Pith Number

pith:UBX6XQH2

pith:2016:UBX6XQH2ZAFKF3IQOOWDKLZJY2

not attested not anchored not stored refs pending

Anisotropic, Mixed-Norm Lizorkin--Triebel Spaces and Diffeomorphic Maps

Jon Johnsen, Sabrina Munch Hansen, Winfried Sickel

arxiv:1608.04573 v1 · 2016-08-16 · 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{UBX6XQH2ZAFKF3IQOOWDKLZJY2}

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	2026-05-18T01:08:36.825700Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a06febc0fac80aa2ed1073ac352f29c6825044acf5fa925ef8e4c918dfd39a0f

Aliases

arxiv: 1608.04573 · arxiv_version: 1608.04573v1 · doi: 10.48550/arxiv.1608.04573 · pith_short_12: UBX6XQH2ZAFK · pith_short_16: UBX6XQH2ZAFKF3IQ · pith_short_8: UBX6XQH2

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/UBX6XQH2ZAFKF3IQOOWDKLZJY2 \
  | 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: a06febc0fac80aa2ed1073ac352f29c6825044acf5fa925ef8e4c918dfd39a0f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f5761e596543d245b29167d7f0b243448a6fb276d747a155818bd6102ecb0251",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-08-16T12:38:52Z",
    "title_canon_sha256": "e843a813ddf5c8e6d7722689559295cfa91e146ea3fca5988a01edb09375a66f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.04573",
    "kind": "arxiv",
    "version": 1
  }
}