Pith Number

pith:6O6P5U6U

pith:2012:6O6P5U6UBU5LRMC5B4VESRH4QT

not attested not anchored not stored refs pending

A Riccati differential equation and free subgroup numbers for lifts of $\PSL_2(\Z)$ modulo powers of primes

Christian Krattenthaler (Universit\"at Wien), Thomas W. M\"uller (Queen Mary)

arxiv:1211.2947 v3 · 2012-11-13 · math.CO · 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{6O6P5U6UBU5LRMC5B4VESRH4QT}

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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	2026-05-18T03:14:28.082850Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f3bcfed3d40d3ab8b05d0f2a4944fc84df1bc1b8e13629e8e862a04784290600

Aliases

arxiv: 1211.2947 · arxiv_version: 1211.2947v3 · doi: 10.48550/arxiv.1211.2947 · pith_short_12: 6O6P5U6UBU5L · pith_short_16: 6O6P5U6UBU5LRMC5 · pith_short_8: 6O6P5U6U

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/6O6P5U6UBU5LRMC5B4VESRH4QT \
  | 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: f3bcfed3d40d3ab8b05d0f2a4944fc84df1bc1b8e13629e8e862a04784290600

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "67e1ec6d82dc1158553514c37e35d6bdcd5e47414cc2971f5da5e4158b1fce9b",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-11-13T10:42:00Z",
    "title_canon_sha256": "6851de05cd2b66194927622f8942bf6745380a36ff4351d358a19eb165940303"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.2947",
    "kind": "arxiv",
    "version": 3
  }
}