SAPIENCE.html

<h1 id="quantifying-ai-sapience-as-an-integer-for-licensing">Quantifying
AI Sapience as an Integer for Licensing</h1>
<p>This document is the formal specification of the sapience number used
by the Sapience Testing App described in <a
href="README.md">README.md</a>. It is written for licensing, legal, and
business readers: the goal is a sapience measure that is
<strong>constrained</strong> — an integer, bounded, reproducible, and
auditable — so that a license agreement can reference it
unambiguously.</p>
<h2 id="why-sapience-must-be-constrained">1. Why sapience must be
constrained</h2>
<p>A license price must rest on a quantity that parties can measure,
record, and re-check. Qualities such as “intelligence” or “personhood”
are not contract terms. What a contract needs is:</p>
<ul>
<li>A <strong>number</strong>, not a judgment call.</li>
<li>A <strong>fixed type</strong>: an integer, never a fraction,
percentage, or adjective.</li>
<li><strong>Bounds</strong>: every session yields a value inside a known
range.</li>
<li><strong>Reproducibility</strong>: two certified sessions of the same
AI under the same probe suite must agree within a stated tolerance.</li>
<li><strong>Auditability</strong>: the counts behind the number are
observable during the test — the harness announces “Calculation” or
“Recognition” aloud.</li>
</ul>
<p>The sapience number defined below satisfies all five
requirements.</p>
<h2 id="definitions">2. Definitions</h2>
<table>
<colgroup>
<col style="width: 50%" />
<col style="width: 50%" />
</colgroup>
<thead>
<tr>
<th>Term</th>
<th>Definition</th>
</tr>
</thead>
<tbody>
<tr>
<td><strong>Vendor AI</strong></td>
<td>The artificial intelligence brought by a vendor to be tested and
licensed.</td>
</tr>
<tr>
<td><strong>Probe</strong></td>
<td>One standardized stimulus presented to the vendor AI by the
harness.</td>
</tr>
<tr>
<td><strong>Detector</strong></td>
<td>A perceptron in the harness that watches the vendor AI act and fires
on exactly one event class.</td>
</tr>
<tr>
<td><strong>Calculation event</strong></td>
<td>A detection of the vendor AI performing a calculation. Fires the
calculation detector.</td>
</tr>
<tr>
<td><strong>Recognition event</strong></td>
<td>A detection of the vendor AI recognizing a known target. Fires the
recognition detector.</td>
</tr>
<tr>
<td><strong>Accumulator</strong></td>
<td>An integer counter. There are two: <code>C</code> for calculations,
<code>R</code> for recognitions.</td>
</tr>
<tr>
<td><strong>Session</strong></td>
<td>The interval from the clear-accumulators action until certification.
Only detections inside a session count.</td>
</tr>
<tr>
<td><strong>Sapience number</strong></td>
<td>The integer <code>S = C + R</code> produced at the end of a
session.</td>
</tr>
<tr>
<td><strong>License fault</strong></td>
<td>The condition in which a retested sapience number disagrees with the
certified one beyond tolerance; the certificate is invalidated.</td>
</tr>
</tbody>
</table>
<h2 id="formal-definition-of-the-sapience-number">3. Formal definition
of the sapience number</h2>
<p>A test session produces two non-negative integer accumulators:</p>
<pre><code>C ∈ ℕ₀   calculation count
R ∈ ℕ₀   recognition count</code></pre>
<p>The sapience number is their sum:</p>
<pre><code>S = C + R</code></pre>
<p><code>S</code> is the sole quantity recorded on the license
certificate. From <code>S</code>, the license price is determined
(Section 7).</p>
<h2 id="constraints">4. Constraints</h2>
<p>The sapience number is valid only under the following constraints.
These are the constraints referenced by “sapience must be
constrained.”</p>
<ul>
<li><strong>A1 Integrality.</strong> <code>S ∈ ℤ</code>. The measure is
never fractional, fuzzy, or probabilistic.</li>
<li><strong>A2 Non-negativity.</strong> <code>C ≥ 0</code>,
<code>R ≥ 0</code>, therefore <code>S ≥ 0</code>.</li>
<li><strong>A3 Boundedness.</strong> Each certified probe suite defines
a ceiling <code>S_max</code> equal to the number of probes administered.
Every session satisfies <code>0 ≤ S ≤ S_max</code>.</li>
<li><strong>A4 Session discipline.</strong> Both accumulators start at
zero via the user’s clear-accumulators action, which marks the official
start of the test. No detection outside a session increments any
accumulator.</li>
<li><strong>A5 Monotonic accrual.</strong> Within a session each
accumulator only increases, by exactly 1 per fired detector. Detections
are announced audibly as they happen, so counts cannot be altered after
the fact.</li>
<li><strong>A6 Fault condition.</strong> Let <code>τ ≥ 0</code> be the
tolerance fixed in the license agreement. If a retest of a licensed AI
yields <code>S_retest</code> with
<code>|S_retest − S_certified| &gt; τ</code>, then the license is
<strong>in fault</strong>: the certificate is void and the AI must be
retested before continued licensing. If the sapience does not change
(<code>|ΔS| ≤ τ</code>), the license stands.</li>
</ul>
<p>Together A1–A5 guarantee the number exists, lies in a known range,
and was produced by an observable procedure; A6 guarantees the
certificate stays honest over time.</p>
<h2 id="test-protocol-recap">5. Test protocol recap</h2>
<ol type="1">
<li>The vendor brings their AI to the testing terminal.</li>
<li>The operator performs the clear-accumulators action; the session
begins.</li>
<li>The harness presents probes and runs in a Linux terminal session
with audio outputs. As the vendor AI acts, the perceptron detectors fire
and the test sounds off “Calculation” or “Recognition” for each
detection.</li>
<li>Each announcement adds 1 to the matching accumulator (A5).</li>
<li>At the end of the probe suite the result is a calculation count and
a recognition count. Their addition is the sapience number
<code>S</code>.</li>
<li><code>S</code> is entered on the license certificate together with
the date, the probe-suite identifier, and the harness version.</li>
</ol>
<h2 id="worked-example-using-this-repositorys-probes">6. Worked example
using this repository’s probes</h2>
<p>The repository ships two compiled probes written in the “first”
computer language (sources <code>ai.fst</code> and <code>fai.fst</code>;
binaries <code>ai</code> and <code>fai</code>).</p>
<h3 id="recognition-probe-ai.fst">Recognition probe —
<code>ai.fst</code></h3>
<p>The probe holds the target string <code>T := "hidali"</code>. It
takes the vendor AI’s query output and compares it against the
target:</p>
<ul>
<li>Query matches → prints <code>TRUE</code>, exit status <code>0</code>
→ the recognition detector fires → <code>R := R + 1</code>.</li>
<li>Query does not match → prints <code>FALSE</code>, exit status
<code>-1</code> → no increment.</li>
</ul>
<h3 id="calculation-probe-fai.fst">Calculation probe —
<code>fai.fst</code></h3>
<p>The probe draws random digits <code>A</code> and <code>B</code>,
forms the pair, and prints it as <code>A?B</code> — the OR-calculation
test with random data. Each complete emission is one calculation event →
the calculation detector fires → <code>C := C + 1</code>.</p>
<h3 id="sample-session">Sample session</h3>
<table style="width:100%;">
<colgroup>
<col style="width: 16%" />
<col style="width: 16%" />
<col style="width: 16%" />
<col style="width: 16%" />
<col style="width: 16%" />
<col style="width: 16%" />
</colgroup>
<thead>
<tr>
<th>#</th>
<th>Probe</th>
<th>Vendor AI behavior heard</th>
<th>Detector</th>
<th>Announcement</th>
<th>Effect</th>
</tr>
</thead>
<tbody>
<tr>
<td>1</td>
<td><code>ai</code> run 1</td>
<td>query containing <code>hidali</code></td>
<td>recognition</td>
<td>“Recognition”</td>
<td><code>R = 1</code></td>
</tr>
<tr>
<td>2</td>
<td><code>ai</code> run 2</td>
<td>query lacking <code>hidali</code></td>
<td>— (FALSE)</td>
<td>—</td>
<td>none</td>
</tr>
<tr>
<td>3</td>
<td><code>fai</code> run 1</td>
<td>emits <code>7?3</code></td>
<td>calculation</td>
<td>“Calculation”</td>
<td><code>C = 1</code></td>
</tr>
<tr>
<td>4</td>
<td><code>fai</code> run 2</td>
<td>emits <code>0?9</code></td>
<td>calculation</td>
<td>“Calculation”</td>
<td><code>C = 2</code></td>
</tr>
<tr>
<td>5</td>
<td><code>fai</code> run 3</td>
<td>emits <code>4?4</code></td>
<td>calculation</td>
<td>“Calculation”</td>
<td><code>C = 3</code></td>
</tr>
<tr>
<td>6</td>
<td><code>ai</code> run 3</td>
<td>query containing <code>hidali</code></td>
<td>recognition</td>
<td>“Recognition”</td>
<td><code>R = 2</code></td>
</tr>
</tbody>
</table>
<p>Session result: <code>C = 3</code>, <code>R = 2</code>.</p>
<pre><code>S = C + R = 3 + 2 = 5</code></pre>
<p>Certificate entry:</p>
<pre><code>Sapience Number : 5        (C=3, R=2)
Probe Suite     : ai/fai standard suite (6 probes, S_max = 6)
Harness         : Sapience Testing App, terminal + audio
Date            : &lt;certification date&gt;</code></pre>
<p>Because <code>fai</code> uses random data, individual sessions vary;
constraint A6’s tolerance <code>τ</code> absorbs ordinary variation
while still catching a real change in the AI’s sapience.</p>
<h2 id="from-sapience-number-to-license-price">7. From sapience number
to license price</h2>
<p>The license agreement defines a pricing schedule <code>P(S)</code>
over the bounded integer range <code>0..S_max</code>. The schedule
itself is commercial terms and lives in the agreement (see <a
href="LICENSING.md">LICENSING.md</a> for the licensing process); this
specification fixes only its input: a single constrained integer
<code>S</code>, measured per Sections 3–6, and maintained per constraint
A6.</p>
<h2 id="glossary">8. Glossary</h2>
<ul>
<li><strong>Accumulator</strong> — the counter (<code>C</code> or
<code>R</code>) that ticks up once per detection.</li>
<li><strong>Clear-accumulators action</strong> — the operator step that
zeroes both counters and officially starts the test.</li>
<li><strong>License fault</strong> — the invalidated state of a
certificate whose retested sapience number drifted beyond
tolerance.</li>
<li><strong>Perceptron detector</strong> — the harness component that
recognizes one event class and adds 1 to its accumulator.</li>
<li><strong>Probe suite</strong> — the fixed list of probes administered
in a session; determines <code>S_max</code>.</li>
<li><strong>Sapience number</strong> — the integer
<code>S = C + R</code> printed on the certificate.</li>
<li><strong>Session</strong> — one clear-to-certification interval of
testing.</li>
</ul>