Pith Number

pith:FEYXWZ75

pith:2015:FEYXWZ75X7U37PGYRWBZXBF4UV

not attested not anchored not stored refs pending

Invariance principle for the periodic Lorentz gas in the Boltzmann-Grad limit

Balint Toth, Jens Marklof

arxiv:1506.03619 v2 · 2015-06-11 · math-ph · math.DS · math.MP · math.PR · nlin.CD

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FEYXWZ75X7U37PGYRWBZXBF4UV}

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	2026-05-18T01:26:57.566379Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

29317b67fdbfe9bfbcd88d839b84bca5625514d09d5d1333bf48496d30bbeeec

Aliases

arxiv: 1506.03619 · arxiv_version: 1506.03619v2 · doi: 10.48550/arxiv.1506.03619 · pith_short_12: FEYXWZ75X7U3 · pith_short_16: FEYXWZ75X7U37PGY · pith_short_8: FEYXWZ75

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/FEYXWZ75X7U37PGYRWBZXBF4UV \
  | 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: 29317b67fdbfe9bfbcd88d839b84bca5625514d09d5d1333bf48496d30bbeeec

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a4b04bdf7a09699d274391c7037eb1eef28029b17a75205880e6012d56c2a4f3",
    "cross_cats_sorted": [
      "math.DS",
      "math.MP",
      "math.PR",
      "nlin.CD"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2015-06-11T10:50:10Z",
    "title_canon_sha256": "1e28f9dfe5d6fcf58c417dc23cc42f47c8b757919506a6e7511af3b198e13538"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.03619",
    "kind": "arxiv",
    "version": 2
  }
}