Pith Number

pith:PNTPDU5E

pith:2015:PNTPDU5E3OH7AQ7QBEX2AUSCIY

not attested not anchored not stored refs pending

Representation growth of the Heisenberg group over $\mathcal{O}[x]/(x^n)$

Duong Hoang Dung

arxiv:1508.03507 v1 · 2015-08-14 · math.GR · math.NT · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PNTPDU5E3OH7AQ7QBEX2AUSCIY}

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	2026-05-18T01:35:17.568924Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7b66f1d3a4db8ff043f0092fa052424603e110c6fd8e854f3e27e9193d97ed25

Aliases

arxiv: 1508.03507 · arxiv_version: 1508.03507v1 · doi: 10.48550/arxiv.1508.03507 · pith_short_12: PNTPDU5E3OH7 · pith_short_16: PNTPDU5E3OH7AQ7Q · pith_short_8: PNTPDU5E

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/PNTPDU5E3OH7AQ7QBEX2AUSCIY \
  | 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: 7b66f1d3a4db8ff043f0092fa052424603e110c6fd8e854f3e27e9193d97ed25

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "31b0ee9f04d6e8f648dbd8e000dbcb8e7944a153914c75e4833d397959b601f3",
    "cross_cats_sorted": [
      "math.NT",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-08-14T14:08:50Z",
    "title_canon_sha256": "8f684be8b72475a9feec651d2420e454a69da3b02fcab3c5e4f74f2967694fdb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.03507",
    "kind": "arxiv",
    "version": 1
  }
}