Pith Number

pith:YY3ZHB6D

pith:2013:YY3ZHB6D4TYWUGMK5OWMXMUVQX

not attested not anchored not stored refs pending

Continued fractions on the Heisenberg group

Anton Lukyanenko, Joseph Vandehey

arxiv:1302.6121 v2 · 2013-02-25 · math.NT · math.DS · math.GR · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YY3ZHB6D4TYWUGMK5OWMXMUVQX}

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	2026-05-18T01:12:19.013222Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c6379387c3e4f16a198aebaccbb29585fcdcbb981601ed5bbfb226ead17b0848

Aliases

arxiv: 1302.6121 · arxiv_version: 1302.6121v2 · doi: 10.48550/arxiv.1302.6121 · pith_short_12: YY3ZHB6D4TYW · pith_short_16: YY3ZHB6D4TYWUGMK · pith_short_8: YY3ZHB6D

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/YY3ZHB6D4TYWUGMK5OWMXMUVQX \
  | 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: c6379387c3e4f16a198aebaccbb29585fcdcbb981601ed5bbfb226ead17b0848

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9de35d05406e7cc69f61666e7b68746b4814f5b03e90e86d8c4c5dae57c4b5ad",
    "cross_cats_sorted": [
      "math.DS",
      "math.GR",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-02-25T15:25:34Z",
    "title_canon_sha256": "0f7db501500a6eb96f2bacf7d728f29b6d7947315e44d3a8cf2dbd7131def1f2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.6121",
    "kind": "arxiv",
    "version": 2
  }
}