{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:2AB6P33HLMANHZMFE6SRVI566F","short_pith_number":"pith:2AB6P33H","schema_version":"1.0","canonical_sha256":"d003e7ef675b00d3e58527a51aa3bef1470f66926290d7785563c00e6f3363ed","source":{"kind":"arxiv","id":"2411.19713","version":3},"attestation_state":"computed","paper":{"title":"CantorNet: A Sandbox for Testing Geometrical and Topological Complexity Measures","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI","stat.ML"],"primary_cat":"cs.NE","authors_text":"Bernhard A.Moser, Hamid Eghbalzadeh, Michal Lewandowski","submitted_at":"2024-11-29T14:01:34Z","abstract_excerpt":"Many natural phenomena are characterized by self-similarity, for example the symmetry of human faces, or a repetitive motif of a song. Studying of such symmetries will allow us to gain deeper insights into the underlying mechanisms of complex systems. Recognizing the importance of understanding these patterns, we propose a geometrically inspired framework to study such phenomena in artificial neural networks. To this end, we introduce \\emph{CantorNet}, inspired by the triadic construction of the Cantor set, which was introduced by Georg Cantor in the $19^\\text{th}$ century. In mathematics, the"},"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":"2411.19713","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.NE","submitted_at":"2024-11-29T14:01:34Z","cross_cats_sorted":["cs.AI","stat.ML"],"title_canon_sha256":"37679ec17e295489ca332af4e8aa48be690e1ed4dda0ac9ec583e0da6ca5a8b2","abstract_canon_sha256":"9aa962095cc7d0d4ff64e2ed24dd04fee47a5791cb7e62a02c978265aff9e27b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:06:09.484813Z","signature_b64":"Nfdy51nfy9Rq9OXGvHJNC6LS3pLXBul3F0HFoVEm4krrVhjhwrGQHze4komUdIQTDR7IFPaSNqGUyI14aOIMBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d003e7ef675b00d3e58527a51aa3bef1470f66926290d7785563c00e6f3363ed","last_reissued_at":"2026-07-05T10:06:09.484302Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:06:09.484302Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"CantorNet: A Sandbox for Testing Geometrical and Topological Complexity Measures","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI","stat.ML"],"primary_cat":"cs.NE","authors_text":"Bernhard A.Moser, Hamid Eghbalzadeh, Michal Lewandowski","submitted_at":"2024-11-29T14:01:34Z","abstract_excerpt":"Many natural phenomena are characterized by self-similarity, for example the symmetry of human faces, or a repetitive motif of a song. Studying of such symmetries will allow us to gain deeper insights into the underlying mechanisms of complex systems. Recognizing the importance of understanding these patterns, we propose a geometrically inspired framework to study such phenomena in artificial neural networks. To this end, we introduce \\emph{CantorNet}, inspired by the triadic construction of the Cantor set, which was introduced by Georg Cantor in the $19^\\text{th}$ century. In mathematics, the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.19713","kind":"arxiv","version":3},"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/2411.19713/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":"2411.19713","created_at":"2026-07-05T10:06:09.484375+00:00"},{"alias_kind":"arxiv_version","alias_value":"2411.19713v3","created_at":"2026-07-05T10:06:09.484375+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.19713","created_at":"2026-07-05T10:06:09.484375+00:00"},{"alias_kind":"pith_short_12","alias_value":"2AB6P33HLMAN","created_at":"2026-07-05T10:06:09.484375+00:00"},{"alias_kind":"pith_short_16","alias_value":"2AB6P33HLMANHZMF","created_at":"2026-07-05T10:06:09.484375+00:00"},{"alias_kind":"pith_short_8","alias_value":"2AB6P33H","created_at":"2026-07-05T10:06:09.484375+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/2AB6P33HLMANHZMFE6SRVI566F","json":"https://pith.science/pith/2AB6P33HLMANHZMFE6SRVI566F.json","graph_json":"https://pith.science/api/pith-number/2AB6P33HLMANHZMFE6SRVI566F/graph.json","events_json":"https://pith.science/api/pith-number/2AB6P33HLMANHZMFE6SRVI566F/events.json","paper":"https://pith.science/paper/2AB6P33H"},"agent_actions":{"view_html":"https://pith.science/pith/2AB6P33HLMANHZMFE6SRVI566F","download_json":"https://pith.science/pith/2AB6P33HLMANHZMFE6SRVI566F.json","view_paper":"https://pith.science/paper/2AB6P33H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2411.19713&json=true","fetch_graph":"https://pith.science/api/pith-number/2AB6P33HLMANHZMFE6SRVI566F/graph.json","fetch_events":"https://pith.science/api/pith-number/2AB6P33HLMANHZMFE6SRVI566F/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2AB6P33HLMANHZMFE6SRVI566F/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2AB6P33HLMANHZMFE6SRVI566F/action/storage_attestation","attest_author":"https://pith.science/pith/2AB6P33HLMANHZMFE6SRVI566F/action/author_attestation","sign_citation":"https://pith.science/pith/2AB6P33HLMANHZMFE6SRVI566F/action/citation_signature","submit_replication":"https://pith.science/pith/2AB6P33HLMANHZMFE6SRVI566F/action/replication_record"}},"created_at":"2026-07-05T10:06:09.484375+00:00","updated_at":"2026-07-05T10:06:09.484375+00:00"}