Pith Number

pith:BRRZGLHR

pith:2026:BRRZGLHRGL4NGRU3L75GHSHTWF

not attested not anchored not stored refs pending

Diameters and mixing times for giant components of random graphs with given degrees

Bruce Reed, Corrine Yap, Louigi Addario-Berry

arxiv:2605.16511 v1 · 2026-05-15 · math.CO · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BRRZGLHRGL4NGRU3L75GHSHTWF}

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	2026-05-20T00:02:26.530677Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0c63932cf132f8d3469b5ffa63c8f3b17f0c52a8281f58c6aee40822ea9cc5e1

Aliases

arxiv: 2605.16511 · arxiv_version: 2605.16511v1 · doi: 10.48550/arxiv.2605.16511 · pith_short_12: BRRZGLHRGL4N · pith_short_16: BRRZGLHRGL4NGRU3 · pith_short_8: BRRZGLHR

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/BRRZGLHRGL4NGRU3L75GHSHTWF \
  | 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: 0c63932cf132f8d3469b5ffa63c8f3b17f0c52a8281f58c6aee40822ea9cc5e1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "05fb26ec74f49ff6159bd0c637f8074d4590bfce5044956bafb00f3eb2de3be7",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-15T18:06:24Z",
    "title_canon_sha256": "3d553bf2f5b95fda895c1cd7a75d742d6ee3a18b1b27388442414a40482ed803"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16511",
    "kind": "arxiv",
    "version": 1
  }
}