Pith Number

pith:VNGLQ6VA

pith:2015:VNGLQ6VAX2KGWE3XCAQ6NHQQCE

not attested not anchored not stored refs pending

Free loci of matrix pencils and domains of noncommutative rational functions

Igor Klep, Jurij Vol\v{c}i\v{c}

arxiv:1512.02648 v4 · 2015-12-08 · math.RA · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VNGLQ6VAX2KGWE3XCAQ6NHQQCE}

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	2026-05-18T00:17:30.838686Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ab4cb87aa0be946b13771021e69e1011043fb82bfdfc45ec81fe6a79d84f64ef

Aliases

arxiv: 1512.02648 · arxiv_version: 1512.02648v4 · doi: 10.48550/arxiv.1512.02648 · pith_short_12: VNGLQ6VAX2KG · pith_short_16: VNGLQ6VAX2KGWE3X · pith_short_8: VNGLQ6VA

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/VNGLQ6VAX2KGWE3XCAQ6NHQQCE \
  | 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: ab4cb87aa0be946b13771021e69e1011043fb82bfdfc45ec81fe6a79d84f64ef

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "800fdc12a853a75718fc744479df11cde838357a2c92ae7f4f593dd76ca00b52",
    "cross_cats_sorted": [
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2015-12-08T21:00:11Z",
    "title_canon_sha256": "6d828177463bb42861b0126f795bd7703fbb54b50bb5d4044546d6bc5d8d43aa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.02648",
    "kind": "arxiv",
    "version": 4
  }
}