Pith Number

pith:XR3JU7QJ

pith:2026:XR3JU7QJYHIOZ6KZBYTSWIKQIO

not attested not anchored not stored refs pending

Edge-based mean-field approximation of dynamics on networks via approximate lumping of Markov chains

G\'abor Tim\'ar, Jonathan A. Ward, P\'eter L. Simon

arxiv:2607.05425 v1 · 2026-06-30 · physics.soc-ph · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XR3JU7QJYHIOZ6KZBYTSWIKQIO}

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	2026-07-08T01:18:09.631162Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bc769a7e09c1d0ecf9590e272b215043b62ac8e5e54a03600cffaf2c449f9e45

Aliases

arxiv: 2607.05425 · arxiv_version: 2607.05425v1 · doi: 10.48550/arxiv.2607.05425 · pith_short_12: XR3JU7QJYHIO · pith_short_16: XR3JU7QJYHIOZ6KZ · pith_short_8: XR3JU7QJ

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/XR3JU7QJYHIOZ6KZBYTSWIKQIO \
  | 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: bc769a7e09c1d0ecf9590e272b215043b62ac8e5e54a03600cffaf2c449f9e45

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "317ee995b0e423b891c45eb9885aa2b1ebffef69da923dfd73d3dd4cbce28ba2",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.soc-ph",
    "submitted_at": "2026-06-30T15:56:04Z",
    "title_canon_sha256": "918a19540e19072b932135aa1dd97e91ae8a1281fe5ad7d8556020e124e6c586"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.05425",
    "kind": "arxiv",
    "version": 1
  }
}