Pith Number

pith:SKBQMN2S

pith:2010:SKBQMN2SJO2B76OX2Q2BAXMQZT

not attested not anchored not stored refs pending

Lane-Emden stars, selfgravitating disks and the Sobolev inequality

Edward Malec, Patryk Mach

arxiv:1007.1652 v1 · 2010-07-09 · astro-ph.SR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SKBQMN2SJO2B76OX2Q2BAXMQZT}

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	2026-05-18T02:06:23.298065Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

92830637524bb41ff9d7d434105d90ccdec2ceb6c53df0ebead779c08c1c0c6c

Aliases

arxiv: 1007.1652 · arxiv_version: 1007.1652v1 · doi: 10.48550/arxiv.1007.1652 · pith_short_12: SKBQMN2SJO2B · pith_short_16: SKBQMN2SJO2B76OX · pith_short_8: SKBQMN2S

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/SKBQMN2SJO2B76OX2Q2BAXMQZT \
  | 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: 92830637524bb41ff9d7d434105d90ccdec2ceb6c53df0ebead779c08c1c0c6c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3baaaa6116ec5962de2057edd58a908cd601b1762857ed7a290e6ecc85f76d49",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.SR",
    "submitted_at": "2010-07-09T19:35:00Z",
    "title_canon_sha256": "8f55fd1457b50e5e7e2a75711422b86886ae642a1b6bed6243f31b44a2e05bf4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1007.1652",
    "kind": "arxiv",
    "version": 1
  }
}