Pith Number

pith:K3PI2HE5

pith:2025:K3PI2HE5IR6DYSEJQZSYF6KA6P

not attested not anchored not stored refs pending

Lin-Lu-Yau Ricci curvature on hypergraphs

Liang Zhao, Yulu Tian

arxiv:2507.04109 v1 · 2025-07-05 · 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{K3PI2HE5IR6DYSEJQZSYF6KA6P}

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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.

Cited by

1 paper in Pith

Edge-connectivity and LLY curvature of hypergraphs

Receipt and verification

First computed	2026-07-05T11:32:42.088726Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

56de8d1c9d447c3c4889866582f940f3ce82962eb5a63ab244ae7b758160a2e0

Aliases

arxiv: 2507.04109 · arxiv_version: 2507.04109v1 · doi: 10.48550/arxiv.2507.04109 · pith_short_12: K3PI2HE5IR6D · pith_short_16: K3PI2HE5IR6DYSEJ · pith_short_8: K3PI2HE5

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/K3PI2HE5IR6DYSEJQZSYF6KA6P \
  | 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: 56de8d1c9d447c3c4889866582f940f3ce82962eb5a63ab244ae7b758160a2e0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8f728a8114c3936ced9e234992679fee9bfd0ad68eccd5019a065ee64b8efcbf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2025-07-05T17:39:25Z",
    "title_canon_sha256": "72ba524e09687331078c0f452204fb1a9842404725ea17ed3521757fad0fa162"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.04109",
    "kind": "arxiv",
    "version": 1
  }
}