Pith Number

pith:NPGUMGBF

pith:2016:NPGUMGBFMDMMLUYG2BHBZGR5NR

not attested not anchored not stored refs pending

Characterisation by Local Means of Anisotropic Lizorkin--Triebel Spaces with Mixed Norms

Jon Johnsen, Sabrina Munch Hansen, Winfried Sickel

arxiv:1609.06970 v1 · 2016-09-22 · 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{NPGUMGBFMDMMLUYG2BHBZGR5NR}

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	2026-05-18T01:04:04.721688Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6bcd46182560d8c5d306d04e1c9a3d6c5ac5191936ec3c2c654ab7eba1647c88

Aliases

arxiv: 1609.06970 · arxiv_version: 1609.06970v1 · doi: 10.48550/arxiv.1609.06970 · pith_short_12: NPGUMGBFMDMM · pith_short_16: NPGUMGBFMDMMLUYG · pith_short_8: NPGUMGBF

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/NPGUMGBFMDMMLUYG2BHBZGR5NR \
  | 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: 6bcd46182560d8c5d306d04e1c9a3d6c5ac5191936ec3c2c654ab7eba1647c88

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e7bd45413421242e328db89a85e794e0997328326a0689d9f416ca91c0d905a0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2016-09-22T13:41:09Z",
    "title_canon_sha256": "e931179a9c6e305b11019b00a64ae8c6430743f2a72ef14e130632a534b4b9e4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.06970",
    "kind": "arxiv",
    "version": 1
  }
}