{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:LKEB2MUZQF7SDOGZQDNDQGTG24","short_pith_number":"pith:LKEB2MUZ","schema_version":"1.0","canonical_sha256":"5a881d3299817f21b8d980da381a66d72f31b397749ed0ae47c9e06338ebb183","source":{"kind":"arxiv","id":"2608.06180","version":1},"attestation_state":"computed","paper":{"title":"The Intersection Euler Characteristic Profile: Euler Calculus and Stability for Topological Interaction of Ball Unions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.AT","authors_text":"Atish Mitra, Kazuhiro Kawamura, Sushovan Majhi","submitted_at":"2026-08-06T15:41:07Z","abstract_excerpt":"The Intersection Euler Characteristic Profile (Intersection ECP) of $k$ colored point clouds $X_1, \\ldots, X_k \\subset \\mathbb{R}^d$ is the Euler characteristic $\\chi(\\bigcap_{i=1}^k \\mathcal{U}(X_i; t_i))$ of the overlap of their ball unions---an integer-valued, multiparameter invariant of their topological interaction across scales. Its organizing framework is the Euler calculus on constructible functions: the profile is equally the Euler integral $\\int \\prod_{i=1}^k \\mathbf{1}_{\\mathcal{U}(X_i; t_i)} \\, d\\chi$ of the product of the $k$ data-dependent offsets, and this identity---our Interse"},"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":false},"canonical_record":{"source":{"id":"2608.06180","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2026-08-06T15:41:07Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"e2e04f89fe84ebea971e39c0a342f07504fa61ac471f1914cb9101eb9ecb4bf6","abstract_canon_sha256":"ac34a5cd30f1395f8638dffd236f2ca08e5747d63c712150b53401567c45b47c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-07T01:40:53.292402Z","signature_b64":"FP9KtaAcbzhgVzOpVKuqBedv1y+4iKMLQTIdyufSoCkFThcpbKH24W0CYWUoFQcG/BV+Jjhsh7nTLRC/wFlnAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a881d3299817f21b8d980da381a66d72f31b397749ed0ae47c9e06338ebb183","last_reissued_at":"2026-08-07T01:40:53.290625Z","signature_status":"signed_v1","first_computed_at":"2026-08-07T01:40:53.290625Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Intersection Euler Characteristic Profile: Euler Calculus and Stability for Topological Interaction of Ball Unions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.AT","authors_text":"Atish Mitra, Kazuhiro Kawamura, Sushovan Majhi","submitted_at":"2026-08-06T15:41:07Z","abstract_excerpt":"The Intersection Euler Characteristic Profile (Intersection ECP) of $k$ colored point clouds $X_1, \\ldots, X_k \\subset \\mathbb{R}^d$ is the Euler characteristic $\\chi(\\bigcap_{i=1}^k \\mathcal{U}(X_i; t_i))$ of the overlap of their ball unions---an integer-valued, multiparameter invariant of their topological interaction across scales. Its organizing framework is the Euler calculus on constructible functions: the profile is equally the Euler integral $\\int \\prod_{i=1}^k \\mathbf{1}_{\\mathcal{U}(X_i; t_i)} \\, d\\chi$ of the product of the $k$ data-dependent offsets, and this identity---our Interse"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.06180","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.06180/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"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":"2608.06180","created_at":"2026-08-07T01:40:53.293177+00:00"},{"alias_kind":"arxiv_version","alias_value":"2608.06180v1","created_at":"2026-08-07T01:40:53.293177+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.06180","created_at":"2026-08-07T01:40:53.293177+00:00"},{"alias_kind":"pith_short_12","alias_value":"LKEB2MUZQF7S","created_at":"2026-08-07T01:40:53.293177+00:00"},{"alias_kind":"pith_short_16","alias_value":"LKEB2MUZQF7SDOGZ","created_at":"2026-08-07T01:40:53.293177+00:00"},{"alias_kind":"pith_short_8","alias_value":"LKEB2MUZ","created_at":"2026-08-07T01:40:53.293177+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LKEB2MUZQF7SDOGZQDNDQGTG24","json":"https://pith.science/pith/LKEB2MUZQF7SDOGZQDNDQGTG24.json","graph_json":"https://pith.science/api/pith-number/LKEB2MUZQF7SDOGZQDNDQGTG24/graph.json","events_json":"https://pith.science/api/pith-number/LKEB2MUZQF7SDOGZQDNDQGTG24/events.json","paper":"https://pith.science/paper/LKEB2MUZ"},"agent_actions":{"view_html":"https://pith.science/pith/LKEB2MUZQF7SDOGZQDNDQGTG24","download_json":"https://pith.science/pith/LKEB2MUZQF7SDOGZQDNDQGTG24.json","view_paper":"https://pith.science/paper/LKEB2MUZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2608.06180&json=true","fetch_graph":"https://pith.science/api/pith-number/LKEB2MUZQF7SDOGZQDNDQGTG24/graph.json","fetch_events":"https://pith.science/api/pith-number/LKEB2MUZQF7SDOGZQDNDQGTG24/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LKEB2MUZQF7SDOGZQDNDQGTG24/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LKEB2MUZQF7SDOGZQDNDQGTG24/action/storage_attestation","attest_author":"https://pith.science/pith/LKEB2MUZQF7SDOGZQDNDQGTG24/action/author_attestation","sign_citation":"https://pith.science/pith/LKEB2MUZQF7SDOGZQDNDQGTG24/action/citation_signature","submit_replication":"https://pith.science/pith/LKEB2MUZQF7SDOGZQDNDQGTG24/action/replication_record"}},"created_at":"2026-08-07T01:40:53.293177+00:00","updated_at":"2026-08-07T01:40:53.293177+00:00"}