Pith Number

pith:4GFHPZV3

pith:2013:4GFHPZV3R2R4HD5YUD4D2GJUCR

not attested not anchored not stored refs pending

Moore-Penrose inverse and doubly commuting elements in $C^*$-algebras

Enrico Boasso

arxiv:1309.6911 v1 · 2013-09-26 · 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{4GFHPZV3R2R4HD5YUD4D2GJUCR}

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	2026-05-18T03:12:09.774499Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e18a77e6bb8ea3c38fb8a0f83d1934147bb8d86ddd1ebc34e7b8400066046655

Aliases

arxiv: 1309.6911 · arxiv_version: 1309.6911v1 · doi: 10.48550/arxiv.1309.6911 · pith_short_12: 4GFHPZV3R2R4 · pith_short_16: 4GFHPZV3R2R4HD5Y · pith_short_8: 4GFHPZV3

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/4GFHPZV3R2R4HD5YUD4D2GJUCR \
  | 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: e18a77e6bb8ea3c38fb8a0f83d1934147bb8d86ddd1ebc34e7b8400066046655

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "60c6a09af5d308f4d00e8cf9f4da11ca8f79fabba8e7c6fb10e29d7a581b6e54",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2013-09-26T14:17:45Z",
    "title_canon_sha256": "6e05c52dccf3931e8a5446e15d2cb9f049fb55cbbbb6c4a30e1130a4d7fe0539"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.6911",
    "kind": "arxiv",
    "version": 1
  }
}