Pith Number

pith:LAC4FKEK

pith:2009:LAC4FKEK4Z7X6GR3IID2E3K4BD

not attested not anchored not stored refs pending

The Relation between Ann-Categories and Ring Categories

Che Thi Kim Phung, Nguyen Thu Thuy, Nguyen Tien Quang

arxiv:0904.1099 v1 · 2009-04-07 · math.CT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LAC4FKEK4Z7X6GR3IID2E3K4BD}

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	2026-05-18T03:37:09.563422Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5805c2a88ae67f7f1a3b4207a26d5c08e461792161bf35d3961991e29976e44d

Aliases

arxiv: 0904.1099 · arxiv_version: 0904.1099v1 · doi: 10.48550/arxiv.0904.1099 · pith_short_12: LAC4FKEK4Z7X · pith_short_16: LAC4FKEK4Z7X6GR3 · pith_short_8: LAC4FKEK

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/LAC4FKEK4Z7X6GR3IID2E3K4BD \
  | 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: 5805c2a88ae67f7f1a3b4207a26d5c08e461792161bf35d3961991e29976e44d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ad8409ecc3b44fa373a15955e5acd28a1780de2b9897469e00c6caef3bcf00ca",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2009-04-07T10:04:20Z",
    "title_canon_sha256": "fed2a9d472a951447fe11f9aee0b42daa6a35fabe9841d1935064d5a07b32d80"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0904.1099",
    "kind": "arxiv",
    "version": 1
  }
}