Pith Number

pith:ZS2WXCLE

pith:2024:ZS2WXCLELIVTOSFPWM3PKX6DPK

not attested not anchored not stored refs pending

Iwasawa theory and ranks of elliptic curves in quadratic twist families

Anwesh Ray, Jeffrey Hatley

arxiv:2412.07308 v2 · 2024-12-10 · 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{ZS2WXCLELIVTOSFPWM3PKX6DPK}

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

Iwasawa invariants of sharp/flat $2$-adic $L$-functions for quadratic twists of elliptic curves

Receipt and verification

First computed	2026-07-05T09:48:17.876673Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ccb56b89645a2b3748afb336f55fc37abb26842cca8bf3a5ed609477cd600bab

Aliases

arxiv: 2412.07308 · arxiv_version: 2412.07308v2 · doi: 10.48550/arxiv.2412.07308 · pith_short_12: ZS2WXCLELIVT · pith_short_16: ZS2WXCLELIVTOSFP · pith_short_8: ZS2WXCLE

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/ZS2WXCLELIVTOSFPWM3PKX6DPK \
  | 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: ccb56b89645a2b3748afb336f55fc37abb26842cca8bf3a5ed609477cd600bab

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0fe05d1b49b5fa683867c0163993e395b180586c1ef21f17b9a2d1f62aa5d452",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2024-12-10T08:44:19Z",
    "title_canon_sha256": "fdb7f3585de2f2ded752a766c6bbf618d58d6163006975e9e8213bb3a3674f7b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.07308",
    "kind": "arxiv",
    "version": 2
  }
}