Pith Number

pith:OGM7BXFH

pith:2010:OGM7BXFHTIVP6V7UM3KBPZ573X

not attested not anchored not stored refs pending

Ballistic regime for random walks in random environment with unbounded jumps and Knudsen billiards

Francis Comets, Serguei Popov

arxiv:1009.0048 v2 · 2010-08-31 · 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{OGM7BXFHTIVP6V7UM3KBPZ573X}

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	2026-05-18T03:52:12.589912Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7199f0dca79a2aff57f466d417e7bfddc1d8073111ec77f2fa1780e6d5957d38

Aliases

arxiv: 1009.0048 · arxiv_version: 1009.0048v2 · doi: 10.48550/arxiv.1009.0048 · pith_short_12: OGM7BXFHTIVP · pith_short_16: OGM7BXFHTIVP6V7U · pith_short_8: OGM7BXFH

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/OGM7BXFHTIVP6V7UM3KBPZ573X \
  | 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: 7199f0dca79a2aff57f466d417e7bfddc1d8073111ec77f2fa1780e6d5957d38

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f8ad3f5684e5789a8c88d9b673019c2de506ece56c12ce790ec7ecc38b3580e5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-08-31T23:10:54Z",
    "title_canon_sha256": "6904e64e2936c33bc86f3fc9f477095e45343e0a5c101cd53c3d2579c31fb143"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.0048",
    "kind": "arxiv",
    "version": 2
  }
}