Pith Number

pith:P5FZ5L56

pith:2015:P5FZ5L56XANSQA6U6NBUGORNTY

not attested not anchored not stored refs pending

On the Maximal Error of Spectral Approximation of Graph Bisection

John C. Urschel, Ludmil T. Zikatanov

arxiv:1512.06325 v1 · 2015-12-20 · math.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{P5FZ5L56XANSQA6U6NBUGORNTY}

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	2026-05-18T01:24:00.833883Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7f4b9eafbeb81b2803d4f343433a2d9e0ea4b87e7c4b1b68a6584fc583e4825c

Aliases

arxiv: 1512.06325 · arxiv_version: 1512.06325v1 · doi: 10.48550/arxiv.1512.06325 · pith_short_12: P5FZ5L56XANS · pith_short_16: P5FZ5L56XANSQA6U · pith_short_8: P5FZ5L56

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/P5FZ5L56XANSQA6U6NBUGORNTY \
  | 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: 7f4b9eafbeb81b2803d4f343433a2d9e0ea4b87e7c4b1b68a6584fc583e4825c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ee45907fc8800ef138e4ee9e2afbd8c7ae8421456a8c0940031791319bc2e852",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2015-12-20T06:04:48Z",
    "title_canon_sha256": "2059e6a9c374c4c7f7d19c8662001d9870ebdaa49333f096ba87c9d034787022"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.06325",
    "kind": "arxiv",
    "version": 1
  }
}