Signal Theory — Universal Signal Detection Framework
Signal detection tools grounded in 6 axioms and 5 theorems. Includes threshold-based detection, SDT decision matrix (d-prime, sensitivity, specificity, MCC), conservation law verification, multi-stage
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Get Axioms
List all 6 axioms of signal theory with their primitive mappings. A1 Data Generation (ν), A2 Noise Dominance (∅), A3 Sig
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Get Theorems
List all 5 theorems of signal theory with their prerequisites and formal statements.
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Detect
Run signal detection: compare observed count vs expected count against a threshold. Returns ratio, difference, detection
observedexpected
Decision Matrix
Compute SDT decision matrix metrics from a 2×2 classification table (hits, misses, false alarms, correct rejections). Re
hitsmissesfalse_alarmscorrect_rejections
Conservation Check
Verify conservation laws (L1-L4) on a decision matrix. Checks total count conservation and information conservation (d-p
hitsmissesfalse_alarmscorrect_rejections
Pipeline
Run a multi-stage signal detection pipeline. A value passes through sequential stages, each with its own threshold. Repo
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Cascade
Cascading threshold evaluation — find the highest severity level exceeded. Thresholds in ascending order with labels. Re
valuethresholdslabels
Parallel
Parallel signal detection across two independent detectors. Mode 'both' (AND) requires both to fire. Mode 'either' (OR)
valuethreshold_1threshold_2