Pith Number

pith:ZDRGNGKO

pith:2024:ZDRGNGKO7XWTOFLVCPSLAF5XHR

not attested not anchored not stored refs pending

Exceptional zeros for Heegner points and $p$-converse to the theorem of Gross-Zagier and Kolyvagin

Francesc Castella

arxiv:2409.01360 v1 · 2024-09-02 · 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{ZDRGNGKO7XWTOFLVCPSLAF5XHR}

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

A $p$-Converse theorem for Real Quadratic Fields

Receipt and verification

First computed	2026-07-05T09:02:28.173142Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c8e266994efded37157513e4b017b73c6b327aa890293709e5e7add4f20eeac5

Aliases

arxiv: 2409.01360 · arxiv_version: 2409.01360v1 · doi: 10.48550/arxiv.2409.01360 · pith_short_12: ZDRGNGKO7XWT · pith_short_16: ZDRGNGKO7XWTOFLV · pith_short_8: ZDRGNGKO

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/ZDRGNGKO7XWTOFLVCPSLAF5XHR \
  | 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: c8e266994efded37157513e4b017b73c6b327aa890293709e5e7add4f20eeac5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3259d93aed7380fdbf36ef9abba0b6a38a4df043febeb71b80647217b1512ebd",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2024-09-02T16:24:43Z",
    "title_canon_sha256": "2eae7af9c26b2ab708cc244e000406aaa04cef73cff152fbc5d3c4727b6e05b6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2409.01360",
    "kind": "arxiv",
    "version": 1
  }
}