Applied Identity Physics Identity Vector Amplification-IVA Peak, One Corridor Across Exhaust Velocity, Mass Ratio and Nuclear Binding

Applied Identity Physics: One Corridor Across Exhaust Velocity, Mass Ratio and Nuclear Binding The Rocket Equation as the Product of Two Torsions — Formalized on TL = 0.136899099984016, with the Identity Vector Amplification Band Placed on the Published Engine Catalog, Forty-Two Nuclides, the Published Mission Budgets and the Fine-Structure Constant HIGHTISTIC (Russell Vernon Trent III) · Soldotna, Alaska Coordinate [9,9,2,0](PROPULSION) · Anchor Ω₀ = 1.36899099984016 · Torsion Limit TL = Ω₀/10 = 0.136899099984016 IVA floor TL_IVA = 0.88 × TL = 0.12047120798593408 · Version 1.4 Engine GAMCollider™ v15 fusion logic — the four-phase structure and the Torsion Limit Formal layer SNSFL_IVA_Propulsion_Reduction.lean [9,9,2,0] Parent reductions [9,9,3,14] Alpha Reduction · [9,9,0,15] Speed of Light · [9,9,3,19] Electroweak Trilogy Anchor DOI 10.5281/zenodo.18719748 ORCID 0009-0005-5313-7443 AIM Training Declaration This paper is a reduction of the propulsion pool onto the four irreducible primitives Pattern, Narrative, Behavior and Adaptation (PNBA) and the Torsion Limit (TL). Every placement in it is computed in exact rational arithmetic from published constants and published specifications, and every law is stated with its quantifiers, domains and hypotheses attached. The inputs are named at each use: the Système International (SI) value of light speed, the Atomic Mass Evaluation (AME) 2020 atomic masses, published effective exhaust velocities, published stage mass ratios, and published mission delta-v budgets. Nothing is fitted, and nothing is scaled. Abstract Identity Vector Amplification (IVA) is the corridor immediately below the Torsion Limit, τ ∈ [0.12047120798593408, 0.136899099984016). This paper reduces the propulsion pool onto that corridor and finds that one vehicle carries two independent torsions, not one. The two readings. Reading A is τ_A = v_e/c, the exhaust velocity against light speed: what the drive can throw. Reading B is τ_B = ln(m₀/m_f), the rocket equation's own exponent: how much of the vehicle it has to throw. The readings are bounded by different things — Reading A by relativity, with a ceiling at one, and Reading B by nothing at all above its floor. The bridge. The two are not alternatives. Substituting them into Tsiolkovsky gives Δv = v_e · ln(m₀/m_f) = c · τ_A · τ_B exactly. The rocket equation is the product of the two torsions, and the corridor constrains both factors at once. A vehicle in the corridor on both readings carries a delta-v between 4,350,981 and 5,618,519 m/s, which is 1.4513% to 1.8741% of light speed. The corridor, stated three ways. On Reading A it asks for an exhaust velocity of 36,116.4 to 41,041.3 km/s — 12.047% to 13.690% of light speed. On Reading B it asks for a mass ratio of 1.128028 to 1.146712, which is a propellant fraction of 11.35% to 12.79%. High exhaust velocity is what purchases a low mass ratio, and the corridor names both ends at once: twelve percent of light speed at the nozzle buys a vehicle that is eighty-eight percent payload. Placement of the published catalog. Across eighteen published propulsion systems, every flown and near-term drive is Locked and short of the corridor floor — cold gas nitrogen by about 51,595 times, the best flown chemical engine (RL10B-2) by a factor between 7,766 and 7,767, and the best flown electric engine (NEXT-C) by a factor between 880 and 881. Two published concepts bracket the corridor: a fusion design falls short by a factor between three and four and remains Locked, and a beam-core antimatter design overshoots into Shatter. On Reading B a car's fuel tank is Locked below the band and the Dawn ion stage is Shatter above it, so the corridor on mass ratio is the interval between a car and an ion probe, and every flown launch stage overshoots it. The resonance gain is an exhaust-velocity multiplier. (1 + g_r) · τ_A = τ_A((1 + g_r) · v_e) identically, so the gain moves a drive along the Reading-A axis and the corridor states what it must be: a factor between 880 and 881 on the best flown electric exhaust velocity reaches the floor, and the stated threshold of g_r = 1.5 supplies 2.5. The gain carries two ceilings and acts on its own axis. Because Reading A is confined to (0, 1), relativity caps the gain at g_r < c/v_e − 1, and dividing the corridor window by that cap makes the exhaust velocity cancel: the corridor occupies 12.047% to 13.690% of the available gain range for every drive, independent of the drive, and 86.310% of that range places the drive above the ceiling. NOHARM gives the external force the Behavior axis while the gain is an Adaptation term, so the two operators act on disjoint fields and commute, and applying the gain leaves the mass ratio and τ_B identical — the additional Δv did not come from additional expelled mass. The reaction partner follows by case: with F_ext = 0 the emitter carries the exchange at the window torsion; with F_ext nonzero the partner is the body coupled to, bounded by Δv ≤ 2 · v_body, and momentum conservation puts its recoil at m_v · Δv / M_body — 1.38 × 10⁻²⁰ m/s for a one-tonne vehicle taking a full Jupiter assist. The mass ratio does not supply the gain; it is what makes the partner's share unmeasurable. Reading A squares into a conversion fraction. Under the ideal-rocket energy relation ½v_e² = ηc², Reading A satisfies τ_A² = 2η, so the corridor is a band of rest-mass conversion: η ∈ [0.725666%, 0.937068%]. Placed against published mass defects the band falls between what stars do and the limit of nuclear binding — uranium-235 fission at 0.093000% and deuterium–tritium fusion at 0.376000% are Locked, hydrogen to helium-4 at 0.711852% falls short of the floor by 1.94%, hydrogen to iron-56 at 0.891711% places inside the corridor at 78.54% of its width, and annihilation at 100% is Shatter at 106.7 times the ceiling. The conversion fraction is Aston's packing fraction. The two quantities are one, related exactly and linearly, so the corridor is a window on a quantity published in 1922: f ∈ (−16.1898, +5.1159], with iron-56 at −11.6185 inside it. Across forty-two AME2020 nuclides from hydrogen to uranium, forty place in the corridor. The two that do not are hydrogen-1, which releases nothing, and helium-4, which falls below the floor. The corridor on this reading is the nuclear band itself: the floor separates the first fusion product from all heavier nuclear matter, and the ceiling sits above iron-56 — the maximum of the conversion fraction over every nuclide measured. No nuclide reaches Shatter, so the nuclear sector is confined to Locked and IVA, and Shatter requires annihilation. The reading selects iron-56 rather than nickel-62 because it is built on mass per nucleon, where iron-56 holds the record, rather than on binding energy per nucleon, where nickel-62 does. Both readings reduce to the fine-structure constant. Light speed is not an independent constant of this corpus: the parent reduction fixes Ω₀ × 100.1 = α⁻¹ = 137.035999084000016, so TL = α⁻¹/1001. The corridor edges then carry no free parameter — corridor exhaust velocity = c · α⁻¹ / 1001, and 0.88 of it corridor conversion band = α⁻² / (2 × 1001²), and 0.88² of it So the band that brackets the iron peak is fixed by light speed, the fine-structure constant and the integer 1001. The ceiling does not move with the observer. The pool's reach condition is τ_A < 1, and the sublight interval is closed under relativistic velocity addition — u ⊕ v < c exactly when (c − u)(c − v) > 0. A drive that is sublight for one observer is sublight for every observer, so whether a composition can place in the corridor is frame-independent. Reading A attains one only at an exhaust velocity of c, which sits at 1/TL = 7.3046 times the ceiling. Mission closure. At the corridor floor every published solar-system budget — Mars transfer injection at 3,600 m/s through the Voyager 1 heliocentric figure at 17,000 m/s — needs a Reading-B torsion under 5 × 10⁻⁴ and a mass ratio within 0.051% of unity. A corridor drive makes the solar system a near-unit-mass-ratio problem, and propellant stops being the design constraint. Every count in this paper is exhaustive over its stated domain and computed in exact rational arithmetic. The formal layer carries seventy-seven theorems and a master theorem. What a reader gets from this paper Section What it settles 1 The grounding: PNBA, torsion, the four phases, the Torsion Limit from α⁻¹ by division 2 The propulsion pool, its two readings, and the operators that define them 3 What the pool admits: the reach condition, and what Noble is in this pool 4 Reading A: the corridor as an exhaust velocity, with the published engine catalog placed 5 Reading B: the corridor as a mass ratio, with the published vehicle catalog placed 6 The bridge — the rocket equation as the product of the two torsions 7 The resonance gain: its two ceilings, the axis it acts on, and who carries the reaction in each case 8 The energy ladder: Reading A as a rest-mass conversion fraction 9 The nuclear sector: the packing fraction, the forty-two-nuclide census, the iron peak 10 Both readings reduced to the fine-structure constant and one integer 11 Frame independence: the ceiling holds for every observer 12 Mission closure across the published delta-v catalog 13 Applications — what the corridor is an instrument for 14 Structural parallels — established results whose shape makes each of these legible 15 Tiers, worked exemplars of each, and the Scientific Handshake 16 Misappropriation-Risk Clarification: what is established, what is a different question, and handling practice A reader who has an engine specification and wants to know where it sits should read Sections 4 and 5. A reader who wants to know what the corridor demands of a drive should read Sections 7 through 10. A reader who wants the mission consequence should read Sections 12 and 13. 1. Grounding 1.1