Pith Number

pith:I3XGNGSS

pith:2026:I3XGNGSSX4NDEF7IEWOZEYCEL2

not attested not anchored not stored refs pending

Leaderless Collective Motion in Affine Formation Control over the Complex Plane

Enric Morella, Hector Garcia de Marina, Jesus Bautista, Lili Wang

Modifying the Laplacian weights allows leaderless swarms to perform any affine transformation of a reference shape in the plane.

arxiv:2604.05648 v2 · 2026-04-07 · cs.RO · cs.SY · eess.SY

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\pithnumber{I3XGNGSSX4NDEF7IEWOZEYCEL2}

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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

The resulting collective motion is characterized as a time-varying affine transformation of a reference configuration, or shape, with an analytic solution governing the motion via explicitly designed eigenvectors and eigenvalues of the modified Laplacian.

C2weakest assumption

The analysis assumes that the modified weights produce a Laplacian matrix whose eigenvectors and eigenvalues can be designed to exactly realize any desired affine motion while preserving formation stability, without specifying how to choose weights for arbitrary graphs or under disturbances.

C3one line summary

Modifying Laplacian weights produces leaderless affine formation motions in the plane, with an analytic solution via complex-number eigenvectors and eigenvalues.

Receipt and verification

First computed	2026-06-23T01:12:04.436630Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

46ee669a52bf1a3217e8259d9260445e9773f2c9d8bbb66f7deb5f6b68f18b28

Aliases

arxiv: 2604.05648 · arxiv_version: 2604.05648v2 · doi: 10.48550/arxiv.2604.05648 · pith_short_12: I3XGNGSSX4ND · pith_short_16: I3XGNGSSX4NDEF7I · pith_short_8: I3XGNGSS

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/I3XGNGSSX4NDEF7IEWOZEYCEL2 \
  | 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: 46ee669a52bf1a3217e8259d9260445e9773f2c9d8bbb66f7deb5f6b68f18b28

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8b1d2254620f0ec068416c1a12053556f5a34f25da1638fc773e998d49d5f484",
    "cross_cats_sorted": [
      "cs.SY",
      "eess.SY"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "cs.RO",
    "submitted_at": "2026-04-07T09:53:48Z",
    "title_canon_sha256": "6e85d941bebb227f0bd46bb69bd979c71e2ec333272a4990289b25b0c07b3a6b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.05648",
    "kind": "arxiv",
    "version": 2
  }
}