Pith Number

pith:APFB7O4J

pith:2003:APFB7O4JI5GTKL3UEMBPKGHG4M

not attested not anchored not stored refs pending

A Phase Transition for the Metric Distortion of Percolation on the Hypercube

Itai Benjamini, Omer Angel

arxiv:math/0306355 v1 · 2003-06-25 · 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{APFB7O4JI5GTKL3UEMBPKGHG4M}

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	2026-07-04T14:37:32.979516Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

03ca1fbb89474d352f742302f518e6e33564ac7350d4bf61a2d39e6922357522

Aliases

arxiv: math/0306355 · arxiv_version: math/0306355v1 · doi: 10.48550/arxiv.math/0306355 · pith_short_12: APFB7O4JI5GT · pith_short_16: APFB7O4JI5GTKL3U · pith_short_8: APFB7O4J

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/APFB7O4JI5GTKL3UEMBPKGHG4M \
  | 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: 03ca1fbb89474d352f742302f518e6e33564ac7350d4bf61a2d39e6922357522

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e35ce430be13ed9e3ad2eb3c34c476dd5ec80c49081e22fab8b84edeb0d2cb25",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2003-06-25T07:22:29Z",
    "title_canon_sha256": "075eac14feca4f55b698514f51b636061c73d14d842db1edcd5225cf01a3cd1b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0306355",
    "kind": "arxiv",
    "version": 1
  }
}