Pith Number

pith:67NFJ6FK

pith:2021:67NFJ6FKIDXMNX5BAR4KG6KRV7

not attested not anchored not stored refs pending

The real symplectic Stiefel and Grassmann manifolds: metrics, geodesics and applications

Ralf Zimmermann, Thomas Bendokat

arxiv:2108.12447 v1 · 2021-08-27 · math.DG · cs.NA · math.NA

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\usepackage{pith}
\pithnumber{67NFJ6FKIDXMNX5BAR4KG6KRV7}

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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.

Cited by

4 papers in Pith

A Riemannian gradient descent method for optimization on the indefinite Stiefel manifold

An inexact variable metric proximal linearization method for composite optimization on manifolds

A generalized canonical metric for optimization on the indefinite Stiefel manifold

A polar-factor retraction on the symplectic Stiefel manifold with closed-form inverse

Receipt and verification

First computed	2026-07-05T03:09:32.074252Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f7da54f8aa40eec6dfa10478a37951afe2a4b6e6d0d6bf13ef68c6df46dacb55

Aliases

arxiv: 2108.12447 · arxiv_version: 2108.12447v1 · doi: 10.48550/arxiv.2108.12447 · pith_short_12: 67NFJ6FKIDXM · pith_short_16: 67NFJ6FKIDXMNX5B · pith_short_8: 67NFJ6FK

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/67NFJ6FKIDXMNX5BAR4KG6KRV7 \
  | 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: f7da54f8aa40eec6dfa10478a37951afe2a4b6e6d0d6bf13ef68c6df46dacb55

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b6676db26a061087d1496afcb1b34ede1cc22c56c35db98a59bc8d346752278f",
    "cross_cats_sorted": [
      "cs.NA",
      "math.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2021-08-27T18:11:51Z",
    "title_canon_sha256": "fed9769c817ab7549c0cb62f43c7e1b08697242620cfb50fc2374ddd63d1c71b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2108.12447",
    "kind": "arxiv",
    "version": 1
  }
}