Pith Number

pith:NKM6J45Y

pith:2015:NKM6J45YW2P23DVTWBHK4GGSWY

not attested not anchored not stored refs pending

Littlewood-Paley Characterizations of Fractional Sobolev Spaces via Averages on Balls

Dachun Yang, Feng Dai, Jun Liu, Wen Yuan

arxiv:1511.07598 v1 · 2015-11-24 · math.CA · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NKM6J45YW2P23DVTWBHK4GGSWY}

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	2026-05-18T01:26:04.288975Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6a99e4f3b8b69fad8eb3b04eae18d2b6105c61e5e0bd1e5f6dbd45625e22a2d7

Aliases

arxiv: 1511.07598 · arxiv_version: 1511.07598v1 · doi: 10.48550/arxiv.1511.07598 · pith_short_12: NKM6J45YW2P2 · pith_short_16: NKM6J45YW2P23DVT · pith_short_8: NKM6J45Y

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/NKM6J45YW2P23DVTWBHK4GGSWY \
  | 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: 6a99e4f3b8b69fad8eb3b04eae18d2b6105c61e5e0bd1e5f6dbd45625e22a2d7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b53472d1dd44d0cb58b603f2c6b936ebf9c184da518ea0863532f4b14f2f9192",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-11-24T07:31:13Z",
    "title_canon_sha256": "9da5773bead48a355b23936e29fce7883e8f9765433e5023afe520ea3483a43a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.07598",
    "kind": "arxiv",
    "version": 1
  }
}