Pith Number

pith:2XBI43S5

pith:2012:2XBI43S56GZZNMIGBY4ESQQXVQ

not attested not anchored not stored refs pending

An expansion estimate for dispersing planar billiards with corner points

Imre P\'eter T\'oth, Jacopo De Simoi

arxiv:1212.6897 v1 · 2012-12-31 · 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{2XBI43S56GZZNMIGBY4ESQQXVQ}

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	2026-05-18T03:37:29.570813Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d5c28e6e5df1b396b1060e38494217ac3de4532ea7b8285a36dd91ebdff1df90

Aliases

arxiv: 1212.6897 · arxiv_version: 1212.6897v1 · doi: 10.48550/arxiv.1212.6897 · pith_short_12: 2XBI43S56GZZ · pith_short_16: 2XBI43S56GZZNMIG · pith_short_8: 2XBI43S5

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/2XBI43S56GZZNMIGBY4ESQQXVQ \
  | 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: d5c28e6e5df1b396b1060e38494217ac3de4532ea7b8285a36dd91ebdff1df90

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "039fc3b8519c2c0b6869d08909fe2ba8a0cec35a25ded4e06ab08fb12d9c1230",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-12-31T14:28:07Z",
    "title_canon_sha256": "6eed12c0d1ec766ee74a93e7d668593d1746a620633610cc02742b3ee7b00b53"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.6897",
    "kind": "arxiv",
    "version": 1
  }
}