{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:FEIULSPCLXSNA342HWYG6A4WJS","short_pith_number":"pith:FEIULSPC","schema_version":"1.0","canonical_sha256":"291145c9e25de4d06f9a3db06f03964c8bf71a22bef87116486eae3e7f624eab","source":{"kind":"arxiv","id":"2605.09706","version":2},"attestation_state":"computed","paper":{"title":"A dyadic construction of a three-dimensional attractive point interaction Markov family","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Iterated Doob transforms along dyadic partitions construct a Markov family for three-dimensional attractive point interactions.","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Barkat Mian","submitted_at":"2026-05-10T19:07:12Z","abstract_excerpt":"We discuss a probabilistic approximation framework for the three-dimensional attractive point interaction on a finite time horizon. By iterating the Doob transforms of the explicit heat kernel associated with the singular Schr\\\"odinger operator formally given by \\[ \\frac12\\Delta \\,+\\, \\frac{\\beta}{2}\\, \\delta_0(\\cdot), \\qquad \\beta>0, \\] we obtain sub-probability kernels along finite partitions on the punctured domain \\[ E_\\varepsilon=\\{x\\in\\mathbb R^3:\\ |x|>\\varepsilon\\}, \\] which yield a limiting sub-probability kernel via refinement along global dyadic partitions, and we extend this limit t"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":true},"canonical_record":{"source":{"id":"2605.09706","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-05-10T19:07:12Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"84089f58718e7300bf9d9e1826e35a38f2e6c163db90dc9dbd69575538f1c330","abstract_canon_sha256":"17c3f412e13f84a96d8cdeca6928dd881e8530e48b038dc685fce9b4ad527cf3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-26T01:03:33.032726Z","signature_b64":"4TcOuyqboNqyhMWU6JO6L4N/FcLf/uIqMPhJigkr+I6p8L8pPz9Y8706UbOZ14CYQPKXSOu3t6YaYU2PfhvwDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"291145c9e25de4d06f9a3db06f03964c8bf71a22bef87116486eae3e7f624eab","last_reissued_at":"2026-05-26T01:03:33.031764Z","signature_status":"signed_v1","first_computed_at":"2026-05-26T01:03:33.031764Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A dyadic construction of a three-dimensional attractive point interaction Markov family","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Iterated Doob transforms along dyadic partitions construct a Markov family for three-dimensional attractive point interactions.","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Barkat Mian","submitted_at":"2026-05-10T19:07:12Z","abstract_excerpt":"We discuss a probabilistic approximation framework for the three-dimensional attractive point interaction on a finite time horizon. By iterating the Doob transforms of the explicit heat kernel associated with the singular Schr\\\"odinger operator formally given by \\[ \\frac12\\Delta \\,+\\, \\frac{\\beta}{2}\\, \\delta_0(\\cdot), \\qquad \\beta>0, \\] we obtain sub-probability kernels along finite partitions on the punctured domain \\[ E_\\varepsilon=\\{x\\in\\mathbb R^3:\\ |x|>\\varepsilon\\}, \\] which yield a limiting sub-probability kernel via refinement along global dyadic partitions, and we extend this limit t"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"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.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"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.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"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.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Iterated Doob transforms along dyadic partitions construct a Markov family for three-dimensional attractive point interactions.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"a96ed308fa6c17f2e378d1edefdc99933ba0c017d3fb6ac9823120ed9db8618d"},"source":{"id":"2605.09706","kind":"arxiv","version":2},"verdict":{"id":"044633c8-15a4-4990-bb5c-b937514b7924","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-12T03:36:09.388796Z","strongest_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.","one_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.","pipeline_version":"pith-pipeline@v0.9.0","weakest_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.","pith_extraction_headline":"Iterated Doob transforms along dyadic partitions construct a Markov family for three-dimensional attractive point interactions."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.09706/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-20T07:22:01.339250Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T16:37:31.154118Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T12:31:18.230698Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T10:00:11.761163Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"126e8107c7ef82104394edd3013c50a383eddc8fb2a92d7587f31e5a3ee321bd"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"c2c75ab65df4c6adb46c61c07de50201bd32afcc5d0584a66a70ec8a26ef31d4"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2605.09706","created_at":"2026-05-26T01:03:33.031929+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.09706v2","created_at":"2026-05-26T01:03:33.031929+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.09706","created_at":"2026-05-26T01:03:33.031929+00:00"},{"alias_kind":"pith_short_12","alias_value":"FEIULSPCLXSN","created_at":"2026-05-26T01:03:33.031929+00:00"},{"alias_kind":"pith_short_16","alias_value":"FEIULSPCLXSNA342","created_at":"2026-05-26T01:03:33.031929+00:00"},{"alias_kind":"pith_short_8","alias_value":"FEIULSPC","created_at":"2026-05-26T01:03:33.031929+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":2,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FEIULSPCLXSNA342HWYG6A4WJS","json":"https://pith.science/pith/FEIULSPCLXSNA342HWYG6A4WJS.json","graph_json":"https://pith.science/api/pith-number/FEIULSPCLXSNA342HWYG6A4WJS/graph.json","events_json":"https://pith.science/api/pith-number/FEIULSPCLXSNA342HWYG6A4WJS/events.json","paper":"https://pith.science/paper/FEIULSPC"},"agent_actions":{"view_html":"https://pith.science/pith/FEIULSPCLXSNA342HWYG6A4WJS","download_json":"https://pith.science/pith/FEIULSPCLXSNA342HWYG6A4WJS.json","view_paper":"https://pith.science/paper/FEIULSPC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.09706&json=true","fetch_graph":"https://pith.science/api/pith-number/FEIULSPCLXSNA342HWYG6A4WJS/graph.json","fetch_events":"https://pith.science/api/pith-number/FEIULSPCLXSNA342HWYG6A4WJS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FEIULSPCLXSNA342HWYG6A4WJS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FEIULSPCLXSNA342HWYG6A4WJS/action/storage_attestation","attest_author":"https://pith.science/pith/FEIULSPCLXSNA342HWYG6A4WJS/action/author_attestation","sign_citation":"https://pith.science/pith/FEIULSPCLXSNA342HWYG6A4WJS/action/citation_signature","submit_replication":"https://pith.science/pith/FEIULSPCLXSNA342HWYG6A4WJS/action/replication_record"}},"created_at":"2026-05-26T01:03:33.031929+00:00","updated_at":"2026-05-26T01:03:33.031929+00:00"}