Pith Number

pith:PVBAAMI6

pith:2016:PVBAAMI6BCOKJQ7UL3OQP6BM4U

not attested not anchored not stored refs pending

A Bishop type inequality on metric measure spaces with Ricci curvature bounded below

Yu Kitabeppu

arxiv:1603.04162 v1 · 2016-03-14 · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PVBAAMI6BCOKJQ7UL3OQP6BM4U}

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	2026-05-18T01:19:09.233361Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7d4200311e089ca4c3f45edd07f82ce50a631c91829861e4fbfffebf0ebe4155

Aliases

arxiv: 1603.04162 · arxiv_version: 1603.04162v1 · doi: 10.48550/arxiv.1603.04162 · pith_short_12: PVBAAMI6BCOK · pith_short_16: PVBAAMI6BCOKJQ7U · pith_short_8: PVBAAMI6

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/PVBAAMI6BCOKJQ7UL3OQP6BM4U \
  | 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: 7d4200311e089ca4c3f45edd07f82ce50a631c91829861e4fbfffebf0ebe4155

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d9ad6121732bac36d0018ec61fdf61e3950ee35f95fa9909f87e7f26899283c0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2016-03-14T08:14:13Z",
    "title_canon_sha256": "edb60c2740c853a8306a2df972b8a6ceafb5b0be21c3eb406ee86d6cff01c8e1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1603.04162",
    "kind": "arxiv",
    "version": 1
  }
}