Pith Number

pith:NPTV7FS5

pith:2013:NPTV7FS5J5MLZB6NBYST7LGEDJ

not attested not anchored not stored refs pending

Curvature-dimension inequalities and Li-Yau inequalities in sub-Riemannian spaces

Nicola Garofalo

arxiv:1301.6581 v1 · 2013-01-28 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NPTV7FS5J5MLZB6NBYST7LGEDJ}

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	2026-05-18T03:35:14.983466Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6be75f965d4f58bc87cd0e253facc41a7c1ee81c890e5bd31e1cc965a3c48fd6

Aliases

arxiv: 1301.6581 · arxiv_version: 1301.6581v1 · doi: 10.48550/arxiv.1301.6581 · pith_short_12: NPTV7FS5J5ML · pith_short_16: NPTV7FS5J5MLZB6N · pith_short_8: NPTV7FS5

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/NPTV7FS5J5MLZB6NBYST7LGEDJ \
  | 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: 6be75f965d4f58bc87cd0e253facc41a7c1ee81c890e5bd31e1cc965a3c48fd6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e9f408c7a88d5c6575467055c47d1397528a961ac9b5382c2f1c528685a3c868",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-01-28T15:52:13Z",
    "title_canon_sha256": "b263e42e84aeac417e0a7c137d70d343bda33abcbfcad237f340ebee14b4d7d8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.6581",
    "kind": "arxiv",
    "version": 1
  }
}