Pith Number

pith:XXIMCWSP

pith:2015:XXIMCWSPRFS4JECB27LA77W256

not attested not anchored not stored refs pending

Critical density of activated random walks on transitive graphs

Alexandre Stauffer, Lorenzo Taggi

arxiv:1512.02397 v3 · 2015-12-08 · math.PR · 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{XXIMCWSPRFS4JECB27LA77W256}

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	2026-05-18T00:28:07.413065Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bdd0c15a4f8965c49041d7d60ffedaefb6ef287c0f83821487217cb37faf7b37

Aliases

arxiv: 1512.02397 · arxiv_version: 1512.02397v3 · doi: 10.48550/arxiv.1512.02397 · pith_short_12: XXIMCWSPRFS4 · pith_short_16: XXIMCWSPRFS4JECB · pith_short_8: XXIMCWSP

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/XXIMCWSPRFS4JECB27LA77W256 \
  | 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: bdd0c15a4f8965c49041d7d60ffedaefb6ef287c0f83821487217cb37faf7b37

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6ed3c2c4bf23e37056e09b1134252b2b634e20f0a62dbc3e091e7e4f2c87e567",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-12-08T10:49:24Z",
    "title_canon_sha256": "3a91c3cfa7031e7238a32931b2c349481ab7002ef1050573e5838488aea1a63c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.02397",
    "kind": "arxiv",
    "version": 3
  }
}