Pith Number

pith:PBCNIIFV

pith:2005:PBCNIIFVLDM7SWMH7NHQUKPVYZ

not attested not anchored not stored refs pending

The Grone Merris Conjecture and a quadratic eigenvalue problem

Nets Hawk Katz

arxiv:math/0512647 v1 · 2005-12-29 · math.CA · 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{PBCNIIFVLDM7SWMH7NHQUKPVYZ}

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

Sums of Laplacian eigenvalues and sums of degrees

Receipt and verification

First computed	2026-07-04T14:52:18.289463Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7844d420b558d9f95987fb4f0a29f5c66422334f8dea457aa648cd4e16a36809

Aliases

arxiv: math/0512647 · arxiv_version: math/0512647v1 · doi: 10.48550/arxiv.math/0512647 · pith_short_12: PBCNIIFVLDM7 · pith_short_16: PBCNIIFVLDM7SWMH · pith_short_8: PBCNIIFV

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/PBCNIIFVLDM7SWMH7NHQUKPVYZ \
  | 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: 7844d420b558d9f95987fb4f0a29f5c66422334f8dea457aa648cd4e16a36809

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fc80f28b665db1d523e33552b90d1d7b9454a08eb82485c3c51d3507fcbc3968",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "",
    "primary_cat": "math.CA",
    "submitted_at": "2005-12-29T21:16:25Z",
    "title_canon_sha256": "071b2a415d6df1939b6e5047a17802d526a2da5ce1aa3be4d365874e15ba974e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0512647",
    "kind": "arxiv",
    "version": 1
  }
}