Pith Number

pith:PJ4IBWBU

pith:2015:PJ4IBWBUDZ54DP7ZJR3MNA6SFD

not attested not anchored not stored refs pending

Reducibility of invertible tuples to the principal component in commutative Banach algebras

Raymond Mortini, Rudolf Rupp

arxiv:1511.04568 v1 · 2015-11-14 · 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{PJ4IBWBUDZ54DP7ZJR3MNA6SFD}

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	2026-05-18T01:02:45.494691Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7a7880d8341e7bc1bff94c76c683d228e9b75cc6f609b4d8cd67ffcaacc3fc66

Aliases

arxiv: 1511.04568 · arxiv_version: 1511.04568v1 · doi: 10.48550/arxiv.1511.04568 · pith_short_12: PJ4IBWBUDZ54 · pith_short_16: PJ4IBWBUDZ54DP7Z · pith_short_8: PJ4IBWBU

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/PJ4IBWBUDZ54DP7ZJR3MNA6SFD \
  | 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: 7a7880d8341e7bc1bff94c76c683d228e9b75cc6f609b4d8cd67ffcaacc3fc66

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "329d4bf6c34d69d94370f89531879f0dab7cde44b077a933a9706470cd25f593",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2015-11-14T15:11:21Z",
    "title_canon_sha256": "b96f1392f3a789adb2704abe94ca3c9ddd95205a635f00ea83f54ab5d913e95c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.04568",
    "kind": "arxiv",
    "version": 1
  }
}