Pith Number

pith:I5KHUYMF

pith:2013:I5KHUYMFZPUNP3TBVS5HOYSPYS

not attested not anchored not stored refs pending

Coarse Ricci curvature on the space of probability measures

Yu Kitabeppu

arxiv:1301.0978 v1 · 2013-01-06 · math.MG · 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{I5KHUYMFZPUNP3TBVS5HOYSPYS}

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	2026-05-18T03:37:07.127828Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

47547a6185cbe8d7ee61acba77624fc48b41a17c373aa31a01ab6607b7e28fa1

Aliases

arxiv: 1301.0978 · arxiv_version: 1301.0978v1 · doi: 10.48550/arxiv.1301.0978 · pith_short_12: I5KHUYMFZPUN · pith_short_16: I5KHUYMFZPUNP3TB · pith_short_8: I5KHUYMF

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/I5KHUYMFZPUNP3TBVS5HOYSPYS \
  | 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: 47547a6185cbe8d7ee61acba77624fc48b41a17c373aa31a01ab6607b7e28fa1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "437e14ec139ce409e5fb3b3412aa7c14bee6fc49420518039029be95bea31a08",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2013-01-06T06:20:47Z",
    "title_canon_sha256": "3fd140eec4815b71f3c0edf3d475050cc741f1997320462a4a605679ab297829"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.0978",
    "kind": "arxiv",
    "version": 1
  }
}