Pith Number

pith:NG4YRVSJ

pith:2009:NG4YRVSJGVOPOQFNIEODE5YEKB

not attested not anchored not stored refs pending

Spectra of Upper-triangular Operator Matrix

Wu Junde, Zhang Shifang, Zhong Huaijie

arxiv:0906.5055 v1 · 2009-06-27 · 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{NG4YRVSJGVOPOQFNIEODE5YEKB}

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	2026-05-18T00:31:05.863206Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

69b988d649355cf740ad411c3277045069a9cd3df1479d32729fefc075cdfc57

Aliases

arxiv: 0906.5055 · arxiv_version: 0906.5055v1 · doi: 10.48550/arxiv.0906.5055 · pith_short_12: NG4YRVSJGVOP · pith_short_16: NG4YRVSJGVOPOQFN · pith_short_8: NG4YRVSJ

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/NG4YRVSJGVOPOQFNIEODE5YEKB \
  | 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: 69b988d649355cf740ad411c3277045069a9cd3df1479d32729fefc075cdfc57

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "35ea410d232ebc91cf300c4dbd1b916550a5e25f2ec08e6e42f04e63d763360e",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/3.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2009-06-27T09:25:45Z",
    "title_canon_sha256": "2cbff2d83c30cec2a657acf63fe327c8f9b5ee90397e62295232f1bc5e35baf7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0906.5055",
    "kind": "arxiv",
    "version": 1
  }
}