Pith Number

pith:N3WI7QWJ

pith:2012:N3WI7QWJ4JSZUQ25BRLEHAQJB7

not attested not anchored not stored refs pending

The graphic nature of Gaussian periods

Bob Lutz, Stephan Ramon Garcia, William Duke

arxiv:1212.6825 v5 · 2012-12-31 · 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{N3WI7QWJ4JSZUQ25BRLEHAQJB7}

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	2026-05-18T02:54:21.629084Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6eec8fc2c9e2659a435d0c564382090fd37d8203b912449235f1102e443d6813

Aliases

arxiv: 1212.6825 · arxiv_version: 1212.6825v5 · doi: 10.48550/arxiv.1212.6825 · pith_short_12: N3WI7QWJ4JSZ · pith_short_16: N3WI7QWJ4JSZUQ25 · pith_short_8: N3WI7QWJ

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/N3WI7QWJ4JSZUQ25BRLEHAQJB7 \
  | 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: 6eec8fc2c9e2659a435d0c564382090fd37d8203b912449235f1102e443d6813

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aac8ec3fc47000106b07432b07cdda44f7c317f3d7d4591e88a582dddc252902",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-12-31T06:19:19Z",
    "title_canon_sha256": "2314b38b90b632b52cf57f8236c3e8af1acf3064faa41bd0abd258bf99cc7930"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.6825",
    "kind": "arxiv",
    "version": 5
  }
}