RTLI Corridor Update v5: Pluto-Constrained Geometry, KQ14 Validation, and a Collapsed Single-Tile Apex for a ~7 M⊕, ~620 AU, i ≈ 32° Hidden Massive Body

Additional technical notes and experimental reports related to the IVT, corridor width, and variance-mediated phase transitions are available on Zenodo.To locate the full body of related work, please use the Zenodo search box and enter the author name with quotation marks: "De Jesus, Elias" Using quotation marks ensures accurate retrieval of all associated records and avoids fragmentation due to name variations. Update (18 Jan 2026) New document uploaded: Saturation Diagnostic Stability Under Domain Transfer: Application to Exoplanet Systems This update extends the previously introduced saturation diagnostic to a physically distinct domain: Kepler exoplanet systems (4,556 confirmed and candidate planets). The goal of this extension is not to assert universality, but to evaluate diagnostic stability under domain transfer, where constraints are externally mediated, noisy, and subject to selection effects. Three saturation signatures were tested: Correlation inversion Diversity inversion (entropy peak followed by decline) Regime discretization (emergent gaps / bimodality) The results reveal a clear diagnostic hierarchy. Correlation inversion weakens and becomes partial under external constraint mediation, while diversity inversion remains robust and non-monotonic. Regime discretization emerges as the most stable signature, exemplified by the well-documented exoplanet radius gap (~1.7 R⊕), which is interpreted here as a failed-configuration zone rather than a sampling artifact. The analysis supports a constrained interpretation: saturation diagnostics persist under domain transfer, but with ordered degradation reflecting increased contextual complexity. Discretization survives where correlation does not, indicating that digital-like architectural outcomes can emerge from underlying analog dynamics when reconciliation limits are exceeded. This document refines the scope of the framework, clarifies its failure modes, and strengthens its role as a diagnostic tool for constraint-limited systems, rather than as a universal explanatory theory. ______________________________________________________________________________________________________________________________ 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) 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. Brief Summary: Pluto-Constrained HMB Location and Method Location Prediction (December 10, 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. 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 future N-body and survey-bias studies: constraining λ more tightly will automatically reduce the allowed mass range. Internal Consistency Check for RTLI The fact that the RTLI+ inversion and PCA geometry converge on a narrow corridor (rather than div