Pith Number

pith:YNYH7SAR

pith:2012:YNYH7SARDVGXP4JQ4OV3O56K4W

not attested not anchored not stored refs pending

On the notion(s) of duality for Markov processes

Noemi Kurt, Sabine Jansen

arxiv:1210.7193 v2 · 2012-10-26 · math.PR · 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{YNYH7SARDVGXP4JQ4OV3O56K4W}

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	2026-05-18T02:58:57.660400Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c3707fc8111d4d77f130e3abb777cae5a00fef55d2720c1f8f544e39721c9ca4

Aliases

arxiv: 1210.7193 · arxiv_version: 1210.7193v2 · doi: 10.48550/arxiv.1210.7193 · pith_short_12: YNYH7SARDVGX · pith_short_16: YNYH7SARDVGXP4JQ · pith_short_8: YNYH7SAR

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/YNYH7SARDVGXP4JQ4OV3O56K4W \
  | 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: c3707fc8111d4d77f130e3abb777cae5a00fef55d2720c1f8f544e39721c9ca4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f29ee9cd22f31cc03545965ec22f7d50c8b3506a3e01c287290d48f91b69d5a5",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-10-26T16:57:54Z",
    "title_canon_sha256": "d7eabeaffceb1407d06a8a14a494c3b0652d2b9a19afd5f87f5746a8d6bdd43f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.7193",
    "kind": "arxiv",
    "version": 2
  }
}