Pith Number

pith:QG2MKLN4

pith:2010:QG2MKLN4LRNHZ5GICH63SPJS6G

not attested not anchored not stored refs pending

Analogues of the adjoint matrix for generalized inverses and corresponding Cramer rules

Ivan Kyrchei

arxiv:1004.4761 v1 · 2010-04-27 · math.RA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QG2MKLN4LRNHZ5GICH63SPJS6G}

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	2026-05-18T02:24:15.978293Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

81b4c52dbc5c5a7cf4c811fdb93d32f1a0b6ed8fec7774a2747f14c2d3d451b9

Aliases

arxiv: 1004.4761 · arxiv_version: 1004.4761v1 · doi: 10.48550/arxiv.1004.4761 · pith_short_12: QG2MKLN4LRNH · pith_short_16: QG2MKLN4LRNHZ5GI · pith_short_8: QG2MKLN4

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/QG2MKLN4LRNHZ5GICH63SPJS6G \
  | 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: 81b4c52dbc5c5a7cf4c811fdb93d32f1a0b6ed8fec7774a2747f14c2d3d451b9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "29ac26ba806a4c90905355624043af444b245735d218c5a70db75181651583cd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2010-04-27T10:58:56Z",
    "title_canon_sha256": "191997e5d81c7b6e064e42d21f7f1096aa51f9d3b2a3e321bb83565345f8dfce"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.4761",
    "kind": "arxiv",
    "version": 1
  }
}