FOPT-Assisted Resonant Leptogenesis: A Ratio-Threshold Framework with Gravitational Wave and Collider Falsifiers

This preprint presents a constrained synthesis framing first-order phase transition (FOPT) assisted resonant leptogenesis as a ratio-threshold mechanism governed by the invariant R = ε/W, where ε is the CP-asymmetric decay bias and W is the washout factor. A real scalar field φ undergoing a first-order phase transition at T* ~ 1–10 TeV generates right-handed neutrino (RHN) masses via M_N = λ_φN v_φ, suppresses washout through bubble-wall dynamics, and produces a stochastic gravitational wave (GW) background. Under symmetry-protected near-degeneracy ΔM ~ Γ_N, resonant CP enhancement yields ε_res ~ O(10⁻³), sufficient to produce the observed baryon asymmetry η_B ~ 6×10⁻¹⁰ within standard sphaleron conversion. Semi-analytic estimates place the GW peak frequency at f_peak ~ 0.1–1 Hz with Ω_GW h² ~ 10⁻¹³ to 10⁻¹⁰, potentially within DECIGO/BBO sensitivity and at the edge of LISA reach for favourable transition parameters. Three primary falsifiers are identified: (1) departure from the resonance condition ΔM ~ Γ_N; (2) null stochastic GW signal in the predicted frequency and amplitude window; (3) absence of lepton-number-violating same-sign dilepton signatures at FCC-hh (100 TeV). T3 (experimental confirmation) requires joint observation of signals (2) and (3) at mutually consistent parameter values. Neither observation alone is sufficient. The invariant framing adopted here is organisational rather than foundational. It preserves explicit separation between asymmetry generation (ε) and asymmetry survival (W), allowing corrections, phase-transition effects, and detector-linked falsifiers to be traced through a common threshold structure without altering the underlying leptogenesis formalism. All quantitative results are semi-analytic or order-of-magnitude estimates. Full numerical treatment using CosmoTransitions, PTPlot/GWfast, and density-matrix Boltzmann transport is required before precision claims can be made. The dominant open uncertainty is β/H*, estimated at 10³–5×10³ by semi-analytic thick-wall expansion; numerical bounce-action computation is the defined next step. Supplementary Material S1 contains the complete correction and audit log, recording all variable redefinitions, gate failures, and repairs applied during framework development. The invariant R = ε/W remained stable under all corrections.Classification: Structured T2 framework / constrained synthesisEmpirical status: Unconfirmed — T3 blocked pending DECIGO/BBO and FCC-hh observationPrimary numerical dependency: β/H* from CosmoTransitions bounce-action computationInvariant status: Stable under all applied corrections Supplementary audit trail: S1 Keywords: leptogenesis · resonant leptogenesis · first-order phase transition · gravitational waves · right-handed neutrinos · baryogenesis · bubble-wall leptogenesis · washout suppression · LISA · DECIGO · BBO · FCC-hh · scalar field · thermal phase transition · stochastic gravitational wave background · inverse seesaw · CP asymmetry · early universe cosmology · beyond the Standard Model · hep-ph This work forms part of a broader structured-framework corpus focused on invariant-preserving transfer analysis, falsifier-linked reasoning, and boundary-conditioned dynamical systems. Related methodological and framework records are included for corpus continuity and audit traceability.