Pith Number

pith:KKLLZCQE

pith:2012:KKLLZCQEI6QMQOX2WBBYHTNNII

not attested not anchored not stored refs pending

Koplienko Trace Formula

Arup Chattopadhyay, Kalyan B. Sinha

arxiv:1204.0167 v1 · 2012-04-01 · 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{KKLLZCQEI6QMQOX2WBBYHTNNII}

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	2026-05-18T03:58:50.172295Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5296bc8a0447a0c83afab04383cdad4228212bd39b582b137281972921c7b6a6

Aliases

arxiv: 1204.0167 · arxiv_version: 1204.0167v1 · doi: 10.48550/arxiv.1204.0167 · pith_short_12: KKLLZCQEI6QM · pith_short_16: KKLLZCQEI6QMQOX2 · pith_short_8: KKLLZCQE

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/KKLLZCQEI6QMQOX2WBBYHTNNII \
  | 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: 5296bc8a0447a0c83afab04383cdad4228212bd39b582b137281972921c7b6a6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2dedfeba6655bbc045d0e1dcd1b8437d113f4190bad0842d63b0e5e3c6ae79cf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-04-01T05:16:25Z",
    "title_canon_sha256": "2a3b9f815b34bc2c6024875009b81aa1650824401fdfc0700991527e656e4fa9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.0167",
    "kind": "arxiv",
    "version": 1
  }
}