Pith Number

pith:XCNCU6CH

pith:2008:XCNCU6CHMFJUKMVSRRTRHUCZKY

not attested not anchored not stored refs pending

Least-Squares Approximation by Elements from Matrix Orbits Achieved by Gradient Flows on Compact Lie Groups

C.K. Li, T. Schulte-Herbrueggen, Y.T. Poon

arxiv:0812.1817 v1 · 2008-12-09 · math.NA · math.DS · math.OC · quant-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XCNCU6CHMFJUKMVSRRTRHUCZKY}

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	2026-05-18T03:37:19.267538Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b89a2a784761534532b28c6713d059560985d64f44ec2d2fec7ed87e1a5dabe4

Aliases

arxiv: 0812.1817 · arxiv_version: 0812.1817v1 · doi: 10.48550/arxiv.0812.1817 · pith_short_12: XCNCU6CHMFJU · pith_short_16: XCNCU6CHMFJUKMVS · pith_short_8: XCNCU6CH

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/XCNCU6CHMFJUKMVSRRTRHUCZKY \
  | 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: b89a2a784761534532b28c6713d059560985d64f44ec2d2fec7ed87e1a5dabe4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fc60004a9220edabb5c2787bb94aa3539080585ec72366d7212518c9c554e3b7",
    "cross_cats_sorted": [
      "math.DS",
      "math.OC",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2008-12-09T23:48:37Z",
    "title_canon_sha256": "0dfdd4c05418582401fda8858b187841275d24abf01eb8a1dbf05b897cdb0b67"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0812.1817",
    "kind": "arxiv",
    "version": 1
  }
}