Pith Number

pith:NRJ7QZ7Y

pith:2014:NRJ7QZ7YMOEP56EWAIF5IR5ZC5

not attested not anchored not stored refs pending

Counting and equidistribution in Heisenberg groups

Fr\'ed\'eric Paulin, Jouni Parkkonen

arxiv:1402.7225 v2 · 2014-02-28 · math.DG · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NRJ7QZ7YMOEP56EWAIF5IR5ZC5}

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	2026-05-18T02:18:40.987748Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6c53f867f86388fef896020bd447b91779bdb283a0efbfca9f736486d83d2453

Aliases

arxiv: 1402.7225 · arxiv_version: 1402.7225v2 · doi: 10.48550/arxiv.1402.7225 · pith_short_12: NRJ7QZ7YMOEP · pith_short_16: NRJ7QZ7YMOEP56EW · pith_short_8: NRJ7QZ7Y

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/NRJ7QZ7YMOEP56EWAIF5IR5ZC5 \
  | 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: 6c53f867f86388fef896020bd447b91779bdb283a0efbfca9f736486d83d2453

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "91259569c74d359d573dd27cb4846feda23f7d67625cb6201deb3b57f54d2c8d",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2014-02-28T12:39:29Z",
    "title_canon_sha256": "b63bd084ec8650e577ada4d1d46a446300f314e95439abd594c863b8d0a6cd18"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1402.7225",
    "kind": "arxiv",
    "version": 2
  }
}