Pith Number

pith:POSBKRCE

pith:2012:POSBKRCEKJSXEG7Y7A6Q6FW4E4

not attested not anchored not stored refs pending

Phase space analysis and functional calculus for the linearized Landau and Boltzmann operators

Chao-Jiang Xu, Karel Pravda-Starov, Nicolas Lerner, Yoshinori Morimoto

arxiv:1205.3688 v3 · 2012-05-16 · math-ph · math.AP · math.FA · 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{POSBKRCEKJSXEG7Y7A6Q6FW4E4}

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	2026-05-18T03:39:43.516674Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7ba41544445265721bf8f83d0f16dc2718efd54311dc39b480bcd2d4f61f75c2

Aliases

arxiv: 1205.3688 · arxiv_version: 1205.3688v3 · doi: 10.48550/arxiv.1205.3688 · pith_short_12: POSBKRCEKJSX · pith_short_16: POSBKRCEKJSXEG7Y · pith_short_8: POSBKRCE

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/POSBKRCEKJSXEG7Y7A6Q6FW4E4 \
  | 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: 7ba41544445265721bf8f83d0f16dc2718efd54311dc39b480bcd2d4f61f75c2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bd60c0fc4826dcfeb24502f6bdc5b94b9f1f8e5dfdfdaf2816444f2f43923ad1",
    "cross_cats_sorted": [
      "math.AP",
      "math.FA",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2012-05-16T14:39:24Z",
    "title_canon_sha256": "2c80387ce6380da20d58013d321b6bcbb1ae0fadd9261c60e29cc3d80c8c0bfd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.3688",
    "kind": "arxiv",
    "version": 3
  }
}