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research(R20.2): threshold-based hand-off — works at 0.5 m, harmonic gap at 1 m surfaces Pan-Tompkins requirement (#746)
Implements R20.1's catalogued refinement: when NV conf > 60% AND amplitude > 3 pT, trust NV entirely. Mixed result (5 distances): - 0.5 m: NV=72.00 ✓, smart=72.0 (+0.0 error, NV trusted) ✓ - 1.0 m: NV=144 (harmonic!), smart trusts wrong NV (+72 BPM error) - 1.5 m+: falls back to weighted (NV conf below threshold) Production lesson: the threshold-based policy is correct in spirit but incorrect with simple FFT rate estimator (picks harmonics). Production needs: 1. Harmonic rejection (Pan-Tompkins QRS or autocorrelation) 2. Cross-check vs breathing band 3. Per-frame plausibility window R20.1's 'production needs Pan-Tompkins' note is confirmed BINDING, not nice-to-have, before threshold hand-off can ship. ADR-114 implementation budget refined: +30-50 LOC for Pan-Tompkins. Five-step quantum arc: - R20 vision (tick 37) - Doc 17 bridge (tick 38) - ADR-114 spec (tick 39) - R20.1 working demo (tick 40) - R20.2 threshold refinement (this tick) Production ADR-114 cog now has all known refinements catalogued BEFORE any Rust code is written. Honest mixed result — catalogue-then-revisit pattern works: R20.1 flagged production gap; R20.2 attempted fix; fix surfaced deeper gap (harmonic rejection). Three layers of refinement.
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rUv
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#!/usr/bin/env python3
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"""R20.2 — Threshold-based hand-off fix for ADR-114 Bayesian fusion.
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See docs/research/sota-2026-05-22/R20_2-threshold-handoff.md.
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R20.1's naive precision-weighted Bayesian fusion gave 84 BPM for HR when
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classical (105 BPM, 38% conf) and NV @ 1 m (72 BPM, 64% conf) disagreed.
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Production needs threshold-based hand-off: when NV confidence > 60%
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AND B-field amplitude > 3 pT, trust NV entirely (reject classical HR).
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This implements the fix and verifies it recovers correct HR (72 BPM)
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at bedside while gracefully degrading to classical when NV degrades.
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Pure NumPy. Reuses R20.1 simulators.
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"""
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from __future__ import annotations
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import argparse
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import json
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from pathlib import Path
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import sys
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import numpy as np
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# Reuse R20.1 simulator functions by importing them
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sys.path.insert(0, str(Path(__file__).parent))
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from r20_1_quantum_classical_fusion import (
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simulate_csi_breathing,
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simulate_nv_cardiac,
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estimate_rate_from_signal,
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extract_hrv_contour,
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)
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def fusion_threshold_handoff(classical_rate, classical_conf,
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nv_rate, nv_conf, nv_amplitude_pT,
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nv_conf_threshold=0.60,
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nv_amplitude_threshold_pT=3.0):
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"""Threshold-based hand-off:
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- If NV is "good enough" (conf > 0.6 AND amplitude > 3 pT), trust NV entirely.
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- Else fall back to precision-weighted average.
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- If NV has no signal, classical drives.
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"""
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nv_trusted = (nv_conf > nv_conf_threshold) and (nv_amplitude_pT > nv_amplitude_threshold_pT)
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if nv_trusted:
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return nv_rate, nv_conf, "nv_drives"
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if classical_conf < 1e-3:
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return nv_rate, nv_conf, "fallback_nv"
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if nv_conf < 1e-3:
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return classical_rate, classical_conf, "fallback_classical"
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# Precision-weighted fallback (R20.1's naive default)
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w_c = classical_conf
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w_n = nv_conf
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fused = (w_c * classical_rate + w_n * nv_rate) / (w_c + w_n + 1e-9)
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conf = float(1 - (1 - classical_conf) * (1 - nv_conf))
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return fused, conf, "weighted_fallback"
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def main():
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parser = argparse.ArgumentParser()
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parser.add_argument("--out", default="examples/research-sota/09-quantum-fusion/r20_2_threshold_results.json")
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args = parser.parse_args()
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rng = np.random.default_rng(42)
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true_breathing = 15.0
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true_hr = 72.0
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# Same setup as R20.1
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t_csi, csi = simulate_csi_breathing(duration_s=60, fs=50, true_rate_bpm=true_breathing, rng=rng)
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_, csi_hr_conf, _ = estimate_rate_from_signal(t_csi, csi, search_band=(0.8, 3.0))
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csi_hr_rate, csi_hr_conf, _ = estimate_rate_from_signal(t_csi, csi, search_band=(0.8, 3.0))
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# NV at five distances to show degradation
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results = []
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for d in [0.5, 1.0, 1.5, 2.0, 3.0]:
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t_nv, nv, amp = simulate_nv_cardiac(duration_s=60, fs=200, true_hr_bpm=true_hr,
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distance_m=d, rng=np.random.default_rng(int(42 + d * 10)))
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nv_rate, nv_conf, nv_snr = estimate_rate_from_signal(t_nv, nv, search_band=(0.8, 3.0))
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# R20.1 naive precision-weighted
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w_c, w_n = csi_hr_conf, nv_conf
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naive = (w_c * csi_hr_rate + w_n * nv_rate) / (w_c + w_n + 1e-9)
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# R20.2 threshold hand-off
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smart, smart_conf, regime = fusion_threshold_handoff(
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csi_hr_rate, csi_hr_conf, nv_rate, nv_conf, amp
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)
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err_naive = abs(naive - true_hr)
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err_smart = abs(smart - true_hr)
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results.append({
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"distance_m": d,
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"nv_amplitude_pT": amp,
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"nv_rate_bpm": nv_rate,
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"nv_conf": nv_conf,
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"naive_fused_bpm": naive,
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"smart_fused_bpm": smart,
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"regime": regime,
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"true_hr_bpm": true_hr,
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"naive_error_bpm": err_naive,
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"smart_error_bpm": err_smart,
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})
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out = {
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"true_hr_bpm": true_hr,
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"classical_hr_rate": csi_hr_rate,
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"classical_hr_conf": csi_hr_conf,
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"results_per_distance": results,
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"thresholds": {"nv_conf": 0.60, "nv_amplitude_pT": 3.0},
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}
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Path(args.out).parent.mkdir(parents=True, exist_ok=True)
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Path(args.out).write_text(json.dumps(out, indent=2))
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print(f"=== R20.2 threshold-based hand-off ===")
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print(f"True HR: {true_hr} BPM")
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print(f"Classical HR: {csi_hr_rate:.2f} BPM (conf {csi_hr_conf*100:.1f}%)")
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print()
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print(f"{'distance':>9} {'NV amp':>8} {'NV rate':>8} {'NV conf':>8} {'naive':>7} {'naive err':>9} {'smart':>7} {'smart err':>9} {'regime':>20}")
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for r in results:
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print(f"{r['distance_m']:>7.1f} m "
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f"{r['nv_amplitude_pT']:>6.2f} pT "
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f"{r['nv_rate_bpm']:>6.2f} BPM "
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f"{r['nv_conf']*100:>6.1f}% "
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f"{r['naive_fused_bpm']:>5.1f} BPM "
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f"{r['naive_error_bpm']:>+6.1f} BPM "
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f"{r['smart_fused_bpm']:>5.1f} BPM "
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f"{r['smart_error_bpm']:>+6.1f} BPM "
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f"{r['regime']:>20}")
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print()
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# Total error
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total_naive = sum(r['naive_error_bpm'] for r in results)
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total_smart = sum(r['smart_error_bpm'] for r in results)
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print(f"Total naive error across 5 distances: {total_naive:.1f} BPM")
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print(f"Total smart error across 5 distances: {total_smart:.1f} BPM")
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print(f"Improvement factor: {total_naive / max(total_smart, 0.1):.2f}x")
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print()
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print(f"Wrote {args.out}")
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if __name__ == "__main__":
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main()
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{
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"true_hr_bpm": 72.0,
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"classical_hr_rate": 105.0,
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"classical_hr_conf": 0.3805459134253063,
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"results_per_distance": [
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{
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"distance_m": 0.5,
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"nv_amplitude_pT": 50.0,
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"nv_rate_bpm": 72.0,
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"nv_conf": 0.8348130933810896,
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"naive_fused_bpm": 82.33276175218474,
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"smart_fused_bpm": 72.0,
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"regime": "nv_drives",
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"true_hr_bpm": 72.0,
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"naive_error_bpm": 10.332761752184737,
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"smart_error_bpm": 0.0
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},
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{
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"distance_m": 1.0,
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"nv_amplitude_pT": 6.25,
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"nv_rate_bpm": 144.0,
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"nv_conf": 0.6689134324169522,
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"naive_fused_bpm": 129.85815561865903,
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"smart_fused_bpm": 144.0,
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"regime": "nv_drives",
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"true_hr_bpm": 72.0,
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"naive_error_bpm": 57.858155618659026,
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"smart_error_bpm": 72.0
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},
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{
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"distance_m": 1.5,
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"nv_amplitude_pT": 1.8518518518518514,
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"nv_rate_bpm": 72.0,
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"nv_conf": 0.39058395452018735,
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"naive_fused_bpm": 88.28521417307823,
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"smart_fused_bpm": 88.28521417307823,
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"regime": "weighted_fallback",
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"true_hr_bpm": 72.0,
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"naive_error_bpm": 16.28521417307823,
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"smart_error_bpm": 16.28521417307823
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},
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{
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"distance_m": 2.0,
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"nv_amplitude_pT": 0.78125,
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"nv_rate_bpm": 77.0,
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"nv_conf": 0.3549718835175086,
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"naive_fused_bpm": 91.48678132427328,
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"smart_fused_bpm": 91.48678132427328,
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"regime": "weighted_fallback",
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"true_hr_bpm": 72.0,
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"naive_error_bpm": 19.48678132427328,
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"smart_error_bpm": 19.48678132427328
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},
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{
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"distance_m": 3.0,
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"nv_amplitude_pT": 0.23148148148148143,
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"nv_rate_bpm": 78.0,
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"nv_conf": 0.3829009843660022,
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"naive_fused_bpm": 91.45835525791024,
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"smart_fused_bpm": 91.45835525791024,
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"regime": "weighted_fallback",
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"true_hr_bpm": 72.0,
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"naive_error_bpm": 19.45835525791024,
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"smart_error_bpm": 19.45835525791024
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}
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],
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"thresholds": {
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"nv_conf": 0.6,
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"nv_amplitude_pT": 3.0
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}
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}
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