Pith Number

pith:EN2B5TSZ

pith:2025:EN2B5TSZQF4DVII2ZXGPERIFTO

not attested not anchored not stored refs pending

Strengthened upper bound on the third eigenvalue of graphs

Sida Li

arxiv:2501.07494 v1 · 2025-01-13 · 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{EN2B5TSZQF4DVII2ZXGPERIFTO}

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

Graph Eigenvalues and Projection Constants

Receipt and verification

First computed	2026-07-05T10:00:29.327132Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

23741ece5981783aa11acdccf245059ba1f19c75eee37fdc51c60ffbaf682a60

Aliases

arxiv: 2501.07494 · arxiv_version: 2501.07494v1 · doi: 10.48550/arxiv.2501.07494 · pith_short_12: EN2B5TSZQF4D · pith_short_16: EN2B5TSZQF4DVII2 · pith_short_8: EN2B5TSZ

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/EN2B5TSZQF4DVII2ZXGPERIFTO \
  | 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: 23741ece5981783aa11acdccf245059ba1f19c75eee37fdc51c60ffbaf682a60

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d09fa637ff22e4cde8b4d8c6943ba74a8b11f11b1c249e82754e0375e231a444",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-01-13T17:12:57Z",
    "title_canon_sha256": "e01e6cc97ac45549d27364d98aa7f0d0897096c9c553dc2326036566408a4d91"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2501.07494",
    "kind": "arxiv",
    "version": 1
  }
}