Pith Number

pith:3WOH7R4B

pith:2018:3WOH7R4BTEIZAVPKRPWX3P2CCJ

not attested not anchored not stored refs pending

Billiards with Markovian reflection laws

Carl-Erik Gauthier, Clayton Barnes, Krzysztof Burdzy

arxiv:1811.02529 v1 · 2018-11-06 · 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{3WOH7R4BTEIZAVPKRPWX3P2CCJ}

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	2026-05-18T00:01:23.982586Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dd9c7fc78199119055ea8bed7dbf42127f817fad9d5824cfa7152304ad8619a5

Aliases

arxiv: 1811.02529 · arxiv_version: 1811.02529v1 · doi: 10.48550/arxiv.1811.02529 · pith_short_12: 3WOH7R4BTEIZ · pith_short_16: 3WOH7R4BTEIZAVPK · pith_short_8: 3WOH7R4B

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/3WOH7R4BTEIZAVPKRPWX3P2CCJ \
  | 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: dd9c7fc78199119055ea8bed7dbf42127f817fad9d5824cfa7152304ad8619a5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "360ffb45b2f1babb459603e8a23e2205c0dbfc5cd526ebc6d0aaadba6f67c2ba",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2018-11-06T17:54:54Z",
    "title_canon_sha256": "646b473ec179c694f67a1f4790e78d7676eb8f4d9d66d522f5fcdeddd177655a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1811.02529",
    "kind": "arxiv",
    "version": 1
  }
}