Pith Number

pith:BJKZ3HYP

pith:2016:BJKZ3HYPZLF6Q2JDPS7JNFTFZP

not attested not anchored not stored refs pending

Commutativity of normal compact operator via projective spectrum

Penghui Wang, Tong Mao, Yikun Qiao

arxiv:1609.07258 v3 · 2016-09-23 · 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{BJKZ3HYPZLF6Q2JDPS7JNFTFZP}

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	2026-05-18T00:45:22.317276Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0a559d9f0fcacbe869237cbe969665cbd3db71700d8888f974a8d21b512cc46f

Aliases

arxiv: 1609.07258 · arxiv_version: 1609.07258v3 · doi: 10.48550/arxiv.1609.07258 · pith_short_12: BJKZ3HYPZLF6 · pith_short_16: BJKZ3HYPZLF6Q2JD · pith_short_8: BJKZ3HYP

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/BJKZ3HYPZLF6Q2JDPS7JNFTFZP \
  | 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: 0a559d9f0fcacbe869237cbe969665cbd3db71700d8888f974a8d21b512cc46f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e03cab33d5387530b1c4dada7c59efb1646376259b8a7b8828dbccad9dc7021d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2016-09-23T07:40:17Z",
    "title_canon_sha256": "b6a688cdc3bd6b40d0a15e6747ef74cc818e01323a1e8805540a3fb0095c4964"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.07258",
    "kind": "arxiv",
    "version": 3
  }
}