Pith Number

pith:2H6MHGH4

pith:2019:2H6MHGH4YQNHS2MR7PCSL2JLMQ

not attested not anchored not stored refs pending

Geometric and spectral properties of directed graphs under a lower Ricci curvature bound

Ryunosuke Ozawa, Taiki Yamada, Yohei Sakurai

arxiv:1909.07715 v3 · 2019-09-17 · math.DG · math.CO · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2H6MHGH4YQNHS2MR7PCSL2JLMQ}

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	2026-07-05T01:16:09.621909Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d1fcc398fcc41a796991fbc525e92b642cfd4ac030a269aa79dbb9c1f618aca1

Aliases

arxiv: 1909.07715 · arxiv_version: 1909.07715v3 · doi: 10.48550/arxiv.1909.07715 · pith_short_12: 2H6MHGH4YQNH · pith_short_16: 2H6MHGH4YQNHS2MR · pith_short_8: 2H6MHGH4

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/2H6MHGH4YQNHS2MR7PCSL2JLMQ \
  | 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: d1fcc398fcc41a796991fbc525e92b642cfd4ac030a269aa79dbb9c1f618aca1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e04ed88f0623d2e5befc340ff02aba1a0be01c7e8af672d5fa24260bfebabf57",
    "cross_cats_sorted": [
      "math.CO",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2019-09-17T11:01:25Z",
    "title_canon_sha256": "5e9a823b2310710a0c6868c44609d20a443e9582d4c0ff3dcf99fb38ccc570af"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1909.07715",
    "kind": "arxiv",
    "version": 3
  }
}