Pith Number

pith:VBRFT3PI

pith:2026:VBRFT3PIHQFER2N6TYEKTBJWDN

not attested not anchored not stored refs resolved

Strong well-posedness of a singular SDE for signed Coulomb particles

Patrick van Meurs, Yoan Tardy

Signed Coulomb particles in two dimensions have unique strong global solutions despite singular collisions.

arxiv:2605.16788 v1 · 2026-05-16 · math.AP · math.PR

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\pithnumber{VBRFT3PIHQFER2N6TYEKTBJWDN}

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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

Our main results are the existence and uniqueness of strong global solutions and the characterization of all possible collisions.

C2weakest assumption

The proofs rely on scaling invariance of the process together with several tools developed in [FT25] for the Keller-Segel particle system; if those tools do not transfer directly to the signed Coulomb case with annihilation, the global well-posedness argument fails.

C3one line summary

Proves strong well-posedness and full collision characterization for an SDE of signed Coulomb particles in R^2 that annihilate on contact.

References

18 extracted · 18 resolved · 0 Pith anchors

[1] L. Ambrosio, E. Mainini, and S. Serfaty. Gradient flow of the C hapman-- R ubinstein-- S chatzman model for signed vortices. In Annales de l'Institut Henri Poincare (C) Non Linear Analysis , volume 28 2011

[2] F. Bethuel, G. Orlandi, and D. Smets. Dynamics of multiple degree G inzburg- L andau vortices. Communications in Mathematical Physics , 272:229--261, 2007 2007

[3] J. Boursier and S. Serfaty. Dipole formation in the two-component plasma. arXiv:2410.01025 , 2024 2024

[4] J. Boursier and S. Serfaty. Multipole and B erezinskii-- K osterlitz-- T houless transitions in the two-component plasma. arXiv:2509.09449 , 2025 2025

[5] P. Cattiaux and L. P\'ed\`eches. The 2-D stochastic Keller-Segel particle model: existence and uniqueness . Latin American Journal of Probability and Mathematical Statistics , 13:447--463, 2016 2016

Receipt and verification

First computed	2026-05-20T00:03:22.023486Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a86259ede83c0a48e9be9e08a985361b50fde9e1cba121a6a7beae0869e97e95

Aliases

arxiv: 2605.16788 · arxiv_version: 2605.16788v1 · doi: 10.48550/arxiv.2605.16788 · pith_short_12: VBRFT3PIHQFE · pith_short_16: VBRFT3PIHQFER2N6 · pith_short_8: VBRFT3PI

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/VBRFT3PIHQFER2N6TYEKTBJWDN \
  | 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: a86259ede83c0a48e9be9e08a985361b50fde9e1cba121a6a7beae0869e97e95

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2dd572c2d63f76605d8d70d84c3bc1d540cfae2bf8dbd421bedfad238448fdcb",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-16T03:44:52Z",
    "title_canon_sha256": "5dec28056c2dddeeacc6d3395e5647838f73581b93af97266f12bcfdb6b2dd1f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16788",
    "kind": "arxiv",
    "version": 1
  }
}