Pith Number

pith:SH42LVJS

pith:2015:SH42LVJSYUTUOKNMQLVNLVOO7B

not attested not anchored not stored refs pending

On the existence and blow-up of solutions for a mean field equation with variable intensities

Gabriella Zecca, Ryo Takahashi, Tonia Ricciardi, Xiao Zhang

arxiv:1509.05204 v1 · 2015-09-17 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SH42LVJSYUTUOKNMQLVNLVOO7B}

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	2026-05-18T01:32:49.619632Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

91f9a5d532c5274729ac82ead5d5cef866d809ea2662fa4ec15fbca0fb58aa83

Aliases

arxiv: 1509.05204 · arxiv_version: 1509.05204v1 · doi: 10.48550/arxiv.1509.05204 · pith_short_12: SH42LVJSYUTU · pith_short_16: SH42LVJSYUTUOKNM · pith_short_8: SH42LVJS

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/SH42LVJSYUTUOKNMQLVNLVOO7B \
  | 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: 91f9a5d532c5274729ac82ead5d5cef866d809ea2662fa4ec15fbca0fb58aa83

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "77c320bc1a17ceb39d901060523f7193cdd13f8bd53ab96de990e322eab0c368",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-09-17T11:03:16Z",
    "title_canon_sha256": "ae14fa36289d856b41646ac67287a02749bdfc87c9225ee7ef1b4c4d69e8f8bc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.05204",
    "kind": "arxiv",
    "version": 1
  }
}