Pith Number

pith:AUFYCKXW

pith:2017:AUFYCKXWRJFQDQRTD3WHUQAHR4

not attested not anchored not stored refs pending

Limit theorems in bi-free probability theory

Hao-Wei Huang, Jiun-Chau Wang, Takahiro Hasebe

arxiv:1705.05523 v1 · 2017-05-16 · math.PR · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AUFYCKXWRJFQDQRTD3WHUQAHR4}

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	2026-05-18T00:44:22.506652Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

050b812af68a4b01c2331eec7a40078f1a75e910c7cc16001043f2160171004a

Aliases

arxiv: 1705.05523 · arxiv_version: 1705.05523v1 · doi: 10.48550/arxiv.1705.05523 · pith_short_12: AUFYCKXWRJFQ · pith_short_16: AUFYCKXWRJFQDQRT · pith_short_8: AUFYCKXW

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/AUFYCKXWRJFQDQRTD3WHUQAHR4 \
  | 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: 050b812af68a4b01c2331eec7a40078f1a75e910c7cc16001043f2160171004a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ec0b4d5af2af4e60b85d891b53e9090d594adeb04a2d14ed98b5c02b66d7ccb2",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2017-05-16T04:30:20Z",
    "title_canon_sha256": "2ce47c70f5cd52ee25092bba076b6572a40d04225343ed2c3ba8b62852fcc1da"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1705.05523",
    "kind": "arxiv",
    "version": 1
  }
}