Pith Number

pith:CSXSAH22

pith:2011:CSXSAH222R6BPD6PHFQK7TMJKJ

not attested not anchored not stored refs pending

Behaviors of entropy on finitely generated groups

J\'er\'emie Brieussel

arxiv:1110.5099 v3 · 2011-10-23 · math.GR · 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{CSXSAH222R6BPD6PHFQK7TMJKJ}

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	2026-05-18T03:04:38.716899Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

14af201f5ad47c178fcf3960afcd8952595371bb4933d3206cbaa467c856cc7f

Aliases

arxiv: 1110.5099 · arxiv_version: 1110.5099v3 · doi: 10.48550/arxiv.1110.5099 · pith_short_12: CSXSAH222R6B · pith_short_16: CSXSAH222R6BPD6P · pith_short_8: CSXSAH22

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/CSXSAH222R6BPD6PHFQK7TMJKJ \
  | 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: 14af201f5ad47c178fcf3960afcd8952595371bb4933d3206cbaa467c856cc7f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b94b45c31e0462a1c70072f84211e9be6fece709d7e8404654198710a72cda63",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-10-23T23:48:57Z",
    "title_canon_sha256": "f5762f08d6709285e898cbf081bcfebec101891600daee9e38c70da8b9287695"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.5099",
    "kind": "arxiv",
    "version": 3
  }
}