Pith Number

pith:CXCADRI2

pith:2026:CXCADRI2Y73XOQHYDV7FJELAH5

not attested not anchored not stored refs resolved

Irregular SLE(4) martingales and isomonodromic deformations

Aleksandra Korzhenkova, Eveliina Peltola, Harini Desiraju

Deriving the Loewner evolution of isomonodromic parameters constructs martingale observables for SLE(4) with double poles.

arxiv:2605.13802 v1 · 2026-05-13 · math-ph · math.MP · math.PR

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Claims

C1strongest claim

Our first main result is the derivation of the Loewner evolution of these isomonodromic deformation parameters. Using this result, we construct martingale observables for Schramm-Loewner evolution (SLE(4)) processes in the presence of double poles. Furthermore, we characterize these SLE(4) observables uniquely in terms of confluent BPZ equations of a CFT with central charge c=1.

C2weakest assumption

The deformations are non-Fuchsian monodromy-preserving on the Riemann sphere, with the associated parameters comprising positions of singularities together with Birkhoff invariants due to irregular singularities; the derivation assumes these parameters admit a well-defined Loewner evolution under the SLE(4) driving function.

C3one line summary

Derives Loewner evolution for isomonodromic parameters with irregular singularities and constructs unique SLE(4) martingales with double poles via confluent BPZ equations.

References

76 extracted · 76 resolved · 2 Pith anchors

[1] Ablowitz and Athanassios S 2003

[2] SLE_ growth processes and conformal field theories 2002

[3] Conformal field theories of stochastic L oewner evolutions 2003

[4] SLE martingales and the V irasoro algebra 2003

[5] Conformal transformations and the SLE partition function martingale 2004

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T02:44:15.497456Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

15c401c51ac7f77740f81d7e5491603f6285856edcff14c8cf7b5dcfa5d49c59

Aliases

arxiv: 2605.13802 · arxiv_version: 2605.13802v1 · doi: 10.48550/arxiv.2605.13802 · pith_short_12: CXCADRI2Y73X · pith_short_16: CXCADRI2Y73XOQHY · pith_short_8: CXCADRI2

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/CXCADRI2Y73XOQHYDV7FJELAH5 \
  | 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: 15c401c51ac7f77740f81d7e5491603f6285856edcff14c8cf7b5dcfa5d49c59

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a461474fe0ba6c966c559e2674643749bf288f30d4e0ce455846fad156b07880",
    "cross_cats_sorted": [
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-05-13T17:24:46Z",
    "title_canon_sha256": "c9e4ef775885284a9a81cf6ea5c764ece42860912b225dbaedaa58157280873d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13802",
    "kind": "arxiv",
    "version": 1
  }
}