Pith Number

pith:JQK7NYJ5

pith:2016:JQK7NYJ5QIZG735CWNCCOZG3XD

not attested not anchored not stored refs pending

Geometric quantities arising from bubbling analysis of mean field equations

Chang-shou Lin, Chin-Lung Wang

arxiv:1609.07204 v1 · 2016-09-23 · 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{JQK7NYJ5QIZG735CWNCCOZG3XD}

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	2026-05-18T01:04:01.984571Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4c15f6e13d82326fefa2b3442764dbb8d4dca04acf9bccfd5ca617ecc9136f2b

Aliases

arxiv: 1609.07204 · arxiv_version: 1609.07204v1 · doi: 10.48550/arxiv.1609.07204 · pith_short_12: JQK7NYJ5QIZG · pith_short_16: JQK7NYJ5QIZG735C · pith_short_8: JQK7NYJ5

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/JQK7NYJ5QIZG735CWNCCOZG3XD \
  | 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: 4c15f6e13d82326fefa2b3442764dbb8d4dca04acf9bccfd5ca617ecc9136f2b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "829fe9773bd7867894c32dea4fc6cf6e1656449a7d0e89efb5d1b8a9143d4d50",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-09-23T02:00:56Z",
    "title_canon_sha256": "b873fa83e2e666cdabd5daf726320acd6113168c5cf7d8c157fa2c027d2ae68d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.07204",
    "kind": "arxiv",
    "version": 1
  }
}