Pith Number

pith:FTCNJ6NP

pith:2012:FTCNJ6NPW5ORDY53O5HZYDXBSY

not attested not anchored not stored refs pending

Margulis Lemma, entropy and free products

Filippo Cerocchi

arxiv:1204.1619 v2 · 2012-04-07 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FTCNJ6NPW5ORDY53O5HZYDXBSY}

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	2026-05-18T03:55:01.430064Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2cc4d4f9afb75d11e3bb774f9c0ee196211de8eb958db28e25346b2060e54470

Aliases

arxiv: 1204.1619 · arxiv_version: 1204.1619v2 · doi: 10.48550/arxiv.1204.1619 · pith_short_12: FTCNJ6NPW5OR · pith_short_16: FTCNJ6NPW5ORDY53 · pith_short_8: FTCNJ6NP

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/FTCNJ6NPW5ORDY53O5HZYDXBSY \
  | 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: 2cc4d4f9afb75d11e3bb774f9c0ee196211de8eb958db28e25346b2060e54470

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3035195b654542e9ba03b6b76b7409a4496d764c6193470ee13f459c4c46ca0f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2012-04-07T11:43:17Z",
    "title_canon_sha256": "f4b9613ddd00c178ab162edff0f859dd788070b717b161a728652a43ed0d98c8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.1619",
    "kind": "arxiv",
    "version": 2
  }
}