Pith Number

pith:ERRI5MNS

pith:2015:ERRI5MNSFFR4L7OA7XRFHDXUN5

not attested not anchored not stored refs pending

On Operator-Valued Bi-Free Distributions

Paul Skoufranis

arxiv:1510.03896 v1 · 2015-10-13 · math.OA · math.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{ERRI5MNSFFR4L7OA7XRFHDXUN5}

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	2026-05-18T01:05:12.688094Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

24628eb1b22963c5fdc0fde2538ef46f45cf9cf47d323537db33928a7bdb4e57

Aliases

arxiv: 1510.03896 · arxiv_version: 1510.03896v1 · doi: 10.48550/arxiv.1510.03896 · pith_short_12: ERRI5MNSFFR4 · pith_short_16: ERRI5MNSFFR4L7OA · pith_short_8: ERRI5MNS

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/ERRI5MNSFFR4L7OA7XRFHDXUN5 \
  | 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: 24628eb1b22963c5fdc0fde2538ef46f45cf9cf47d323537db33928a7bdb4e57

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6b51b57a12437837e66caae7336feed7cef1e77c4341bbd675df01afc5ab39dd",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2015-10-13T21:04:46Z",
    "title_canon_sha256": "fc361bb9ab9ce90b4f205ea5e8cb056cc8ef2f3f6c6eb9516f4b3802bba9635a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.03896",
    "kind": "arxiv",
    "version": 1
  }
}