Pith Number

pith:CMUN3MMU

pith:2018:CMUN3MMUQZEZLVXZM7ZAKWH6TO

not attested not anchored not stored refs pending

Critical exponents of invariant random subgroups in negative curvature

Arie Levit, Ilya Gekhtman

arxiv:1804.02995 v4 · 2018-04-09 · math.GR · math.DS · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CMUN3MMUQZEZLVXZM7ZAKWH6TO}

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	2026-05-18T00:04:37.447970Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1328ddb194864995d6f967f20558fe9b99435424a7d996df59cbcd339e3fecd2

Aliases

arxiv: 1804.02995 · arxiv_version: 1804.02995v4 · doi: 10.48550/arxiv.1804.02995 · pith_short_12: CMUN3MMUQZEZ · pith_short_16: CMUN3MMUQZEZLVXZ · pith_short_8: CMUN3MMU

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/CMUN3MMUQZEZLVXZM7ZAKWH6TO \
  | 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: 1328ddb194864995d6f967f20558fe9b99435424a7d996df59cbcd339e3fecd2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d3cbbea257004c571603e552475117d39509833f38a31a87f9db6bc6b024583b",
    "cross_cats_sorted": [
      "math.DS",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2018-04-09T14:05:14Z",
    "title_canon_sha256": "84f751f9d43d2c3ab8d652a450d8bab26ebcc20ca57dc71d03930550aedc28ab"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1804.02995",
    "kind": "arxiv",
    "version": 4
  }
}