Pith Number

pith:COJZTPKL

pith:2008:COJZTPKL4GJ45UIFUNDZRTEIJQ

not attested not anchored not stored refs pending

Quenched invariance principle for the Knudsen stochastic billiard in a random tube

Francis Comets, Gunter M. Sch\"utz, Marina Vachkovskaia, Serguei Popov

arxiv:0811.0366 v3 · 2008-11-03 · math.PR · math-ph · math.MP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{COJZTPKL4GJ45UIFUNDZRTEIJQ}

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	2026-05-18T01:09:24.356471Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

139399bd4be193ced105a34798cc884c059558b10ee594dbc43f50fe59ff6477

Aliases

arxiv: 0811.0366 · arxiv_version: 0811.0366v3 · doi: 10.48550/arxiv.0811.0366 · pith_short_12: COJZTPKL4GJ4 · pith_short_16: COJZTPKL4GJ45UIF · pith_short_8: COJZTPKL

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/COJZTPKL4GJ45UIFUNDZRTEIJQ \
  | 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: 139399bd4be193ced105a34798cc884c059558b10ee594dbc43f50fe59ff6477

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "95fb30fc73eda1a1e27aad64598f83e6c15a2db60a7881705b77534a3774ff75",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2008-11-03T18:52:24Z",
    "title_canon_sha256": "009c6fe8e40489d1834273107ce4a7bdfc50278e348b6f66df88ab5b6db20022"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0811.0366",
    "kind": "arxiv",
    "version": 3
  }
}