Pith Number

pith:SPHQU2W6

pith:2009:SPHQU2W63AGYMASHAJ7OSDUW2M

not attested not anchored not stored refs pending

A rapidly-converging lower bound for the joint spectral radius via multiplicative ergodic theory

Ian D. Morris

arxiv:0906.0260 v1 · 2009-06-01 · math.DS · cs.NA · 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{SPHQU2W63AGYMASHAJ7OSDUW2M}

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	2026-06-03T23:06:26.731550Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

93cf0a6aded80d860247027ee90e96d328454017b181f19e2d0eb9f19df94694

Aliases

arxiv: 0906.0260 · arxiv_version: 0906.0260v1 · doi: 10.48550/arxiv.0906.0260 · pith_short_12: SPHQU2W63AGY · pith_short_16: SPHQU2W63AGYMASH · pith_short_8: SPHQU2W6

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/SPHQU2W63AGYMASHAJ7OSDUW2M \
  | 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: 93cf0a6aded80d860247027ee90e96d328454017b181f19e2d0eb9f19df94694

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "63a106c94d5ccc7685c832bb14502484585f0d4b3e477bacd9af86e25c492579",
    "cross_cats_sorted": [
      "cs.NA",
      "math.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2009-06-01T11:01:24Z",
    "title_canon_sha256": "94c563b93c4157ee58463b3e7ba56aad3c50ce4431ec18f3f6db2cb381117aab"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0906.0260",
    "kind": "arxiv",
    "version": 1
  }
}