Gravit Open Network

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weight of evidence deciban verifiable trust This document defines the Graviteron, a unit that states how much signed, independent evidence supports or contradicts a claim. A Graviteron reading is the weight of evidence of Turing and Good, expressed in decibans: ten times the base-10 logarithm of the factor by which independent checks change the odds of the claim. The document specifies the computation from operator verdicts and measured operator reliability, eight properties that every conforming implementation must satisfy, a reading format that is never a bare number, and language-neutral test vectors. It does not define a decision rule.

Introduction Systems that check claims about AI outputs, data or actions often report a confidence score whose meaning differs from one system to the next. Scores are added when they should not be, keys of one party are counted as independent voices, old checks keep full weight forever, and contradictions disappear into an average. The Graviteron addresses this by fixing the quantity being reported. It does not measure truth. It measures how far the available independent, signed evidence moves the odds of a claim, on a logarithmic scale whose zero means "no evidence either way". The quantity is the weight of evidence introduced by A. M. Turing and I. J. Good , measured in decibans. Two implementations conform to this document if they produce the same readings, within the stated tolerances, for the test vectors of . A unit is useful only when independent implementations agree; the vectors exist for that purpose. This document is related to the Gravit Epistemic Verification Protocol , which defines signed evidence Records and grouping by independent source. The Graviteron can be computed from such Records, but it is defined independently of any product or protocol, and the decision of whether a claim may be called a fact is out of scope.

Conventions and Terminology The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in BCP 14 when, and only when, they appear in all capitals, as shown here.

Claim:

A statement that can be true or false, for example that a payment occurred or that an output was produced by a given model.

Operator:

An independent party that checks claims. One operator may hold several signing keys; they remain one operator.

Verdict:

The signed result of an operator for a claim: true, false, or null (no result).

Sensitivity, specificity:

The measured probability that the operator returns true for a true claim, and false for a false claim. They are estimated from data, for example with the Dawid-Skene method .

Deciban (dB):

Ten times the base-10 logarithm of a likelihood ratio or odds factor.

Definition The Graviteron G of a claim, given the evidence E, is: where O denotes odds. With independent operators this equals the sum of the operators' contributions: Implementations MUST clamp sensitivity and specificity to the interval [1e-6, 1 - 1e-6] before computing g_i.

One Verdict per Operator All records of one operator, under any number of keys, MUST be reduced to one verdict: the majority of its non-null results. If there are no non-null results, or the results are tied, the operator's verdict is null.

Decay A reading MAY use a half life h. A contribution whose verdict is a seconds old then becomes g_i * 2^(-a / h). A renewed check has age 0 and full weight. Without a half life, contributions do not decay.

Required Properties A conforming implementation MUST satisfy all of the following.

1. Zero point: with no counted evidence, G = 0.
2. Sign: a confirmation by an operator better than chance gives a positive contribution; a contradiction gives a negative one.
3. Additivity: contributions of independent operators add.
4. Sybil invariance: adding keys to one operator does not change G.
5. Dynamics: with a half life, a contribution halves after one half life and is restored when the check is renewed.
6. No silent evidence: an operator with a null verdict, or without measured sensitivity and specificity, contributes nothing, and the reading MUST say so in its notes.
7. Never a bare point: every reading carries an interval () that narrows as independent operators are added.
8. Visible contradiction: if any counted operator signed false, the reading MUST be flagged as contested, and the flag MUST NOT be removed by averaging.

The Reading A Graviteron reading MUST contain: the value G in decibans; an interval; a verbal band; the number of independent operators that contributed; the contradiction flag; the contribution of each operator; and notes for every record that counted nothing.

Verbal Bands The band follows the scale of Jeffreys on the absolute value of G: below 5 dB "inconclusive"; 5 to below 10 "substantial"; 10 to below 15 "strong"; 15 to below 20 "very strong"; 20 and more "decisive". Except for "inconclusive", the band is followed by "support" when G is positive and "contradiction" when G is negative. A contested reading is prefixed by "contested: ". The bands are a communication scale. They are not a decision rule and MUST NOT be presented as one.

Interval Each contribution c is converted to a pseudo-count 1 - 2^(-|c| / 10). Let pos be the sum of pseudo-counts of positive contributions and neg that of negative ones, and let a = 1 + pos and b = 1 + neg. With the quantiles q_lo and q_hi of the Beta(a, b) distribution at (1 - L)/2 and (1 + L)/2 for the interval level L (default 0.9), and d(p) = 10 * log10(p / (1 - p)), the interval is: This interval is provisional: it reflects how much independent evidence there is, not yet the uncertainty in the operators' measured reliability. A future version is expected to carry the sample sizes of the reliability estimates into the interval.

Test Vectors Twenty-one test vectors, with inputs (records, operator parameters, ages, half life, interval level) and expected readings, are published as JSON . Tolerances are 1e-6 dB for G and for each contribution, and 1e-4 dB for the interval bounds. Four of them, for operators with sensitivity and specificity of 0.9/0.9 and 0.8/0.95:

Situation	G (dB)	90 % interval	Band
one operator confirms	9.542425	-0.32 to 22.37	substantial support
three operators confirm	31.126	23.54 to 43.98	decisive support
two confirm, one signs false	12.318	4.01 to 22.50	contested: strong support
three confirm, 60 days old, half life 30 days	7.782	-2.05 to 20.61	substantial support

Implementation Status One reference implementation exists (Python, Apache-2.0) ; it passes the test vectors in continuous integration. No independent implementation exists yet. An open call for independent implementations is made through the Open Verifiable AI Consortium. This section is to be removed before publication as an RFC.

Security Considerations The Graviteron is only as sound as the independence of the operators and the measurement of their reliability. An attacker who controls several operators that appear independent inflates G; Sybil invariance protects only against several keys of one known operator. Deciding which operators are independent is out of scope and SHOULD follow a documented procedure, for example the grouping by independent source in . Overstated sensitivity or specificity inflates every contribution of that operator. Reliability estimates SHOULD be published with their data and sample sizes. A high G is not a proof. Presenting a reading without its interval, operator count and contradiction flag invites false precision and is not conforming.

IANA Considerations This document has no IANA actions.

References Normative References Gravit Open Network Informative References Gravit Open Network Charles Griffin, London Oxford University Press Journal of the Royal Statistical Society, Series C, 28(1), 20-28 Gravit Open Network