vera C. Rubin Observatory's Legacy Survey of Space and Time, the boundary model predicts ~ 59 per cent of new objects inside the declared 60° cap against the ~ 42 per cent footprint-only expectation — a separation that ~ 123 discoveries resolve at 95 per cent power for a one-per-cent test (~ 83 at five per cent). The counterweights are registered alongside: the modern reconstruction channel reverses at the declared axis, the newest 2025–26 provisional cohort sits at its footprint baseline (2/21 in-cap, at anti-axis pointings) and Ammonite (2023 KQ14) lies 134^° off-axis; a mundane watch-flag is carried for the axis longitude itself — Neptune's mean varpi lies 4.0^° away (a priori p = 0.022), though the coincidence does not extend to Neptune's forced secular directions (112^° off-axis, p = 0.62); and the mechanism's required field excursion remains an open condition on the solved profile rather than a derived output. Keywords: Kuiper belt: general – comets: general – gravitation – celestial mechanics – astrometry Website: https://mlsmawfield.com/tep/9/Repository: https://github.com/matthewsmawfield/TEP-9 DOI: 10.5281/zenodo.22858191 Open Science Statement: This work is a preprint and is open to community review, ideas, and collaboration. All materials required for full reproducibility—including data downloads, analysis scripts, code, and manuscripts—are open-source. Feedback and contributions to further test these results are welcome.