Pith Number

pith:2PL5QABO

pith:2015:2PL5QABOOAIERZGY3VAYB62WU2

not attested not anchored not stored refs pending

Sharp geometric and functional inequalities in metric measure spaces with lower Ricci curvature bounds

Andrea Mondino, Fabio Cavalletti

arxiv:1505.02061 v2 · 2015-05-08 · math.MG · math.AP · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2PL5QABOOAIERZGY3VAYB62WU2}

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	2026-05-17T23:46:55.962239Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d3d7d8002e701048e4d8dd4180fb56a692305e61a659c393204eca71b942f148

Aliases

arxiv: 1505.02061 · arxiv_version: 1505.02061v2 · doi: 10.48550/arxiv.1505.02061 · pith_short_12: 2PL5QABOOAIE · pith_short_16: 2PL5QABOOAIERZGY · pith_short_8: 2PL5QABO

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/2PL5QABOOAIERZGY3VAYB62WU2 \
  | 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: d3d7d8002e701048e4d8dd4180fb56a692305e61a659c393204eca71b942f148

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5d8f70a2515ccb7e69773408ee7013336de793206ef3f56bc02b4c32b34c8ce0",
    "cross_cats_sorted": [
      "math.AP",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2015-05-08T15:26:43Z",
    "title_canon_sha256": "237c59462b33b1dc52906bcb41b219ad47a6e1ba341f71366c65642a0640fe30"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.02061",
    "kind": "arxiv",
    "version": 2
  }
}