Pith Number

pith:YF32Z3GH

pith:2024:YF32Z3GHVUJDDPGV364662JJDL

not attested not anchored not stored refs pending

On $\mu$-invariants and isogenies for abelian varieties over function fields

Jishnu Ray, Sohan Ghosh, Takashi Suzuki

arxiv:2407.21431 v3 · 2024-07-31 · 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{YF32Z3GHVUJDDPGV364662JJDL}

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	2026-06-03T01:05:43.001727Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c177acecc7ad1231bcd5dfb9ef69291ad5e5c7cc695052bfe81fe18eab83a72b

Aliases

arxiv: 2407.21431 · arxiv_version: 2407.21431v3 · doi: 10.48550/arxiv.2407.21431 · pith_short_12: YF32Z3GHVUJD · pith_short_16: YF32Z3GHVUJDDPGV · pith_short_8: YF32Z3GH

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/YF32Z3GHVUJDDPGV364662JJDL \
  | 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: c177acecc7ad1231bcd5dfb9ef69291ad5e5c7cc695052bfe81fe18eab83a72b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9110d0d9d5cf4d39433c341dcf6bb0040ef66837d04db9ab54e306584f943cd5",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2024-07-31T08:33:25Z",
    "title_canon_sha256": "679786bd31e94be5507e36b833426df0781977a6ac60e1684257b9e90f1ccd33"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2407.21431",
    "kind": "arxiv",
    "version": 3
  }
}