Add visual primitives goxel witness research note

0-Core-Formalism/otom/docs/visual_primitives_goxel_witness.md

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+---
+project: OTOM
+domain: axis-04-formalization
+type: ResearchNote
+settlement: FORMING
+authority: registry
+route_signature: otom/axis-04-formalization/researchnote/visual-primitives-goxel-witness/v0
+source_url: https://www.alphaxiv.org/abs/visual-primitives
+---
+
+# Visual Primitives as Goxel Witnesses
+
+## External anchor
+
+The linked visual-primitives work frames a multimodal reasoning bottleneck as a
+reference problem: language alone is often too ambiguous to identify the exact
+spatial object or region involved in a visual reasoning step.
+
+The project-facing interpretation is narrow and engineering-safe:
+
+> Coordinate-bearing visual primitives can act as witness objects that bind a
+> linguistic claim to a bounded visual/manifold region.
+
+This note does **not** treat the external work as validation of the full OTOM or
+TSM ontology. It only records the bridge:
+
+```text
+language-only reference is under-bound
+coordinate witness reduces reference ambiguity
+reduced reference ambiguity can reduce replay/compression cost
+bounded witness can be formalized as a Goxel-facing primitive
+```
+
+## Stack translation
+
+| External phrase | Stack phrase | Meaning |
+|---|---|---|
+| visual primitive | coordinate-bearing witness | point/box/mask-like spatial reference unit |
+| reference gap | binding ambiguity | language does not uniquely bind to a field region |
+| point while reasoning | witness trace atom | reasoning emits a spatial receipt |
+| bounding box / point | bounded region | finite coordinate support |
+| visual token efficiency | witness compression pressure | spatial grounding may reduce reference entropy |
+
+## Canonical formal bridge
+
+Lean module:
+
+```text
+0-Core-Formalism/otom/tools/lean/Semantics/Semantics/VisualPrimitive.lean
+```
+
+Primary objects:
+
+```text
+PrimitiveKind
+BoundedRegion
+VisualPrimitive
+GoxelWitness
+```
+
+First theorem-level gates:
+
+```text
+BoundedRegion.Nonempty
+VisualPrimitive.Binds
+GoxelWitness.Grounded
+area_positive_of_grounded
+```
+
+## Proposed compression objective
+
+A visual primitive is useful when the cost of storing the witness is lower than
+the ambiguity it removes:
+
+```text
+minimize:
+  H(reference | primitive)
++ lambda * primitive_cost
++ mu     * replay_cost
++ nu     * hallucination_penalty
+```
+
+Equivalent operational rule:
+
+> A good primitive reduces reference entropy more than it costs to encode and
+> replay.
+
+## Relationship to TSM
+
+The TSM direction should treat a visual primitive as a finite state-transition
+receipt, not as passive annotation:
+
+```text
+VisualPrimitive -> GoxelWitness -> TSM register / checkpoint trace
+```
+
+This preserves the important distinction:
+
+- annotation: a label attached after perception
+- witness: a bounded coordinate receipt used during reasoning/replay
+
+## Evidence discipline
+
+Allowed claim state: `BEAUTIFUL_PROVISIONAL` until benchmarked.
+
+Acceptable near-term claims:
+
+1. A coordinate-bearing primitive can be represented as a finite bounded region.
+2. A Goxel witness can bind a semantic tag to a nonempty coordinate region.
+3. A grounded witness has positive spatial receipt cost.
+
+Blocked claims without evidence receipts:
+
+1. Any universal claim about multimodal model capability.
+2. Any claim that this validates OTOM as a full ontology.
+3. Any claim of compression improvement without measured baselines.
+4. Any claim of hallucination reduction without controlled evaluation.
+
+## Next tests
+
+1. Add a small synthetic scene corpus with known reference targets.
+2. Compare text-only references against point/box witness references.
+3. Measure reference entropy, replay cost, and error rate.
+4. Add evidence receipts before promoting beyond `BEAUTIFUL_PROVISIONAL`.