Pith Number

pith:7P64CKET

pith:2015:7P64CKETMJFLHJWJO7SLFPML5G

not attested not anchored not stored refs pending

Lace expansion for dummies

Erwin Bolthausen, Gady Kozma, Remco van der Hofstad

arxiv:1512.01481 v2 · 2015-12-04 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7P64CKETMJFLHJWJO7SLFPML5G}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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	2026-05-18T01:16:16.933811Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fbfdc12893624ab3a6c977e4b2bd8be98bfe57d1bb97cdfdd34504bfd20e2055

Aliases

arxiv: 1512.01481 · arxiv_version: 1512.01481v2 · doi: 10.48550/arxiv.1512.01481 · pith_short_12: 7P64CKETMJFL · pith_short_16: 7P64CKETMJFLHJWJ · pith_short_8: 7P64CKET

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/7P64CKETMJFLHJWJO7SLFPML5G \
  | 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: fbfdc12893624ab3a6c977e4b2bd8be98bfe57d1bb97cdfdd34504bfd20e2055

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f83de4d1fc2bd270f1367b8303415f6782c2cd5783b6f769ab12cc9b1ccd494b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-12-04T17:03:20Z",
    "title_canon_sha256": "302711b188fd5a38d102f370abd511e3a64212f26598866158df0aeebbaeac0d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.01481",
    "kind": "arxiv",
    "version": 2
  }
}