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Applied Identity Physics: The Terraformable Band — Locked Planets Between the IVA Floor and the Forcing Ceiling, 101 Placed, With Required Warming in Kelvin From Luminosity and Distance Alone

Year: 2026
Type: article
Abstract: Applied Identity Physics: The Terraformable Band — Locked Planets Between the IVA Floor and the Forcing Ceiling, 101 Placed, With Required Warming in Kelvin From Luminosity and Distance Alone Brightening on Fractional Main-Sequence Age, the Far Bound as a Property of the Working Fluid, and Mars Carried From Both Directions — Formally Verified, 0 Sorry, 0 Free Parameters, CI Green Architect HIGHTISTIC (Russell Vernon Trent III) · SNSFT Foundation · Kenai, Alaska Coordinate [9,9,3,28](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 · [9,9,3,27] IMatter™ · [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 Companion tool AtlasGoldilocks™ · uuia.app/atlasgoldilocks Formal layer SNSFL_TerraformableBand_Reduction.lean [9,9,3,28](COSM) · 50 theorems + master · 551 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 The Goldilocks annulus of [9,9,3,26] places a planet between the boil at τ = TL and the IVA floor at τ = 0.88 × TL. A planet already inside that annulus is reading IVA. A planet inside the boil is reading Shatter. Locked is the one phase with headroom, and this reduction gives the band inside Locked where that headroom can be spent. Three results follow, and each is stated against the published record. The brightening law runs on fractional main-sequence age. Writing f = age / t_MS and normalizing the Gough 1981 solar track to zero-age main sequence gives L(f)/L_zams = 1.4 / (1.4 − (400/457) f) — one law, every stellar mass, no free parameters, and the substitution is a change of variable that maps the Gough denominator term for term rather than approximating it. Earth crosses s = 0.88 at f = 0.351138, which is 1,059 Myr ago, the figure carried in [9,9,3,26]. The crossing has a closed form and needs no iteration. The far bound belongs to the working fluid. The published outer edge of the habitable zone stands at effective flux 0.3853 for a Sun-like host under carbon dioxide and at 0.19 to 0.22 for an M8V host, and it moves with carbon dioxide partial pressure across the 1 to 35 bar range of the published parametrization. Engineered conductive aerosols warm per unit mass by a factor of 5 × 10³ over the best gases. Reduced, the near bound is geometric — s = 0.88 exactly, with luminosity, effective temperature and stellar radius all cancelling — and the far bound is a property of the forcing agent and the spectrum it sits under. The two bounds are different kinds of object, and the band between them is read accordingly. Required warming computes from luminosity and distance alone. For a planet reading reduced flux s, the warming that carries it to the IVA floor is ΔT = T_eq · [(0.88/s)^¼ − 1], with no interior model and no atmosphere model in it. Across the band the figure runs from 0.2 K to 74.9 K. Applied to the NASA Exoplanet Archive, 101 planets stand inside the band. Of the 47 whose host age and mass are both published, the star carries 31 of them to the IVA floor within its main sequence, and for 16 the main sequence closes first. Each route is certified across the published error bars: 35 of the 47 hold across the host age bar, 14 hold across all five bars taken at once, and ten of the forcing-route rows are certified. Mars is carried from both directions. Run through the identical path with nothing specific to it, Mars reads s = 0.41417, stands 8.6% across the band, requires 46.8 K, and returns a retention figure 10.6× worse than Earth's from mass and radius alone. The Sun reaches the IVA floor at Mars in 6.05 Gyr with about 5.4 Gyr of main sequence left. The published volatile inventory for Mars reaches about 7% of one bar against the tens of bars that near-ceiling forcing takes. Geometry and inventory are measured independently and they meet. LHS 1140 b stands at 0.0865 across the band against Mars at 0.0857 and requires 46.7 K against Mars at 46.8 K — the same placement to a tenth of a Kelvin, with an escape velocity of 20.13 km/s and a retention figure 24× better than Earth's, under a main sequence of 685 Gyr. What a reader gets from this paper A planet's distance from its star and its host luminosity are published numbers. From those two and the Torsion Limit, this paper gives the reader the band a Locked planet stands in, the warming in Kelvin that carries it to the IVA floor, and whether its own star will deliver that warming before the main sequence closes. Every step is arithmetic a reader can run, and the full placement of all 101 band members is carried in Appendix A so that nothing has to be reconstructed. 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, the load, is the vapor pressure; Pattern, the structure, is the ambient pressure; Shatter is the boil, where vapor pressure reaches ambient; and IVA Peak is vapor pressure between 0.88 and 1.00 of ambient — the simmer, shaking at the bottom of the pot before the rolling boil. 1.5 The temperature mapping Vapor pressure and temperature are linked by the Clausius–Clapeyron relation (Clapeyron 1834; Clausius 1850), which works in absolute temperature:
DOI: 10.5281/zenodo.24148005
Language: English
Open Access status: green
OpenAlex ID: W7225817302
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