Pith Number

pith:A5DZZANW

pith:2011:A5DZZANWJOLCFF3GCVEFWWHQFF

not attested not anchored not stored refs pending

On a Devil's staircase associated to the joint spectral radii of a family of pairs of matrices

Ian D. Morris, Nikita Sidorov

arxiv:1107.3506 v3 · 2011-07-18 · math.OC · cs.DM · math.DS · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{A5DZZANWJOLCFF3GCVEFWWHQFF}

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	2026-05-18T02:25:11.972792Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

07479c81b64b9622976615485b58f02979b03485bb8d0783549c2d24c5ef1b6b

Aliases

arxiv: 1107.3506 · arxiv_version: 1107.3506v3 · doi: 10.48550/arxiv.1107.3506 · pith_short_12: A5DZZANWJOLC · pith_short_16: A5DZZANWJOLCFF3G · pith_short_8: A5DZZANW

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/A5DZZANWJOLCFF3GCVEFWWHQFF \
  | 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: 07479c81b64b9622976615485b58f02979b03485bb8d0783549c2d24c5ef1b6b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "985eb84e028a1c0d56be9d85500b476192650968fac15d8faf3ef7b24af233ab",
    "cross_cats_sorted": [
      "cs.DM",
      "math.DS",
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2011-07-18T17:18:19Z",
    "title_canon_sha256": "628996c038617ac3f69d313309a91a1ad7b9933c6337f66a0fc2de93c6ee7b72"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.3506",
    "kind": "arxiv",
    "version": 3
  }
}