Pith Number

pith:LRZ7TKI4

pith:2011:LRZ7TKI4YRPAJ5BF4HJASDACRO

not attested not anchored not stored refs pending

Relations among Besov-Type Spaces, Triebel-Lizorkin-Type Spaces and Generalized Carleson Measure Spaces

Dachun Yang, Wen Yuan

arxiv:1109.0789 v2 · 2011-09-05 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LRZ7TKI4YRPAJ5BF4HJASDACRO}

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	2026-05-18T03:52:26.332609Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5c73f9a91cc45e04f425e1d2090c028b99379abd807f59e0f3a78f031ae86aca

Aliases

arxiv: 1109.0789 · arxiv_version: 1109.0789v2 · doi: 10.48550/arxiv.1109.0789 · pith_short_12: LRZ7TKI4YRPA · pith_short_16: LRZ7TKI4YRPAJ5BF · pith_short_8: LRZ7TKI4

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/LRZ7TKI4YRPAJ5BF4HJASDACRO \
  | 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: 5c73f9a91cc45e04f425e1d2090c028b99379abd807f59e0f3a78f031ae86aca

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "81431b427e017cccb75e007e6d7fcef7af6997af955465f2ad830cdd48b8c866",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2011-09-05T02:48:40Z",
    "title_canon_sha256": "9041d804bbaa3c1a0f2054be2326da17ba385ca790691f4949818f9906a05cef"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.0789",
    "kind": "arxiv",
    "version": 2
  }
}