Pith Number

pith:NMY4DVTI

pith:2018:NMY4DVTIYMSFZ6MA7E3WWCQLLZ

not attested not anchored not stored refs pending

The parallel sum for adjointable operators on Hilbert $C^*$-modules

Chuanning Song, Qingxiang Xu, Wei Luo

arxiv:1806.04227 v3 · 2018-06-11 · math.OA · 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{NMY4DVTIYMSFZ6MA7E3WWCQLLZ}

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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	2026-05-18T00:10:51.689667Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6b31c1d668c3245cf980f9376b0a0b5e5c2d5fb130cb599d807c708a438da4ba

Aliases

arxiv: 1806.04227 · arxiv_version: 1806.04227v3 · doi: 10.48550/arxiv.1806.04227 · pith_short_12: NMY4DVTIYMSF · pith_short_16: NMY4DVTIYMSFZ6MA · pith_short_8: NMY4DVTI

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/NMY4DVTIYMSFZ6MA7E3WWCQLLZ \
  | 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: 6b31c1d668c3245cf980f9376b0a0b5e5c2d5fb130cb599d807c708a438da4ba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a7ffe711626dc71408a0cc90b6b682180414a14841e7cc2ac1f30feaed6e6d1b",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2018-06-11T20:28:21Z",
    "title_canon_sha256": "4797a3b94da7114374f4b52ca28f60479d02c5f211c7b44a51d49e966f4f931d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1806.04227",
    "kind": "arxiv",
    "version": 3
  }
}