Pith Number

pith:ABMXUJE2

pith:2018:ABMXUJE2S3K5NZ63DOBMC7KFPQ

not attested not anchored not stored refs pending

How to hear the shape of a billiard table

Aaron Calderon, Andre Oliveira, Diana Davis, Justin Lanier, Solly Coles

arxiv:1806.09644 v1 · 2018-06-25 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ABMXUJE2S3K5NZ63DOBMC7KFPQ}

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	2026-05-18T00:12:23.880708Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

00597a249a96d5d6e7db1b82c17d457c2238199224e6353652f2600227b13d39

Aliases

arxiv: 1806.09644 · arxiv_version: 1806.09644v1 · doi: 10.48550/arxiv.1806.09644 · pith_short_12: ABMXUJE2S3K5 · pith_short_16: ABMXUJE2S3K5NZ63 · pith_short_8: ABMXUJE2

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/ABMXUJE2S3K5NZ63DOBMC7KFPQ \
  | 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: 00597a249a96d5d6e7db1b82c17d457c2238199224e6353652f2600227b13d39

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eab41d0e494f5748702eaa95daf1d215ae09cba7b21991c7cf902882484b4d8e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2018-06-25T18:01:02Z",
    "title_canon_sha256": "2ef5462af8e51a3c53bbc8ecb044ae8819fc59ccc367503f13f664e5818cfd8e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1806.09644",
    "kind": "arxiv",
    "version": 1
  }
}