Pith Number

pith:N4ZXKVIS

pith:2015:N4ZXKVISCI3ENMLQ4UEK2AR2LT

not attested not anchored not stored refs pending

Variational proof of the existence of eigenvalues for star graphs

Konstantin Pankrashkin

arxiv:1511.09227 v1 · 2015-11-30 · math-ph · math.MP · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{N4ZXKVISCI3ENMLQ4UEK2AR2LT}

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	2026-05-18T00:45:35.119661Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6f33755512123646b170e508ad023a5cf307062d9b91f19014f52915f1317012

Aliases

arxiv: 1511.09227 · arxiv_version: 1511.09227v1 · doi: 10.48550/arxiv.1511.09227 · pith_short_12: N4ZXKVISCI3E · pith_short_16: N4ZXKVISCI3ENMLQ · pith_short_8: N4ZXKVIS

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/N4ZXKVISCI3ENMLQ4UEK2AR2LT \
  | 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: 6f33755512123646b170e508ad023a5cf307062d9b91f19014f52915f1317012

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6eca26cbe0c503ce338fa2d1142585ed29f1b7ed556830786248df9a43b2d6ad",
    "cross_cats_sorted": [
      "math.MP",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2015-11-30T10:16:52Z",
    "title_canon_sha256": "aefe3c98065c1e462f95c0a8fd1b5e8290b1944fc350cd0cae061b2c679805a9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.09227",
    "kind": "arxiv",
    "version": 1
  }
}