Pith Number

pith:A4QABK5V

pith:2026:A4QABK5V5ZU7JFN4EXND7IMCEP

not attested not anchored not stored refs pending

Asymptotic independence of class-group 4-ranks in correlated pairs of imaginary quadratic fields

Xiuwu Zhu, Yue Xu

arxiv:2608.00387 v1 · 2026-08-01 · 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{A4QABK5V5ZU7JFN4EXND7IMCEP}

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	2026-08-04T00:35:37.625023Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

072000abb5ee69f495bc25da3fa18223fc83e3954262ceaed51a76d3e3707837

Aliases

arxiv: 2608.00387 · arxiv_version: 2608.00387v1 · doi: 10.48550/arxiv.2608.00387 · pith_short_12: A4QABK5V5ZU7 · pith_short_16: A4QABK5V5ZU7JFN4 · pith_short_8: A4QABK5V

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/A4QABK5V5ZU7JFN4EXND7IMCEP \
  | 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: 072000abb5ee69f495bc25da3fa18223fc83e3954262ceaed51a76d3e3707837

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "489c7b9e09037ee67fef2a64aa0e071ec0b7f295512506b678fcf0b0a62c8d09",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-08-01T01:55:26Z",
    "title_canon_sha256": "6c0f68e9d88006af6fe8406447f8ef5b00e035ae44832a1440fe634d79f9962a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.00387",
    "kind": "arxiv",
    "version": 1
  }
}