Pith Number

pith:K3KRYTXQ

pith:2016:K3KRYTXQWU7GFVSJNLILWBEKEI

not attested not anchored not stored refs pending

Yamabe type equations on graphs

Alexander Grigor'yan, Yong Lin, Yunyan Yang

arxiv:1607.04521 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{K3KRYTXQWU7GFVSJNLILWBEKEI}

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	2026-05-18T01:11:00.983464Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

56d51c4ef0b53e62d6496ad0bb048a2237de22d89ec7fadf749419c21bff8f29

Aliases

arxiv: 1607.04521 · arxiv_version: 1607.04521v1 · doi: 10.48550/arxiv.1607.04521 · pith_short_12: K3KRYTXQWU7G · pith_short_16: K3KRYTXQWU7GFVSJ · pith_short_8: K3KRYTXQ

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/K3KRYTXQWU7GFVSJNLILWBEKEI \
  | 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: 56d51c4ef0b53e62d6496ad0bb048a2237de22d89ec7fadf749419c21bff8f29

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aa643cb0c5ff4d4fad40ba943389ca00e78d35148ec9bf2dbe7f8656267901df",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-07-15T14:20:39Z",
    "title_canon_sha256": "8d2f92876c1b41d374b10650ec37d154291ee76220bd93fde1f77014d1217f3c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.04521",
    "kind": "arxiv",
    "version": 1
  }
}