Pith Number

pith:SGQZ7ND5

pith:2026:SGQZ7ND52GPNO2GB2FAT6PAQAL

not attested not anchored not stored refs pending

Modular abelian surfaces of small conductor with nontrivial Tate--Shafarevich groups

Dylan Laird, Sam Frengley

arxiv:2602.19813 v2 · 2026-02-23 · 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{SGQZ7ND52GPNO2GB2FAT6PAQAL}

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	2026-07-24T01:23:05.800176Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

91a19fb47dd19ed768c1d1413f3c1002c4003962e56544e0ee88113d42a0afd3

Aliases

arxiv: 2602.19813 · arxiv_version: 2602.19813v2 · doi: 10.48550/arxiv.2602.19813 · pith_short_12: SGQZ7ND52GPN · pith_short_16: SGQZ7ND52GPNO2GB · pith_short_8: SGQZ7ND5

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/SGQZ7ND52GPNO2GB2FAT6PAQAL \
  | 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: 91a19fb47dd19ed768c1d1413f3c1002c4003962e56544e0ee88113d42a0afd3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fbe0e4b32ef4c1107db724cf5e863fe99a1d1ab65fd58bc7ca1815aacdd96492",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-02-23T13:13:12Z",
    "title_canon_sha256": "347b376fc9da692e11c838571c040bd764f5d932b342b6913d66886f5e5b36f2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2602.19813",
    "kind": "arxiv",
    "version": 2
  }
}