Pith Number

pith:6ZS5UQFK

pith:2012:6ZS5UQFKIWIHSBW7SUDJXTM2XP

not attested not anchored not stored refs pending

Explicit representation formulas for the minimum norm least squares solutions of some quaternion matrix equations

Ivan Kyrchei

arxiv:1204.1986 v1 · 2012-04-09 · 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{6ZS5UQFKIWIHSBW7SUDJXTM2XP}

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	2026-05-18T03:35:25.967228Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f665da40aa45907906df95069bcd9abbc67b985322076fc059d455275fecf61d

Aliases

arxiv: 1204.1986 · arxiv_version: 1204.1986v1 · doi: 10.48550/arxiv.1204.1986 · pith_short_12: 6ZS5UQFKIWIH · pith_short_16: 6ZS5UQFKIWIHSBW7 · pith_short_8: 6ZS5UQFK

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/6ZS5UQFKIWIHSBW7SUDJXTM2XP \
  | 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: f665da40aa45907906df95069bcd9abbc67b985322076fc059d455275fecf61d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e9be6ee3076014ca539c16f24230048e14be2df5230966647e3f3201090adfad",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2012-04-09T20:44:56Z",
    "title_canon_sha256": "0ccba682e65e14444e5094a7a6570a73ce1d1f7e797047f63a25b0006ef2335f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.1986",
    "kind": "arxiv",
    "version": 1
  }
}