FOR THE LARP — Every prediction has a provenance.

1 The runtime pipeline

Two vision models read pixels; one router reads text; a human confirms; deterministic code does all the math. Select a stage.

2 Recorded traces

Real trace arrays returned by production, copied from the repo's evidence docs. Static data: replaying them here costs no quota.

3 Topology & validation

Models never hand the solver a picture. They hand it this typed graph, which validateGraph (zod schema + graph walk from GND) must accept before anything is solved. The checks below run in your browser.

// src/lib/circuit/types.ts (canonical contract, docs/API_CONTRACT.md v1)
export type CircuitComponent = {
  id: string;
  kind: 'resistor' | 'dc_voltage';
  value: number; // SI units: ohm or volt
  positiveNode: string;
  negativeNode: string;
  sourceBoundingBox?: [number, number, number, number];
};
export type CircuitGraph = {
  schemaVersion: 1;
  components: CircuitComponent[];
  groundNode: 'GND';
  measureNode: string;
};

{
 "schemaVersion": 1,
 "components": [
  {
   "id": "V1",
   "kind": "dc_voltage",
   "value": 5,
   "positiveNode": "VIN",
   "negativeNode": "GND"
  },
  {
   "id": "R1",
   "kind": "resistor",
   "value": 10000,
   "positiveNode": "VIN",
   "negativeNode": "VOUT"
  },
  {
   "id": "R2",
   "kind": "resistor",
   "value": 10000,
   "positiveNode": "VOUT",
   "negativeNode": "GND"
  }
 ],
 "groundNode": "GND",
 "measureNode": "VOUT"
}

4 MNA solver: the only math authority

Modified Nodal Analysis stamps each resistor as a conductance into G and each ideal source as a row/column pair (B, C), then solves [G B; C D]·[v; j] = [i; e] by Gaussian elimination with partial pivoting. solveDC keeps its matrix private, so this page re-derives it with the same stamps (src/app/for-the-larp/math.ts) and checks the result against solveDC live; a unit test pins it. Fixture: Divider 5 V, 10k/10k.

G[VIN, VIN] = 1/R1 S. Select a conductance cell to inspect its resistor contributions.

G conductances (S) B/C source incidence D zero for ideal sources. Source current follows MNA sign: current into the + terminal, so a source delivering power reads negative.

solveDC() in this browser returns VIN = 5 V, VOUT = 2.5 V: bit-for-bit identical to the displayed x.

5 Predictions & evidence

Drag the meter reading. diagnose() re-solves the circuit with each part open, shorted, off-value or each supply off-rail, and ranks single-fault hypotheses that reproduce your reading. No model, no network: everything below recomputes in your browser.

1. R2 may be 1 kΩ instead of 10 kΩ

   Expected 2.5 V at VOUT but measured 0.45 V. Hypothesis: a 1 kΩ R2 would give 0.455 V (exact fit 989 Ω), instead of the 10 kΩ in the diagram. A wrong resistor value or misread color band is one possible explanation. This is a hypothesis, not a confirmed fault.

   Next: Disconnect power first, then measure R2's resistance with a multimeter and compare to 10 kΩ.

2. R1 may be 100 kΩ instead of 10 kΩ

   Expected 2.5 V at VOUT but measured 0.45 V. Hypothesis: a 100 kΩ R1 would give 0.455 V (exact fit 101 kΩ), instead of the 10 kΩ in the diagram. A wrong resistor value or misread color band is one possible explanation. This is a hypothesis, not a confirmed fault.

   Next: Disconnect power first, then measure R1's resistance with a multimeter and compare to 10 kΩ.

3. Supply V1 may be 0.9 V instead of 5 V

   Expected 2.5 V at VOUT but measured 0.45 V. Hypothesis: if V1 were actually delivering about 0.9 V instead of 5 V, the reading would match (low battery, wrong supply or regulator setting). This is a hypothesis, not a confirmed fault.

   Next: With the circuit powered, measure the voltage directly across V1's terminals (low-voltage DC only) and compare to 5 V.

6 Probe Guide: where to measure next

probeStep() builds 1 nominal + 13 single-fault hypotheses (each resistor open, shorted, ×10, ×0.1; supply dead), re-solves each with MNA, and weights them by a Gaussian meter model (σ = 2% + 10 mV). For each unmeasured node it groups hypotheses whose predicted readings a meter can't tell apart and computes expected information gain IG = H(posterior) − Σ P(outcome)·H(posterior | outcome) in bits. Highest gain wins. Computed live below.

7 Usage, latency, limits & economics

Measured anecdotes, not distributions. Unknown is written as unknown, never as $0. Sources: docs/UNIT_ECONOMICS.md, docs/MODEL_ACCESS.md, docs/VISION_FALLBACK.md, docs/demo/README.md.

Measured (2026-10-11, production)

Free-plan ceilings and listed prices (accessed 2026-10-11)

Usage charges in this deployment: $0 by construction (free plans), which is not a production marginal-cost claim. Hypothetical paid cost per analysis (scripts/cost-model.mjs): Jev $0.0000200; Groq and Gemini unknown until their prices are listed, so the total is incomplete. No routing-savings claim: there is no same-case baseline yet.

8 Supported today vs planned