Pith Number

pith:YE64UVUR

pith:2019:YE64UVURHHCQBXTNQEBDEZQ5K4

not attested not anchored not stored refs pending

Divisibility of Selmer groups and class groups

Azizul Hoque, Kalyan Banerjee, Kalyan Chakraborty

arxiv:1912.02420 v1 · 2019-12-05 · math.AG · math.KT · 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{YE64UVURHHCQBXTNQEBDEZQ5K4}

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	2026-07-05T00:24:13.486044Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c13dca569139c500de6d810232661d57181c2fe35f6eec55b25b6c56130dc2ec

Aliases

arxiv: 1912.02420 · arxiv_version: 1912.02420v1 · doi: 10.48550/arxiv.1912.02420 · pith_short_12: YE64UVURHHCQ · pith_short_16: YE64UVURHHCQBXTN · pith_short_8: YE64UVUR

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/YE64UVURHHCQBXTNQEBDEZQ5K4 \
  | 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: c13dca569139c500de6d810232661d57181c2fe35f6eec55b25b6c56130dc2ec

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ec62a9c9ce22c8c2ca699bdc10f54907802ffdd433acefd74e06caf728722dd7",
    "cross_cats_sorted": [
      "math.KT",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2019-12-05T07:47:49Z",
    "title_canon_sha256": "a36f0f9e3d5bd8667e08e68be1b96d051045ede31aa8374f2199db1ba1dabea5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1912.02420",
    "kind": "arxiv",
    "version": 1
  }
}