Pith Number

pith:GR4IZD3I

pith:2012:GR4IZD3ICP6YS5X6EKXUJUOXZB

not attested not anchored not stored refs pending

The Williams Bjerknes Model on Regular Trees

Alexander Vandenberg-Rodes, Oren Louidor, Ran J. Tessler

arxiv:1211.5694 v2 · 2012-11-24 · math.PR · cs.SI · math-ph · math.MP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GR4IZD3ICP6YS5X6EKXUJUOXZB}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

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.

Receipt and verification

First computed	2026-05-18T03:37:52.256301Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

34788c8f6813fd8976fe22af44d1d7c8744dfc7e9599df4fdd5075639ba17fd3

Aliases

arxiv: 1211.5694 · arxiv_version: 1211.5694v2 · doi: 10.48550/arxiv.1211.5694 · pith_short_12: GR4IZD3ICP6Y · pith_short_16: GR4IZD3ICP6YS5X6 · pith_short_8: GR4IZD3I

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/GR4IZD3ICP6YS5X6EKXUJUOXZB \
  | 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: 34788c8f6813fd8976fe22af44d1d7c8744dfc7e9599df4fdd5075639ba17fd3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eb549b8982b80843db0af2e030d4b4a08bbd23c0a50c1067088f0d8a7d7d3560",
    "cross_cats_sorted": [
      "cs.SI",
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-11-24T18:56:39Z",
    "title_canon_sha256": "b449c27c9f14ee231c1ba39881bd60254ddd17af94fb481ca17261e007889125"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.5694",
    "kind": "arxiv",
    "version": 2
  }
}