Pith Number

pith:Y5TYZPBU

pith:2012:Y5TYZPBUFQET7I7PK2EK6YQDCG

not attested not anchored not stored refs pending

Lorentz spaces with variable exponents

Henning Kempka, Jan Vyb\'iral

arxiv:1210.1738 v2 · 2012-10-05 · 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{Y5TYZPBUFQET7I7PK2EK6YQDCG}

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	2026-05-18T03:15:06.424777Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c7678cbc342c093fa3ef5688af62031199fec3161b2464f1d3521c8b58be5aec

Aliases

arxiv: 1210.1738 · arxiv_version: 1210.1738v2 · doi: 10.48550/arxiv.1210.1738 · pith_short_12: Y5TYZPBUFQET · pith_short_16: Y5TYZPBUFQET7I7P · pith_short_8: Y5TYZPBU

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/Y5TYZPBUFQET7I7PK2EK6YQDCG \
  | 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: c7678cbc342c093fa3ef5688af62031199fec3161b2464f1d3521c8b58be5aec

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6f7bad03d8af0c7d13156e499404fbb51d2968aeec5ecd0dc28e8457309cfd60",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-10-05T12:43:05Z",
    "title_canon_sha256": "d817fa8cb23201e060b4fcedee73664a1f991ab80de8b86f9c8893605b4330a7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.1738",
    "kind": "arxiv",
    "version": 2
  }
}