# ontology-asi-interleave <<<<<<< HEAD

> > Bridge connecting plurigrid/ontology to ASI skill graph. Wires autopoietic ergodicity, Open Games, Gromov-Wasserstein theory, Arena CRDT, Nexus Nodes, and transactive energy into decentralized energy coordination, digital twin multi-agent systems, and grid intelligence. Use when connecting ontology concepts to ASI skills, designing transactive energy markets, or bridging Arena CRDT to DuckDB. >>>>>>> origin/main

- Skill: `plurigrid/ontology-asi-interleave-head` (Agent Skill, multi-file: 2 files)
- Install (CLI): `npx skillmds@latest add plurigrid/ontology-asi-interleave-head`
- Raw SKILL.md: https://api.skillmd.com/api/skills/plurigrid/ontology-asi-interleave-head/raw
- Safety review: pending
- Works with: Claude Code, Claude.ai, OpenAI Codex
- Category: AI & ML
- Author: plurigrid (https://skillmd.com/u/plurigrid)
- Updated: 2026-09-17
- Page: https://skillmd.com/skills/plurigrid/ontology-asi-interleave-head

---


# Ontology x ASI Interleave

Bridge connecting `plurigrid/ontology` (the Plurigrid protocol's mathematical and systems foundation) to the ASI skill graph.

## plurigrid/ontology -- 7 Core Concepts

```
<<<<<<< HEAD
plurigrid/ontology
  1. Autopoietic Ergodicity    -- self-org + time-avg = ensemble-avg convergence
  2. Open Games Framework      -- compositional game theory, Markov categories
  3. Gromov-Wasserstein Theory  -- metric measure space comparison, entropic reg.
  4. Arena System              -- local-first graph DB, Rust + Yrs CRDTs, DuckDB
  5. Digital Twin Architecture -- multi-agent value elicitation, mutual recursion
  6. Nexus Nodes               -- 3-tier hardware: Apple Silicon / RPi4 / Pico W
  7. Transactive Energy        -- stigmergic markets, multi-agent RL + Open Games
```

## GF(3) Tripartite Tag

`arena-crdt(-1) * ontology-asi-interleave(0) * open-games(+1) = 0`

Infrastructure (-1) x Bridge (0) x Strategy (+1) = balanced energy coordination.

---

=======
1. Autopoietic Ergodicity    -- self-org + time-avg = ensemble-avg convergence
2. Open Games Framework      -- compositional game theory, Markov categories
3. Gromov-Wasserstein Theory  -- metric measure space comparison, entropic reg.
4. Arena System              -- local-first graph DB, Rust + Yrs CRDTs, DuckDB
5. Digital Twin Architecture -- multi-agent value elicitation, mutual recursion
6. Nexus Nodes               -- 3-tier hardware: Apple Silicon / RPi4 / Pico W
7. Transactive Energy        -- stigmergic markets, multi-agent RL + Open Games
```

>>>>>>> origin/main
## Integration Points

### 1. Autopoietic Ergodicity <-> autopoiesis, ergodicity, dynamic-sufficiency

<<<<<<< HEAD
Ontology defines autopoietic ergodicity as the convergence criterion: a system that self-organizes (autopoiesis) such that time averages equal ensemble averages (ergodicity), minimizing surprise through continuous learning (active inference).

```
  ontology                         ASI skills
  +-----------------------+        +-------------------------+
  | autopoietic ergodicity|------->| autopoiesis             |
  |   time-avg = ens-avg  |------->| ergodicity              |
  |   minimize surprise   |------->| dynamic-sufficiency(145)|
  |   embodied gradualism |        | active-inference        |
  +-----------------------+        +-------------------------+
```

`dynamic-sufficiency` (145 references, central hub) is the primary landing point: it already connects autopoiesis and ergodicity within ASI. Ontology's "embodied gradualism" maps to dynamic-sufficiency's gradual capability accumulation.
=======
A system that self-organizes (autopoiesis) such that time averages equal ensemble averages (ergodicity), minimizing surprise through continuous learning (active inference).

`dynamic-sufficiency` (145 references, central hub) is the primary landing point. Ontology's "embodied gradualism" maps to dynamic-sufficiency's gradual capability accumulation.
>>>>>>> origin/main

### 2. Open Games Framework <-> open-games, cybernetic-open-game

The Plurigrid protocol IS a compositional open game. Agents are morphisms in a Markov category with generative (play) and recognition (coplay) channels.

<<<<<<< HEAD
```
  ontology                         ASI skills
  +-----------------------+        +-------------------------+
  | Open Games            |------->| open-games              |
  |   Markov categories   |------->| cybernetic-open-game    |
  |   correlated equilib. |------->| equilibrium             |
  |   sense-making / AI   |------->| nashator (9999)         |
  +-----------------------+        +-------------------------+
```

=======
>>>>>>> origin/main
Grid = composed game: `node_game @ transmission_game @ market_game`. The correlated equilibrium = autopoietically ergodic state = Nash equilibrium that is also thermodynamically stable.

### 3. Gromov-Wasserstein Theory <-> gflownet, duckdb-spatial

<<<<<<< HEAD
GW theory compares metric measure spaces and does graph matching across heterogeneous energy networks. Entropic regularization + Bregman projections for efficient optimization.

```
  ontology                         ASI skills
  +-----------------------+        +-------------------------+
  | Gromov-Wasserstein    |------->| gflownet (OT sampling)  |
  |   entropic reg.       |------->| duckdb-spatial (graphs) |
  |   Bregman projections |------->| geohash-coloring        |
  |   graph matching      |------->| map-projection          |
  +-----------------------+        +-------------------------+
```

GFlowNet samples from energy-proportional distributions over combinatorial structures -- the same optimal transport problem that GW solves for network matching. The entropic regularization in GW parallels the entropy bonus in GFlowNet training.
=======
GW theory compares metric measure spaces and does graph matching across heterogeneous energy networks. Entropic regularization + Bregman projections for efficient optimization. GFlowNet samples from energy-proportional distributions over combinatorial structures -- the same optimal transport problem that GW solves for network matching.
>>>>>>> origin/main

### 4. Arena CRDT System <-> crdt, time-travel-crdt, duckdb-ies

Arena is a local-first graph-based data store in Rust with DuckDB backend and Yrs CRDTs for real-time peer synchronization.

<<<<<<< HEAD
```
  ontology                         ASI skills
  +-----------------------+        +-------------------------+
  | Arena System          |        |                         |
  |   Yrs (Y-CRDT)       |------->| crdt                    |
  |   peer sync           |------->| time-travel-crdt        |
  |   DuckDB backend      |------->| duckdb-ies              |
  |   graph store         |------->| duckdb-spatial          |
  |   nodes/edges tables  |------->| duckdb-quadruple-interl.|
  +-----------------------+        +-------------------------+
```

Arena schema: `nodes(id, label, properties)` + `edges(id, src, dst, label, properties)` -- maps directly to DuckDB graph patterns in `duckdb-ies` and `duckdb-spatial`. The CRDT layer (Yrs) provides exactly the merge semantics that `time-travel-crdt` formalizes for ASI skill state.

### 5. Digital Twin Architecture <-> dynamic-sufficiency, agent-o-rama

Virtual representations of physical entities. Multi-agent loop in Chat Arena. Agent profiles with value systems and behavior models. Value elicitation via mutual recursion.

```
  ontology                         ASI skills
  +-----------------------+        +-------------------------+
  | Digital Twin          |------->| dynamic-sufficiency     |
  |   agent profiles      |------->| agent-o-rama (hub)      |
  |   value elicitation   |------->| cognitive-surrogate     |
  |   active inference    |------->| active-inference        |
  |   mutual recursion    |------->| skill-dispatch          |
  +-----------------------+        +-------------------------+
```

The digital twin's active inference loop (predict -> act -> observe -> update) is the same loop that `dynamic-sufficiency` implements for ASI skill selection. Each agent twin maintains a GF(3)-colored value system that evolves via CRDT merge with peer twins.

### 6. Nexus Nodes <-> hvm-runtime, world-runtime, iot-device-provisioning

3-tier hardware architecture, all targeting wasm32-unknown-unknown with WASI + capability plugins:

```
  Tier          Hardware           Compute        ASI Skill
  +-----------+------------------+-------------+-------------------------+
  | High Power| Apple Silicon    | Full WASM   | hvm-runtime             |
  |           | (M-series Mac)   | + TF ext.   | world-runtime-capability|
  +-----------+------------------+-------------+-------------------------+
  | Low Power | Raspberry Pi 4   | WASI core   | iot-device-provisioning |
  |           | (4GB ARM)        |             |                         |
  +-----------+------------------+-------------+-------------------------+
  | Embedded  | RPi Pico W       | Minimal WASI| iot-device-provisioning |
  |           | (264KB SRAM)     | (sensor hub)|                         |
  +-----------+------------------+-------------+-------------------------+
  Runtime: WasmEdge for high-perf WASM with TensorFlow extensions
```

`hvm-runtime` handles the high-performance interaction net reduction on Apple Silicon. `world-runtime-capability` provides the capability-secure plugin system that maps to WASI capability plugins. `iot-device-provisioning` covers the provisioning and attestation workflow for the Low Power and Embedded tiers.

### 7. Transactive Energy <-> nashator, open-games, equilibrium

Market-based transactions between energy grids. Stigmergic feedback for energy availability, demand, and prices. Multi-agent RL + mutual information optimization + Open Games.

```
  ontology                         ASI skills
  +-----------------------+        +-------------------------+
  | Transactive Energy    |------->| nashator (market engine) |
  |   stigmergic feedback |------->| open-games (formalism)  |
  |   market clearing     |------->| equilibrium (solver)    |
  |   multi-agent RL      |------->| gym (RL environments)   |
  |   mutual info opt.    |------->| gflownet (sampling)     |
  +-----------------------+        +-------------------------+
```

Nashator at 127.0.0.1:9999 is the direct implementation target: each energy node submits bids as open game moves, the Nashator resolves to correlated equilibrium = market clearing price.

---

## Gap Registry

Capabilities in plurigrid/ontology not yet covered by ASI skills:

| Ontology Concept | Gap | Priority | Candidate Skill Name |
|-----------------|-----|----------|---------------------|
| Gromov-Wasserstein distance | No dedicated GW/OT skill; gflownet is tangential | HIGH | `gromov-wasserstein` |
| Arena graph store (Rust+Yrs) | No Rust CRDT skill; `crdt` is language-agnostic | MED | `arena-crdt` |
| Stigmergic feedback loops | No stigmergy skill; nashator handles markets only | MED | `stigmergy` |
| WasmEdge runtime | `hvm-runtime` covers HVM, not WasmEdge specifically | LOW | `wasmedge-runtime` |
| Value elicitation protocols | `dynamic-sufficiency` is close but not explicit | LOW | `value-elicitation` |
| Embodied gradualism | Philosophical concept; `autopoiesis` partially covers | LOW | (extend autopoiesis) |
| RPi Pico W sensor hub | `iot-device-provisioning` exists but no Pico W target | LOW | (extend iot-device) |

---

## Plurigrid Protocol Summary

The Plurigrid protocol = self-rebalancing, self-infrastructuring electricity grid:
=======
Arena schema: `nodes(id, label, properties)` + `edges(id, src, dst, label, properties)` -- maps directly to DuckDB graph patterns.

### 5. Digital Twin Architecture <-> dynamic-sufficiency, agent-o-rama

The digital twin's active inference loop (predict -> act -> observe -> update) is the same loop that `dynamic-sufficiency` implements for ASI skill selection.

### 6. Nexus Nodes <-> hvm-runtime, world-runtime, iot-device-provisioning

3-tier hardware architecture targeting wasm32-unknown-unknown with WASI + capability plugins:

| Tier | Hardware | Compute | ASI Skill |
|---|---|---|---|
| High Power | Apple Silicon (M-series) | Full WASM + TF ext. | hvm-runtime |
| Low Power | Raspberry Pi 4 (4GB ARM) | WASI core | iot-device-provisioning |
| Embedded | RPi Pico W (264KB SRAM) | Minimal WASI | iot-device-provisioning |

Runtime: WasmEdge for high-perf WASM with TensorFlow extensions.

### 7. Transactive Energy <-> nashator, open-games, equilibrium

Market-based transactions between energy grids. Stigmergic feedback for energy availability, demand, and prices.

Nashator at 127.0.0.1:9999 is the direct implementation target: each energy node submits bids as open game moves, the Nashator resolves to correlated equilibrium = market clearing price.

## Concrete Affordances

### Arena CRDT Schema in DuckDB

Create the Arena graph schema and insert sample energy-grid nodes:

```sql
-- File: /Users/alice/v/asi/skills/ontology-asi-interleave/arena_schema.sql
-- Run: duckdb /Users/alice/v/arena.duckdb < arena_schema.sql

CREATE TABLE IF NOT EXISTS arena_nodes (
    id        VARCHAR PRIMARY KEY,
    label     VARCHAR NOT NULL,
    properties JSON,
    created_at TIMESTAMP DEFAULT current_timestamp,
    yrs_clock  BIGINT DEFAULT 0  -- Yrs CRDT logical clock
);

CREATE TABLE IF NOT EXISTS arena_edges (
    id    VARCHAR PRIMARY KEY,
    src   VARCHAR NOT NULL REFERENCES arena_nodes(id),
    dst   VARCHAR NOT NULL REFERENCES arena_nodes(id),
    label VARCHAR NOT NULL,
    properties JSON,
    weight DOUBLE DEFAULT 1.0
);

-- Sample: three Nexus Nodes forming a transactive energy triangle
INSERT OR IGNORE INTO arena_nodes VALUES
  ('nexus-m4',  'apple-silicon', '{"tier":"high","watt_capacity":150}',  now(), 1),
  ('nexus-rpi', 'rpi4',          '{"tier":"low","watt_capacity":15}',    now(), 1),
  ('nexus-pico','pico-w',        '{"tier":"embedded","watt_capacity":1}', now(), 1);

INSERT OR IGNORE INTO arena_edges VALUES
  ('e1', 'nexus-m4',  'nexus-rpi',  'energy-link', '{"latency_ms":2}',   1.0),
  ('e2', 'nexus-rpi', 'nexus-pico', 'energy-link', '{"latency_ms":50}',  0.5),
  ('e3', 'nexus-pico','nexus-m4',   'energy-link', '{"latency_ms":45}',  0.3);

-- Query: neighbor energy capacity
SELECT n.id, n.label, n.properties->>'watt_capacity' AS watts,
       COUNT(e.id) AS degree
FROM arena_nodes n
LEFT JOIN arena_edges e ON n.id = e.src OR n.id = e.dst
GROUP BY n.id, n.label, watts;
```

### Nashator Transactive Energy API

Submit energy bids and query equilibrium via the Nashator service:

```bash
# Check Nashator is running
curl -s http://127.0.0.1:9999/health

# Submit an energy bid (open game move)
curl -X POST http://127.0.0.1:9999/api/v1/bid \
  -H 'Content-Type: application/json' \
  -d '{
    "node_id": "nexus-m4",
    "bid_type": "supply",
    "quantity_kwh": 5.0,
    "price_per_kwh": 0.12,
    "timestamp": "'"$(date -u +%Y-%m-%dT%H:%M:%SZ)"'"
  }'

# Query current correlated equilibrium (market clearing price)
curl -s http://127.0.0.1:9999/api/v1/equilibrium | python3 -m json.tool
```

### Open Games Grid Model (Julia)

Compose a transactive energy game using Open Games:

```julia
# Requires: using Pkg; Pkg.add(["OpenGames", "Catlab"])
using OpenGames, Catlab

# Each Nexus Node is a player choosing (quantity, price)
node_game = OpenGame(
    name = :nexus_node,
    strategies = [(0.0:0.5:10.0, 0.05:0.01:0.30)],  # (kWh, $/kWh)
    payoff = (s, ctx) -> s[2] * s[1] - generation_cost(s[1])
)

# Transmission: pairwise latency cost
transmission_game = OpenGame(
    name = :transmission,
    payoff = (s, ctx) -> -ctx[:latency_ms] * 0.001 * s[:quantity]
)

# Compose: node @ transmission @ market
grid_game = compose(node_game, transmission_game)

# Find Nash equilibrium via Lemke-Howson or support enumeration
eq = solve(grid_game, method=:support_enumeration)
println("Equilibrium price: ", eq.clearing_price, " \$/kWh")
```

### Gromov-Wasserstein Network Matching (Python)

Compare two energy network topologies using entropic GW distance:

```python
# pip install pot numpy
import numpy as np
import ot

# Adjacency / cost matrices for two energy networks
C1 = np.array([[0, 1, 0], [1, 0, 1], [0, 1, 0]], dtype=float)  # linear
C2 = np.array([[0, 1, 1], [1, 0, 1], [1, 1, 0]], dtype=float)  # triangle

p = ot.unif(C1.shape[0])
q = ot.unif(C2.shape[0])

# Entropic Gromov-Wasserstein distance
gw_dist, log = ot.gromov.entropic_gromov_wasserstein2(
    C1, C2, p, q, loss_fun='square_loss', epsilon=0.1, log=True
)
print(f"Entropic GW distance: {gw_dist:.6f}")
print(f"Transport plan:\n{log['T']}")
```

## Gap Registry

| Ontology Concept | Gap | Priority | Candidate Skill |
|---|---|---|---|
| Gromov-Wasserstein distance | No dedicated GW/OT skill | HIGH | `gromov-wasserstein` |
| Arena graph store (Rust+Yrs) | No Rust CRDT skill | MED | `arena-crdt` |
| Stigmergic feedback loops | No stigmergy skill | MED | `stigmergy` |
| WasmEdge runtime | hvm-runtime covers HVM, not WasmEdge | LOW | `wasmedge-runtime` |

## Plurigrid Protocol Summary

>>>>>>> origin/main
- **Math core**: Open Games + Gromov-Wasserstein + Active Inference
- **Data layer**: Arena (local-first CRDT graph DB, Rust + Yrs + DuckDB)
- **Agent arch**: Digital twins with value elicitation + mutual recursion
- **Equilibrium**: Autopoietically ergodic state = Nash eq. that is thermodynamically stable
<<<<<<< HEAD
- **Energy market**: Stigmergic feedback -> decentralized price discovery -> transactive coordination
- **Hardware**: Nexus Nodes (Apple Silicon / RPi4 / Pico W) all running WASI

## Related Skills

- `autopoiesis` -- self-organization; the Plurigrid node model
- `ergodicity` -- time-average = ensemble-average convergence criterion
- `dynamic-sufficiency` -- 145-ref hub; autopoiesis + ergodicity nexus
- `open-games` -- compositional game theory; Plurigrid protocol formalization
- `cybernetic-open-game` -- cybernetic feedback in open game frameworks
- `crdt` / `time-travel-crdt` -- Arena CRDT patterns for distributed skill state
- `duckdb-ies` / `duckdb-spatial` -- Arena DuckDB backend patterns
- `gflownet` -- energy-proportional sampling; GW optimal transport analog
- `hvm-runtime` -- high-perf WASM on Apple Silicon Nexus tier
- `world-runtime-capability` -- WASI capability plugin system
- `iot-device-provisioning` -- Nexus Nodes Low Power + Embedded tiers
- `nashator` -- transactive energy market engine (127.0.0.1:9999)
- `agent-o-rama` -- universal hub; digital twin orchestration
- `equilibrium` -- Nash/correlated equilibria solver
- `ordered-locale` -- GF(3)->GF(9)->GF(27) tower; mathematical spine
- `catcolab-stock-flow` / `catcolab-causal-loop` -- energy system modeling
- `vertex-asi-interleave` / `bigquery-asi-interleave` -- sibling GCP bridges
=======
- **Energy market**: Stigmergic feedback -> decentralized price discovery
- **Hardware**: Nexus Nodes (Apple Silicon / RPi4 / Pico W) all running WASI
>>>>>>> origin/main