ifc-0279

18.13 Intervals, abstention, and active acquisition

NI-2C changed the type of the relation rather than weakening its threshold. If person \(i\) has \(k_i\) confident keypoints, its public log-area uncertainty is

\[ r(k_i)=0.25+0.05(17-k_i). \]

For reference person \(0\), the relative log-area interval is

\[ I_{i0}=\left[ \log \frac{\widehat A_i}{\widehat A_0}-r(k_i)-r(k_0), \log \frac{\widehat A_i}{\widehat A_0}+r(k_i)+r(k_0) \right]. \]

A categorical claim is emitted only when the entire interval lies beyond the registered indifference band: \(\inf I_{i0}{\gt}0.15\) certifies larger, \(\sup I_{i0}{\lt}-0.15\) certifies smaller, and every other case abstains.

This repaired calibration: all eight sealed annotation-derived ratios and all twenty-four output ratios lay in their intervals, and no certified claim was false. But only one of eight comparisons was certified. NI-2C therefore passed twelve of thirteen clauses and failed the frozen \(25\% \) claim-coverage requirement. Reliable ignorance was preferable to false precision, but was not yet useful enough.

Interval relation	Emitted claim	Epistemic reading	Permitted action
\(\inf I_{i0}{\gt}0.15\)	person \(i\) is larger	The complete uncertainty interval clears the indifference band.	Preserve the certified ordering through repair.
\(\sup I_{i0}{\lt}-0.15\)	person \(i\) is smaller	The complete uncertainty interval clears the band in the opposite direction.	Preserve the certified ordering through repair.
\(I_{i0}\cap [-0.15,0.15]\ne \varnothing \)	abstain	Available evidence does not determine a stable categorical relation.	Acquire another registered view or leave the relation unspecified.

Table 18.2 The NI-2C decision rule makes abstention part of the typed observer. The system may preserve a relation only when the entire interval supports it; a point estimate alone cannot authorize repair.

NI-2D made acquisition conditional on that ignorance. When a base interval abstained, the observer acquired a horizontally reflected view, inverse-mapped its person masks, and tested agreement in the original coordinates. An interval narrowed only when both relevant masks had IoU at least \(0.70\) across views and absolute log-area change at most \(0.15\). The fused radius used the preregistered sharper rule

\[ r_{\mathrm{active}}(k)=0.18+0.03(17-k). \]

Disagreement left the original interval untouched. The second view is a registered equivariance probe of the same frozen segmenter, not an independent semantic observer.

Stage	Admission	Annotation coverage	Claim precision	Claim coverage
NI–2B: point relation	8/11 clauses	not represented	brittle	incomplete
NI–2C: interval and abstention	12/13 clauses	\(100\% \)	\(100\% \)	\(12.5\% \)
NI–2D: active second view	13/13 clauses	\(100\% \)	\(100\% \)	\(25.0\% \)

Seven of NI-2D’s eight base comparisons triggered acquisition. Five passed the agreement gate and were narrowed; two retained wide intervals because the reference-person observation was inconsistent. Mean half-width fell from \(0.9375\) in NI-2C to \(0.7550\), while sealed-annotation coverage remained \(100\% \). Certified coverage doubled to two of eight comparisons, with precision still \(100\% \). All thirteen preregistered clauses passed.

The same distinction between public observation and sealed structural audit can be made concrete in a robot-only testbed. In the robot-baseball example, each visible player is assigned a typed role and compared with the frozen role-slot declaration; the overlay exposes omissions, duplicates, and misplacements rather than scoring the scene as an undifferentiated image.

Figure 18.4 Typed structural audit in the robot-baseball testbed. Bounding boxes identify the batter, catcher, pitcher, umpire, three runners, and nine defenders by role. The audit tests cardinality, role identity, and spatial incidence rather than relying on holistic visual similarity.

The generated-output audit was conjunctive. Before localized repair, instance IoU was \(0.787\), keypoint PCK \(0.975\), interval coverage \(91.7\% \), and structural score \(0.875\). After repair these became \(0.836\), \(0.997\), \(100\% \), and \(0.912\). Identity order and triangle geometry passed in all twelve cells. Subject RGB error fell from \(0.0633\) to \(0.00329\), and the incremental repair-area ratio was \(0.191\), below the frozen \(0.75\) ceiling.

A complementary pose experiment shows how such an audit becomes a localized repair. The first realization places the catcher in the wrong orientation; the second enforces the registered catcher pose; the third harmonizes that typed insertion with the surrounding image while preserving the other player roles and field layout.

Observer-localized pose repair using robot players. Left: the catcher faces the wrong direction. Center: the registered pose is enforced. Right: the inserted catcher is harmonized with the scene. The sequence makes the repair target explicit while leaving unrelated roles and… — Figure 18.5 Observer-localized pose repair using robot players. Left: the catcher faces the wrong direction. Center: the registered pose is enforced. Right: the inserted catcher is harmonized with the scene. The sequence makes the repair target explicit while leaving unrelated roles and geometry fixed.

. Active observation is creative only in a restricted sense: the system changes what evidence it seeks to decide whether its declaration can be sharpened. The key result is not that another view always helps, but that agreement licenses refinement while disagreement preserves abstention.