Pith Number

pith:Y756JH5B

pith:2024:Y756JH5BV2M44MYWMYXFWYVH4M

not attested not anchored not stored refs pending

The Rank of the Normal Functions of the Ceresa and Gross--Schoen Cycles

Richard Hain

arxiv:2408.07809 v4 · 2024-08-14 · 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{Y756JH5BV2M44MYWMYXFWYVH4M}

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

What makes an algebraic curve special?

Receipt and verification

First computed	2026-07-05T11:41:19.058775Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c7fbe49fa1ae99ce3316662e5b62a7e319f9dcf2192c850f9da7144670fd800f

Aliases

arxiv: 2408.07809 · arxiv_version: 2408.07809v4 · doi: 10.48550/arxiv.2408.07809 · pith_short_12: Y756JH5BV2M4 · pith_short_16: Y756JH5BV2M44MYW · pith_short_8: Y756JH5B

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/Y756JH5BV2M44MYWMYXFWYVH4M \
  | 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: c7fbe49fa1ae99ce3316662e5b62a7e319f9dcf2192c850f9da7144670fd800f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9fcb885224716ef0bb80da3bae47195d78896478c3dfa0905f44735ec2d11d2a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2024-08-14T20:40:01Z",
    "title_canon_sha256": "ff1043d2a9fbcdfe55958dce2cd85bb132e8621abffe503700fd3fdc96845b9f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2408.07809",
    "kind": "arxiv",
    "version": 4
  }
}