Pith Number

pith:UQKKHLAE

pith:2015:UQKKHLAEF5W3VSHAGSTH657TNV

not attested not anchored not stored refs pending

Perturbation of closed range operators and Moore-Penrose inverse

G. Ramesh, S. H. Kulkarni

arxiv:1510.01534 v2 · 2015-10-06 · 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{UQKKHLAEF5W3VSHAGSTH657TNV}

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	2026-05-18T01:30:50.510694Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a414a3ac042f6dbac8e034a67f77f36d6cd02388f1f7c664e8dd927024b83995

Aliases

arxiv: 1510.01534 · arxiv_version: 1510.01534v2 · doi: 10.48550/arxiv.1510.01534 · pith_short_12: UQKKHLAEF5W3 · pith_short_16: UQKKHLAEF5W3VSHA · pith_short_8: UQKKHLAE

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/UQKKHLAEF5W3VSHAGSTH657TNV \
  | 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: a414a3ac042f6dbac8e034a67f77f36d6cd02388f1f7c664e8dd927024b83995

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "33d38890f595c1fbf595219b256f8735b5d60ef161ebd1f8ca7ae71c9e46b0e9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2015-10-06T11:35:22Z",
    "title_canon_sha256": "2820e251d01bced11801aa1c1581d0658ef6ada061c6b4c5573b63b274f67856"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.01534",
    "kind": "arxiv",
    "version": 2
  }
}