Pith Number

pith:5Q3AL6G2

pith:2015:5Q3AL6G2XSV4X7ZHFDGVGZQAST

not attested not anchored not stored refs pending

Sobolev, Besov and Triebel-Lizorkin spaces on quantum tori

Quanhua Xu, Xiao Xiong, Zhi Yin

arxiv:1507.01789 v2 · 2015-07-07 · math.OA · 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{5Q3AL6G2XSV4X7ZHFDGVGZQAST}

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	2026-05-18T00:21:05.366768Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ec3605f8dabcabcbff2728cd53660094f0563d4835bd7f0a5c96bbcfffcc0e71

Aliases

arxiv: 1507.01789 · arxiv_version: 1507.01789v2 · doi: 10.48550/arxiv.1507.01789 · pith_short_12: 5Q3AL6G2XSV4 · pith_short_16: 5Q3AL6G2XSV4X7ZH · pith_short_8: 5Q3AL6G2

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/5Q3AL6G2XSV4X7ZHFDGVGZQAST \
  | 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: ec3605f8dabcabcbff2728cd53660094f0563d4835bd7f0a5c96bbcfffcc0e71

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cf89771dccbd92bf300ceb5974e48f03a194be59a2d3bf5db515c452cb689687",
    "cross_cats_sorted": [
      "math.CA",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2015-07-07T13:21:33Z",
    "title_canon_sha256": "9712a6048a6fd188cf5650728cd10f2b0af7496164f2c8825a32dbc305f9581e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.01789",
    "kind": "arxiv",
    "version": 2
  }
}