Pith Number

pith:FNBMLVDJ

pith:2016:FNBMLVDJMIH6PUESHZRES5WI3R

not attested not anchored not stored refs pending

The Vlasov-Poisson-Boltzmann system for a disparate mass binary mixture

Renjun Duan, Shuangqian Liu

arxiv:1601.01051 v1 · 2016-01-06 · math.AP · 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{FNBMLVDJMIH6PUESHZRES5WI3R}

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	2026-05-18T00:32:15.286594Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2b42c5d469620fe7d0923e624976c8dc56ca09d4b6a3700672772a4e63343dee

Aliases

arxiv: 1601.01051 · arxiv_version: 1601.01051v1 · doi: 10.48550/arxiv.1601.01051 · pith_short_12: FNBMLVDJMIH6 · pith_short_16: FNBMLVDJMIH6PUES · pith_short_8: FNBMLVDJ

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/FNBMLVDJMIH6PUESHZRES5WI3R \
  | 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: 2b42c5d469620fe7d0923e624976c8dc56ca09d4b6a3700672772a4e63343dee

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "97bca580d9c8c3542eb9d87f89aee4063e938edfcee4e5850fd8899ad2daead5",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-01-06T02:12:33Z",
    "title_canon_sha256": "2de7a543215607eefb20844a0f8940b10dbeaf66f45543e1bcf7a8645e919442"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.01051",
    "kind": "arxiv",
    "version": 1
  }
}