Pith Number

pith:P67LUSJZ

pith:2017:P67LUSJZ6MKFZ4P2OAMSAC4DFE

not attested not anchored not stored refs pending

On The Absolute Value of The Product and the Sum of Linear Operators

Mohammed Hichem Mortad

arxiv:1702.08671 v1 · 2017-02-28 · 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{P67LUSJZ6MKFZ4P2OAMSAC4DFE}

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	2026-05-18T00:49:48.130535Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7fbeba4939f3145cf1fa7019200b83293cdb20e5eba57244a250c38d315d577c

Aliases

arxiv: 1702.08671 · arxiv_version: 1702.08671v1 · doi: 10.48550/arxiv.1702.08671 · pith_short_12: P67LUSJZ6MKF · pith_short_16: P67LUSJZ6MKFZ4P2 · pith_short_8: P67LUSJZ

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/P67LUSJZ6MKFZ4P2OAMSAC4DFE \
  | 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: 7fbeba4939f3145cf1fa7019200b83293cdb20e5eba57244a250c38d315d577c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d6245375a900a54b8fd1c5d2aa75574023509b73d3e4517cb5c3373b4f47211c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2017-02-28T07:09:30Z",
    "title_canon_sha256": "69a1f4127a8e7a7828d4cff4570fab5e2eb41bdf412305fa4a2856aa8580022d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1702.08671",
    "kind": "arxiv",
    "version": 1
  }
}