> 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.*