Pith Number

pith:EKHXVFC5

pith:2019:EKHXVFC5MPLXMEAUNCYJGHYNEO

not attested not anchored not stored refs pending

Li-Yau inequality under $CD(0,n)$ on graphs

Florentin M\"unch

arxiv:1909.10242 v1 · 2019-09-23 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{EKHXVFC5MPLXMEAUNCYJGHYNEO}

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	2026-07-05T00:06:19.077750Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

228f7a945d63d776101468b0931f0d23997c1325e1991c957b7bb061e143ea99

Aliases

arxiv: 1909.10242 · arxiv_version: 1909.10242v1 · doi: 10.48550/arxiv.1909.10242 · pith_short_12: EKHXVFC5MPLX · pith_short_16: EKHXVFC5MPLXMEAU · pith_short_8: EKHXVFC5

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/EKHXVFC5MPLXMEAUNCYJGHYNEO \
  | 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: 228f7a945d63d776101468b0931f0d23997c1325e1991c957b7bb061e143ea99

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e4750e632c2b108cff6e7688639531c5a8442650b3ef95acd969ae0725b0c9fc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2019-09-23T09:34:30Z",
    "title_canon_sha256": "5cafd2c0294bb574f6e4bf2149e00bebf1942051cddca99118b2dd42966091f8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1909.10242",
    "kind": "arxiv",
    "version": 1
  }
}