Pith Number

pith:MMRMYBUX

pith:2026:MMRMYBUXI3IE2GVK5V4EMQFRQM

not attested not anchored not stored refs pending

Equivalence of Lin--Lu--Yau curvature and 1/2-Ollivier curvature on weighted graphs

Shiping Liu, Yunyan Yang

arxiv:2608.05939 v1 · 2026-08-06 · math.DG · math.AP · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MMRMYBUXI3IE2GVK5V4EMQFRQM}

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	2026-08-07T00:53:43.544631Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6322cc069746d04d1aaaed784640b1833363883a35134e9c1f41d77bbe247274

Aliases

arxiv: 2608.05939 · arxiv_version: 2608.05939v1 · doi: 10.48550/arxiv.2608.05939 · pith_short_12: MMRMYBUXI3IE · pith_short_16: MMRMYBUXI3IE2GVK · pith_short_8: MMRMYBUX

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/MMRMYBUXI3IE2GVK5V4EMQFRQM \
  | 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: 6322cc069746d04d1aaaed784640b1833363883a35134e9c1f41d77bbe247274

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bcbaeda1a546486fb78d92fce17bf80c41a015c962a82da4ebfacbb8f111d85d",
    "cross_cats_sorted": [
      "math.AP",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2026-08-06T12:06:40Z",
    "title_canon_sha256": "91a363698f529c561001fafce0e9a915ad57fa30a769748675e33cf5346abda7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.05939",
    "kind": "arxiv",
    "version": 1
  }
}