Pith Number

pith:GBBGASQY

pith:2013:GBBGASQYOEITHXWYCXA5ZENOE2

not attested not anchored not stored refs pending

An asymptotic estimate of the variance of the self-intersections of a planar periodic Lorentz process

Francoise Pene (LM)

arxiv:1303.3034 v1 · 2013-03-12 · math.DS · 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{GBBGASQYOEITHXWYCXA5ZENOE2}

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	2026-05-18T03:31:05.994989Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3042604a18711133ded815c1dc91ae26ac4f55e8b1d317665389d6322032274c

Aliases

arxiv: 1303.3034 · arxiv_version: 1303.3034v1 · doi: 10.48550/arxiv.1303.3034 · pith_short_12: GBBGASQYOEIT · pith_short_16: GBBGASQYOEITHXWY · pith_short_8: GBBGASQY

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/GBBGASQYOEITHXWYCXA5ZENOE2 \
  | 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: 3042604a18711133ded815c1dc91ae26ac4f55e8b1d317665389d6322032274c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3e50eccb1e70c73fd2bfa78ea4047cfd30c5ec187b13dc9fdbb52b7d8943d3d9",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2013-03-12T21:04:56Z",
    "title_canon_sha256": "9e762114588e2798a064475471fcbf81e0de9c520f3933bd4139908ac698a0bd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.3034",
    "kind": "arxiv",
    "version": 1
  }
}