Pith Number

pith:BHQSYWEW

pith:2012:BHQSYWEWRBQC77QTQ6KZJBNDAK

not attested not anchored not stored refs pending

The Abresch-Gromoll inequality in a non-smooth setting

Nicola Gigli, Sunra Mosconi

arxiv:1209.3813 v1 · 2012-09-17 · math.MG · 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{BHQSYWEWRBQC77QTQ6KZJBNDAK}

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	2026-05-18T03:45:22.443445Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

09e12c589688602ffe1387959485a302a24a950efb483784073539e53ee4443c

Aliases

arxiv: 1209.3813 · arxiv_version: 1209.3813v1 · doi: 10.48550/arxiv.1209.3813 · pith_short_12: BHQSYWEWRBQC · pith_short_16: BHQSYWEWRBQC77QT · pith_short_8: BHQSYWEW

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/BHQSYWEWRBQC77QTQ6KZJBNDAK \
  | 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: 09e12c589688602ffe1387959485a302a24a950efb483784073539e53ee4443c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a5ac90613b207f22c713de56cddbfa9fc091792a9b438f2b925681d4050fec5e",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2012-09-17T23:26:11Z",
    "title_canon_sha256": "fc2b3c2a270af229fe13b43d9441a07efeae67644540798183120eb0f91e35a3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.3813",
    "kind": "arxiv",
    "version": 1
  }
}