Pith Number

pith:NQ3F5D7G

pith:2017:NQ3F5D7GRUWL3UAYEHQACO5E73

not attested not anchored not stored refs pending

$2^\infty$-Selmer groups, $2^\infty$-class groups, and Goldfeld's conjecture

Alexander Smith

arxiv:1702.02325 v2 · 2017-02-08 · 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{NQ3F5D7GRUWL3UAYEHQACO5E73}

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	2026-05-18T00:42:51.293222Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6c365e8fe68d2cbdd01821e0013ba4fec7d65311407692f42796650541696429

Aliases

arxiv: 1702.02325 · arxiv_version: 1702.02325v2 · doi: 10.48550/arxiv.1702.02325 · pith_short_12: NQ3F5D7GRUWL · pith_short_16: NQ3F5D7GRUWL3UAY · pith_short_8: NQ3F5D7G

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/NQ3F5D7GRUWL3UAYEHQACO5E73 \
  | 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: 6c365e8fe68d2cbdd01821e0013ba4fec7d65311407692f42796650541696429

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e5d6ae7f44df76dd7884b8b51a9c21035b80fca80596e0134b0f29d6cf20b07c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2017-02-08T08:42:41Z",
    "title_canon_sha256": "ddf6a2f02f15d957857b06cc516d5fba58e03714e2c8a88202fad06262fe6a57"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1702.02325",
    "kind": "arxiv",
    "version": 2
  }
}