Pith Number

pith:G4B4LP4S

pith:2018:G4B4LP4SUZLFVFD7JN4AJOU3FO

not attested not anchored not stored refs pending

Reducible and irreducible approximation of complex symmetric operators

Jiayin Zhao, Sen Zhu, Ting Liu

arxiv:1812.04733 v1 · 2018-12-11 · math.FA · math.OA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{G4B4LP4SUZLFVFD7JN4AJOU3FO}

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	2026-05-17T23:58:29.650011Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3703c5bf92a6565a947f4b7804ba9b2b9fc210d6b86ac2f9d6ff34ab9828a3fc

Aliases

arxiv: 1812.04733 · arxiv_version: 1812.04733v1 · doi: 10.48550/arxiv.1812.04733 · pith_short_12: G4B4LP4SUZLF · pith_short_16: G4B4LP4SUZLFVFD7 · pith_short_8: G4B4LP4S

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/G4B4LP4SUZLFVFD7JN4AJOU3FO \
  | 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: 3703c5bf92a6565a947f4b7804ba9b2b9fc210d6b86ac2f9d6ff34ab9828a3fc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fdeeeb8986888c3791cb9c88f8cd48c17a18b18f25f1c54d1417cf35613a9bf5",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2018-12-11T22:39:47Z",
    "title_canon_sha256": "1191a3bf422824a2570c1aad90270f2094631e45146b2b1a5b548038a5b32a45"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1812.04733",
    "kind": "arxiv",
    "version": 1
  }
}