Pith Number

pith:ZWWHIQDR

pith:2015:ZWWHIQDRDFPBG2HFKCPHMQMWNW

not attested not anchored not stored refs pending

Cramer's Rule for Generalized Inverse Solutions of Some Matrices Equations

Ivan Kyrchei

arxiv:1503.06997 v2 · 2015-03-24 · 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{ZWWHIQDRDFPBG2HFKCPHMQMWNW}

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	2026-05-18T01:22:50.772211Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cdac744071195e1368e5509e7641966daa2ca368891e875ab231538d75815688

Aliases

arxiv: 1503.06997 · arxiv_version: 1503.06997v2 · doi: 10.48550/arxiv.1503.06997 · pith_short_12: ZWWHIQDRDFPB · pith_short_16: ZWWHIQDRDFPBG2HF · pith_short_8: ZWWHIQDR

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/ZWWHIQDRDFPBG2HFKCPHMQMWNW \
  | 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: cdac744071195e1368e5509e7641966daa2ca368891e875ab231538d75815688

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "50fe2d25e04f0dbb09dcdaff4013324eec3a34a8108ef582db317b3fc54e08f7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2015-03-24T11:54:40Z",
    "title_canon_sha256": "4bef05c62190f40047dd3037d55a3527713ac92c4701239b01a2199001040750"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.06997",
    "kind": "arxiv",
    "version": 2
  }
}