Pith Number

pith:VKOJ25D4

pith:2001:VKOJ25D4NX2TIPXIDBVAWGI5KC

not attested not anchored not stored refs pending

percolation on finite graphs

Itai Benjamini

arxiv:math/0106022 v1 · 2001-06-04 · math.PR · 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{VKOJ25D4NX2TIPXIDBVAWGI5KC}

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	2026-07-04T14:35:21.740682Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aa9c9d747c6df5343ee8186a0b191d50a91441c74c95dd2e6d652b85142e6a61

Aliases

arxiv: math/0106022 · arxiv_version: math/0106022v1 · doi: 10.48550/arxiv.math/0106022 · pith_short_12: VKOJ25D4NX2T · pith_short_16: VKOJ25D4NX2TIPXI · pith_short_8: VKOJ25D4

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/VKOJ25D4NX2TIPXIDBVAWGI5KC \
  | 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: aa9c9d747c6df5343ee8186a0b191d50a91441c74c95dd2e6d652b85142e6a61

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fcc7ccf5655f85de68500590b2176eb49270846e224846ada6e5fc4ca58d14f2",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2001-06-04T19:13:22Z",
    "title_canon_sha256": "6a8d899ee7405012e7f28cc67714e58ed6577a169647fc42cea5e1a0e2065fe0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0106022",
    "kind": "arxiv",
    "version": 1
  }
}