Pith Number

pith:YIDXCUAP

pith:2007:YIDXCUAPIBZ5CLNGMR63CVP75T

not attested not anchored not stored refs pending

Covers of the integers with odd moduli and their applications to the forms $x^m-2^n$ and $x^2-F_{3n}/2$

Ke-Jian Wu, Zhi-Wei Sun

arxiv:math/0702382 v5 · 2007-02-13 · math.NT · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YIDXCUAPIBZ5CLNGMR63CVP75T}

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	2026-07-04T15:32:46.467006Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c20771500f4073d12da6647db155ffecce3efe3fae22de9d7692b335a39b830a

Aliases

arxiv: math/0702382 · arxiv_version: math/0702382v5 · doi: 10.48550/arxiv.math/0702382 · pith_short_12: YIDXCUAPIBZ5 · pith_short_16: YIDXCUAPIBZ5CLNG · pith_short_8: YIDXCUAP

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/YIDXCUAPIBZ5CLNGMR63CVP75T \
  | 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: c20771500f4073d12da6647db155ffecce3efe3fae22de9d7692b335a39b830a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6c2e617a3d0d9d9fd8ef62a32f9a0e4991168636cbd65e5f19795b2c0f1ddb83",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2007-02-13T17:34:18Z",
    "title_canon_sha256": "b4a3deef17835a379be0d1734d1a2116f5f3b173f9a37ced2b6ebf3e8efb3cbf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0702382",
    "kind": "arxiv",
    "version": 5
  }
}