Pith Number

pith:PNK3KWPQ

pith:2017:PNK3KWPQFHRFRLOFUTXZQWYVLI

not attested not anchored not stored refs pending

Horizontal variation of Tate--Shafarevich groups

Ashay A. Burungale, Haruzo Hida, Ye Tian

arxiv:1712.02148 v2 · 2017-12-06 · 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{PNK3KWPQFHRFRLOFUTXZQWYVLI}

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	2026-05-18T00:26:59.949384Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7b55b559f029e258adc5a4ef985b155a14a020482286040445a11ac42e237588

Aliases

arxiv: 1712.02148 · arxiv_version: 1712.02148v2 · doi: 10.48550/arxiv.1712.02148 · pith_short_12: PNK3KWPQFHRF · pith_short_16: PNK3KWPQFHRFRLOF · pith_short_8: PNK3KWPQ

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/PNK3KWPQFHRFRLOFUTXZQWYVLI \
  | 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: 7b55b559f029e258adc5a4ef985b155a14a020482286040445a11ac42e237588

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "97ea1d1f4655564051b7db34cdd611b92d194c2181ee515a3df8dddb624e912e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2017-12-06T12:04:10Z",
    "title_canon_sha256": "b704efb21ae66045c0f2837c80c9b558e21a1bead6ae39f398045b0ee9da52b7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1712.02148",
    "kind": "arxiv",
    "version": 2
  }
}