The workspace DSP (vital_signs, multistatic, pose_tracker, tomography)
implicitly assumes a forward model that maps scatterer geometry to
per-subcarrier phase shifts. Nobody had written it down. This tick
makes it explicit.
Closed-form first-Fresnel-zone radius + point-scatterer path-delta +
per-subcarrier phase prediction over 802.11n/ac 20 MHz channels (52
subcarriers, 312.5 kHz spacing). Pure NumPy demo + JSON output for
downstream consumers.
Headline numbers:
- 5 m link first-Fresnel radius @ midpoint: 40 cm (2.4 GHz), 27 cm (5 GHz)
- Inside zone-1: phase spread <0.5 deg across 52 subcarriers (band-flat)
- Outside zone-1: phase spread up to 16 deg (band-dispersed)
This unifies R5 + R6: R5's experimentally measured band-spread top
subcarriers is exactly what the Fresnel forward model predicts for
zone-1 occupancy.
Closes the loop on three earlier threads:
- R7 (mincut adversarial) gets a precise definition of 'physically
inconsistent' instead of a learned classifier
- R10 (foliage range) needs to retract 100 m sparse estimate to ~70 m
to account for Fresnel-zone obstruction
- R12 (eigenshift negative result) gets its revision basis: PABS over
Fresnel-grounded forward operator
Honest scope: point-scatterer only, first Fresnel only, frequency-flat
reflectivity, LOS-only (no multipath). The scalar version is the right
first-order approximation; volume-integral / multi-zone / multipath
extensions catalogued as R6.1+R6.2 follow-ups.
Coordination: ticks/tick-8.md, no PROGRESS.md edit.
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