Pith Number

pith:FXFSZ5CX

pith:2020:FXFSZ5CXPNFPCV4JHBAAF4EPLV

not attested not anchored not stored refs pending

The Hasse invariant of the Tate normal form $E_5$ and the class number of $\mathbb{Q}(\sqrt{-5l})$

Patrick Morton

arxiv:2002.04134 v4 · 2020-02-10 · 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{FXFSZ5CXPNFPCV4JHBAAF4EPLV}

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	2026-07-05T02:23:04.829422Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2dcb2cf4577b4af15789384002f08f5d56db0af654a39a8e40795f52dd791a44

Aliases

arxiv: 2002.04134 · arxiv_version: 2002.04134v4 · doi: 10.48550/arxiv.2002.04134 · pith_short_12: FXFSZ5CXPNFP · pith_short_16: FXFSZ5CXPNFPCV4J · pith_short_8: FXFSZ5CX

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/FXFSZ5CXPNFPCV4JHBAAF4EPLV \
  | 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: 2dcb2cf4577b4af15789384002f08f5d56db0af654a39a8e40795f52dd791a44

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a5049bda802f10aca934e6308d013e1d06001c1ced7c29f9805c48b653d223a5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2020-02-10T23:36:30Z",
    "title_canon_sha256": "d762b28b0c8ddf634e56c2dc27b4feaa23019cbf8c0efa307ef6bee88916f776"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2002.04134",
    "kind": "arxiv",
    "version": 4
  }
}