Pith Number

pith:IZFHBOYH

pith:2012:IZFHBOYHGJ6XTAHHTSHVW4OUY2

not attested not anchored not stored refs pending

On balanced subgroups of the multiplicative group

Carl Pomerance, Douglas Ulmer

arxiv:1204.6705 v1 · 2012-04-30 · 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{IZFHBOYHGJ6XTAHHTSHVW4OUY2}

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	2026-05-18T03:56:44.080496Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

464a70bb07327d7980e79c8f5b71d4c6a023b89ea985f58f7e2f711bead9273b

Aliases

arxiv: 1204.6705 · arxiv_version: 1204.6705v1 · doi: 10.48550/arxiv.1204.6705 · pith_short_12: IZFHBOYHGJ6X · pith_short_16: IZFHBOYHGJ6XTAHH · pith_short_8: IZFHBOYH

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/IZFHBOYHGJ6XTAHHTSHVW4OUY2 \
  | 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: 464a70bb07327d7980e79c8f5b71d4c6a023b89ea985f58f7e2f711bead9273b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "729a04092d62c87ac5061b006ab6d7e7cac1a243a041b831d0a2ca4a3063deb6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-04-30T17:11:11Z",
    "title_canon_sha256": "0e783ac6e87ea665b8f8db5fdaf0db47b437ad5c2edd54d22290a2fc2a8e3f79"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.6705",
    "kind": "arxiv",
    "version": 1
  }
}