Pith Number

pith:NNZN7XKI

pith:2012:NNZN7XKI5X7WKUBHOOR2CUDLGV

not attested not anchored not stored refs pending

Unbounded subnormal weighted shifts on directed trees I

Il Bong Jung, Piotr Budzy\'nski, Zenon Jan Jab{\l}o\'nski

arxiv:1203.0140 v1 · 2012-03-01 · 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{NNZN7XKI5X7WKUBHOOR2CUDLGV}

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	2026-05-18T03:10:37.492220Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6b72dfdd48edff65502773a3a1506b3564788f211eba110231efda7f33006507

Aliases

arxiv: 1203.0140 · arxiv_version: 1203.0140v1 · doi: 10.48550/arxiv.1203.0140 · pith_short_12: NNZN7XKI5X7W · pith_short_16: NNZN7XKI5X7WKUBH · pith_short_8: NNZN7XKI

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/NNZN7XKI5X7WKUBHOOR2CUDLGV \
  | 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: 6b72dfdd48edff65502773a3a1506b3564788f211eba110231efda7f33006507

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bd1e2ec42f37701ee4c786a7a9073cdf83a530c51ddcb31063eec7a81c0f9aac",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-03-01T10:46:38Z",
    "title_canon_sha256": "81994fce71c6013049e85d4bff2eaf55983d28a8d04cb4036a3e504e8af090ec"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.0140",
    "kind": "arxiv",
    "version": 1
  }
}