Pith Number

pith:LDOC4P5H

pith:2026:LDOC4P5HAHAK7EPX3ISWYVXOV6

not attested not anchored not stored refs pending

Time-periodic solutions of the Vlasov-Poisson-Boltzmann system with a general external force in $\mathbb{R}^3$

Jinkai Ni, Renjun Duan

arxiv:2608.05637 v1 · 2026-08-06 · 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{LDOC4P5HAHAK7EPX3ISWYVXOV6}

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	2026-08-07T00:52:06.334217Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

58dc2e3fa701c0af91f7da256c56eeaf99bf44941fbee8d065e90c2e1ab47502

Aliases

arxiv: 2608.05637 · arxiv_version: 2608.05637v1 · doi: 10.48550/arxiv.2608.05637 · pith_short_12: LDOC4P5HAHAK · pith_short_16: LDOC4P5HAHAK7EPX · pith_short_8: LDOC4P5H

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/LDOC4P5HAHAK7EPX3ISWYVXOV6 \
  | 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: 58dc2e3fa701c0af91f7da256c56eeaf99bf44941fbee8d065e90c2e1ab47502

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d0474b3b2ca2d8e189eede8161c2c2f3172bbc42a5457a2f899fa1b857f876e1",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-08-06T06:25:03Z",
    "title_canon_sha256": "1296fc39082893017833b78f960c15ce900ff1d29026d3cea73feb1f73dc9265"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.05637",
    "kind": "arxiv",
    "version": 1
  }
}