Pith Number

pith:7WJ7WK7K

pith:2018:7WJ7WK7KYSW7YRVNV3T7LGZBUF

not attested not anchored not stored refs pending

Monotonicity and rigidity of the W-entropy on RCD(0, N) spaces

Kazumasa Kuwada, Xiang-Dong Li

arxiv:1811.07228 v1 · 2018-11-17 · math.PR · math.AP · math.DG · 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{7WJ7WK7KYSW7YRVNV3T7LGZBUF}

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	2026-05-18T00:00:28.579163Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fd93fb2beac4adfc46adaee7f59b21a147e3aa81bdedd1e7fde52caecd54507c

Aliases

arxiv: 1811.07228 · arxiv_version: 1811.07228v1 · doi: 10.48550/arxiv.1811.07228 · pith_short_12: 7WJ7WK7KYSW7 · pith_short_16: 7WJ7WK7KYSW7YRVN · pith_short_8: 7WJ7WK7K

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/7WJ7WK7KYSW7YRVNV3T7LGZBUF \
  | 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: fd93fb2beac4adfc46adaee7f59b21a147e3aa81bdedd1e7fde52caecd54507c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a285fab5bfb413bc0aa616dcb3005eff06d9a26cb1f0cbb897a6f63ea15c89b0",
    "cross_cats_sorted": [
      "math.AP",
      "math.DG",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2018-11-17T21:54:30Z",
    "title_canon_sha256": "d6bb88693743524a7bbe845a91bf8a3142c6c88c7e90e13dd59d24cc06886a61"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1811.07228",
    "kind": "arxiv",
    "version": 1
  }
}