Pith Number

pith:6WM2VSPF

pith:2018:6WM2VSPFL3HIJCDRFBXVH2DOZJ

not attested not anchored not stored refs pending

Poincar\'e inequality on complete Riemannian manifolds with Ricci curvature bounded below

G\'erard Besson, Gilles Courtois, Sa'ar Hersonsky

arxiv:1801.04216 v1 · 2018-01-12 · 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{6WM2VSPFL3HIJCDRFBXVH2DOZJ}

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	2026-05-18T00:26:09.472737Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f599aac9e55ece848871286f53e86eca4afbd932f6527433cfabf9957647049f

Aliases

arxiv: 1801.04216 · arxiv_version: 1801.04216v1 · doi: 10.48550/arxiv.1801.04216 · pith_short_12: 6WM2VSPFL3HI · pith_short_16: 6WM2VSPFL3HIJCDR · pith_short_8: 6WM2VSPF

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/6WM2VSPFL3HIJCDRFBXVH2DOZJ \
  | 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: f599aac9e55ece848871286f53e86eca4afbd932f6527433cfabf9957647049f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "26512a57e6d2c0a23a5ca90523d7b4912357d1f6f77dbeeef6431edda0e147eb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2018-01-12T16:20:47Z",
    "title_canon_sha256": "4487f00c2b1340fa4440f85b6e67af92e0617b6165063cc969c349ce24d906e9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1801.04216",
    "kind": "arxiv",
    "version": 1
  }
}