Pith Number

pith:E3CHYSFH

pith:2010:E3CHYSFH3UZXGHATAJBYLBFY6Q

not attested not anchored not stored refs pending

Rank-preserving geometric means of positive semi-definite matrices

Anne Collard, Rodolphe Sepulchre, Silvere Bonnabel

arxiv:1007.5494 v3 · 2010-07-30 · math.OC · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{E3CHYSFH3UZXGHATAJBYLBFY6Q}

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	2026-05-18T03:28:19.886365Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

26c47c48a7dd33731c1302438584b8f43c8dcfd98ab4ef41185a2e286a1eba4d

Aliases

arxiv: 1007.5494 · arxiv_version: 1007.5494v3 · doi: 10.48550/arxiv.1007.5494 · pith_short_12: E3CHYSFH3UZX · pith_short_16: E3CHYSFH3UZXGHAT · pith_short_8: E3CHYSFH

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/E3CHYSFH3UZXGHATAJBYLBFY6Q \
  | 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: 26c47c48a7dd33731c1302438584b8f43c8dcfd98ab4ef41185a2e286a1eba4d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f016d70ba3023980634b4caf8e92744ec45af6637ad6b51baf1de6bb654dfef0",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2010-07-30T16:44:00Z",
    "title_canon_sha256": "820865c6beccaaa1de9bb797d61824d8503804e3f465be330217b0d8484da82d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1007.5494",
    "kind": "arxiv",
    "version": 3
  }
}