Pith Number

pith:4AJ4DKF6

pith:2016:4AJ4DKF6XWZ7FN22VRBYRKV3KW

not attested not anchored not stored refs pending

Symmetries and ergodic properties in quantum probability

Francesco Fidaleo, Vitonofrio Crismale

arxiv:1609.09856 v1 · 2016-09-30 · 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{4AJ4DKF6XWZ7FN22VRBYRKV3KW}

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	2026-05-18T01:03:33.171666Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e013c1a8bebdb3f2b75aac4388aabb559acd909f573f0bcc060c7581b5296bf7

Aliases

arxiv: 1609.09856 · arxiv_version: 1609.09856v1 · doi: 10.48550/arxiv.1609.09856 · pith_short_12: 4AJ4DKF6XWZ7 · pith_short_16: 4AJ4DKF6XWZ7FN22 · pith_short_8: 4AJ4DKF6

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/4AJ4DKF6XWZ7FN22VRBYRKV3KW \
  | 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: e013c1a8bebdb3f2b75aac4388aabb559acd909f573f0bcc060c7581b5296bf7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "43ea282c8dc789ca42fdc4d54e8279d9915f1920a08425285fe84bf70ec94525",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-09-30T18:47:46Z",
    "title_canon_sha256": "1e49dfd2ea16d3bf1725ef1da193190f427e81418c0dd0bfba71f8385d1eecad"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.09856",
    "kind": "arxiv",
    "version": 1
  }
}