Pith Number

pith:26ZEGW6Y

pith:2026:26ZEGW6YNE55YSSOYE6HZCNFMX

not attested not anchored not stored refs pending

Confocal families of plane algebraic curves

Boris Shapiro, Ragni Piene

Confocality of plane algebraic curves is reformulated via a focal map on equiclassical families whose fibers are analyzed with deformation theory.

arxiv:2604.25293 v2 · 2026-04-28 · math.AG · math.CV

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\usepackage{pith}
\pithnumber{26ZEGW6YNE55YSSOYE6HZCNFMX}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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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

We reformulate confocality via a focal map on equiclassical families and analyze its fibers using deformation theory.

C2weakest assumption

That confocality admits a well-defined focal map on equiclassical families whose fibers can be meaningfully analyzed by deformation theory without further restrictions on the curves or base field.

C3one line summary

Confocality for plane algebraic curves is reformulated as a focal map on equiclassical families, with fibers analyzed via deformation theory.

Cited by

1 paper in Pith

Plane rectifiable curves: old and new

Receipt and verification

First computed	2026-05-20T00:05:45.257179Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d7b2435bd8693bdc4a4ec13c7c89a565ce203de35511c41ce61eda7b14fa2d76

Aliases

arxiv: 2604.25293 · arxiv_version: 2604.25293v2 · doi: 10.48550/arxiv.2604.25293 · pith_short_12: 26ZEGW6YNE55 · pith_short_16: 26ZEGW6YNE55YSSO · pith_short_8: 26ZEGW6Y

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/26ZEGW6YNE55YSSOYE6HZCNFMX \
  | 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: d7b2435bd8693bdc4a4ec13c7c89a565ce203de35511c41ce61eda7b14fa2d76

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "38dd03f939ac94d653b27fa91c2aceade10b9365c083a68152a93445a5b39898",
    "cross_cats_sorted": [
      "math.CV"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-04-28T07:01:39Z",
    "title_canon_sha256": "647341922df7d75e4e5861fc67da3a298c4f0ffeb2f9571c30dd97d31544f3f7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.25293",
    "kind": "arxiv",
    "version": 2
  }
}