Pith Number

pith:J6IBEQUL

pith:2010:J6IBEQULKPCAPAHSK5YIDJVNNC

not attested not anchored not stored refs pending

On rings of integers generated by their units

Christopher Frei

arxiv:1009.0447 v3 · 2010-09-02 · 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{J6IBEQULKPCAPAHSK5YIDJVNNC}

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	2026-05-18T03:58:51.733671Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4f9012428b53c40780f2577081a6ad689845b581ef9f817859804234c3b4639a

Aliases

arxiv: 1009.0447 · arxiv_version: 1009.0447v3 · doi: 10.48550/arxiv.1009.0447 · pith_short_12: J6IBEQULKPCA · pith_short_16: J6IBEQULKPCAPAHS · pith_short_8: J6IBEQUL

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/J6IBEQULKPCAPAHSK5YIDJVNNC \
  | 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: 4f9012428b53c40780f2577081a6ad689845b581ef9f817859804234c3b4639a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a50eeefbdf43361ec5f8bd024ac7b2e2e850b37cbdd6a6af3a5e4f8fdbf36e36",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2010-09-02T15:11:46Z",
    "title_canon_sha256": "13a86159b1322441bb56c622d501880fa06bcebf82f1b47cdf4251baf50a4ce3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.0447",
    "kind": "arxiv",
    "version": 3
  }
}