Pith Number

pith:GYBJISE7

pith:2019:GYBJISE7HTSSW2KRMJM3HAYSIF

not attested not anchored not stored refs pending

Quadratic points on modular curves with infinite Mordell--Weil group

Josha Box

arxiv:1906.05206 v3 · 2019-06-12 · 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{GYBJISE7HTSSW2KRMJM3HAYSIF}

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.

Cited by

1 paper in Pith

The rational cuspidal divisor class group of $X_0(N)$

Receipt and verification

First computed	2026-07-05T00:37:45.512550Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

360294489f3ce52b69516259b383124160d908c49a1bb2568a1113e01b00b5f2

Aliases

arxiv: 1906.05206 · arxiv_version: 1906.05206v3 · doi: 10.48550/arxiv.1906.05206 · pith_short_12: GYBJISE7HTSS · pith_short_16: GYBJISE7HTSSW2KR · pith_short_8: GYBJISE7

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/GYBJISE7HTSSW2KRMJM3HAYSIF \
  | 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: 360294489f3ce52b69516259b383124160d908c49a1bb2568a1113e01b00b5f2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6d84a42766e47c2e99ac145b27d08ecee26c7c1f1ff8054f0b56eefbf4676b49",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2019-06-12T15:22:30Z",
    "title_canon_sha256": "cf3f6552f731c7506e544e91cde031354aaad623dfd6c2d21f14ed23264418c8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1906.05206",
    "kind": "arxiv",
    "version": 3
  }
}