Pith Number

pith:WPI2V23K

pith:2014:WPI2V23KMLSQ3BPIE7F5E7QSMU

not attested not anchored not stored refs pending

Kernel and symbol criteria for Schatten classes and $r$-nuclearity on compact manifolds

Julio Delgado, Michael Ruzhansky

arxiv:1408.6170 v1 · 2014-08-26 · math.FA · math.AP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WPI2V23KMLSQ3BPIE7F5E7QSMU}

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	2026-05-18T02:40:53.745837Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b3d1aaeb6a62e50d85e827cbd27e126528496427525e57682a26daac2f601a7d

Aliases

arxiv: 1408.6170 · arxiv_version: 1408.6170v1 · doi: 10.48550/arxiv.1408.6170 · pith_short_12: WPI2V23KMLSQ · pith_short_16: WPI2V23KMLSQ3BPI · pith_short_8: WPI2V23K

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/WPI2V23KMLSQ3BPIE7F5E7QSMU \
  | 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: b3d1aaeb6a62e50d85e827cbd27e126528496427525e57682a26daac2f601a7d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e9604aedbd4cc504120f3c5b3bcd027a0b85bbf71ffebc1f263ebcddea160269",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2014-08-26T15:58:15Z",
    "title_canon_sha256": "2b9c0d35400d92b74c908a8822f1737209432191a8c21ff2b0f377eacbc68897"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1408.6170",
    "kind": "arxiv",
    "version": 1
  }
}