Pith Number

pith:WPUGQ7GW

pith:2013:WPUGQ7GW2MRFLMG577NOMOD6LE

not attested not anchored not stored refs pending

Special precovers and preenvelopes of complexes

Zhanping Wang, Zhongkui Liu

arxiv:1301.6595 v1 · 2013-01-28 · math.KT · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WPUGQ7GW2MRFLMG577NOMOD6LE}

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	2026-05-18T03:35:14.946149Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b3e8687cd6d32255b0ddffdae6387e5939a918b4151cc2799ae401ec979dfc37

Aliases

arxiv: 1301.6595 · arxiv_version: 1301.6595v1 · doi: 10.48550/arxiv.1301.6595 · pith_short_12: WPUGQ7GW2MRF · pith_short_16: WPUGQ7GW2MRFLMG5 · pith_short_8: WPUGQ7GW

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/WPUGQ7GW2MRFLMG577NOMOD6LE \
  | 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: b3e8687cd6d32255b0ddffdae6387e5939a918b4151cc2799ae401ec979dfc37

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8f73a970c097ee1071df427ef9b828ae7576d36df48453a7068aa5777522fc4e",
    "cross_cats_sorted": [
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.KT",
    "submitted_at": "2013-01-28T16:34:05Z",
    "title_canon_sha256": "bfe770f6928e20b1a8a4dce8a57f47dddbaddf1086282257cb34012ed8abfc9f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.6595",
    "kind": "arxiv",
    "version": 1
  }
}