Pith Number

pith:QVGK2ZDR

pith:2015:QVGK2ZDRA7EYVGMTEM6WUTSVVT

not attested not anchored not stored refs pending

Lyapunov-maximising measures for pairs of weighted shift operators

Ian D. Morris

arxiv:1510.00162 v1 · 2015-10-01 · math.DS · 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{QVGK2ZDRA7EYVGMTEM6WUTSVVT}

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	2026-05-18T01:31:20.563334Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

854cad647107c98a9993233d6a4e55acc1376ed63f6609ea2a9c773757062a2a

Aliases

arxiv: 1510.00162 · arxiv_version: 1510.00162v1 · doi: 10.48550/arxiv.1510.00162 · pith_short_12: QVGK2ZDRA7EY · pith_short_16: QVGK2ZDRA7EYVGMT · pith_short_8: QVGK2ZDR

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/QVGK2ZDRA7EYVGMTEM6WUTSVVT \
  | 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: 854cad647107c98a9993233d6a4e55acc1376ed63f6609ea2a9c773757062a2a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9e4ecb412b595726383f5d638fafba2be9c4213ed585be93bef787676b312ba0",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2015-10-01T09:41:05Z",
    "title_canon_sha256": "718b26f30d047b4ba714063e4234f361a5e274ac99c8a9c342f5e293c4beff9e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.00162",
    "kind": "arxiv",
    "version": 1
  }
}