Pith Number

pith:CB5BCOFX

pith:2013:CB5BCOFX4O672LAEUCC2UJETZ2

not attested not anchored not stored refs pending

An approximation principle for congruence subgroups

Erez Lapid, Tobias Finis

arxiv:1308.3604 v4 · 2013-08-16 · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CB5BCOFX4O672LAEUCC2UJETZ2}

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	2026-05-18T00:05:08.246769Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

107a1138b7e3bdfd2c04a085aa2493ce9fbd263d9b6699a6e50c308e3cac890c

Aliases

arxiv: 1308.3604 · arxiv_version: 1308.3604v4 · doi: 10.48550/arxiv.1308.3604 · pith_short_12: CB5BCOFX4O67 · pith_short_16: CB5BCOFX4O672LAE · pith_short_8: CB5BCOFX

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/CB5BCOFX4O672LAEUCC2UJETZ2 \
  | 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: 107a1138b7e3bdfd2c04a085aa2493ce9fbd263d9b6699a6e50c308e3cac890c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9c0e1041e7ddceb37bc66ab2cdb373f5fda7997ea0ce96a947d93a1d7c34f0ca",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-08-16T11:16:10Z",
    "title_canon_sha256": "b1895bf0af49efba43f8360d1ceb624a38a953761fa17b593f2be4e95d10a7cd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.3604",
    "kind": "arxiv",
    "version": 4
  }
}