Pith Number

pith:KNJUNMXJ

pith:2011:KNJUNMXJRGESQXMQP3U55PPEQI

not attested not anchored not stored refs pending

Normal extensions escape from the class of weighted shifts on directed trees

Il Bong Jung, Jan Stochel, Zenon Jan Jablonski

arxiv:1104.4428 v1 · 2011-04-22 · 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{KNJUNMXJRGESQXMQP3U55PPEQI}

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	2026-05-18T03:10:37.657365Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

535346b2e98989285d907ee9debde4821a2603ffa3c055fa326a6d94e87377c0

Aliases

arxiv: 1104.4428 · arxiv_version: 1104.4428v1 · doi: 10.48550/arxiv.1104.4428 · pith_short_12: KNJUNMXJRGES · pith_short_16: KNJUNMXJRGESQXMQ · pith_short_8: KNJUNMXJ

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/KNJUNMXJRGESQXMQP3U55PPEQI \
  | 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: 535346b2e98989285d907ee9debde4821a2603ffa3c055fa326a6d94e87377c0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d70bc321b890547c5f9f13fd61cb3d260619dd25eee7fa55c3b2e33c6438423a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2011-04-22T12:29:54Z",
    "title_canon_sha256": "6bcb26e45001427d2186733bdeb6e8cd05f369dae7d1a61edbf42645f2d8f262"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.4428",
    "kind": "arxiv",
    "version": 1
  }
}