Ch. 161 / 2026z — One Number: The Causal-Loop Test — Pre-registration

This is a pre-registration, not a claim of experimental success. It states in advance one quantitative prediction that differs from standard quantum optics, one protocol to test it, and one set of falsification criteria. Claim: A causal loop with H^1_causal != 0 adds an extra erasure factor gamma_causal(L), even when the which-way marker W is held fixed. Setup: Mach-Zehnder interferometer, heralded single photons at 810 nm, which-way marker overlap |<W0|W1>| = 0.60, one arm through a fiber delay loop of length L. Standard prediction (Englert 1996):V_standard = 0.600, D = 0.800, D^2 + V^2 = 1.000, flat in L. Tseglin prediction:gamma_causal(L) = 0.30 * (1 - exp(-L / 2.0 m))V_Tseglin(L) = 0.600 * (1 - gamma_causal(L)) Headline number at L = 3.0 m:Standard: V = 0.600 +/- 0.010Tseglin: V = 0.460 +/- 0.010Difference: Delta V = 0.140 Vindicated if: V(3.0 m) = 0.460 +/- 0.030 and V(L) follows the predicted curve within +/- 0.03.Falsified if: V(3.0 m) = 0.600 +/- 0.030 and V is flat in L within +/- 0.02.Inconclusive if: D drifts, control drifts, or error bars exceed 0.03. No experimental data are reported herein. Keywords: quantum eraserMach-Zehnder interferometercomplementaritypre-registrationcausal topologyfalsifiable prediction