arborist/docs/tickets/ticket-000013-spatial-temporal-substrate.md

Ticket #000013 — Spatial-temporal substrate (Merkle-AGI v7-W)

Status: closed · landed 2026-05-09 (substrate paper + frontier catalog + namespace stub) Opened: 2026-05-07 Scope: Spec for a third commitment substrate — spatial-temporal world-state — sister to Merkle-AGI v7 (logic/math substrate) and arborist v9.8 (language/claim-lattice substrate). Doc-only — this ticket commissions the substrate paper. Implementation tickets cite it. Audience: fox + future blackops shifts + downstream world-model authors. Hard constraint: stays inside A1–A3 (canonical encoding, public quantization, collision-resistant hash). No new axiom. World-state canonical projection π*_w must be definable on quantized integer state, not on continuous tensors.

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1. Problem statement

Fox's own framing identifies three substrates needed for ASI:

3 > (language, logic, substrate)
1 = recursive-falsification merkle-agi (logic / math)
2 = language / claim-lattice (arborist v9.8)
3 = spatial-temporal vision / world-models  ← MISSING

Without a world-state substrate, an agent cannot:

Capability	Failure under language+logic only
Persistent identity across time	Cache is keyed on text; physical "where am I" has no commitment.
Causal physics reasoning	Logic substrate verifies proof steps; world substrate verifies "what happened next."
Multi-modal grounding	A claim about an object's location can't be falsified without a state commitment.
Robotic / embodied use	No way to commit "I observed X at (t, x, y, z) with confidence c."
Video / time-series audit	No π* for temporal signals; no equivalent of wikitext-base-v1.

v7 § 11 multimodal composition handles vision + language structurally (commit the conv kernel, the bridge, the projection). It does not commit world-state: the abstract scene representation, the spatial relations, the temporal predicates. Those are derived from the model's forward pass and never committed as first-class objects.

1.1 What world-state means here

Not raw pixels. Not raw audio. The derived state an agent maintains:

- objects:    { id, class, bbox, pose, confidence }
- relations:  { subject_id, predicate, object_id, time_window }
- events:     { type, t_start, t_end, participants, place }
- places:     { id, frame_of_reference, geometry, parent_place }
- agents:     { id, position_trace, pose_trace, attention_trace }

This is the substrate of a world-model. It's what a SLAM system exports, what a Genie/SORA-style world-model dreams about, what a robotics planner consumes. None of it has a canonical commitment form today.

1.2 The verifiability challenge

Unlike text (where to_base() canonicalizes prose) and unlike model weights (where Q(Θ) gives integer commitment), world-state is:

• Continuous in space and time — needs canonical discretization (a π*_w with explicit grid choice).
• Probabilistic — every observation has confidence; commitments must bind the confidence, not just the claim.
• Frame-dependent — same scene, different observers, different coordinates. π*_w must canonicalize frame.
• Temporally extended — events span intervals. Canonical interval representation needed.

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2. Design choices

2.1 Canonical discretization

A. Fixed grid (per-substrate constant). Δ_x, Δ_t fixed in the substrate manifest. Simple. Brittle for multi-scale tasks.

B. Per-claim grid. Each commitment declares its grid in attrs. Flexible. Spec-brittleness explosion (every claim becomes its own canonicalization).

C. Hierarchical grid (octree / quadtree levels). Substrate declares a finite set of grid levels; each commitment names which level it's anchored at. Compositional.

Recommendation: C. Hierarchical octree-style grids match how spatial reasoning actually works (coarse-to-fine), match established standards (e.g., S2 / H3 for geographic indexing), and keep π*_w finitely specified.

2.2 Frame canonicalization

A. Single canonical frame (e.g., ECEF, object-fixed). Forces every observation into a global frame. Loses local-frame ergonomics.

B. Frame as part of commitment. Each observation declares its frame; cross-frame reasoning needs explicit transforms (also committed).

C. Equivalence classes (like arborist's question_hash strict / equivalence_class). π*_w accepts multiple frames; equivalence class membership is committed.

Recommendation: B. Forces explicit frame at every observation, and frame transforms become first-class committed objects (matching v7's "every causally relevant transformation must be committed" axiom).

2.3 Temporal canonicalization

A. Discrete tick (e.g., milliseconds since epoch). Trivial. Locks substrate into one clock domain.

B. Per-substrate clock (declared in manifest). Substrate manifest declares Δ_t and reference epoch. Cross-substrate joins need explicit clock transforms.

C. Logical time (Lamport / vector clocks). Decouples from wall-clock. Required for distributed observation merging without trusting clocks.

Recommendation: B for single-agent, C for multi-agent. Substrate manifest declares which mode. Mixed deployments use B locally + C across agents.

2.4 Probabilistic commitment

Two viable approaches:

A. Quantize confidence to integer (e.g., centi-confidence 0-100). Commits the discretized confidence as part of claim. Simple. Coarse.

B. Range commitment. Each claim commits a confidence interval [lo, hi] as integers. More expressive. More disclosure surface.

Recommendation: A by default; B opt-in for safety-critical deployments where confidence intervals matter (medical, robotics).

2.5 ε-frontiers in v7-W

What's the equivalent of "affine preactivation" for world-models?

Candidates:

• Pose update step (ego-motion / kinematic integration). Linear in state under small-time-step assumption. ε-frontier candidate.
• Observation-to-state update (Kalman update step). Affine. ε-frontier candidate.
• Object detection logits (already covered by v7).
• Scene-graph edge prediction logits (affine projections on pair embeddings). ε-frontier candidate.

Recommendation: declare four canonical ε-frontiers in v7-W: pose_integration, observation_update, object_logits, relation_logits. Each is affine after appropriate canonical projection.

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3. Recommendation

A v7-W substrate paper specifying:

1. Hierarchical-grid spatial discretization (S2/H3-like).
2. Frame as committed object with explicit transforms.
3. Substrate-declared clock (single-agent) + Lamport (multi-agent).
4. Quantized confidence (centi-confidence) default; range opt-in.
5. Four canonical ε-frontiers: pose, observation, object, relation.
6. Standard π*_w on the (object, relation, event, place, agent) tuple-space defined above.

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4. Implementation sketch

This ticket commissions the substrate paper. v7-W structure follows v7:

• Part 1 — Introduction & motivation. Why world-state needs its own substrate; why v7 multimodal composition isn't enough.
• Part 2 — Substrate definition (π_w).* Hierarchical grid, frame, clock, confidence. Canonical encoding.
• Part 3 — Theorems. T1-W (state binding), T2-W (causal completeness), T3-W (frame-transform soundness), T4-W (ε at affine frontiers).
• Part 4 — Verifier kernels. Pose integration, Kalman update, scene-graph edge predictor (each as deterministic integer kernel).
• Part 5 — Multimodal composition with v7. When does a v7 vision encoder feed v7-W state, and where do ε-proofs anchor.
• Part 6 — Adversarial corners. Frame spoofing, time-skew, observation injection.
• Appendix — Worked example. A toy SLAM scenario with full commitment trail.

4.1 Concrete artifacts this ticket produces

• docs/merkle-agi-v7w-spatial-temporal.rst — substrate paper.
• docs/v7w-frontier-catalog.md — canonical ε-frontier catalog for world-models.
• Stub arborist/world/__init__.py reserving the namespace; no implementation yet.

4.2 What does not change

• arborist's text/claim-lattice substrate. v7-W is parallel, not replacement.
• v7's affine-frontier ε-proof discipline. v7-W's frontiers follow the same pattern at different op types.

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5. Out of scope

• Actually running a SLAM stack inside arborist. v7-W defines the commitment substrate; world-model engines (SLAM, Gaussian splatting, predictive video) plug into it via adapters that are separate tickets.
• Cross-modal joint reasoning (text claim + spatial state). That needs the cross-domain π* composition theorem (ticket #000015).
• Specific sensor adapters (LIDAR, RGB-D, IMU). Each is a separate source-adapter ticket once v7-W lands.

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6. Risks & open questions

• Discretization tax. Every spatial claim incurs grid-rounding cost. Need empirical bench on whether ε at world-model frontiers remains tight enough to be useful.
• Standards adoption. S2/H3 vs custom octree vs Cesium 3D Tiles. Picking a standard reduces interop friction; picking custom keeps permacomputer values intact. Recommend S2 + Lamport as default, custom escape hatch.
• Privacy. A world-state commitment substrate is also a surveillance substrate. Frame discipline + Phase-2 ZK (ticket #000016) more important here than for text/logic.

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7. Status

Open · awaiting go/no-go. Research-paper-scope ticket. Closure criterion: docs/merkle-agi-v7w-spatial-temporal.rst lands and is reviewed.