Pith Number

pith:4YCNTBK2

pith:2018:4YCNTBK2YJQ7UHPABYEVLPYFPQ

not attested not anchored not stored refs pending

Operator-valued Triebel-Lizorkin spaces

Runlian Xia, Xiao Xiong

arxiv:1804.01930 v1 · 2018-04-05 · math.OA · 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{4YCNTBK2YJQ7UHPABYEVLPYFPQ}

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	2026-05-18T00:19:09.535704Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e604d9855ac261fa1de00e0955bf057c175e5da20671d9ce4109f1649263dc40

Aliases

arxiv: 1804.01930 · arxiv_version: 1804.01930v1 · doi: 10.48550/arxiv.1804.01930 · pith_short_12: 4YCNTBK2YJQ7 · pith_short_16: 4YCNTBK2YJQ7UHPA · pith_short_8: 4YCNTBK2

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/4YCNTBK2YJQ7UHPABYEVLPYFPQ \
  | 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: e604d9855ac261fa1de00e0955bf057c175e5da20671d9ce4109f1649263dc40

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "39785d320101258b82a9f9b2eacd687a4e586512396bf2460a1c67caa61bf445",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2018-04-05T16:06:28Z",
    "title_canon_sha256": "c5958e98db6f68235fef66bc5d7e8e5ab7a520030714cf314988a938d9424556"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1804.01930",
    "kind": "arxiv",
    "version": 1
  }
}