Pith Number

pith:AYOLXPJZ

pith:2013:AYOLXPJZXIOCH2WIGWUPYHSFT6

not attested not anchored not stored refs pending

An alternative proof of a result of Takaoka

Shiqi Song

arxiv:1306.1062 v1 · 2013-06-05 · math.PR · q-fin.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AYOLXPJZXIOCH2WIGWUPYHSFT6}

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	2026-05-18T03:21:44.481343Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

061cbbbd39ba1c23eac835a8fc1e459f807a8aa9e0a9e6aa181e1d82e7886f26

Aliases

arxiv: 1306.1062 · arxiv_version: 1306.1062v1 · doi: 10.48550/arxiv.1306.1062 · pith_short_12: AYOLXPJZXIOC · pith_short_16: AYOLXPJZXIOCH2WI · pith_short_8: AYOLXPJZ

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/AYOLXPJZXIOCH2WIGWUPYHSFT6 \
  | 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: 061cbbbd39ba1c23eac835a8fc1e459f807a8aa9e0a9e6aa181e1d82e7886f26

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5ee5037146360c2e1a87afb5f74e993f9b3d476211a88d3539073bcc73eda430",
    "cross_cats_sorted": [
      "q-fin.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-06-05T11:26:28Z",
    "title_canon_sha256": "9a37260d38cd11d9034f0e8ff5031c0ba8ebc6e5bb825d07cff2270e3287d373"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.1062",
    "kind": "arxiv",
    "version": 1
  }
}