Pith Number

pith:XJI2XHQO

pith:2012:XJI2XHQOSXSQHNSPG2I3NZXXCU

not attested not anchored not stored refs pending

Statistics of Different Reduction Types of Fermat Curves

David Harvey, Igor Shparlinski

arxiv:1212.0915 v1 · 2012-12-05 · 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{XJI2XHQOSXSQHNSPG2I3NZXXCU}

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	2026-05-18T03:39:06.973541Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ba51ab9e0e95e503b64f3691b6e6f7152c9c8db348bd470aa33f0aca2a7129d4

Aliases

arxiv: 1212.0915 · arxiv_version: 1212.0915v1 · doi: 10.48550/arxiv.1212.0915 · pith_short_12: XJI2XHQOSXSQ · pith_short_16: XJI2XHQOSXSQHNSP · pith_short_8: XJI2XHQO

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/XJI2XHQOSXSQHNSPG2I3NZXXCU \
  | 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: ba51ab9e0e95e503b64f3691b6e6f7152c9c8db348bd470aa33f0aca2a7129d4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "13edc795b8ae272a080b743e46bcb371f60e2a1c3fd26eac53de59726678a461",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-12-05T01:58:41Z",
    "title_canon_sha256": "b9791687ebd9c03af6cb644c5823efaf79c8ae85a2a8e1c10995950ea4dd7a7c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.0915",
    "kind": "arxiv",
    "version": 1
  }
}