Pith Number

pith:N6YVHBEJ

pith:2021:N6YVHBEJCYY7EZHNTF2PMR3HJC

not attested not anchored not stored refs pending

The second moment of the size of the $2$-Selmer group of elliptic curves

Arul Shankar, Ashvin Swaminathan, Manjul Bhargava

arxiv:2110.09063 v1 · 2021-10-18 · 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{N6YVHBEJCYY7EZHNTF2PMR3HJC}

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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

Tamagawa ratios and unbounded Selmer moments

Receipt and verification

First computed	2026-07-05T03:23:23.716246Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6fb15384891631f264ed9974f64767488f70e4fa849ac13c78532a7f59f05852

Aliases

arxiv: 2110.09063 · arxiv_version: 2110.09063v1 · doi: 10.48550/arxiv.2110.09063 · pith_short_12: N6YVHBEJCYY7 · pith_short_16: N6YVHBEJCYY7EZHN · pith_short_8: N6YVHBEJ

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/N6YVHBEJCYY7EZHNTF2PMR3HJC \
  | 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: 6fb15384891631f264ed9974f64767488f70e4fa849ac13c78532a7f59f05852

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7cbd26479cd065d4dfc7bcc8e77e2d47e30a54d745e17b009ad4c418fb4916d7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2021-10-18T07:11:58Z",
    "title_canon_sha256": "7bcebb600928eaeac596c55e5fdffba7400c3433db75c924a7d052b127735df6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2110.09063",
    "kind": "arxiv",
    "version": 1
  }
}