Delta Zero: A Two-Ledger Framework for Change (r/i)

1-liner (punchy) A two-ledger model of change that splits every variable into visible r and hidden i branches, enforces closed-cycle balance, and predicts gated |i|² spillover into real observables. Short (2–3 sentences) Delta Zero Theory treats unified change as the core signal and records forward/observable effects in r and reverse/latent effects in i. Over closed cycles, the net balance is zero, while measurements only see hidden dynamics through |i|² under gates. Energy splits as (with past information in ), and identity can be modeled via the self-integral . Abstract (≈120 words) Delta Zero Theory is a minimalist framework for reasoning about complex dynamics with two ledgers of change: a visible forward branch (r) and a hidden reverse/latent branch (i). Unified change integrates to a self-state , while conservation is enforced over closed cycles (net or complex-square forms). Hidden dynamics never signal directly; they influence observables only through gated |i|² terms, keeping causality and standard laws intact (e.g., ). Past information—memory, genetic programs, abstract data—is encoded as . The framework is reparameterization-invariant and comes with concrete tests: Backward Segments, Möbius Phase Flip, and Hidden→Real Spillover. This write-up includes paste-ready equations, intuition, and parameter guidance for applying the model to physical, biological, or informational systems. Keywords r/i split, unified change , self-integral , closed-cycle balance, |i|² spillover, no-signaling, energy decomposition , reparam invariance, memory as energy, Möbius phase flip, backward segments.