Pith Number

pith:7X6MFE7F

pith:2013:7X6MFE7F4TXYBWLIO7HMIVTGLG

not attested not anchored not stored refs pending

On the Ordering of Spectral Radius Product r(A) r(AD) Versus r(A^2 D) and Related Applications

Lee Altenberg

arxiv:1301.4969 v3 · 2013-01-21 · math.SP · q-bio.PE

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7X6MFE7F4TXYBWLIO7HMIVTGLG}

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	2026-05-18T03:27:34.151690Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fdfcc293e5e4ef80d96877cec456665991f3d9f30839e1a3d79a9bb69527b141

Aliases

arxiv: 1301.4969 · arxiv_version: 1301.4969v3 · doi: 10.48550/arxiv.1301.4969 · pith_short_12: 7X6MFE7F4TXY · pith_short_16: 7X6MFE7F4TXYBWLI · pith_short_8: 7X6MFE7F

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/7X6MFE7F4TXYBWLIO7HMIVTGLG \
  | 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: fdfcc293e5e4ef80d96877cec456665991f3d9f30839e1a3d79a9bb69527b141

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4cbea2e3cac03706dbd3c0503e75d3544035821085ebe9da482d47627b709ed4",
    "cross_cats_sorted": [
      "q-bio.PE"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2013-01-21T19:24:42Z",
    "title_canon_sha256": "c638e4d899d9b8747ae931afc9d2a76972be682e091a85d8a08e4a5cac720a3c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.4969",
    "kind": "arxiv",
    "version": 3
  }
}