{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:KEPWWYGIFQ4DFO6C7T3D7G5PHM","short_pith_number":"pith:KEPWWYGI","canonical_record":{"source":{"id":"2605.17494","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-05-17T15:05:53Z","cross_cats_sorted":[],"title_canon_sha256":"022ea897f5f64ffaa77e57fe3d904208660aa5b878e16c6b72f808569995f36a","abstract_canon_sha256":"1d419cc6f782be4e667fcba392ed0a95647774c404025693f7fe37304bf9b9b0"},"schema_version":"1.0"},"canonical_sha256":"511f6b60c82c3832bbc2fcf63f9baf3b31a170b2ead9d26685f663718abb1117","source":{"kind":"arxiv","id":"2605.17494","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.17494","created_at":"2026-05-20T00:04:42Z"},{"alias_kind":"arxiv_version","alias_value":"2605.17494v1","created_at":"2026-05-20T00:04:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.17494","created_at":"2026-05-20T00:04:42Z"},{"alias_kind":"pith_short_12","alias_value":"KEPWWYGIFQ4D","created_at":"2026-05-20T00:04:42Z"},{"alias_kind":"pith_short_16","alias_value":"KEPWWYGIFQ4DFO6C","created_at":"2026-05-20T00:04:42Z"},{"alias_kind":"pith_short_8","alias_value":"KEPWWYGI","created_at":"2026-05-20T00:04:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:KEPWWYGIFQ4DFO6C7T3D7G5PHM","target":"record","payload":{"canonical_record":{"source":{"id":"2605.17494","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-05-17T15:05:53Z","cross_cats_sorted":[],"title_canon_sha256":"022ea897f5f64ffaa77e57fe3d904208660aa5b878e16c6b72f808569995f36a","abstract_canon_sha256":"1d419cc6f782be4e667fcba392ed0a95647774c404025693f7fe37304bf9b9b0"},"schema_version":"1.0"},"canonical_sha256":"511f6b60c82c3832bbc2fcf63f9baf3b31a170b2ead9d26685f663718abb1117","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:04:42.096086Z","signature_b64":"kcYuyPUTSe0qmg1WsALpAxvm2SONWfrfF4NdWdGaOqwHY9sSjo4PJBvqycmTyy6lLAxtpl6c1tiR7HEgvCxeBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"511f6b60c82c3832bbc2fcf63f9baf3b31a170b2ead9d26685f663718abb1117","last_reissued_at":"2026-05-20T00:04:42.095240Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:04:42.095240Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.17494","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-20T00:04:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vaDb7ieC4Dahzg4MvQ36jnnEfF3PpZAEN19QYKDSErb2rfGRWNZigxsY+DpP3MoLGHcMTINRDcG2xXNwLKD9Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T19:40:08.709989Z"},"content_sha256":"73a863f2e8d0c6c5412a791886a374f3ef401dc9265df36f19c2a065891700eb","schema_version":"1.0","event_id":"sha256:73a863f2e8d0c6c5412a791886a374f3ef401dc9265df36f19c2a065891700eb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:KEPWWYGIFQ4DFO6C7T3D7G5PHM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized intersection exponents and local cut points for three-dimensional Brownian loop soup","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Generalized intersection exponents exist for the three-dimensional Brownian loop soup and relate to the dimension of its local cut points.","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ruixuan Li, Xinyi Li, Yifan Gao","submitted_at":"2026-05-17T15:05:53Z","abstract_excerpt":"We study generalized non-intersection probabilities for the three-dimensional Brownian loop soup at subcritical intensities. We establish the existence of generalized intersection exponents (GIE) and prove an up-to-constants estimate for these probabilities by means of a separation lemma tailored to this setting. We also relate the Hausdorff dimension of the set of local cut points of the three-dimensional Brownian loop soup to the GIE, and show that the GIE is continuous at intensity zero, where it reduces to the classical Brownian intersection exponent. In particular, this implies that, for "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We establish the existence of generalized intersection exponents (GIE) and prove an up-to-constants estimate for these probabilities by means of a separation lemma tailored to this setting. We also relate the Hausdorff dimension of the set of local cut points of the three-dimensional Brownian loop soup to the GIE, and show that the GIE is continuous at intensity zero, where it reduces to the classical Brownian intersection exponent. In particular, this implies that, for sufficiently small intensity parameters, the set of local cut points has Hausdorff dimension strictly larger than 1.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The separation lemma tailored to the loop-soup setting holds and supplies the up-to-constants bounds needed to define the generalized intersection exponents; without it the existence claim and the dimension relation cannot be established from the non-intersection probabilities.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The authors establish generalized intersection exponents for the 3D Brownian loop soup, prove an up-to-constants estimate via a separation lemma, relate them to the Hausdorff dimension of local cut points, and show continuity at zero intensity implying dimension strictly larger than 1 for small sub-","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Generalized intersection exponents exist for the three-dimensional Brownian loop soup and relate to the dimension of its local cut points.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"88d2724b1f84072ad55f8a2478632731a4152f9c9e7099dc9c6bed7d8cb14f0d"},"source":{"id":"2605.17494","kind":"arxiv","version":1},"verdict":{"id":"228d6d60-4d44-4041-8b0c-19f37ba501a3","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T22:41:39.804603Z","strongest_claim":"We establish the existence of generalized intersection exponents (GIE) and prove an up-to-constants estimate for these probabilities by means of a separation lemma tailored to this setting. We also relate the Hausdorff dimension of the set of local cut points of the three-dimensional Brownian loop soup to the GIE, and show that the GIE is continuous at intensity zero, where it reduces to the classical Brownian intersection exponent. In particular, this implies that, for sufficiently small intensity parameters, the set of local cut points has Hausdorff dimension strictly larger than 1.","one_line_summary":"The authors establish generalized intersection exponents for the 3D Brownian loop soup, prove an up-to-constants estimate via a separation lemma, relate them to the Hausdorff dimension of local cut points, and show continuity at zero intensity implying dimension strictly larger than 1 for small sub-","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The separation lemma tailored to the loop-soup setting holds and supplies the up-to-constants bounds needed to define the generalized intersection exponents; without it the existence claim and the dimension relation cannot be established from the non-intersection probabilities.","pith_extraction_headline":"Generalized intersection exponents exist for the three-dimensional Brownian loop soup and relate to the dimension of its local cut points."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.17494/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T23:01:19.529213Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T22:51:32.058059Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T21:41:57.676422Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T21:33:23.640633Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"6bb14c4c2ddb440ca1473bb296edfe1c6da7bed3773fc4e2437a6f13ffab5921"},"references":{"count":31,"sample":[{"doi":"","year":1990,"title":"K. Burdzy and G. F. Lawler. Nonintersection exponents for Brownian paths. II. Estimates and applications to a random fractal. Ann. Probab., 18(3):981–1009, 1990","work_id":"14a016dd-255c-4b29-bfd2-858590b4968f","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2024,"title":"arXiv preprint arXiv:2406.02397 , year=","work_id":"d58b182f-8251-453d-881f-b1d2b2ca98b4","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"Z. Cai and J. Ding. Heterochromatic two-arm probabilities for metric graph Gaussian free fields. arXiv preprint arXiv:2510.20492 , 2025","work_id":"c1dfbc92-8410-4687-8d0c-551509e40e8f","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"Z. Cai and J. Ding. On the gap between cluster dimensions of loop soups on R3 and the metric graph of Z3. arXiv preprint arXiv:2510.20526 , 2025","work_id":"78edfe45-0d58-4eb3-aa32-9c6aecec7067","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"Z. Cai and J. Ding. Separation and cut edge in macroscopic clusters for metric graph Gaussian free fields. arXiv preprint arXiv:2510.20516 , 2025","work_id":"f8533a21-b57c-479b-993e-954cc3a85d80","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":31,"snapshot_sha256":"d2f724883e3cc1537b10adddd8772e9ddc4e7df3fb66ee62140bf45ba4f82f41","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"6b03de93f3b38ba3784a02a18d60de61bc422b914f940fb3082d0a835b25001a"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":"228d6d60-4d44-4041-8b0c-19f37ba501a3"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-20T00:04:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C1d3UgngWq9jW0+O07qz/c3YgOzQNEX9Y+0aP4oRptvkzOW6xoOcpJaY20CYynriRSx1Or824XayqPqnXB0kBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T19:40:08.710981Z"},"content_sha256":"d0fcfaeea1bc9402edfd9d8f77519837c682390f238367a8507a7c31f36258d1","schema_version":"1.0","event_id":"sha256:d0fcfaeea1bc9402edfd9d8f77519837c682390f238367a8507a7c31f36258d1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KEPWWYGIFQ4DFO6C7T3D7G5PHM/bundle.json","state_url":"https://pith.science/pith/KEPWWYGIFQ4DFO6C7T3D7G5PHM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KEPWWYGIFQ4DFO6C7T3D7G5PHM/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-25T19:40:08Z","links":{"resolver":"https://pith.science/pith/KEPWWYGIFQ4DFO6C7T3D7G5PHM","bundle":"https://pith.science/pith/KEPWWYGIFQ4DFO6C7T3D7G5PHM/bundle.json","state":"https://pith.science/pith/KEPWWYGIFQ4DFO6C7T3D7G5PHM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KEPWWYGIFQ4DFO6C7T3D7G5PHM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:KEPWWYGIFQ4DFO6C7T3D7G5PHM","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"1d419cc6f782be4e667fcba392ed0a95647774c404025693f7fe37304bf9b9b0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-05-17T15:05:53Z","title_canon_sha256":"022ea897f5f64ffaa77e57fe3d904208660aa5b878e16c6b72f808569995f36a"},"schema_version":"1.0","source":{"id":"2605.17494","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.17494","created_at":"2026-05-20T00:04:42Z"},{"alias_kind":"arxiv_version","alias_value":"2605.17494v1","created_at":"2026-05-20T00:04:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.17494","created_at":"2026-05-20T00:04:42Z"},{"alias_kind":"pith_short_12","alias_value":"KEPWWYGIFQ4D","created_at":"2026-05-20T00:04:42Z"},{"alias_kind":"pith_short_16","alias_value":"KEPWWYGIFQ4DFO6C","created_at":"2026-05-20T00:04:42Z"},{"alias_kind":"pith_short_8","alias_value":"KEPWWYGI","created_at":"2026-05-20T00:04:42Z"}],"graph_snapshots":[{"event_id":"sha256:d0fcfaeea1bc9402edfd9d8f77519837c682390f238367a8507a7c31f36258d1","target":"graph","created_at":"2026-05-20T00:04:42Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"We establish the existence of generalized intersection exponents (GIE) and prove an up-to-constants estimate for these probabilities by means of a separation lemma tailored to this setting. We also relate the Hausdorff dimension of the set of local cut points of the three-dimensional Brownian loop soup to the GIE, and show that the GIE is continuous at intensity zero, where it reduces to the classical Brownian intersection exponent. In particular, this implies that, for sufficiently small intensity parameters, the set of local cut points has Hausdorff dimension strictly larger than 1."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The separation lemma tailored to the loop-soup setting holds and supplies the up-to-constants bounds needed to define the generalized intersection exponents; without it the existence claim and the dimension relation cannot be established from the non-intersection probabilities."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"The authors establish generalized intersection exponents for the 3D Brownian loop soup, prove an up-to-constants estimate via a separation lemma, relate them to the Hausdorff dimension of local cut points, and show continuity at zero intensity implying dimension strictly larger than 1 for small sub-"},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Generalized intersection exponents exist for the three-dimensional Brownian loop soup and relate to the dimension of its local cut points."}],"snapshot_sha256":"88d2724b1f84072ad55f8a2478632731a4152f9c9e7099dc9c6bed7d8cb14f0d"},"formal_canon":{"evidence_count":2,"snapshot_sha256":"6b03de93f3b38ba3784a02a18d60de61bc422b914f940fb3082d0a835b25001a"},"integrity":{"available":true,"clean":true,"detectors_run":[{"findings_count":0,"name":"doi_title_agreement","ran_at":"2026-05-19T23:01:19.529213Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"doi_compliance","ran_at":"2026-05-19T22:51:32.058059Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"claim_evidence","ran_at":"2026-05-19T21:41:57.676422Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"ai_meta_artifact","ran_at":"2026-05-19T21:33:23.640633Z","status":"skipped","version":"1.0.0"}],"endpoint":"/pith/2605.17494/integrity.json","findings":[],"snapshot_sha256":"6bb14c4c2ddb440ca1473bb296edfe1c6da7bed3773fc4e2437a6f13ffab5921","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study generalized non-intersection probabilities for the three-dimensional Brownian loop soup at subcritical intensities. We establish the existence of generalized intersection exponents (GIE) and prove an up-to-constants estimate for these probabilities by means of a separation lemma tailored to this setting. We also relate the Hausdorff dimension of the set of local cut points of the three-dimensional Brownian loop soup to the GIE, and show that the GIE is continuous at intensity zero, where it reduces to the classical Brownian intersection exponent. In particular, this implies that, for ","authors_text":"Ruixuan Li, Xinyi Li, Yifan Gao","cross_cats":[],"headline":"Generalized intersection exponents exist for the three-dimensional Brownian loop soup and relate to the dimension of its local cut points.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-05-17T15:05:53Z","title":"Generalized intersection exponents and local cut points for three-dimensional Brownian loop soup"},"references":{"count":31,"internal_anchors":0,"resolved_work":31,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"K. Burdzy and G. F. Lawler. Nonintersection exponents for Brownian paths. II. Estimates and applications to a random fractal. Ann. Probab., 18(3):981–1009, 1990","work_id":"14a016dd-255c-4b29-bfd2-858590b4968f","year":1990},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"arXiv preprint arXiv:2406.02397 , year=","work_id":"d58b182f-8251-453d-881f-b1d2b2ca98b4","year":2024},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"Z. Cai and J. Ding. Heterochromatic two-arm probabilities for metric graph Gaussian free fields. arXiv preprint arXiv:2510.20492 , 2025","work_id":"c1dfbc92-8410-4687-8d0c-551509e40e8f","year":2025},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"Z. Cai and J. Ding. On the gap between cluster dimensions of loop soups on R3 and the metric graph of Z3. arXiv preprint arXiv:2510.20526 , 2025","work_id":"78edfe45-0d58-4eb3-aa32-9c6aecec7067","year":2025},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"Z. Cai and J. Ding. Separation and cut edge in macroscopic clusters for metric graph Gaussian free fields. arXiv preprint arXiv:2510.20516 , 2025","work_id":"f8533a21-b57c-479b-993e-954cc3a85d80","year":2025}],"snapshot_sha256":"d2f724883e3cc1537b10adddd8772e9ddc4e7df3fb66ee62140bf45ba4f82f41"},"source":{"id":"2605.17494","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-19T22:41:39.804603Z","id":"228d6d60-4d44-4041-8b0c-19f37ba501a3","model_set":{"reader":"grok-4.3"},"one_line_summary":"The authors establish generalized intersection exponents for the 3D Brownian loop soup, prove an up-to-constants estimate via a separation lemma, relate them to the Hausdorff dimension of local cut points, and show continuity at zero intensity implying dimension strictly larger than 1 for small sub-","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Generalized intersection exponents exist for the three-dimensional Brownian loop soup and relate to the dimension of its local cut points.","strongest_claim":"We establish the existence of generalized intersection exponents (GIE) and prove an up-to-constants estimate for these probabilities by means of a separation lemma tailored to this setting. We also relate the Hausdorff dimension of the set of local cut points of the three-dimensional Brownian loop soup to the GIE, and show that the GIE is continuous at intensity zero, where it reduces to the classical Brownian intersection exponent. In particular, this implies that, for sufficiently small intensity parameters, the set of local cut points has Hausdorff dimension strictly larger than 1.","weakest_assumption":"The separation lemma tailored to the loop-soup setting holds and supplies the up-to-constants bounds needed to define the generalized intersection exponents; without it the existence claim and the dimension relation cannot be established from the non-intersection probabilities."}},"verdict_id":"228d6d60-4d44-4041-8b0c-19f37ba501a3"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:73a863f2e8d0c6c5412a791886a374f3ef401dc9265df36f19c2a065891700eb","target":"record","created_at":"2026-05-20T00:04:42Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"1d419cc6f782be4e667fcba392ed0a95647774c404025693f7fe37304bf9b9b0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-05-17T15:05:53Z","title_canon_sha256":"022ea897f5f64ffaa77e57fe3d904208660aa5b878e16c6b72f808569995f36a"},"schema_version":"1.0","source":{"id":"2605.17494","kind":"arxiv","version":1}},"canonical_sha256":"511f6b60c82c3832bbc2fcf63f9baf3b31a170b2ead9d26685f663718abb1117","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"511f6b60c82c3832bbc2fcf63f9baf3b31a170b2ead9d26685f663718abb1117","first_computed_at":"2026-05-20T00:04:42.095240Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:04:42.095240Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kcYuyPUTSe0qmg1WsALpAxvm2SONWfrfF4NdWdGaOqwHY9sSjo4PJBvqycmTyy6lLAxtpl6c1tiR7HEgvCxeBA==","signature_status":"signed_v1","signed_at":"2026-05-20T00:04:42.096086Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.17494","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:73a863f2e8d0c6c5412a791886a374f3ef401dc9265df36f19c2a065891700eb","sha256:d0fcfaeea1bc9402edfd9d8f77519837c682390f238367a8507a7c31f36258d1"],"state_sha256":"bece72727e51a77be31c8fe8aac8d075e0f968c4419b3ba40075ebea1ac4a7bd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vztEpii/3Gt5hsCjvC6Fb8Cz+98XSVIEEEC6hgZIPJ18sPjx49Et3BI23mSH1w/zvB85DzV8rVdx7A9TomVVDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T19:40:08.714954Z","bundle_sha256":"6726f0f95af17fb455fc3e3aed4b94d90e683d75497fca05b5ef0e3ef988bf6f"}}