Pith Number

pith:WOYMQ6XW

pith:2025:WOYMQ6XWC2VJXZJ6SM2ZCXVMKC

not attested not anchored not stored refs pending

Kac's Program for the Landau Equation

Xuanrui Feng, Zhenfu Wang

arxiv:2506.14309 v2 · 2025-06-17 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WOYMQ6XWC2VJXZJ6SM2ZCXVMKC}

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.

Cited by

3 papers in Pith

On the monotonicity of the entropy production in the Landau-Maxwell equation

Propagation of chaos for the Boltzmann equation with very soft potentials

Quantitative propagation of chaos for particle systems with bounded kernels and multiplicative noise

Receipt and verification

First computed	2026-07-05T11:55:19.921307Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b3b0c87af616aa9be53e9335915eac5087ed44b7421e1c4479ad6049a0207a6a

Aliases

arxiv: 2506.14309 · arxiv_version: 2506.14309v2 · doi: 10.48550/arxiv.2506.14309 · pith_short_12: WOYMQ6XWC2VJ · pith_short_16: WOYMQ6XWC2VJXZJ6 · pith_short_8: WOYMQ6XW

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/WOYMQ6XWC2VJXZJ6SM2ZCXVMKC \
  | 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: b3b0c87af616aa9be53e9335915eac5087ed44b7421e1c4479ad6049a0207a6a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eecbf675becaa7c798de8d0c7fbf2673ff6f8f834cd6ec39eb39f33c8c6ee5a5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2025-06-17T08:36:37Z",
    "title_canon_sha256": "cfe28668ec8008cd59e4b93f18b1680fdff9d937ecc21379cd5818b2e82c5f81"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.14309",
    "kind": "arxiv",
    "version": 2
  }
}