Pith Number

pith:GSO6PTF7

pith:2015:GSO6PTF74F6N4GHOO3DAPUJ6TQ

not attested not anchored not stored refs pending

Right (Or Left) Invertibility of Bounded and Unbounded Operators and Applications to the Spectrum of Products

Mohammed Hichem Mortad, Souheyb Dehimi

arxiv:1505.02719 v2 · 2015-05-11 · 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{GSO6PTF74F6N4GHOO3DAPUJ6TQ}

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	2026-05-18T00:50:02.046421Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

349de7ccbfe17cde18ee76c607d13e9c3b021afeab0d4e52ddd73f7e7915a1f5

Aliases

arxiv: 1505.02719 · arxiv_version: 1505.02719v2 · doi: 10.48550/arxiv.1505.02719 · pith_short_12: GSO6PTF74F6N · pith_short_16: GSO6PTF74F6N4GHO · pith_short_8: GSO6PTF7

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/GSO6PTF74F6N4GHOO3DAPUJ6TQ \
  | 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: 349de7ccbfe17cde18ee76c607d13e9c3b021afeab0d4e52ddd73f7e7915a1f5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "161359231f691ae3bbca07de6110163ae2509988a52229313dd62cd58de829b2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2015-05-11T18:14:51Z",
    "title_canon_sha256": "ca9d44894350052812bfae6cc758c0e456ec00822937b185708e9f040d4f39d8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.02719",
    "kind": "arxiv",
    "version": 2
  }
}