Pith Number

pith:MGRC3JPG

pith:2024:MGRC3JPG5WBCZPE5ZBERURIZYD

not attested not anchored not stored refs pending

A geodesic convexity-like structure for the polar decomposition of a square matrix

Bart Vandereycken, Foivos Alimisis

arxiv:2412.13990 v2 · 2024-12-18 · math.NA · cs.NA · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MGRC3JPG5WBCZPE5ZBERURIZYD}

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	2026-07-05T10:02:56.391479Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

61a22da5e6ed822cbc9dc8491a4519c0fba8edee8a3ac041580fa9e09b80c70d

Aliases

arxiv: 2412.13990 · arxiv_version: 2412.13990v2 · doi: 10.48550/arxiv.2412.13990 · pith_short_12: MGRC3JPG5WBC · pith_short_16: MGRC3JPG5WBCZPE5 · pith_short_8: MGRC3JPG

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/MGRC3JPG5WBCZPE5ZBERURIZYD \
  | 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: 61a22da5e6ed822cbc9dc8491a4519c0fba8edee8a3ac041580fa9e09b80c70d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "04d8c5bc211797b3f0d214ef59a04409435fc2468483533675d1cf6116c72dde",
    "cross_cats_sorted": [
      "cs.NA",
      "math.OC"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2024-12-18T16:10:44Z",
    "title_canon_sha256": "94fad76810bd74ef7dfbe280cae3784f68758134068f2437f10b76175bd9dcc9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.13990",
    "kind": "arxiv",
    "version": 2
  }
}