Pith Number

pith:YQDJ7IGQ

pith:2013:YQDJ7IGQFH66Y3X4SWYQDRGSZD

not attested not anchored not stored refs pending

Isotropic Markov semigroups on ultra-metric spaces

Alexander Bendikov, Alexander Grigor'yan, Christophe Pittet, Wolfgang Woess

arxiv:1304.6271 v3 · 2013-04-23 · math.PR · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YQDJ7IGQFH66Y3X4SWYQDRGSZD}

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	2026-05-18T00:57:32.200213Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c4069fa0d029fdec6efc95b101c4d2c8ca012ee079f8eac9efb4afb6c54dc741

Aliases

arxiv: 1304.6271 · arxiv_version: 1304.6271v3 · doi: 10.48550/arxiv.1304.6271 · pith_short_12: YQDJ7IGQFH66 · pith_short_16: YQDJ7IGQFH66Y3X4 · pith_short_8: YQDJ7IGQ

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/YQDJ7IGQFH66Y3X4SWYQDRGSZD \
  | 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: c4069fa0d029fdec6efc95b101c4d2c8ca012ee079f8eac9efb4afb6c54dc741

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cdc575abf1a320d5a69179da2fae8fbc3236c74bd9d57a7550a2f079a2e6c138",
    "cross_cats_sorted": [
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-04-23T12:55:30Z",
    "title_canon_sha256": "d3ea5c456a21d73776c64cd308a97f1df4e6f80e9b12b206711b13a6da80a278"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.6271",
    "kind": "arxiv",
    "version": 3
  }
}