Pith Number

pith:5ABW663B

pith:2015:5ABW663BCEL5TQHQGTKEHZK4OI

not attested not anchored not stored refs pending

On the Markov commutator

Laurent Miclo (IMT)

arxiv:1505.02540 v1 · 2015-05-11 · 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{5ABW663BCEL5TQHQGTKEHZK4OI}

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	2026-05-18T02:16:18.517478Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e8036f7b611117d9c0f034d443e55c72096ca0f2f0e2111a259e2ecea11a4df4

Aliases

arxiv: 1505.02540 · arxiv_version: 1505.02540v1 · doi: 10.48550/arxiv.1505.02540 · pith_short_12: 5ABW663BCEL5 · pith_short_16: 5ABW663BCEL5TQHQ · pith_short_8: 5ABW663B

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/5ABW663BCEL5TQHQGTKEHZK4OI \
  | 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: e8036f7b611117d9c0f034d443e55c72096ca0f2f0e2111a259e2ecea11a4df4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c6889955943054869bdcfb1d054cd0c92384f308cfe806ad560351fe16edeba8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-05-11T09:50:00Z",
    "title_canon_sha256": "dac43cd0b085fe6451699676d22caa695950c12af8f99a2c03bcfdf78acfcfab"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.02540",
    "kind": "arxiv",
    "version": 1
  }
}