Pith Number

pith:CCZFMO3B

pith:2016:CCZFMO3BLBVBTD5VRUF3BI3DO7

not attested not anchored not stored refs pending

Kazdan-Warner equation on graph

Alexander Grigor'yan, Yong Lin, Yunyan Yang

arxiv:1607.04540 v1 · 2016-07-15 · 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{CCZFMO3BLBVBTD5VRUF3BI3DO7}

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	2026-05-18T01:11:00.928904Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

10b2563b61586a198fb58d0bb0a36377cdb5c44ee00bc610fb81950115a98f53

Aliases

arxiv: 1607.04540 · arxiv_version: 1607.04540v1 · doi: 10.48550/arxiv.1607.04540 · pith_short_12: CCZFMO3BLBVB · pith_short_16: CCZFMO3BLBVBTD5V · pith_short_8: CCZFMO3B

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/CCZFMO3BLBVBTD5VRUF3BI3DO7 \
  | 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: 10b2563b61586a198fb58d0bb0a36377cdb5c44ee00bc610fb81950115a98f53

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2b3d60edd2342d0b668b10c798724f36f4afbb6736706fdc81e00ccd7e3a7d37",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-07-15T14:55:09Z",
    "title_canon_sha256": "b5d9c1d4ce23ed2ace8ae713125882c28bec45168d79b64e8caae7134dbbe941"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.04540",
    "kind": "arxiv",
    "version": 1
  }
}