Pith Number

pith:5ZBIHZTO

pith:2017:5ZBIHZTOYAJSIT3WQTI42QKWCJ

not attested not anchored not stored refs pending

Smallest order closed sublattices and option spanning

Denny H. Leung, Niushan Gao

arxiv:1703.09748 v1 · 2017-03-28 · math.FA · q-fin.MF

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5ZBIHZTOYAJSIT3WQTI42QKWCJ}

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	2026-05-18T00:47:39.630802Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ee4283e66ec013244f7684d1cd41561267e3e33ff7ebf58749c0bdb2e5268b5f

Aliases

arxiv: 1703.09748 · arxiv_version: 1703.09748v1 · doi: 10.48550/arxiv.1703.09748 · pith_short_12: 5ZBIHZTOYAJS · pith_short_16: 5ZBIHZTOYAJSIT3W · pith_short_8: 5ZBIHZTO

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/5ZBIHZTOYAJSIT3WQTI42QKWCJ \
  | 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: ee4283e66ec013244f7684d1cd41561267e3e33ff7ebf58749c0bdb2e5268b5f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1bfaddec8924a13caec7c51e1b5137c3e3df1158273d870e9d4fe9b95451c25c",
    "cross_cats_sorted": [
      "q-fin.MF"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2017-03-28T18:59:21Z",
    "title_canon_sha256": "b7f38153e08a7d35045fed52c82c1ff0619657057dd6dba7c357d2f39bae5d5f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1703.09748",
    "kind": "arxiv",
    "version": 1
  }
}