Pith Number

pith:WVYIAH45

pith:2012:WVYIAH45WL4OY7ADECI54TPCDF

not attested not anchored not stored refs pending

Irreducible Semigroups of Positive Operators on Banach Lattices

Niushan Gao, Vladimir G. Troitsky

arxiv:1208.3498 v1 · 2012-08-16 · 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{WVYIAH45WL4OY7ADECI54TPCDF}

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	2026-05-18T03:48:35.054760Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b570801f9db2f8ec7c032091de4de21940af116f20e1f5b8298946b50cb96f82

Aliases

arxiv: 1208.3498 · arxiv_version: 1208.3498v1 · doi: 10.48550/arxiv.1208.3498 · pith_short_12: WVYIAH45WL4O · pith_short_16: WVYIAH45WL4OY7AD · pith_short_8: WVYIAH45

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/WVYIAH45WL4OY7ADECI54TPCDF \
  | 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: b570801f9db2f8ec7c032091de4de21940af116f20e1f5b8298946b50cb96f82

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0d09145c9e975ab777874c6f7b3b353a626691768f9578ab5d7a3dbcdca750bd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-08-16T21:31:09Z",
    "title_canon_sha256": "9b041397d91b9f19d75b013cff8f20699f1dc77a26178eacacb20c48cf314192"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.3498",
    "kind": "arxiv",
    "version": 1
  }
}