# 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.

---

## 1. Problem statement

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

```text
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:

```text
- 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.

---

## 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.

---

## 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.

---

## 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.

---

## 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.

---

## 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.

---

## 7. Status

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