Decoherence without facts: a one-knob model of where which-path records live

Vanished interference fringes do not by themselves tell us that the environment has recorded which path a particle took. This preprint studies a minimal model that separates the two: a qubit acquires a controlled phase from N environment qubits whose purity is set by one knob η ∈ [0,1]. The loss of fringes is the same for every η; what changes is where the information goes. At η = 1 every fragment of the environment carries a copy of the path; for smaller η records become biased coins, and the number of records needed for 0.9 bit grows as 2.7114/(1 − h_η) in the weak-record limit; at η = 0 the qubit is completely dephased while the modelled environment holds no path record and no system–environment entanglement, only a global parity from which any initial state can be restored. For a single witness the paper gives closed formulas for the path knowledge K and the phase-corrected visibility V along a family of readouts between the "kick" and "path" bases, and shows that this family is optimal: with phase-only feed-forward and no postselection, every readout obeys (K/η)² + V² ≤ 1. A two-path clock is the N = 1 case. The PDF embeds all verification scripts, their outputs, seven key files with expected values, a README and a list of SHA-256 hashes; the same files are in the ZIP. Exploratory calculations are distinguished from subsequent verification checks, and the known errors found during review are documented, not removed. No new physical law is claimed. Calculations, figures and typesetting were assisted by AI tools (Claude, Anthropic), used as tools; the author is responsible for the content.