Pith Number

pith:XEAOLK7U

pith:2021:XEAOLK7UCEID35R2DDXYQSRBVK

not attested not anchored not stored refs pending

The completely delocalized region of the Erd\H{o}s-R\'enyi graph

Antti Knowles, Johannes Alt, Raphael Ducatez

arxiv:2109.03227 v2 · 2021-09-07 · 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{XEAOLK7UCEID35R2DDXYQSRBVK}

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	2026-07-05T03:36:56.931484Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b900e5abf411103df63a18ef884a21aabee2ad091459e4f2984a809ad618db33

Aliases

arxiv: 2109.03227 · arxiv_version: 2109.03227v2 · doi: 10.48550/arxiv.2109.03227 · pith_short_12: XEAOLK7UCEID · pith_short_16: XEAOLK7UCEID35R2 · pith_short_8: XEAOLK7U

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/XEAOLK7UCEID35R2DDXYQSRBVK \
  | 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: b900e5abf411103df63a18ef884a21aabee2ad091459e4f2984a809ad618db33

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a4914a665b6bebeaf155946a664206ce36c1bdccd08470c22705b81d8c56adf9",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2021-09-07T17:55:13Z",
    "title_canon_sha256": "de0c13afd3e342ba11ee647f6c0204ef1c15e1dad7df5d0ffd0a0d33d4f3c046"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2109.03227",
    "kind": "arxiv",
    "version": 2
  }
}