Pith Number

pith:CSI7J4A5

pith:2010:CSI7J4A5JJPRMH7AP3HJVEFBH4

not attested not anchored not stored refs pending

The spectrum of random lifts

Louigi Addario-Berry, Simon Griffiths

arxiv:1012.4097 v3 · 2010-12-18 · 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{CSI7J4A5JJPRMH7AP3HJVEFBH4}

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	2026-05-18T04:09:34.967074Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1491f4f01d4a5f161fe07ece9a90a13f0d50e2394ffa0976df00bdc5a31099f5

Aliases

arxiv: 1012.4097 · arxiv_version: 1012.4097v3 · doi: 10.48550/arxiv.1012.4097 · pith_short_12: CSI7J4A5JJPR · pith_short_16: CSI7J4A5JJPRMH7A · pith_short_8: CSI7J4A5

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/CSI7J4A5JJPRMH7AP3HJVEFBH4 \
  | 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: 1491f4f01d4a5f161fe07ece9a90a13f0d50e2394ffa0976df00bdc5a31099f5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f7778b095c8f43ca370275b916aa3fe3b2f7161638e54d65e5415d7eae27c13a",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-12-18T15:08:11Z",
    "title_canon_sha256": "345d64ad1f247ef1c9b12455a3e0d07313cef9d7448b08757db80bbc4ce6f670"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.4097",
    "kind": "arxiv",
    "version": 3
  }
}