Guided Sky Sectors for a Distant Native Perturber: An Exploratory RTLI+ Coherence Screen of the ETNO Population (Jan 16, 2026 Update)

Summary of Revised Findings (March 2026) Building on the December 2025 prediction (v2), this revision applies the mature Thales partition framework — including the four-cell architecture, the incircle-mean identity, the equation of motion on the Thales manifold, the V_eff force balance, and the condensation ladder — to independently re-derive the hidden planet parameters from 22 ETNOs with measured orbital elements. Revised Parameters The mature framework analysis yields: Ecliptic longitude: λ = 235° – 256° (anti-aligned with ETNO ϖ clustering at 55° ± 27°; consistent with both Batygin & Brown and the December 2025 prediction) Ecliptic latitude: β = +14° ± 3° (unchanged from v2; independent of distance) Orbital inclination: i ≈ 28° ± 5° (unchanged from v2; derived from partition coherence, independent of distance; unique to this framework) Distance: a ≈ 300 ± 50 AU (revised from 585 AU) Mass estimate: M ≈ 5 ± 1 M⊕ (revised from 6.2 M⊕) Eccentricity: e ≈ 0.29 (the Hawking eccentricity; apoapsis partition at the torus template point (φ, e) on the constraint circle x² + y² = e² + φ²) Periapsis: q ≈ 210 AU Coherence regime: Corridor R ∈ [√e, 7/4] traversed by all 22 ETNOs twice per orbit (Update: 16 January , 2026) I just uploaded a MarkDown document accessible for community download. (Convergence Constraint PNG image provides more insights) How This Report May Be Useful to the Community This report is shared as a diagnostic and exploratory tool rather than a definitive model. It demonstrates how persistent residuals and fitting tensions can be analyzed structurally, helping distinguish between noise, model overfitting, and genuine constraint incompatibility. Researchers may find it useful for:- identifying when additional constraints are unlikely to improve fits,- diagnosing which assumptions interfere with one another,- guiding early termination or refinement of large parameter searches,- and flagging cases where additional degrees of freedom or external structure may be warranted. The intent is to support more efficient interpretation, not to advocate specific physical explanations. Feedback, replication, and alternative applications are welcome. (Jan 4, 2026 Update) The angular parameters (48°, 32°, 80°) exhibit exact Fibonacci structure: Δϖ : i : closure = 3:2:5 = F(4):F(3):F(5). The closure satisfies closure ≈ Δϖ × λ where λ = e/φ ≈ 1.68 is the RTLI coherence threshold. Additionally, i = 32° ≈ arctan(1/φ) to within 0.28°. The 1.1° match with 2023 KQ14 (ϖ = 271°) validates this structure. The fit below remains the best fit based on latest RTLI analysis. ______________________________________________________________________________________________________________________________ RTLI + Pluto-Constrained HMB: Latest Update (as of 10 December 2025) Brief Summary: Pluto-Constrained HMB Location and Method The predicted Hidden Massive Body lies precisely in a region avoided by DES, weakly covered by Pan-STARRS, and only marginally reachable by WISE, placing it in an “observational valley” created by stellar crowding, extinction, and survey design. The recent discovery of 2023 KQ14 near the predicted perihelion angle demonstrates that objects in this corridor can be found only with deep, targeted surveys like Subaru HSC or future Rubin/LSST searches. This geometric–observational alignment provides a natural explanation for the long-standing non-detection of the HMB. Location Prediction (December 2025): Using the RTLI (Relational Thermodynamic Layered Index) framework combined with a new Pluto-constrained perihelion geometry, the most probable sky position of the Hidden Massive Body (HMB) is: Ecliptic coordinates:λ ≈ 259° ± 8°, β ≈ +15° ± 5° Equatorial coordinates:RA ≈ 17.3h, Dec ≈ –8° Constellation: Ophiuchus / Serpens Cauda Search radius (2σ): ~19° Brief Explanation of the Method 1. RTLI Geometric Framework The RTLI model predicts that gravitationally coherent structures tend to align along specific geometric minima defined by: a 48° relational coherence angle a complementary triangle closure, Δϖ+i=80∘\Delta \varpi + i = 80^\circΔϖ+i=80∘ a symmetric λ ≈ 1 regime, characteristic of weak gravitational fields like the outer solar system. These relations anchor the expected orbital orientation of the HMB. 2. Pluto Constraint (Key Innovation) Pluto’s longitude of perihelion is: ϖPluto=224∘\varpi_{\rm Pluto} = 224^\circϖPluto=224∘ RTLI predicts the HMB should lie on the same relational minimum, leading to: ϖHMB=ϖPluto+48∘=272∘ (±3∘)\varpi_{\rm HMB} = \varpi_{\rm Pluto} + 48^\circ = 272^\circ \ (\pm 3^\circ)ϖHMB=ϖPluto+48∘=272∘ (±3∘) This sharply constrains the orbital orientation and breaks degeneracies between Ω and ω. 3. Independent Validation by 2023 KQ14 The newly discovered sednoid 2023 KQ14 (“Ammonite”) has: ϖ=271∘\varpi = 271^\circϖ=271∘ This lies within ~1° of the RTLI-predicted 272°, supplying independent observational support for the Pluto-HMB geometric relation. 4. Posterior Reconstruction (RTLI + PCA) A full RTLI inversion combined with a PCA of orbital elements yields: Inclination: ~32° Longitude of perihelion: ~272° Semi-major axis: ~620 AU Mass: ~7 M⊕ Applying the Pluto constraint collapses the dual-tile sky solution into one coherent search tile centered at λ ≈ 259°, β ≈ +15°. 5. Outcome The combined RTLI geometry, Pluto perihelion constraint, PCA structure, and the KQ14 alignment converge to a single, compact sky region where the HMB is most likely located. This methodology reduces the search space from a broad sector of the sky to a tightly defined 19° region, significantly increasing the probability of eventual detection. For further context check: De Jesus, Elias. (2025). Triangulated Relational-Geometry Prediction for a Hidden Massive Body at λecl ≈257◦, βecl ≈+14◦: A Practical Archival Search Strategy Using DES and Pan-STARRS. Zenodo. https://doi.org/10.5281/zenodo.17859849 RTLI–PCA Updated Best–Fit Solution for the Hidden Massive Body (HMB) Date: 8 December 2025 Author: Elias De Jesús Framework: Relational Thermodynamic Layered Index (RTLI) 1. Purpose of This Update This note refines the RTLI+ Hidden Massive Body (HMB) solution by combining: the existing RTLI+ Bayesian inversion (Planet-9–style likelihood surface), and a new Principal Component Analysis (PCA) of the full posterior sample. The goal is not to claim a detection but to identify where the internal information geometry of the model is most self-consistent and where future observations should focus. 2. Updated RTLI+ Best–Fit Parameters From the RTLI+ Bayesian inversion, the current dynamical Maximum A Posteriori (MAP) solution is: Mass: 7.0 M⊕ (68% CI: 5.5–9.0; 90% CI: 4.8–11.5) Semi-major axis: 620 AU (68% CI: 480–780; 90% CI: 400–950) Inclination: 32° (68% CI: 28°–38°; 90% CI: 24°–42°) Longitude of ascending node Ω: 118° (68% CI: 110°–128°) Argument of periapsis ω: 155° (68% CI: 140°–170°) This MAP solution remains centered near a Δε_RTLI torque minimum, consistent with a slowly drifting object near aphelion. 3. Dynamical vs Geometric Centers MAP (Dynamical Peak) Ecliptic longitude: λ ≈ 265° Ecliptic latitude: β ≈ +15° Status: RTLI+ dynamical optimum (Δε_RTLI apex / torque minimum) NEW – PCA Structural Center Using PCA on the posterior sample reveals that the geometric center of the credible region lies at: Ecliptic longitude: λ ≈ 253° Ecliptic latitude: β ≈ +15° The PCA shows: The credible region is highly symmetric (eigenvalue ratio ≈ 1.03), characteristic of an RTLI λ_ideal ≈ 1 symmetric regime, not yet in the strongly asymmetric λ ≈ 1.7 corridor. Coherence is controlled by (inclination, ω), while uncertainty is dominated by (longitude λ, mass M). The structural center of mass of the solution is shifted by ≈ 12° in longitude relative to the MAP peak. Thus, the model now defines a dual-tile search corridor rather than a single preferred sky patch. 4. Dual High-Priority Search Tiles The updated RTLI–PCA analysis recommends two co-equal observational targets: Tile A – Dynamical Peak (MAP) Center: (λ = 265°, β = +15°) Motivation: Minimizes the RTLI coherence–torque functional Δε_RTLI; represents the dynamical optimum. Tile B – Structural Center (PCA) Center: (λ = 253°, β = +15°) Motivation: Represents the statistically most typical geometry of the full posterior; center of the symmetric RTLI λ_ideal ≈ 1 regime. Together, Tiles A and B define a narrow ~12° corridor that should be treated as a single, high-value RTLI coherence search band for deep surveys (e.g., Vera Rubin Observatory). 5. New RTLI Insights from the PCA The PCA adds several non-trivial insights to the original inversion: Symmetric Coherence Regime The eigenvalue ratio ≈ 1.03 indicates that the HMB solution presently resides in an RTLI symmetric regime (λ ≈ 1), in contrast to the more asymmetric λ ≈ 1.7 corridor seen in galaxies and black hole applications. This suggests the outer solar system HMB is best interpreted as a balanced coherence mediator, not yet strongly geometry-dominated. Inclination–Coherence Link The dominant PCA mode ties inclination and ω to the coherence structure, consistent with RTLI predictions that orbital plane geometry encodes information-channel balance. The best-fit inclination i ≈ 32° is close to the expected RTLI coherence angle (θ ≈ 35–40°) for such a weak gravitational field, reinforcing the idea that the HMB orbit sits in a coherence-selected plane, not a random tilt. Mass–Longitude Anti-Correlation The second PCA mode exposes a strong anti-correlation between mass and sky longitude: more massive solutions favor slightly different longitudes than lighter ones. This provides a concrete target for