{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:6FMZTUP6UQZM6ETDCSIIM4537A","short_pith_number":"pith:6FMZTUP6","schema_version":"1.0","canonical_sha256":"f15999d1fea432cf126314908673bbf81898c4c395b9b58c9864615c52105508","source":{"kind":"arxiv","id":"1312.7219","version":4},"attestation_state":"computed","paper":{"title":"Combining persistent homology and invariance groups for shape comparison","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","cs.CV"],"primary_cat":"math.AT","authors_text":"Grzegorz Jablonski, Patrizio Frosini","submitted_at":"2013-12-27T09:09:36Z","abstract_excerpt":"In many applications concerning the comparison of data expressed by $\\mathbb{R}^m$-valued functions defined on a topological space $X$, the invariance with respect to a given group $G$ of self-homeomorphisms of $X$ is required. While persistent homology is quite efficient in the topological and qualitative comparison of this kind of data when the invariance group $G$ is the group $\\mathrm{Homeo}(X)$ of all self-homeomorphisms of $X$, this theory is not tailored to manage the case in which $G$ is a proper subgroup of $\\mathrm{Homeo}(X)$, and its invariance appears too general for several tasks."},"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":"1312.7219","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-12-27T09:09:36Z","cross_cats_sorted":["cs.CG","cs.CV"],"title_canon_sha256":"21bae24c709e40ac96a9a5ac282e28d0129118bb852b59416525885ad9b02ee3","abstract_canon_sha256":"0a7ed94a545afc1d7c311eff4539676d2ec8b236993946562ce0c30be7c0bced"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:45.329240Z","signature_b64":"EXY+gODNAHIeiOXnCorYDEzIwuIejl202GorHZR7ZJj11KVU7XqkDqXCWExP1xZ39a7FOBZh5BvnIs+2qf/NAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f15999d1fea432cf126314908673bbf81898c4c395b9b58c9864615c52105508","last_reissued_at":"2026-05-18T01:21:45.328588Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:45.328588Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Combining persistent homology and invariance groups for shape comparison","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","cs.CV"],"primary_cat":"math.AT","authors_text":"Grzegorz Jablonski, Patrizio Frosini","submitted_at":"2013-12-27T09:09:36Z","abstract_excerpt":"In many applications concerning the comparison of data expressed by $\\mathbb{R}^m$-valued functions defined on a topological space $X$, the invariance with respect to a given group $G$ of self-homeomorphisms of $X$ is required. While persistent homology is quite efficient in the topological and qualitative comparison of this kind of data when the invariance group $G$ is the group $\\mathrm{Homeo}(X)$ of all self-homeomorphisms of $X$, this theory is not tailored to manage the case in which $G$ is a proper subgroup of $\\mathrm{Homeo}(X)$, and its invariance appears too general for several tasks."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.7219","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1312.7219","created_at":"2026-05-18T01:21:45.328687+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.7219v4","created_at":"2026-05-18T01:21:45.328687+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.7219","created_at":"2026-05-18T01:21:45.328687+00:00"},{"alias_kind":"pith_short_12","alias_value":"6FMZTUP6UQZM","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_16","alias_value":"6FMZTUP6UQZM6ETD","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_8","alias_value":"6FMZTUP6","created_at":"2026-05-18T12:27:36.564083+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/6FMZTUP6UQZM6ETDCSIIM4537A","json":"https://pith.science/pith/6FMZTUP6UQZM6ETDCSIIM4537A.json","graph_json":"https://pith.science/api/pith-number/6FMZTUP6UQZM6ETDCSIIM4537A/graph.json","events_json":"https://pith.science/api/pith-number/6FMZTUP6UQZM6ETDCSIIM4537A/events.json","paper":"https://pith.science/paper/6FMZTUP6"},"agent_actions":{"view_html":"https://pith.science/pith/6FMZTUP6UQZM6ETDCSIIM4537A","download_json":"https://pith.science/pith/6FMZTUP6UQZM6ETDCSIIM4537A.json","view_paper":"https://pith.science/paper/6FMZTUP6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.7219&json=true","fetch_graph":"https://pith.science/api/pith-number/6FMZTUP6UQZM6ETDCSIIM4537A/graph.json","fetch_events":"https://pith.science/api/pith-number/6FMZTUP6UQZM6ETDCSIIM4537A/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6FMZTUP6UQZM6ETDCSIIM4537A/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6FMZTUP6UQZM6ETDCSIIM4537A/action/storage_attestation","attest_author":"https://pith.science/pith/6FMZTUP6UQZM6ETDCSIIM4537A/action/author_attestation","sign_citation":"https://pith.science/pith/6FMZTUP6UQZM6ETDCSIIM4537A/action/citation_signature","submit_replication":"https://pith.science/pith/6FMZTUP6UQZM6ETDCSIIM4537A/action/replication_record"}},"created_at":"2026-05-18T01:21:45.328687+00:00","updated_at":"2026-05-18T01:21:45.328687+00:00"}