Pith Number

pith:FV6GPIWO

pith:2016:FV6GPIWOFORRPV4DTU5AUQ5CC7

not attested not anchored not stored refs pending

Noncommutative probability of type D

Marek Bo\.zejko, Takahiro Hasebe, Wiktor Ejsmont

arxiv:1609.01049 v2 · 2016-09-05 · 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{FV6GPIWOFORRPV4DTU5AUQ5CC7}

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	2026-05-18T00:34:57.809305Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2d7c67a2ce2ba317d7839d3a0a43a217ffec4472df77fd11bb83ff3dd9fe3d72

Aliases

arxiv: 1609.01049 · arxiv_version: 1609.01049v2 · doi: 10.48550/arxiv.1609.01049 · pith_short_12: FV6GPIWOFORR · pith_short_16: FV6GPIWOFORRPV4D · pith_short_8: FV6GPIWO

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/FV6GPIWOFORRPV4DTU5AUQ5CC7 \
  | 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: 2d7c67a2ce2ba317d7839d3a0a43a217ffec4472df77fd11bb83ff3dd9fe3d72

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "55fdb5e5c9b21c87fdb2a6ba8c44cd915452ca74ffd73aed7c5c5521db2222d3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2016-09-05T08:11:17Z",
    "title_canon_sha256": "368636b6963dfc5e7a58c5e8a6a31e3b55e69e3db0a29fc82d14131f7f972bcb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.01049",
    "kind": "arxiv",
    "version": 2
  }
}