Pith Number

pith:O7ZWXYO5

pith:2015:O7ZWXYO5QN5H7KTW2K4QNQOV7R

not attested not anchored not stored refs pending

On bi-free De Finetti theorems

Amaury Freslon, Moritz Weber

arxiv:1501.05124 v2 · 2015-01-21 · math.PR · math.OA · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{O7ZWXYO5QN5H7KTW2K4QNQOV7R}

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	2026-05-18T01:36:33.984295Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

77f36be1dd837a7faa76d2b906c1d5fc41d2d05d87fe810607754b4abb06c0e2

Aliases

arxiv: 1501.05124 · arxiv_version: 1501.05124v2 · doi: 10.48550/arxiv.1501.05124 · pith_short_12: O7ZWXYO5QN5H · pith_short_16: O7ZWXYO5QN5H7KTW · pith_short_8: O7ZWXYO5

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/O7ZWXYO5QN5H7KTW2K4QNQOV7R \
  | 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: 77f36be1dd837a7faa76d2b906c1d5fc41d2d05d87fe810607754b4abb06c0e2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bf3c3b7d1c9f19ffb0cb0419b046beedad3166ee3c86eb5677da08b397e3ac8f",
    "cross_cats_sorted": [
      "math.OA",
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-01-21T10:57:11Z",
    "title_canon_sha256": "749c007ad6a566d3dff20957d42fb4017faf5beb591dfa6e84d482a8388d25eb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.05124",
    "kind": "arxiv",
    "version": 2
  }
}