Pith Number

pith:NBSQDTRF

pith:2012:NBSQDTRFII6Y4WB4UBKT3QFSEO

not attested not anchored not stored refs pending

Uniqueness of Kusuoka Representations

Alexander Shapiro, Alois Pichler

arxiv:1210.7257 v4 · 2012-10-26 · math.ST · math.PR · q-fin.RM · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NBSQDTRFII6Y4WB4UBKT3QFSEO}

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	2026-05-18T03:32:19.806810Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

686501ce25423d8e583ca0553dc0b223a002e18001f289a45904e0c0ee160eb2

Aliases

arxiv: 1210.7257 · arxiv_version: 1210.7257v4 · doi: 10.48550/arxiv.1210.7257 · pith_short_12: NBSQDTRFII6Y · pith_short_16: NBSQDTRFII6Y4WB4 · pith_short_8: NBSQDTRF

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/NBSQDTRFII6Y4WB4UBKT3QFSEO \
  | 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: 686501ce25423d8e583ca0553dc0b223a002e18001f289a45904e0c0ee160eb2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9fc495cfeb8b0b6439e590c97dd352471b93f1f8109ffa63f9136d235b629635",
    "cross_cats_sorted": [
      "math.PR",
      "q-fin.RM",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.ST",
    "submitted_at": "2012-10-26T21:34:36Z",
    "title_canon_sha256": "04f180d9f264ac04dee24518608cb0ee61847a0c4ef0431c2d171b4e1d05f8c8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.7257",
    "kind": "arxiv",
    "version": 4
  }
}