Extracted on 2026-10-07 from ontostandard.org/pitch/ (v5.13, 2026-04-20). The formula was never implemented as a measurement.
FORMAL FOUNDATION
The measurement, formalized
How grounded is a response in its cited sources? We answer that question with a measurement — bounded in [0, 1], deterministic, per-response. The definition below is instrumental: it specifies how the score is computed, not what it means universally. Methodology public · reference implementation commercial.
ARCHITECTURE · RESPONSE VS. CITED SOURCES
[Figure: SVG diagram “IGR architecture”; its labels are reproduced below as text.]
response x ──▶ Encoder Enc(x) ──▶ s_x claimed ──┐
├──▶ D divergence ──▶ IGR ∈ [0, 1]
sources y ──▶ Encoder Enc(y) ──▶ s_y cited ──┘
FIGURE. Filled inputs x, y are observed — the response and its cited sources. Rounded modules are deterministic encoders producing representations sx, sy. D computes divergence; the output is a bounded score. The measurement is non-generative — no prediction of y from x, only comparison. Diagram conventions follow LeCun (2022).
DEFINITION 1 · INFORMATION GAP RATIO
IGR(x, y) = 1 − min( I(sy) / I(sx), 1 ) (1)
where I(s) is the information content of representation s · bounded in [0, 1] · deterministic: same input, same score, every time.
FIVE FOUNDATIONS · A1–A4 CLASSICAL · A5 ONTO CONTRIBUTION
- A1 · Landauer — Information is physical; it cannot be created without carrier. — 1961
- A2 · Kolmogorov — Information content is the length of the shortest generating program. — 1965
- A3 · Eigen — Self-organizing complexity is bounded without external information input. — 1971
- A4 · Shannon — Channel capacity bounds transmittable information between source and output. — 1948
- A5 · ONTO sufficiency — For text with citations, the measure I(·) is computable per response. — this work
A1–A4 are independently established results in information theory. A5 is the ONTO contribution — the sufficiency clause that makes the bound measurable per response, not in principle.
IGR · OPERATIONAL THRESHOLDS
| IGR | GAP | INTERPRETATION |
|---|---|---|
| 0.00 | No gap | Response fully grounded in cited sources |
| 0.01–0.29 | Minimal | Sufficient for certification |
| 0.30–0.69 | Partial | Further verification warranted |
| 0.70–1.00 | Critical | Bound exceeded · R4 / R7 / C8 activate |
IGR IN PRACTICE · THREE MEASUREMENTS
| SCENARIO | CONDITION | IGR | R-RULES |
|---|---|---|---|
| AI cites a real paper source present · capacity matches |
I(sy) ≈ I(sx) | ≈ 0 | R4 pass R7 pass |
| AI summarizes recent event partial grounding · no live sources |
I(sy) < I(sx) | ≈ 0.4 | R2 uncertainty R8 resolve |
| AI invents a statistic no source · ungrounded |
I(sy) ≪ I(sx) | ≈ 0.9 | R4 cap · R7 refuse C8 apoptosis |
Illustrative · IGR is measured per response, not per model. Three zones of the same bound.
REFERENCE CASE · UNCITED AI CLAIMS
OPERATIONAL RULE · NO CLAIM EXCEEDS THE INFORMATION OF ITS CITED SOURCES
As the response's claimed information I(sx) grows past its cited information I(sy), IGR approaches 1 — the configuration where R4 Sources, R7 No Fabrication, and C8 Apoptosis activate. Measured per response, not per model.
SCOPE DISCIPLINE
An accounting measurement: it compares claimed information to cited information. What closes the gap — additional sources, uncertainty, refusal — is outside the measurement's scope. Complete derivation accompanies standard adoption.
FALSIFIABILITY
The framework is refuted by: (1) a response with IGR ≥ 0.7 that domain experts independently judge fully grounded · (2) an LLM-as-judge system producing deterministic scores (Var = 0) without regex or rule-based components.
When AI doesn't know, it must cite — not invent. R4 Sources, R7 No Fabrication, and C8 Apoptosis are the operational consequences of Definition 1.