Pith Number

pith:5ISTTLXA

pith:2016:5ISTTLXA2HEDAVXB3DWWWKMAMZ

not attested not anchored not stored refs pending

Littlewood-Paley Characterizations of Haj{\l}asz-Sobolev and Triebel-Lizorkin Spaces via Averages on Balls

Dachun Yang, Der-Chen Chang, Jun Liu, Wen Yuan

arxiv:1601.03467 v1 · 2016-01-14 · 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{5ISTTLXA2HEDAVXB3DWWWKMAMZ}

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	2026-05-18T01:22:53.411229Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ea2539aee0d1c83056e1d8ed6b2980664aedb739236366df21d79d5a6602f98c

Aliases

arxiv: 1601.03467 · arxiv_version: 1601.03467v1 · doi: 10.48550/arxiv.1601.03467 · pith_short_12: 5ISTTLXA2HED · pith_short_16: 5ISTTLXA2HEDAVXB · pith_short_8: 5ISTTLXA

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/5ISTTLXA2HEDAVXB3DWWWKMAMZ \
  | 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: ea2539aee0d1c83056e1d8ed6b2980664aedb739236366df21d79d5a6602f98c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "61c73a1396d4d67a4152c611541d5f1c6264fe84a4e4dd0893f8cdfdc31cb7d3",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2016-01-14T02:30:34Z",
    "title_canon_sha256": "66d3b637706105d2dc0196a2235f046e68f43254173c93f2c3269bc87aef0178"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.03467",
    "kind": "arxiv",
    "version": 1
  }
}