Pith Number

pith:V7JI66NO

pith:2018:V7JI66NOOP53QL3P5AW4LMNYQ2

not attested not anchored not stored refs pending

On the Cheng-Yau gradient estimate for Carnot groups and sub-Riemannian manifolds

Fabrice Baudoin, Maria Gordina, Phanuel Mariano

arxiv:1809.07433 v2 · 2018-09-19 · math.AP · math.DG · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{V7JI66NOOP53QL3P5AW4LMNYQ2}

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	2026-05-18T00:02:53.038757Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

afd28f79ae73fbb82f6fe82dc5b1b88698d1085520e80f5f274850e7b88cf102

Aliases

arxiv: 1809.07433 · arxiv_version: 1809.07433v2 · doi: 10.48550/arxiv.1809.07433 · pith_short_12: V7JI66NOOP53 · pith_short_16: V7JI66NOOP53QL3P · pith_short_8: V7JI66NO

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/V7JI66NOOP53QL3P5AW4LMNYQ2 \
  | 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: afd28f79ae73fbb82f6fe82dc5b1b88698d1085520e80f5f274850e7b88cf102

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2abf7305071556a97e0d190a0b549f86dbd0bbe3514317b6310052f5b905243b",
    "cross_cats_sorted": [
      "math.DG",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2018-09-19T23:58:16Z",
    "title_canon_sha256": "07719974692ad5c68ea31774581f1864ffab2f0210e5393fadded1a000ba0f3d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1809.07433",
    "kind": "arxiv",
    "version": 2
  }
}