Pith Number

pith:M3E45DMM

pith:2020:M3E45DMMF77N25CKHKWPCCMEEA

not attested not anchored not stored refs pending

Delocalization transition for critical Erd\H{o}s-R\'enyi graphs

Antti Knowles, Johannes Alt, Raphael Ducatez

arxiv:2005.14180 v3 · 2020-05-28 · 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{M3E45DMMF77N25CKHKWPCCMEEA}

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	2026-07-05T03:09:55.753381Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

66c9ce8d8c2ffedd744a3aacf1098420352460f5baad3b5346e1754ab9f248ad

Aliases

arxiv: 2005.14180 · arxiv_version: 2005.14180v3 · doi: 10.48550/arxiv.2005.14180 · pith_short_12: M3E45DMMF77N · pith_short_16: M3E45DMMF77N25CK · pith_short_8: M3E45DMM

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/M3E45DMMF77N25CKHKWPCCMEEA \
  | 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: 66c9ce8d8c2ffedd744a3aacf1098420352460f5baad3b5346e1754ab9f248ad

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "82ff4cd5f4491df07245d5833777e30b05e13bcef0e95ca7908e57d5b6bbfd12",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2020-05-28T17:51:16Z",
    "title_canon_sha256": "79e6346b70a5c6d151cc1383dbfee1989f15f663316d835669a802f076ba31bf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2005.14180",
    "kind": "arxiv",
    "version": 3
  }
}