Pith Number

pith:3GKAVNX7

pith:2025:3GKAVNX7Q7DKWRF5GSNEOTAEPI

not attested not anchored not stored refs pending

Spectral bundles on Abelian varieties, complex projective spaces and Grassmannians

Ching-Hao Chang, I-Hsun Tsai, Jih-Hsin Cheng

arxiv:2507.14458 v2 · 2025-07-19 · math.DG · math.CV

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3GKAVNX7Q7DKWRF5GSNEOTAEPI}

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	2026-06-19T16:12:14.256370Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d9940ab6ff87c6ab44bd349a474c047a2f307d8024e2da50d0cb532ec2075a0d

Aliases

arxiv: 2507.14458 · arxiv_version: 2507.14458v2 · doi: 10.48550/arxiv.2507.14458 · pith_short_12: 3GKAVNX7Q7DK · pith_short_16: 3GKAVNX7Q7DKWRF5 · pith_short_8: 3GKAVNX7

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/3GKAVNX7Q7DKWRF5GSNEOTAEPI \
  | 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: d9940ab6ff87c6ab44bd349a474c047a2f307d8024e2da50d0cb532ec2075a0d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ba311f06bba87fbb996edb5ed6c2837b21ecf41c06dd44e7d9ddb0eef5da2795",
    "cross_cats_sorted": [
      "math.CV"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2025-07-19T03:05:48Z",
    "title_canon_sha256": "fd26c4f60c3cc93b963776e79ba9c8d414ea2d6e812e3e933b0d9b8fa452b0f4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.14458",
    "kind": "arxiv",
    "version": 2
  }
}