Pith Number

pith:L2JRJSLB

pith:2018:L2JRJSLBO7EQAJHQNS67P4XGVV

not attested not anchored not stored refs pending

Billiard characterization of spheres

Michael Bialy

arxiv:1807.07712 v1 · 2018-07-20 · math.DG · 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{L2JRJSLBO7EQAJHQNS67P4XGVV}

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	2026-05-18T00:10:15.836747Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5e9314c96177c90024f06cbdf7f2e6ad78a53c96a05765d8034e231fe39d931c

Aliases

arxiv: 1807.07712 · arxiv_version: 1807.07712v1 · doi: 10.48550/arxiv.1807.07712 · pith_short_12: L2JRJSLBO7EQ · pith_short_16: L2JRJSLBO7EQAJHQ · pith_short_8: L2JRJSLB

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/L2JRJSLBO7EQAJHQNS67P4XGVV \
  | 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: 5e9314c96177c90024f06cbdf7f2e6ad78a53c96a05765d8034e231fe39d931c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8a187db4c383268c05954493d239184522000315c03202c915b140c9ee7a4e30",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2018-07-20T06:36:58Z",
    "title_canon_sha256": "c4c48a8abe5c98ae1b9dc45e499f691c0e48afbab9d18b2bbfed2a775caf7e6a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1807.07712",
    "kind": "arxiv",
    "version": 1
  }
}