Pith Number

pith:3Z277PTI

pith:2015:3Z277PTIYWQKSW5HJLLG73NAVO

not attested not anchored not stored refs pending

Gravitational collapse and the Vlasov-Poisson system

Gerhard Rein, Lukas Taegert

arxiv:1509.09154 v1 · 2015-09-30 · math-ph · math.AP · 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{3Z277PTIYWQKSW5HJLLG73NAVO}

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	2026-05-18T01:31:26.942170Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

de75ffbe68c5a0a95ba74ad66feda0ab9e96cae58bcdf4639bf058620c43e26a

Aliases

arxiv: 1509.09154 · arxiv_version: 1509.09154v1 · doi: 10.48550/arxiv.1509.09154 · pith_short_12: 3Z277PTIYWQK · pith_short_16: 3Z277PTIYWQKSW5H · pith_short_8: 3Z277PTI

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/3Z277PTIYWQKSW5HJLLG73NAVO \
  | 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: de75ffbe68c5a0a95ba74ad66feda0ab9e96cae58bcdf4639bf058620c43e26a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8f557f7d496883fdb0775dd0a670fa8b1a385a3fc80503d188e0e96bc9d32524",
    "cross_cats_sorted": [
      "math.AP",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2015-09-30T12:36:41Z",
    "title_canon_sha256": "281c0e91115512f151d63fa1b7b25a397c914739c93d0ff6a5735813c9a53698"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.09154",
    "kind": "arxiv",
    "version": 1
  }
}