Pith Number

pith:TI4QA7AP

pith:2012:TI4QA7APDBT64UX3FYVUWNIWWF

not attested not anchored not stored refs pending

Markov semigroups, monoids, and groups

Alan J. Cain, Victor Maltcev

arxiv:1202.3013 v1 · 2012-02-14 · math.GR · cs.FL

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TI4QA7APDBT64UX3FYVUWNIWWF}

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	2026-05-18T01:29:51.761602Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9a39007c0f1867ee52fb2e2b4b3516b173ebbff641a99f03813c0b2d4d76d942

Aliases

arxiv: 1202.3013 · arxiv_version: 1202.3013v1 · doi: 10.48550/arxiv.1202.3013 · pith_short_12: TI4QA7APDBT6 · pith_short_16: TI4QA7APDBT64UX3 · pith_short_8: TI4QA7AP

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/TI4QA7APDBT64UX3FYVUWNIWWF \
  | 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: 9a39007c0f1867ee52fb2e2b4b3516b173ebbff641a99f03813c0b2d4d76d942

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "80574ab9ef1006a752c3e38db19bd308bfb58cc55d474a4420cc63f561b574d7",
    "cross_cats_sorted": [
      "cs.FL"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-02-14T12:12:06Z",
    "title_canon_sha256": "43948ef3fc71cc1dd3e434f28561e8d71dea2d8a3d40d4ce6a4c4ed352c21cd7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.3013",
    "kind": "arxiv",
    "version": 1
  }
}