TRIP: Trajectory-based Recognition of Identity Proof

This document specifies the Trajectory-based Recognition of Identity Proof (TRIP) protocol, a decentralized mechanism for establishing claims of physical-world presence through cryptographically signed, spatially quantized location attestations called "breadcrumbs." Breadcrumbs are chained into an append-only log, bundled into verifiable epochs, and distilled into a Trajectory Identity Token (TIT) that serves as a persistent pseudonymous identifier. The protocol employs a Criticality Engine grounded in statistical physics to distinguish biological movement from synthetic trajectories. Power Spectral Density (PSD) analysis detects the 1/f signature of Self-Organized Criticality in human mobility through the PSD scaling exponent alpha. A six-component Hamiltonian energy function scores each breadcrumb against the identity's learned behavioral profile in real time. This revision (-03) addresses three areas identified through expert review by researchers in the statistical physics community: it replaces informal terminology with standard spectral analysis nomenclature; it provides the analytical and numerical bridge between the Levy flight displacement exponent and the PSD scaling exponent; and it introduces a convergence analysis framework for quantifying the minimum trajectory length required for reliable single-trajectory classification. Additionally, this revision removes Passive Verification mode entirely, requiring all Attestation Results to be bound to Relying Party nonces via the Active Verification Protocol. TRIP is designed to be transport-agnostic and operates independently of any particular naming system, blockchain, or application layer.