Pith Number

pith:LJGMW3XK

pith:2026:LJGMW3XKXX4V4KN4M2FEJ2K2RA

not attested not anchored not stored refs pending

Analysis of Moment Closures Using $\varphi$-Divergences for Rarefied Dynamics with Binary Collisions and Their Galerkin Discretizations

Irene M. Gamba, Michael R. A. Abdelmalik, Sergej Rjasanow, Torsten Kessler

arxiv:2608.03640 v1 · 2026-08-04 · math.NA · cs.NA · math.AP · physics.comp-ph · physics.flu-dyn

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LJGMW3XKXX4V4KN4M2FEJ2K2RA}

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	2026-08-05T01:36:48.352283Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5a4ccb6eeabdf95e29bc668a44e95a880c2dfef5547b699e072f441a8ad11421

Aliases

arxiv: 2608.03640 · arxiv_version: 2608.03640v1 · doi: 10.48550/arxiv.2608.03640 · pith_short_12: LJGMW3XKXX4V · pith_short_16: LJGMW3XKXX4V4KN4 · pith_short_8: LJGMW3XK

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/LJGMW3XKXX4V4KN4M2FEJ2K2RA \
  | 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: 5a4ccb6eeabdf95e29bc668a44e95a880c2dfef5547b699e072f441a8ad11421

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7964256df630f50409fcaae27181acffe6006468234a66e67a46f60ddd769a9a",
    "cross_cats_sorted": [
      "cs.NA",
      "math.AP",
      "physics.comp-ph",
      "physics.flu-dyn"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-08-04T13:23:53Z",
    "title_canon_sha256": "670daa2f9fc0734c0b8e757104a2c1983c26bc0f43dd0003c8abcf9242bbaf59"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.03640",
    "kind": "arxiv",
    "version": 1
  }
}