Pith Number

pith:P5ADOZ5V

pith:2013:P5ADOZ5V7JEFYMQQNXFRTMWBIV

not attested not anchored not stored refs pending

Compactness in the Lebesgue-Bochner spaces L^p(\mu;X)

Jan van Neerven

arxiv:1305.5688 v1 · 2013-05-24 · 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{P5ADOZ5V7JEFYMQQNXFRTMWBIV}

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	2026-05-18T03:25:03.496719Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7f403767b5fa485c32106dcb19b2c145679fe20c47eb2229495a5477506fd6af

Aliases

arxiv: 1305.5688 · arxiv_version: 1305.5688v1 · doi: 10.48550/arxiv.1305.5688 · pith_short_12: P5ADOZ5V7JEF · pith_short_16: P5ADOZ5V7JEFYMQQ · pith_short_8: P5ADOZ5V

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/P5ADOZ5V7JEFYMQQNXFRTMWBIV \
  | 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: 7f403767b5fa485c32106dcb19b2c145679fe20c47eb2229495a5477506fd6af

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8bccddc6acc4b525ac15dd89ddc498cf5e7dd4337f56214671e9660514d0530e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2013-05-24T11:21:35Z",
    "title_canon_sha256": "85980954c9046cd06cc23a9dbf0b6e3334a390e79df053ab3384f40b702e34b6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1305.5688",
    "kind": "arxiv",
    "version": 1
  }
}