Pith Number

pith:3JGTTLBR

pith:2016:3JGTTLBRCP6JWGV3BZN54IQOY2

not attested not anchored not stored refs pending

Weak factorization of Hardy spaces in the Bessel setting

Brett D. Wick, Roc Oliver

arxiv:1604.02409 v3 · 2016-04-08 · 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{3JGTTLBRCP6JWGV3BZN54IQOY2}

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	2026-05-18T00:32:44.635985Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

da4d39ac3113fc9b1abb0e5bde220ec6863ee6b0af87b69c25ca2dca746124f4

Aliases

arxiv: 1604.02409 · arxiv_version: 1604.02409v3 · doi: 10.48550/arxiv.1604.02409 · pith_short_12: 3JGTTLBRCP6J · pith_short_16: 3JGTTLBRCP6JWGV3 · pith_short_8: 3JGTTLBR

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/3JGTTLBRCP6JWGV3BZN54IQOY2 \
  | 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: da4d39ac3113fc9b1abb0e5bde220ec6863ee6b0af87b69c25ca2dca746124f4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5971a4083cbbf692c614ef3d42aaf2de90ebe878c7c53556861187755aa79df4",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2016-04-08T17:39:45Z",
    "title_canon_sha256": "f71ce5a395baf43071546f64fdec0d330113e8bbc4bf1956c72b9052c118325a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1604.02409",
    "kind": "arxiv",
    "version": 3
  }
}