Pith Number

pith:GQSTGX5K

pith:2016:GQSTGX5KXC6L4K47PYRC3GRLA5

not attested not anchored not stored refs pending

Characterization of pinched Ricci curvature by functional inequalities

Anton Thalmaier, Li-Juan Cheng

arxiv:1611.02160 v1 · 2016-11-07 · 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{GQSTGX5KXC6L4K47PYRC3GRLA5}

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	2026-05-18T01:00:03.543925Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3425335faab8bcbe2b9f7e222d9a2b0767d1ef4a21175e569d0d365977a21578

Aliases

arxiv: 1611.02160 · arxiv_version: 1611.02160v1 · doi: 10.48550/arxiv.1611.02160 · pith_short_12: GQSTGX5KXC6L · pith_short_16: GQSTGX5KXC6L4K47 · pith_short_8: GQSTGX5K

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/GQSTGX5KXC6L4K47PYRC3GRLA5 \
  | 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: 3425335faab8bcbe2b9f7e222d9a2b0767d1ef4a21175e569d0d365977a21578

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "44f091b1df223cde3e499fe19928907bb4af1f853c41a4943cddd3cd920a12f9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-11-07T16:27:26Z",
    "title_canon_sha256": "f1370e067dfb3166a0b8917322ea1ee70a81bef91da7cc2cb34ef119a596f83d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.02160",
    "kind": "arxiv",
    "version": 1
  }
}