Pith Number

pith:7B2RQZBH

pith:2020:7B2RQZBH3C5YISMD77OCR2I76F

not attested not anchored not stored refs pending

On Greenberg's generalized conjecture for imaginary quartic fields

Naoya Takahashi

arxiv:2001.11768 v1 · 2020-01-31 · 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{7B2RQZBH3C5YISMD77OCR2I76F}

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

On the $\mathbb{Z}_p$-extensions of a totally $p$-adic imaginary quadratic field -- With an appendix by Jean-Fran\c{c}ois Jaulent

Receipt and verification

First computed	2026-07-05T00:37:33.714389Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f875186427d8bb844983ffdc28e91ff1468a50c1e121c8141aa78e2b86915234

Aliases

arxiv: 2001.11768 · arxiv_version: 2001.11768v1 · doi: 10.48550/arxiv.2001.11768 · pith_short_12: 7B2RQZBH3C5Y · pith_short_16: 7B2RQZBH3C5YISMD · pith_short_8: 7B2RQZBH

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/7B2RQZBH3C5YISMD77OCR2I76F \
  | 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: f875186427d8bb844983ffdc28e91ff1468a50c1e121c8141aa78e2b86915234

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "73f923cec31ba76614b97da920bae2ffb216acb9cafb6fbb67dbdeefca083cb6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2020-01-31T11:03:29Z",
    "title_canon_sha256": "ee2bcf55e01e0715a25aea837bae8d34a84ae14d60581682431c590bae27df2d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2001.11768",
    "kind": "arxiv",
    "version": 1
  }
}