Pith Number

pith:6CYSYGV7

pith:2003:6CYSYGV72TBNKPNFNMMRXOV7SM

not attested not anchored not stored refs pending

Applications of the Wold decomposition to the study of row contractions associated with directed graphs

David W. Kribs, Elias Katsoulis

arxiv:math/0311178 v2 · 2003-11-12 · math.OA · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6CYSYGV72TBNKPNFNMMRXOV7SM}

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	2026-07-04T14:50:34.491545Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f0b12c1abfd4c2d53da56b191bbabf933bf9c0c0d32d9f9ed00169022247a8e7

Aliases

arxiv: math/0311178 · arxiv_version: math/0311178v2 · doi: 10.48550/arxiv.math/0311178 · pith_short_12: 6CYSYGV72TBN · pith_short_16: 6CYSYGV72TBNKPNF · pith_short_8: 6CYSYGV7

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/6CYSYGV72TBNKPNFNMMRXOV7SM \
  | 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: f0b12c1abfd4c2d53da56b191bbabf933bf9c0c0d32d9f9ed00169022247a8e7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "334e236fcf471a9d65c5ff01d56e50244aa524422c754961fb773c5ec8f8d67d",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "",
    "primary_cat": "math.OA",
    "submitted_at": "2003-11-12T00:38:25Z",
    "title_canon_sha256": "c2d8b94d2bbfac4acbb121b91aa83b83278870f3c4e8a543ce1868924fc73d6f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0311178",
    "kind": "arxiv",
    "version": 2
  }
}