Pith Number

pith:Q4RF4RAO

pith:2018:Q4RF4RAOKQJTXNKEF3MUIQP7PI

not attested not anchored not stored refs pending

On the Invertibility of the Sum of Operators

Mohammed Hichem Mortad

arxiv:1804.07288 v4 · 2018-04-19 · math.FA · 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{Q4RF4RAOKQJTXNKEF3MUIQP7PI}

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	2026-05-18T00:04:13.006603Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

87225e440e54133bb5442ed94441ff7a28976f16851bc46cafd662733dda59ec

Aliases

arxiv: 1804.07288 · arxiv_version: 1804.07288v4 · doi: 10.48550/arxiv.1804.07288 · pith_short_12: Q4RF4RAOKQJT · pith_short_16: Q4RF4RAOKQJTXNKE · pith_short_8: Q4RF4RAO

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/Q4RF4RAOKQJTXNKEF3MUIQP7PI \
  | 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: 87225e440e54133bb5442ed94441ff7a28976f16851bc46cafd662733dda59ec

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "54682e476db62ef2bcb71a59eb13cd1014e700b439043ce92c535dd9069c589f",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2018-04-19T17:46:29Z",
    "title_canon_sha256": "f065dac83531656ba3d0d22c4e5f4abd871d102fdcb2b9c96f9afd1e4af45521"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1804.07288",
    "kind": "arxiv",
    "version": 4
  }
}