Pith Number

pith:CLE66PWB

pith:2018:CLE66PWBB326XUZ6STWNTWR7CE

not attested not anchored not stored refs pending

Orthogonal Dualities of Markov Processes and Unitary Symmetries

Chiara Franceschini, Cristian Giardin\`a, Frank Redig, Gioia Carinci, Wolter Groenevelt

arxiv:1812.08553 v3 · 2018-12-20 · math.PR · math-ph · math.CA · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CLE66PWBB326XUZ6STWNTWR7CE}

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	2026-05-17T23:40:49.263284Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

12c9ef3ec10ef5ebd33e94ecd9da3f11041c8204047bd6ab86d8a11b01e51650

Aliases

arxiv: 1812.08553 · arxiv_version: 1812.08553v3 · doi: 10.48550/arxiv.1812.08553 · pith_short_12: CLE66PWBB326 · pith_short_16: CLE66PWBB326XUZ6 · pith_short_8: CLE66PWB

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/CLE66PWBB326XUZ6STWNTWR7CE \
  | 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: 12c9ef3ec10ef5ebd33e94ecd9da3f11041c8204047bd6ab86d8a11b01e51650

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e36dd0ffed8c45fca35c8fd68ea9f55330f6e92bf1d6715a39321a158419f73e",
    "cross_cats_sorted": [
      "math-ph",
      "math.CA",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2018-12-20T13:38:01Z",
    "title_canon_sha256": "2636c0123fc55b31892e93976e64172cf20deaf9be935f5ef54b4c894f9c38c6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1812.08553",
    "kind": "arxiv",
    "version": 3
  }
}