Pith Number

pith:UYNUOWSX

pith:2022:UYNUOWSXH6U3W73TGPVL5VZWEZ

not attested not anchored not stored refs pending

On average sizes of Selmer groups and ranks in families of elliptic curves having marked points

Manjul Bhargava, Wei Ho

arxiv:2207.03309 v2 · 2022-07-07 · math.NT · math.AG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UYNUOWSXH6U3W73TGPVL5VZWEZ}

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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

2 papers in Pith

Tamagawa ratios and unbounded Selmer moments

Geometry-of-numbers methods over global fields II: Coregular representations

Receipt and verification

First computed	2026-07-05T04:40:28.221722Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a61b475a573fa9bb7f7333eabed7362668ebf2b7bd2ac74cac976f7fe93a08ba

Aliases

arxiv: 2207.03309 · arxiv_version: 2207.03309v2 · doi: 10.48550/arxiv.2207.03309 · pith_short_12: UYNUOWSXH6U3 · pith_short_16: UYNUOWSXH6U3W73T · pith_short_8: UYNUOWSX

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/UYNUOWSXH6U3W73TGPVL5VZWEZ \
  | 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: a61b475a573fa9bb7f7333eabed7362668ebf2b7bd2ac74cac976f7fe93a08ba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ea88a2fc9444b7a4d71e646cf7988631f08882a32163d07665489fd7bfc49926",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2022-07-07T14:14:02Z",
    "title_canon_sha256": "4f51c785e51a639c93d9139d5e2cd7650b366338bd4b78e955aa7ff9cd380dd8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2207.03309",
    "kind": "arxiv",
    "version": 2
  }
}