Pith Number

pith:U32RJAJB

pith:2013:U32RJAJBVG36HXAJ4FHQ7XTGMT

not attested not anchored not stored refs pending

Harmonic functions and stationary distributions for asymptotically homogeneous transition kernels on $Z^+$

Denis Denisov, Dmitry Korshunov, Vitali Wachtel

arxiv:1312.2201 v1 · 2013-12-08 · 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{U32RJAJBVG36HXAJ4FHQ7XTGMT}

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	2026-05-18T03:05:10.994464Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a6f5148121a9b7e3dc09e14f0fde6664eb77463d71390a20277c951ed75aea0f

Aliases

arxiv: 1312.2201 · arxiv_version: 1312.2201v1 · doi: 10.48550/arxiv.1312.2201 · pith_short_12: U32RJAJBVG36 · pith_short_16: U32RJAJBVG36HXAJ · pith_short_8: U32RJAJB

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/U32RJAJBVG36HXAJ4FHQ7XTGMT \
  | 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: a6f5148121a9b7e3dc09e14f0fde6664eb77463d71390a20277c951ed75aea0f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c477983c6c5482fdbb37fa73014b9930c6ba3233eb5d59cd9de106c2fed93ba6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-12-08T12:31:54Z",
    "title_canon_sha256": "a23a462ec874c22c38f3f6c79442540e47b5a79fcb775f2ce3e4d0f52422eddf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.2201",
    "kind": "arxiv",
    "version": 1
  }
}