33.67 turns the nondispersive common-term step into a cone-profile court: under one frozen axis, clustered same-window events above Pth must show a monotone off-axis attenuation H(ρ)/H(0), a stable cone parameter θ0 or θ50, linear ρ50 ∝ d scaling, cross-distance collapse in ρ/(d·θ0), in-cone delays that do not drift with ρ, and sharp failure under pulse-off / below-threshold / axis-permutation / station-label permutation controls.
Use this section as a compact machine-readable EFT reference.
33.67 turns the common-term step into a spatial court. The admissible claim is not that any off-axis detection implies structure, but that above-threshold same-window events show one reproducible beam footprint: monotone attenuation with transverse offset together with a stable coherence cone rather than a station-specific artifact.
Measurement preserves one spatial footprint ledger. The hard outputs are the transverse offset ρ or the equivalent angle θ=ρ/d under one frozen axis, the step height H(ρ), the detection probability P_det(ρ), cone parameters θ0 or θ50 with confidence intervals, the half-power radius ρ50, and the collapse test in the scaled variable ρ/(d·θ0). In-cone events must also show that ΔT does not drift systematically with ρ while nondispersion remains intact.
The workflow freezes geometry and extraction before any verdict. An equal-distance ring or equal-distance multi-point array scans ρ at roughly fixed d, at least two distinct distance settings test the predicted linear relationship between ρ50 and d, all stations share one bandwidth, sign convention, filtering rule, and step-detection algorithm, the onset-extraction method is frozen before acquisition, and station-position, distance, channel, and P-level labels stay blinded during profile fitting.
Controls must destroy false spatial structure instead of merely shrinking it. Under P=0 there may not be reproducible cone-angle scaling or distance proportionality; below threshold the profile and θ0 stability must degrade; axis permutation must break θ0 and the collapse behavior; strong off-axis relocation must sharply reduce H(ρ) and P_det; and station-label permutations must destroy monotone attenuation and the ρ50 versus d law.
Support requires a monotone normalized profile with a stable θ0 or θ50, linear scaling of ρ50 with d, collapse of the normalized profile across distances in the scaled variable, null controls that do not reproduce the same-strength structure, and in-cone delays that do not drift systematically with ρ while nondispersion remains satisfied. Falsification follows from no stable profile, no distance scaling, null tests of comparable strength, or off-axis behavior that introduces a dispersion-like delay. The named adversaries are geometry and ρ-calibration error, station sensitivity differences, and spatial common-mode crosstalk.
So the chapter closes only one tightened common-term coherence-cone and off-axis attenuation ledger aligned with the V03/V08/V09 audit lane. θ0, θ50, and ρ50 may survive only as spatial profile parameters for this geometry court, not as carrier ontology, a universal beam law, or a canon-core propagation verdict. Its clean onward value is to hand a spatially qualified propagation grammar to 33.68.