Pith Number

pith:4EUK6F2X

pith:2020:4EUK6F2X3NKX7WIAZ5C3WUEULP

not attested not anchored not stored refs pending

Minimum stationary values of sparse random directed graphs

Guillem Perarnau, Xing Shi Cai

arxiv:2010.07246 v3 · 2020-10-14 · math.PR · cs.DM · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4EUK6F2X3NKX7WIAZ5C3WUEULP}

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.

Cited by

1 paper in Pith

Voter model on heterogeneous directed networks

Receipt and verification

First computed	2026-07-05T10:12:54.268024Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e128af1757db557fd900cf45bb50945be1f0aaee5098b29ace3614b5829fd26a

Aliases

arxiv: 2010.07246 · arxiv_version: 2010.07246v3 · doi: 10.48550/arxiv.2010.07246 · pith_short_12: 4EUK6F2X3NKX · pith_short_16: 4EUK6F2X3NKX7WIA · pith_short_8: 4EUK6F2X

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/4EUK6F2X3NKX7WIAZ5C3WUEULP \
  | 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: e128af1757db557fd900cf45bb50945be1f0aaee5098b29ace3614b5829fd26a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "30c3b22ef4f062710098a5e1efb2f6389c3d72c15168a8c81647327b197f0744",
    "cross_cats_sorted": [
      "cs.DM",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2020-10-14T17:08:02Z",
    "title_canon_sha256": "7fb9c572c9628feb8944e84fc5a0fb1cd8eea2fd80fd38d0e93f7989ba55a5ab"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2010.07246",
    "kind": "arxiv",
    "version": 3
  }
}