Pith Number

pith:M5UMQQ6B

pith:2025:M5UMQQ6BTPXLDBUKYFG4R4EH3C

not attested not anchored not stored refs pending

Selmer ranks in twists of CM abelian varieties

Jie Shu

arxiv:2504.21274 v2 · 2025-04-30 · 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{M5UMQQ6BTPXLDBUKYFG4R4EH3C}

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.

Cited by

1 paper in Pith

Quadratic spaces and Selmer groups of abelian varieties with multiplication

Receipt and verification

First computed	2026-07-05T11:45:57.842860Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6768c843c19beeb1868ac14dc8f087d8b749e67db299e2cba6da8bb3fc72016d

Aliases

arxiv: 2504.21274 · arxiv_version: 2504.21274v2 · doi: 10.48550/arxiv.2504.21274 · pith_short_12: M5UMQQ6BTPXL · pith_short_16: M5UMQQ6BTPXLDBUK · pith_short_8: M5UMQQ6B

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/M5UMQQ6BTPXLDBUKYFG4R4EH3C \
  | 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: 6768c843c19beeb1868ac14dc8f087d8b749e67db299e2cba6da8bb3fc72016d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "71ac64cd56a58d2aa9f841bba78d50890c9264f7bc61c4d3ecd6202aafe6a369",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2025-04-30T03:06:56Z",
    "title_canon_sha256": "e672144828c36ab68c23319c46ca6963a2bbd61b07aa76f03d7b78007d62f814"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2504.21274",
    "kind": "arxiv",
    "version": 2
  }
}