Pith Number

pith:WZKSE4J4

pith:2017:WZKSE4J4XOKUF3ZEPYUZH22Z3X

not attested not anchored not stored refs pending

Congruence formulae for Legendre modular polynomials

Adel Betina, Emmanuel Lecouturier

arxiv:1704.06941 v1 · 2017-04-23 · math.NT · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WZKSE4J4XOKUF3ZEPYUZH22Z3X}

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	2026-05-18T00:45:55.262215Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b65522713cbb9542ef247e2993eb59ddf56e2185d8de6c8007d960e0e6306123

Aliases

arxiv: 1704.06941 · arxiv_version: 1704.06941v1 · doi: 10.48550/arxiv.1704.06941 · pith_short_12: WZKSE4J4XOKU · pith_short_16: WZKSE4J4XOKUF3ZE · pith_short_8: WZKSE4J4

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/WZKSE4J4XOKUF3ZEPYUZH22Z3X \
  | 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: b65522713cbb9542ef247e2993eb59ddf56e2185d8de6c8007d960e0e6306123

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "10189313a6afb2b5219c606dbe78f9489b0a399ad6511fced8f74487c6871dfe",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2017-04-23T15:37:33Z",
    "title_canon_sha256": "1922aa0bdb4d6bf2c830410f6bd7a9c239c1932d1712324f884184c51e077fd8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1704.06941",
    "kind": "arxiv",
    "version": 1
  }
}