Pith Number

pith:J53GDZI5

pith:2021:J53GDZI5YHYNVL6FDQCJA3R72T

not attested not anchored not stored refs pending

Average radial integrability spaces, tent spaces and integration operators

Petros Galanopoulos, Tanaus\'u Aguilar-Hern\'andez

arxiv:2105.10054 v3 · 2021-05-20 · 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{J53GDZI5YHYNVL6FDQCJA3R72T}

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	2026-07-05T05:32:28.463185Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4f7661e51dc1f0daafc51c04906e3fd4fbcf73c5b9a2c81c72976c8e29e836f2

Aliases

arxiv: 2105.10054 · arxiv_version: 2105.10054v3 · doi: 10.48550/arxiv.2105.10054 · pith_short_12: J53GDZI5YHYN · pith_short_16: J53GDZI5YHYNVL6F · pith_short_8: J53GDZI5

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/J53GDZI5YHYNVL6FDQCJA3R72T \
  | 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: 4f7661e51dc1f0daafc51c04906e3fd4fbcf73c5b9a2c81c72976c8e29e836f2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c6c3b460f7b9ebdcccfd06a08a72f547e4712a94b3703d32d110fdce76d17be9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2021-05-20T22:13:22Z",
    "title_canon_sha256": "17f435b3b83b83eafd802a93c8975c95d733b2d8a5903b7a2181498edfde1f88"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2105.10054",
    "kind": "arxiv",
    "version": 3
  }
}