Pith Number

pith:FEIULSPC

pith:2026:FEIULSPCLXSNA342HWYG6A4WJS

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A dyadic construction of a three-dimensional attractive point interaction Markov family

Barkat Mian

Iterated Doob transforms along dyadic partitions construct a Markov family for three-dimensional attractive point interactions.

arxiv:2605.09706 v2 · 2026-05-10 · math.PR · math-ph · math.MP

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Claims

C1strongest claim

By iterating the Doob-transforms of the fundamental solution of the corresponding singular heat equation, we obtain sub-probability kernels along finite partitions which yield a limiting sub-probability kernel via refinement along global dyadic partitions, and we extend this limit to a transition probability kernel on an enlarged space obtained by adjoining a cemetery state. These kernels determine a time-inhomogeneous Markov process on the set of dyadic times, and its step-function interpolations yield càdlàg processes with consistent finite-dimensional distributions and partial tightness properties.

C2weakest assumption

The existence and regularity of the fundamental solution to the singular heat equation on the punctured domain E_ε together with the convergence of the iterated Doob-transformed kernels under dyadic refinement as the partition mesh tends to zero.

C3one line summary

Iterated Doob transforms along dyadic refinements produce a time-inhomogeneous Markov process on dyadic times that approximates the 3D attractive point interaction via càdlàg paths with consistent finite-dimensional distributions.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-26T01:03:33.031764Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

291145c9e25de4d06f9a3db06f03964c8bf71a22bef87116486eae3e7f624eab

Aliases

arxiv: 2605.09706 · arxiv_version: 2605.09706v2 · doi: 10.48550/arxiv.2605.09706 · pith_short_12: FEIULSPCLXSN · pith_short_16: FEIULSPCLXSNA342 · pith_short_8: FEIULSPC

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/FEIULSPCLXSNA342HWYG6A4WJS \
  | 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: 291145c9e25de4d06f9a3db06f03964c8bf71a22bef87116486eae3e7f624eab

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "17c3f412e13f84a96d8cdeca6928dd881e8530e48b038dc685fce9b4ad527cf3",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-05-10T19:07:12Z",
    "title_canon_sha256": "84089f58718e7300bf9d9e1826e35a38f2e6c163db90dc9dbd69575538f1c330"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.09706",
    "kind": "arxiv",
    "version": 2
  }
}