Pith Number

pith:AM5KWRHB

pith:2026:AM5KWRHBFOS2ACL5UXXS55O3LX

not attested not anchored not stored refs pending

Degree Majorization and Laplacian Eigenvalue Sums for Simplicial Complexes

Huan-Zhi Zhang, Yi-Min Song, Yi-Zheng Fan

arxiv:2607.20910 v1 · 2026-07-23 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AM5KWRHBFOS2ACL5UXXS55O3LX}

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	2026-07-24T01:23:40.042161Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

033aab44e12ba5a0097da5ef2ef5db5dc2b5578d45adb0706d853ee8756ed560

Aliases

arxiv: 2607.20910 · arxiv_version: 2607.20910v1 · doi: 10.48550/arxiv.2607.20910 · pith_short_12: AM5KWRHBFOS2 · pith_short_16: AM5KWRHBFOS2ACL5 · pith_short_8: AM5KWRHB

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/AM5KWRHBFOS2ACL5UXXS55O3LX \
  | 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: 033aab44e12ba5a0097da5ef2ef5db5dc2b5578d45adb0706d853ee8756ed560

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d97a4b35f11312a9441e548ef981b3e7f521f09d4f95868d551268dea743a2fb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-07-23T04:20:41Z",
    "title_canon_sha256": "8675315a0a74e05ad4546ecad985fe1f9e957f3fa57af447d0f9463cc0ee4b4e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.20910",
    "kind": "arxiv",
    "version": 1
  }
}