CP-Odd Information Flow in H → ZZ* → 4ℓ: Imaginary Spin Correlations and Virtuality-Resolved Tomography

CP-Odd Information Flow in H → ZZ* → 4ℓ: Imaginary Spin Correlations and Virtuality-Resolved Tomography We quantify how much CP-odd Higgs information survives compression into spin-correlation moments in H → ZZ* → 4ℓ. In a specified leading-order model, a real ε = a3/a1 deformation changes helicity phases at first order; single-Z marginals, masses, and reflection-even summaries are locally insensitive. Three calibrated imaginary moments retain 96.8% of inclusive angular Fisher information and 85.5% of joint mass–angular information. Four virtuality bins raise the latter fraction to 91.5%, despite their populations having zero linear response. At N = 4500, the three-moment and joint information are 19.54 and 22.86, giving a joint local uncertainty σ(ε) = 0.209. We relate the moments explicitly to established CP-odd angular structures, separate conjugate redundancy from independent measurements, and quantify information lost through mass integration and moment compression. Analytic checks, numerical convergence tests, and pseudo-experiments establish a reproducible baseline for experimental response studies. Version 2.0 — expanded analysis. Adds derivations of phase-information geometry, information-loss budgets, finite-deformation likelihoods, estimator variance, and acceptance, background and nuisance effects, with expanded attribution and clarified notation. The published CP-odd headline benchmarks are unchanged. Appendix D discusses numerical grid dependence; Appendix E records the changes from v1. ECOF research-program foundation. This study forms part of Kate Lynn Blatt’s Energy-Consciousness Observer Framework research program, introduced in The Energy Consciousness Observer Framework: Foundations of Observer-Coupled Physics — Toward a Unified Field for General Relativity’s Mass–Energy Corrections. The calculations use the explicit HZZ model and statistical assumptions specified in the manuscript. Reproduction software. The matching Python package is available as a separate Software record: CP-odd reproduction software — 10.5281/zenodo.23113936. The package reproduces the calculations within this paper’s stated scope. Related studies in the ECOF research program. CP-even information flow · Graph transfer and ultraviolet suppression · Higgs weight concentration.