{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:HFRFWWGSIJ53ZLYCJCY4RWQQ3Y","short_pith_number":"pith:HFRFWWGS","canonical_record":{"source":{"id":"1712.05521","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2017-12-15T04:03:54Z","cross_cats_sorted":[],"title_canon_sha256":"869675083adc521383c499e77c363d9f21f4cd6197b3ecab1fac4a944ec5ad9d","abstract_canon_sha256":"11ce84b865340d5b00b91d608a7da4676af3b68eb3a66d9d0a779e8ea098976c"},"schema_version":"1.0"},"canonical_sha256":"39625b58d2427bbcaf0248b1c8da10de3c8318d980dced1aff71c3c1fb99d250","source":{"kind":"arxiv","id":"1712.05521","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.05521","created_at":"2026-05-18T00:19:16Z"},{"alias_kind":"arxiv_version","alias_value":"1712.05521v4","created_at":"2026-05-18T00:19:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.05521","created_at":"2026-05-18T00:19:16Z"},{"alias_kind":"pith_short_12","alias_value":"HFRFWWGSIJ53","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"HFRFWWGSIJ53ZLYC","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"HFRFWWGS","created_at":"2026-05-18T12:31:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:HFRFWWGSIJ53ZLYCJCY4RWQQ3Y","target":"record","payload":{"canonical_record":{"source":{"id":"1712.05521","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2017-12-15T04:03:54Z","cross_cats_sorted":[],"title_canon_sha256":"869675083adc521383c499e77c363d9f21f4cd6197b3ecab1fac4a944ec5ad9d","abstract_canon_sha256":"11ce84b865340d5b00b91d608a7da4676af3b68eb3a66d9d0a779e8ea098976c"},"schema_version":"1.0"},"canonical_sha256":"39625b58d2427bbcaf0248b1c8da10de3c8318d980dced1aff71c3c1fb99d250","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:16.669430Z","signature_b64":"NesbJyTOueZ4X3P7/g9+ua6+CMmomXomrfdT8NZNh2v3d+IlhbQmnyC7s+lK/ECeJP5Nehbf0a3EM3lHQ6zZBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"39625b58d2427bbcaf0248b1c8da10de3c8318d980dced1aff71c3c1fb99d250","last_reissued_at":"2026-05-18T00:19:16.668609Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:16.668609Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.05521","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:19:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zImvlRv10ceJjy6gkpupd8rHuWUqnZfs0OJDuqEEcmGy2zybuLyqEgrNqZLyongLqCRj0Tg2P6kpPDKweW2dAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T02:37:02.556646Z"},"content_sha256":"605f8347f26ea1a39daacef40de04afb73a3bc7bbe379856371f05a27c2d528a","schema_version":"1.0","event_id":"sha256:605f8347f26ea1a39daacef40de04afb73a3bc7bbe379856371f05a27c2d528a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:HFRFWWGSIJ53ZLYCJCY4RWQQ3Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Maximally almost periodic groups and respecting properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Saak Gabriyelyan","submitted_at":"2017-12-15T04:03:54Z","abstract_excerpt":"For a Tychonoff space $X$, denote by $\\mathfrak{P}$ the family of topological properties $\\mathcal{P}$ of being a convergent sequence or being a compact, sequentially compact, countably compact, pseudocompact and functionally bounded subset of $X$, respectively. A maximally almost periodic $(MAP$) group $G$ respects $\\mathcal{P}$ if $\\mathcal{P}(G)=\\mathcal{P}(G^+)$, where $G^+$ is the group $G$ endowed with the Bohr topology. We study relations between different respecting properties from $\\mathfrak{P}$ and show that the respecting convergent sequences (=the Schur property) is the weakest one"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.05521","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:19:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yLtMG9eQH4dYyyVQN0Y977YLK88G5KaEE0EqEMjZqgB82Iu/X74MO+KO71sAiyoGjPYbiqo2D338Jm+a+bjaCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T02:37:02.557240Z"},"content_sha256":"458d25960d468332d7d0f8b551fb2a09be215f77b22ec09164ac8b7cc7800dfe","schema_version":"1.0","event_id":"sha256:458d25960d468332d7d0f8b551fb2a09be215f77b22ec09164ac8b7cc7800dfe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HFRFWWGSIJ53ZLYCJCY4RWQQ3Y/bundle.json","state_url":"https://pith.science/pith/HFRFWWGSIJ53ZLYCJCY4RWQQ3Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HFRFWWGSIJ53ZLYCJCY4RWQQ3Y/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":"2026-06-07T02:37:02Z","links":{"resolver":"https://pith.science/pith/HFRFWWGSIJ53ZLYCJCY4RWQQ3Y","bundle":"https://pith.science/pith/HFRFWWGSIJ53ZLYCJCY4RWQQ3Y/bundle.json","state":"https://pith.science/pith/HFRFWWGSIJ53ZLYCJCY4RWQQ3Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HFRFWWGSIJ53ZLYCJCY4RWQQ3Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:HFRFWWGSIJ53ZLYCJCY4RWQQ3Y","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":"11ce84b865340d5b00b91d608a7da4676af3b68eb3a66d9d0a779e8ea098976c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2017-12-15T04:03:54Z","title_canon_sha256":"869675083adc521383c499e77c363d9f21f4cd6197b3ecab1fac4a944ec5ad9d"},"schema_version":"1.0","source":{"id":"1712.05521","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.05521","created_at":"2026-05-18T00:19:16Z"},{"alias_kind":"arxiv_version","alias_value":"1712.05521v4","created_at":"2026-05-18T00:19:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.05521","created_at":"2026-05-18T00:19:16Z"},{"alias_kind":"pith_short_12","alias_value":"HFRFWWGSIJ53","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"HFRFWWGSIJ53ZLYC","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"HFRFWWGS","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:458d25960d468332d7d0f8b551fb2a09be215f77b22ec09164ac8b7cc7800dfe","target":"graph","created_at":"2026-05-18T00:19:16Z","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":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"For a Tychonoff space $X$, denote by $\\mathfrak{P}$ the family of topological properties $\\mathcal{P}$ of being a convergent sequence or being a compact, sequentially compact, countably compact, pseudocompact and functionally bounded subset of $X$, respectively. A maximally almost periodic $(MAP$) group $G$ respects $\\mathcal{P}$ if $\\mathcal{P}(G)=\\mathcal{P}(G^+)$, where $G^+$ is the group $G$ endowed with the Bohr topology. We study relations between different respecting properties from $\\mathfrak{P}$ and show that the respecting convergent sequences (=the Schur property) is the weakest one","authors_text":"Saak Gabriyelyan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2017-12-15T04:03:54Z","title":"Maximally almost periodic groups and respecting properties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.05521","kind":"arxiv","version":4},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:605f8347f26ea1a39daacef40de04afb73a3bc7bbe379856371f05a27c2d528a","target":"record","created_at":"2026-05-18T00:19:16Z","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":"11ce84b865340d5b00b91d608a7da4676af3b68eb3a66d9d0a779e8ea098976c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2017-12-15T04:03:54Z","title_canon_sha256":"869675083adc521383c499e77c363d9f21f4cd6197b3ecab1fac4a944ec5ad9d"},"schema_version":"1.0","source":{"id":"1712.05521","kind":"arxiv","version":4}},"canonical_sha256":"39625b58d2427bbcaf0248b1c8da10de3c8318d980dced1aff71c3c1fb99d250","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"39625b58d2427bbcaf0248b1c8da10de3c8318d980dced1aff71c3c1fb99d250","first_computed_at":"2026-05-18T00:19:16.668609Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:16.668609Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NesbJyTOueZ4X3P7/g9+ua6+CMmomXomrfdT8NZNh2v3d+IlhbQmnyC7s+lK/ECeJP5Nehbf0a3EM3lHQ6zZBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:16.669430Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.05521","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:605f8347f26ea1a39daacef40de04afb73a3bc7bbe379856371f05a27c2d528a","sha256:458d25960d468332d7d0f8b551fb2a09be215f77b22ec09164ac8b7cc7800dfe"],"state_sha256":"1ccc73e21f9c2c30a7177530e4846ed50a022fb22cb2dffc84adec38adfef860"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tuaWI+ZR9N9F78VOpfvt5M+LFjjIJriirwSpk2/exTBFyMM9er3nG7uGjg1EHnzzBeEz1VYXaMSr2Gv7sWo0Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T02:37:02.560284Z","bundle_sha256":"259db838cde1784bb1fb65c9bf8356661a73ffcbf988e6d6b5ccef84bf64fde2"}}