Pith Number

pith:4PV4OE5Q

pith:2026:4PV4OE5QZMTF7HINWQHP7OEGKR

not attested not anchored not stored refs pending

Visualising the Attractor Landscape of Neural Cellular Automata

Alexander Mordvintsev, Harald Michael Ludwig, James Stovold, Mia-Katrin Kvalsund, Varun Sharma

Neural cellular automata often show simple behavioral manifolds at the full-state level but complex ones when broken down to individual cells.

arxiv:2604.10639 v2 · 2026-04-12 · cs.NE · cs.ET

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\usepackage{pith}
\pithnumber{4PV4OE5QZMTF7HINWQHP7OEGKR}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

When analysis is performed at a macroscopic level (i.e. taking the entire NCA state as a single data point), the underlying manifold is often quite simple and can be captured and analysed quite well. When analysis is performed at a microscopic level (i.e. taking the state of individual cells as a single data point), the manifold is highly complex and more complicated techniques are required in order to make sense of it.

C2weakest assumption

That the chosen manifold learning and topological techniques faithfully recover the true behavioral manifold without significant distortion or loss of dynamics that matter for the NCA's function.

C3one line summary

Neural Cellular Automata show simple attractor manifolds at the full-state level but complex ones at the individual-cell level when analyzed with PCA, autoencoders, and persistent homology.

Receipt and verification

First computed	2026-06-11T01:10:35.983644Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e3ebc713b0cb265f9d0db40effb8865479a477637e1c330ca76f96dc244af79a

Aliases

arxiv: 2604.10639 · arxiv_version: 2604.10639v2 · doi: 10.48550/arxiv.2604.10639 · pith_short_12: 4PV4OE5QZMTF · pith_short_16: 4PV4OE5QZMTF7HIN · pith_short_8: 4PV4OE5Q

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/4PV4OE5QZMTF7HINWQHP7OEGKR \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: e3ebc713b0cb265f9d0db40effb8865479a477637e1c330ca76f96dc244af79a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5b3e78e1d313b9a712c9a174f40e6769652b5b2c3df54502da262e0983b0b674",
    "cross_cats_sorted": [
      "cs.ET"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "cs.NE",
    "submitted_at": "2026-04-12T13:39:17Z",
    "title_canon_sha256": "cfbcfdb0193add918aaaed68c3fee93648f9c0f75e0ab9a4a40956aac7938876"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.10639",
    "kind": "arxiv",
    "version": 2
  }
}