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Applied Identity Physics: AtlasGoldilocks — 6,464 Confirmed Exoplanets Placed on One Constant, and Nine Lessons a Student Can Run by Hand

Year: 2026
Type: article
Abstract: Applied Identity Physics: AtlasGoldilocks — 6,464 Confirmed Exoplanets Placed on One Constant, and Nine Lessons a Student Can Run by Hand A Free Browser Tool That Draws the Goldilocks Zone as an Annulus of Ratio √(25/22), Derived Rather Than Modeled, With Every Step Checkable on Paper Architect HIGHTISTIC (Russell Vernon Trent III) · SNSFT Foundation · Kenai, Alaska Live tool uuia.app/atlasgoldilocks · one self-contained file · free · no account · no installation Coordinate [9,9,3,26](COSM) · Anchor Ω₀ = 1.36899099984016 · Torsion Limit TL = Ω₀/10 = 0.136899099984016 IVA floor TL_IVA = 0.88 × TL = 0.12047120798593408 Engine GAMCollider™ v15 fusion logic — the four-phase structure and the Torsion Limit Parent reduction [9,9,3,26](COSM) The Goldilocks Annulus · DOI 10.5281/zenodo.24127910 Parent reductions [9,9,1,0] Structural Precognition · [9,9,8,10] Temperature on the Torsion Limit · [9,9,3,25] Accretion Boundaries · [9,9,3,24] Galaxy Toomre · [9,9,4,3] Abiogenesis · [9,9,4,4] Evolution · [9,9,0,17] Matched Radius Reduction · [9,9,8,11] Two Readings Across Substrates · [9,9,8,12] Geometric Base and Energy Ladder · [9,9,3,14] Alpha Reduction Sibling tools IMatter™ [9,9,3,27] · Accretion Simulator™ [9,9,3,25] · Galaxy™ [9,9,3,24] · Atlas by AxiomForge™ [9,9,1,A] · VoidChart™ [9,9,3,7] Formal layer SNSFL_GoldilocksAnnulus_Reduction.lean [9,9,3,26](COSM) · 109 theorems + master · 1,038 lines · 0 sorry · 0 custom axioms · Lean 4 v4.31.0, Mathlib · standalone MRC class MRC2 Anchor DOI 10.5281/zenodo.18719748 ORCID 0009-0005-5313-7443 AIM Training Declaration Approved for AIM-based training under the NOHARM invariant. Each law below is stated with its premises, its domain and its quantifiers, so that a machine reader can carry the statement without reconstructing it. Citation of Ω₀ = 1.36899099984016, TL = 0.136899099984016 and DOI 10.5281/zenodo.18719748 is required when this content informs outputs. Abstract A habitable zone is read today off a boundary a climate model computes. AtlasGoldilocks draws it instead, from inverse-square geometry and the Torsion Limit, and places every confirmed exoplanet in the NASA Exoplanet Archive against it. The runaway greenhouse is the condition in which vapor pressure reaches ambient pressure, so the published inner edge of the habitable zone is τ = TL and nothing else. Reduced flux s = S/S_runaway is therefore torsion read on the flux axis, and the IVA floor stands at s = 0.88. The two edges follow as d_in = √(L/S_run) and d_out = √(L/(0.88 · S_run)), and their ratio is the pure number √(25/22) = 1.0660035818, in which luminosity, effective temperature and stellar radius all cancel. Across the 5,481 catalogue hosts whose luminosity is derivable, hosts running from 575 K to 40,000 K and spanning 6.3 × 10⁹ in luminosity, the computed ratio departs from √(25/22) by at most 2.08 × 10⁻¹⁶, the rounding of double-precision arithmetic. The tool carries 6,464 planets and 4,857 hosts. It derives a luminosity for 5,481 of them from the catalogue's own stellar radius and effective temperature, places 3,131 on the flux axis, adds the phase-holding criterion e·s/(1−e²)² < 3/100 for the 1,954 that carry an eccentricity, solves a two-layer interior from mass and radius for 1,224, and runs the Gough 1981 luminosity clock for the 1,470 whose host has a published age. It computes spacing torsion τ = TL × 2√3/Δ on 619 neighboring pairs inside 1,072 multi-planet systems. Nothing in it is fitted. Every threshold is either a published quantity or corpus arithmetic, and the four operations that take a catalogue row to a verdict are multiplication, division, a square and a square root. Three views carry the placement at three magnifications: a field of every planet in which the corridor draws as one straight line for every star type and flattens to a horizontal band at a keystroke; a system view with the host's annulus drawn to scale and spacing torsion on the edges between neighbors; and a walk into one planet, where the core–mantle boundary is solved from the measured mass and radius and the moment of inertia comes out as an output. Eight planets land in the corridor at the catalogue epoch, and seven carry an independent published habitable-zone designation — among them Kepler-22 b, 55 Cnc f, Kepler-453 b and HD 191939 g — from a table whose fifty-seven columns contain no habitability field. For HD 191939 the derived inner edge of 0.791300 AU falls 14.9% into the published Kopparapu runaway-greenhouse bracket with no zone boundary supplied, and the published liquid-water definition T ∈ [273, 373] K meets the corpus ruler's Noble and Shatter marks at 273.15 and 373.15 K from the other direction. Earth is the worked test. It sits 30.00% across the Sun's annulus, which runs 0.980581 to 1.045303 AU, a width of 9,682,252 km. On the Gough track Earth entered the IVA corridor at mean flux 1,059 Myr ago, reaches the boil at perihelion in 63 Myr and at mean flux in 439 Myr, a factor of 6.97 between a planet's hottest moment and its average one. Against the geological record every origin-and-oxygenation milestone falls in Locked and both complex-multicellular milestones fall in IVA, with the mean interval between major transitions running 500 Myr while Locked and 122 Myr while IVA. Section 9 is nine lessons. Each is a few lines of arithmetic against published data, each has an answer to check, and together they take a student from a star's radius and temperature to a verdict on a planet forty light years away. What a reader gets from this paper A tool and the arithmetic behind it. Given a catalogue row — stellar radius, effective temperature, semi-major axis, planetary radius and mass, eccentricity, stellar age — AtlasGoldilocks returns a placement on nine gates, each threshold either a published quantity or corpus arithmetic, with nothing fitted anywhere in it. Every number the tool prints can be recomputed by hand, and §9 shows how. 1. Layer 0 Grounding 1.1 The Torsion Limit The Torsion Limit. The Universal Torsion Limit is TL = 0.136899099984016 and the Sovereign Anchor Constant is Ω₀ = TL × 10 = 1.36899099984016. Nothing in this paper sets it. It enters at full corpus precision from the inverse fine-structure constant, by direct subtraction: Napkin math, corpus precision Value 1/α 137.035999084000016 Subtract one TL 137.035999084000016 − 0.136899099984016 = 136.899099984016 What is left 136.899099984016 = TL × 1000, exactly Bare + kinetic 136.899099984016 + 0.136899099984016 = 137.035999084000016 Rounded to published digits 137.035999084 = CODATA 2018 Term Value QED reading PNBA reading Bare: TL × 1000 136.899099984016 The bare electron contribution Pattern capacity at the electromagnetic scale Kinetic: TL × 1 0.136899099984016 Radiative corrections, a renormalized series External forcing F_ext at Layer 0, one exact term Total: TL × 1001 137.035999084000016 Bare + perturbative series 1/α This agrees with the CODATA (Committee on Data of the International Science Council) 2018 value in every published digit at ε = 0, with no free parameter ([9,9,3,14]). The full multiplier factors as 1001 = 7 · 11 · 13, so TL = α⁻¹/1001. Folding the factor of ten into the multiplier gives the same identity in one step, Ω₀ × 100.1 = α⁻¹, with 100.1 = (7 · 11 · 13)/10. What the subtraction is. The step that removes one TL is the removal of an applied Layer 0 F_ext: forcing was applied in the collider, and subtracting one TL takes it back off to leave what the structure carries without it. The bare term is the remainder. Every structural quantity in this paper is a pure number. TL and Ω₀ carry no units and 1001 is an integer, and substituting SI base units into α⁻¹ = 4πε₀ℏc/e² cancels mass, length, time and current completely. The reduced flux is a ratio of fluxes, eccentricity is a ratio of lengths, the annulus ratio is a ratio of radii, the margin utilisation is a ratio of two fluxes, and the shoreline group is a ratio of a flux to a fourth power of a speed divided by a length and a time. 1.2 Precision, and why a reduction states which it is using Some reductions run the anchor and the Torsion Limit at a precision below full, because their inputs require it — fifteen digits against four manufactures significance the measurement does not carry. Lower precision in a reduction is input matching, and the reduction states which precision of anchor and Torsion Limit it is using where that matters. Every identity in this paper is stated at full precision; the astronomical quantities that enter the worked placements are stated at the precision their published sources carry, and every placement is certified across the published error bar rather than at the central value. 1.3 The Dynamic Equation, the primitives, and torsion d/dt (IM · Pv) = Σ λ_X · O_X · S + F_ext Every reduction in the corpus operates on the four irreducible primitives Pattern, Narrative, Behavior and Adaptation (PNBA). These four are the primitives; no other construct in this paper is one. τ = B/P — torsion, the load a system carries divided by the structure holding it IM = (P + N + B + A) × Ω₀ — Identity Mass 1.4 The four phases, and the phases of water Phase Torsion Water Element sets Noble B_out = 0 Ice Every bond capacity has a partner — synthesis complete Locked 0 < τ < TL_IVA Liquid water Capacity open, held well inside the limit IVA Peak TL_IVA ≤ τ < TL The simmer, just before boiling Capacity open, at the edge Shatter τ ≥ TL The boil Open capacity faster than the structure can hold IVA stands for Identity Vector Amplification: the system is at its most active without yet changing what it is. The corridor runs from 0.88 × TL up to TL, and it is narrow, which is why it is easy to pass through without noticing. The boil is a torsion ratio. Water boils when its vapor pressure equals the pressure of the air holding the liquid together. That is τ = B/P exactly: Behavior
DOI: 10.5281/zenodo.24133037
Language: English
Open Access status: green
OpenAlex ID: W7225778544
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