Pith Number

pith:KP6QKW6N

pith:2026:KP6QKW6N4N3LTYTX2JGYXR6UTD

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Classification of Double Saddle-Point Systems

Chen Greif, Susanne Bradley

Symmetric double saddle-point systems divide into block-arrow and block-tridiagonal matrix forms that control their invertibility, spectra, and preconditioners.

arxiv:2605.14157 v1 · 2026-05-13 · math.NA · cs.NA

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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.

Claims

C1strongest claim

At the core of the paper is the division of the associated matrices into ``block-arrow'' and ``block-tridiagonal'' forms.

C2weakest assumption

The systems under consideration are symmetric double saddle-point systems whose matrices admit the described block structures.

C3one line summary

A classification of symmetric double saddle-point systems into block-arrow and block-tridiagonal matrix forms is presented, including invertibility conditions, spectral properties, and block preconditioners.

References

86 extracted · 86 resolved · 0 Pith anchors

[1] James H. Adler, Thomas R. Benson, Eric C. Cyr, Patrick E. Farrell, Scott P. MacLachlan, and Ray S. Tuminaro. Monolithic multigrid meth- ods for magnetohydrodynamics.SIAM Journal on Scientific Computin 2021

[2] Safique Ahmad and Pinki Khatun 2025

[3] Safique Ahmad and Pinki Khatun 2026

[4] Ali Beik and M 2018

[5] Antonietti, Jacopo De Ponti, Luca Formaggia, and Anna Scotti 2020

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-17T23:39:11.522867Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

53fd055bcde376b9e277d24d8bc7d498c3110f79f8381a1a33a2111ba3ed2b14

Aliases

arxiv: 2605.14157 · arxiv_version: 2605.14157v1 · doi: 10.48550/arxiv.2605.14157 · pith_short_12: KP6QKW6N4N3L · pith_short_16: KP6QKW6N4N3LTYTX · pith_short_8: KP6QKW6N

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/KP6QKW6N4N3LTYTX2JGYXR6UTD \
  | 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: 53fd055bcde376b9e277d24d8bc7d498c3110f79f8381a1a33a2111ba3ed2b14

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e1367c5c5d396fac435d3631f2a54d815ec0ed718737d5d19bf81d65856320f9",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-05-13T22:16:17Z",
    "title_canon_sha256": "ba1afdede9dcf2a2d7ab28eb5e12396a78be0e80d326bc4c8fa1fde9b392410c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14157",
    "kind": "arxiv",
    "version": 1
  }
}