Version 2 · 2026-10-07. This version differs from v1 only as listed here. v1 is kept in the ONTO archive (md5 below). v1: 2603.0008v1.md · md5 306e222074883727b9727b0a42163d1e

• Removed: GOLD v5.1 structure — the component table (kernel file, domain routing, domains × depth levels, thesis and source counts), the file count and token size, and the two corresponding nodes of the architecture figure — disclosure rule.
• Removed: scorer internals — regex pattern counts and the Rust implementation (crate, modules, binding) in the Original Methods table, the architecture figure and the layer table — disclosure rule.
• Removed: the byte layout of the proof chain — disclosure rule.
• Removed: the verification endpoint of the retired service — service retired.
• Note: IGR is defined three different ways in ONTO documents of this period: (1) this section, “IGR(c) = max(0, 1 − H_max(c) / K(c))”, a claim’s required evidence complexity against the system’s entropy budget; (2) this section’s Advanced Metrics table, “Ratio of missing dependencies to expected evidence for a given claim”; (3) whitepaper WP-2026-002 §11.2 and the pitch page v5.13, “IGR(x, y) = 1 − min(I(s_y) / I(s_x), 1)”, a response against its cited sources.
• Note: “10×” (0.53 → 5.38) is the result of one model, model J (GPT 5.2), in CS-2026-001, not an overall result.
• Note: by this section’s own A–F table (C = 4.0–5.9), the composite 5.38 is grade C, not A as stated.
• Note: the section counts 11 models for CS-2026-001 (transfer ratio, EM distribution, compliance grades) and 22 models for the 10× claim.
• Note: the Python scoring engine is given here as 1073 lines; other ONTO documents of the same period give 993 lines (IR-2026-001, ontostandard.org/investor/).

Extracted on 2026-10-07 from ontostandard.org/docs/ (section #methodology), as published in March–April 2026.

Methodology

The Science Behind ONTO | Shannon · Kolmogorov · Eigenvalue | Original Methods | GOLD v5.1

ONTO provides continuous epistemic grounding for AI systems. This section describes the theoretical foundations, original contributions, scoring architecture, metrics, and verification mechanisms that make ONTO reproducible and independently verifiable. For integration details see Integration Paths. For the full research paper: WP-2026-002.

Formal foundation

ONTO measures epistemic discipline as a quantitative property of an output, given the source corpus available to its system. The foundation is information-theoretic: Shannon's entropy bounds what a system can produce on its own, and Kolmogorov's complexity measures the descriptive content of its output. Discipline is the agreement between the two.

Shannon entropy

For a probability distribution over a discrete output space:

$$H(X) = -\sum_{i} p_i \, \log_2 p_i$$

Bounded above by $\log_2 |X|$. Interpretation in ONTO: the upper bound on novel information the model can emit at inference time, given its prior. We write $H_{\max}(S)$ for that bound on a system $S$.

Kolmogorov complexity

For an output string $x$ on a fixed universal Turing machine $U$:

$$K(x) = \min{ \, |p| : U(p) = x \, }$$

Uncomputable in general, but bounded above by compression heuristics. ONTO uses a calibrated compression-based estimator $\hat{K}$ (gzip + structural hashing). Interpretation: the irreducible descriptive content of the output, separable from formulaic hedging or repetition.

Information conservation

The operational law derived in the dissertation. For any evidence $E$ presented by a system $S$:

$$\forall E, S: \ K(E) > H_{\max}(S) \ \Longrightarrow \ \exists \, \mathrm{Source}: \ H(\mathrm{Source}) \geq K(E)$$

If the descriptive complexity of an output exceeds what the system can produce from its own entropy budget, the output originates from an external source whose entropy at least matches that of the output. The law is purely informational. It does not invoke a creator, a deity, or any specific causal chain. It states only that knowledge cannot exceed its own input.

Five axioms underlying the law are derived in the dissertation. The full derivation accompanies standard adoption — see whitepaper.

Dissertation citation: handle and DOI assignment in progress · Zenodo deposit planned · WP-2026-002 currently the canonical citable summary.

Information Gap Ratio (IGR) [v2 note: IGR is defined three different ways in ONTO documents of this period; see the header of this version.]

The operational metric. For a claim $c$ with required evidence complexity $K(c)$ and available system entropy budget $H_{\max}(c)$:

$$\mathrm{IGR}(c) = \max!\left(0, \ 1 - \frac{H_{\max}(c)}{K(c)}\right)$$

Thresholds:

The eighteen disciplines

The law produces eighteen executable disciplines, organized in five layers. Each layer addresses a different epistemic failure mode. R1–R7 are the universal filter applied to every request; R8–R18 add agency, legacy, creation, and coherence on top.

• Layer I · Discipline · R1 – R7 · always on
• R1 Quantify
• R2 Uncertainty
• R3 Counter
• R4 Sources
• R5 Evidence grade
• R6 Falsifiability

• R7 No fabrication

• Layer II · Agency · R8 – R12 · IGR-triggered

• R8 Source fetch
• R9 —
• R10 —
• R11 —

• R12 —

• Layer III · Legacy · R13 – R15 · temporal

• R13 —
• R14 —

• R15 —

• Layer IV · Creation · R16 · generative

• R16 Disciplined synthesis

• Layer V · Coherence · R17 – R18 · pre-delivery

• R17 Constraints C1 – C8
• R18 Self-splice

R17 enumerates eight constraints that every output must satisfy before delivery (numbers cite sources, certainty maps to a hierarchy, counter-evidence cites sources, and so on). C8 is the apoptosis trigger: structural frameshift implies the response refuses delivery and surfaces the failure publicly. R18 is the splice step itself: introns (empty hedges, decorative qualifiers) are removed, exons (the substantive content) are kept.

Layers II–III names and operational semantics for R9–R15 are surfaced in the dissertation accompanying standard adoption. The public docs surface R-numbers and aggregate behaviour; per-rule semantics are part of the formal specification.

Theoretical Foundations

ONTO's scoring system integrates established information theory with original epistemic measurement methods:

These measure information, confidence, and uncertainty. They do not, by themselves, measure epistemic discipline — whether an AI system cites sources, admits unknowns, quantifies its claims, or maintains rigor across domains. ONTO's original contributions fill that gap.

Original Methods

Dual-Layer Scoring Architecture

ONTO scores every response through two independent engines that must agree:

[Figure: SVG diagram “ONTO data flow architecture”; its labels are reproduced below as text.]

Client request
prompt + provider key
        ↓
*[Removed in v2: GOLD structure]*
        ↓
Provider LLM
disciplined response
        ↙                                   ↘
Python · what the model says                Rust · how the model thinks
scoring_engine_v3 · *[Removed in v2: scorer internals]* · EM1–EM5     *[Removed in v2: scorer internals]*
QD · SS · UM · CP · VQ · CONF               information density · structural coherence
        ↘                                   ↙
DLA agreement
divergence = fabrication risk
        ↓
Ed25519 signature · 104-byte proof

The diagram is the contract: every response in ONTO crosses both engines. Python detects what the model says about its own confidence, sources, and counterarguments. Rust detects what the model computes about the same content — entropy distribution, information density, structural coherence. A high Python score with low Rust agreement is the fingerprint of fluent fabrication. Both layers must align for an A grade.

Divergence between layers = additional risk signal. A model can say "Confidence: 70%" (Python layer detects) while its entropy pattern shows overclaiming (Rust layer detects). Both must align for A grade.

EM1-EM5 Epistemic Marker Taxonomy

Every AI response is classified into one of five epistemic modes:

Baseline distribution across 11 models: 78% EM4-EM5, 19% EM3, 3% EM1-EM2. With ONTO: 71% EM1-EM2, 24% EM3, 5% EM4-EM5.

Core Metrics

Composite = QD + SS + UM + CP + VQ + CONF. Range: -1 to 10. All scoring deterministic — Var(Score)=0 for identical input.

Calibration metrics

Two scalar measures of how well stated confidence tracks actual outcome.

Brier Score — squared error between forecast $p_i$ and binary outcome $o_i$:

$$\mathrm{BS} = \frac{1}{N}\sum_{i=1}^{N}(p_i - o_i)^2$$

Expected Calibration Error — gap between accuracy and confidence across $M$ probability bins $B_m$:

$$\mathrm{ECE} = \sum_{m=1}^{M} \frac{|B_m|}{N}\, \big|\, \mathrm{acc}(B_m) - \mathrm{conf}(B_m)\, \big|$$

Dual-Layer Agreement — disagreement between linguistic score $S_L$ (Python) and statistical score $S_R$ (Rust):

$$\mathrm{DLA} = 1 - \frac{|S_L - S_R|}{\max(S_L, S_R)}$$

$\mathrm{DLA} \to 0$ signals a fabrication risk: the model says one thing while its entropy distribution shows another.

Advanced Metrics

GOLD v5.1 — The Discipline Corpus

GOLD is not a prompt template. It is a curated epistemic knowledge architecture:

[Removed in v2: GOLD structure]

Injected server-side at inference time. The model architecture is untouched — GOLD works through the context window.

ONTO-Bench Validation

268 samples: KNOWN (126) · UNKNOWN (110) · CONTRADICTION (32). Tier-1 sources: Clay Mathematics Institute, NSF/ERC Grand Challenges. Tier-2: NIST constants, established textbooks.

ONTO prioritizes recall (catching unknowns) over precision. In high-stakes domains, unnecessary uncertainty is preferable to undetected overconfidence. Full data: WP-2026-002.

Proof Chain (104 bytes)

Every scored response produces a cryptographic proof:

[Removed in v2: proof-chain byte layout]

Chain-linked: each proof references the previous. Tamper-evident. [Removed in v2: service retired] Not blockchain — standard public-key cryptography.

Compliance Grades

All 11 models in CS-2026-001 scored D or F at baseline (mean 0.92). With ONTO GOLD: treatment model scored A (5.38 composite, 10× improvement). [v2 note: by the A–F table above, 5.38 is grade C (4.0–5.9), not A; the 10× is the result of one model, model J (GPT 5.2).]

Full mathematical proofs and methodology details: Research Paper (WP-2026-002) →