Pith Number

pith:DK5LK6SI

pith:2014:DK5LK6SIGYVYHSBOT3H2X3QRYL

not attested not anchored not stored refs pending

On measure contraction property without Ricci curvature lower bound

Paul W.Y. Lee

arxiv:1412.4345 v1 · 2014-12-14 · 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{DK5LK6SIGYVYHSBOT3H2X3QRYL}

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	2026-05-18T02:31:19.500624Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1abab57a48362b83c82e9ecfabee11c2f8156896bbf435ceeed6f684909773a8

Aliases

arxiv: 1412.4345 · arxiv_version: 1412.4345v1 · doi: 10.48550/arxiv.1412.4345 · pith_short_12: DK5LK6SIGYVY · pith_short_16: DK5LK6SIGYVYHSBO · pith_short_8: DK5LK6SI

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/DK5LK6SIGYVYHSBOT3H2X3QRYL \
  | 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: 1abab57a48362b83c82e9ecfabee11c2f8156896bbf435ceeed6f684909773a8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "934419090f2adaad6e36505d7d74402caa2eaed5ce0892c8d7b9c0d20ed540d1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2014-12-14T12:09:01Z",
    "title_canon_sha256": "50623a6328aa763c2df7892d4c230d4d1d76bb4ad35ec7fbb96946204226ef3c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.4345",
    "kind": "arxiv",
    "version": 1
  }
}