Pith Number

pith:N3HQWNEU

pith:2026:N3HQWNEU6POODZ33WLCOYJ6HGU

not attested not anchored not stored refs pending

Generalized Nordhaus--Gaddum Inequalities for Eigenvalues

Aiden Williams, Carter Antley, George Brooks, Ian Gonzalez, Joseph Aulenbacher, Linyuan Lu, Luke Hawranick, Sahil Agarwal, William Linz

arxiv:2607.15941 v1 · 2026-07-17 · 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{N3HQWNEU6POODZ33WLCOYJ6HGU}

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	2026-07-20T01:19:18.731933Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6ecf0b3494f3dce1e77bb2c4ec27c735356ab6250b3ee43d9681f08caaf1c1d3

Aliases

arxiv: 2607.15941 · arxiv_version: 2607.15941v1 · doi: 10.48550/arxiv.2607.15941 · pith_short_12: N3HQWNEU6POO · pith_short_16: N3HQWNEU6POODZ33 · pith_short_8: N3HQWNEU

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/N3HQWNEU6POODZ33WLCOYJ6HGU \
  | 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: 6ecf0b3494f3dce1e77bb2c4ec27c735356ab6250b3ee43d9681f08caaf1c1d3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4b58591bbc827c4ebed76f9465262193043496b403a8393887ae7cbcb4c8cec2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-07-17T13:24:33Z",
    "title_canon_sha256": "e46e61d9c44b793e125f4395ae6f4a7a45eda8236e5cf953b8bbe00fa4d42659"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.15941",
    "kind": "arxiv",
    "version": 1
  }
}