{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:L3DWDMJJ7H2JL5IU5SQ6GNWD67","short_pith_number":"pith:L3DWDMJJ","schema_version":"1.0","canonical_sha256":"5ec761b129f9f495f514eca1e336c3f7e5d2c23187f3c802005901ce323f933d","source":{"kind":"arxiv","id":"1305.7369","version":1},"attestation_state":"computed","paper":{"title":"Countable powers of compact Abelian groups in the uniform topology and cardinality of their dual groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"D. Dikranjan, E. Mart\\'in-Peinador, V. Tarieladze","submitted_at":"2013-05-31T11:53:53Z","abstract_excerpt":"We equip the product of countably many copies of a compact Abelian group X with the uniform topology, and study some properties of the topological group G thus obtained. In particular, we determine the cardinality of the dual group of G, when X is the circle group: it is precisely 2^c."},"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":"1305.7369","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2013-05-31T11:53:53Z","cross_cats_sorted":[],"title_canon_sha256":"11f115bf244678313d0721f4abd3cfca9475db8e2d749804a7cd8a793b465d82","abstract_canon_sha256":"14e98b2d5517813c8cdb3b47975950cb72c582617f58bc44b36ad3436239af94"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:22:07.072194Z","signature_b64":"O8pDNJUaktb6qRh4AkBWi/8XCcldS/uEMSnrNcE4+CLhzWDRRWNR/L+T1N7NAJqvhPRdu/kDm8cbk1l7z6tCBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ec761b129f9f495f514eca1e336c3f7e5d2c23187f3c802005901ce323f933d","last_reissued_at":"2026-05-18T03:22:07.071595Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:22:07.071595Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Countable powers of compact Abelian groups in the uniform topology and cardinality of their dual groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"D. Dikranjan, E. Mart\\'in-Peinador, V. Tarieladze","submitted_at":"2013-05-31T11:53:53Z","abstract_excerpt":"We equip the product of countably many copies of a compact Abelian group X with the uniform topology, and study some properties of the topological group G thus obtained. In particular, we determine the cardinality of the dual group of G, when X is the circle group: it is precisely 2^c."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.7369","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":""},"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":"1305.7369","created_at":"2026-05-18T03:22:07.071667+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.7369v1","created_at":"2026-05-18T03:22:07.071667+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.7369","created_at":"2026-05-18T03:22:07.071667+00:00"},{"alias_kind":"pith_short_12","alias_value":"L3DWDMJJ7H2J","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_16","alias_value":"L3DWDMJJ7H2JL5IU","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_8","alias_value":"L3DWDMJJ","created_at":"2026-05-18T12:27:51.066281+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/L3DWDMJJ7H2JL5IU5SQ6GNWD67","json":"https://pith.science/pith/L3DWDMJJ7H2JL5IU5SQ6GNWD67.json","graph_json":"https://pith.science/api/pith-number/L3DWDMJJ7H2JL5IU5SQ6GNWD67/graph.json","events_json":"https://pith.science/api/pith-number/L3DWDMJJ7H2JL5IU5SQ6GNWD67/events.json","paper":"https://pith.science/paper/L3DWDMJJ"},"agent_actions":{"view_html":"https://pith.science/pith/L3DWDMJJ7H2JL5IU5SQ6GNWD67","download_json":"https://pith.science/pith/L3DWDMJJ7H2JL5IU5SQ6GNWD67.json","view_paper":"https://pith.science/paper/L3DWDMJJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.7369&json=true","fetch_graph":"https://pith.science/api/pith-number/L3DWDMJJ7H2JL5IU5SQ6GNWD67/graph.json","fetch_events":"https://pith.science/api/pith-number/L3DWDMJJ7H2JL5IU5SQ6GNWD67/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/L3DWDMJJ7H2JL5IU5SQ6GNWD67/action/timestamp_anchor","attest_storage":"https://pith.science/pith/L3DWDMJJ7H2JL5IU5SQ6GNWD67/action/storage_attestation","attest_author":"https://pith.science/pith/L3DWDMJJ7H2JL5IU5SQ6GNWD67/action/author_attestation","sign_citation":"https://pith.science/pith/L3DWDMJJ7H2JL5IU5SQ6GNWD67/action/citation_signature","submit_replication":"https://pith.science/pith/L3DWDMJJ7H2JL5IU5SQ6GNWD67/action/replication_record"}},"created_at":"2026-05-18T03:22:07.071667+00:00","updated_at":"2026-05-18T03:22:07.071667+00:00"}