Pith Number

pith:D4KMQ23K

pith:2018:D4KMQ23KI3IW4PD7DXBY2LCASZ

not attested not anchored not stored refs pending

Parabolic frequency monotonicity on compact manifolds

Kui Wang, Xiaolong Li

arxiv:1804.09806 v1 · 2018-04-25 · math.DG · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{D4KMQ23KI3IW4PD7DXBY2LCASZ}

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	2026-05-18T00:17:27.834332Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1f14c86b6a46d16e3c7f1dc38d2c409646fbd79f1f0b44ca8a61255ba9a91876

Aliases

arxiv: 1804.09806 · arxiv_version: 1804.09806v1 · doi: 10.48550/arxiv.1804.09806 · pith_short_12: D4KMQ23KI3IW · pith_short_16: D4KMQ23KI3IW4PD7 · pith_short_8: D4KMQ23K

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/D4KMQ23KI3IW4PD7DXBY2LCASZ \
  | 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: 1f14c86b6a46d16e3c7f1dc38d2c409646fbd79f1f0b44ca8a61255ba9a91876

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "623b8852345d3c1a0b563be3a9e3c29cabe3c827d132ff62202bfa01f26c2af4",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2018-04-25T21:30:25Z",
    "title_canon_sha256": "f5bbe3b9b04bb0ea5fa51ba0616eb0f799448c020d7f4f3feeb3b50035a2eee8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1804.09806",
    "kind": "arxiv",
    "version": 1
  }
}