Pith Number

pith:7TKJFNLP

pith:2014:7TKJFNLPWB7KVQPTZM5OPC3HFQ

not attested not anchored not stored refs pending

A finite presentation of the level $2$ principal congruence subgroup of $GL(n;\mathbb{Z})$

Ryoma Kobayashi

arxiv:1407.1612 v3 · 2014-07-07 · math.GT · 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{7TKJFNLPWB7KVQPTZM5OPC3HFQ}

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	2026-05-18T02:29:23.412561Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fcd492b56fb07eaac1f3cb3ae78b672c1f57868987f844ee82f886aedaa08430

Aliases

arxiv: 1407.1612 · arxiv_version: 1407.1612v3 · doi: 10.48550/arxiv.1407.1612 · pith_short_12: 7TKJFNLPWB7K · pith_short_16: 7TKJFNLPWB7KVQPT · pith_short_8: 7TKJFNLP

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/7TKJFNLPWB7KVQPTZM5OPC3HFQ \
  | 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: fcd492b56fb07eaac1f3cb3ae78b672c1f57868987f844ee82f886aedaa08430

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "25d98347b0632e6a8ef5b5b641e93d9d85c5c7ccbfad21bb8a96bd69312e388e",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2014-07-07T08:08:55Z",
    "title_canon_sha256": "ef45833b2c912d09614065942a1951eeea737e622e454ef7a7f5d14b371d6667"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1407.1612",
    "kind": "arxiv",
    "version": 3
  }
}