{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:B42UOOGYDXIWCLJAWM2X2HBLT5","short_pith_number":"pith:B42UOOGY","canonical_record":{"source":{"id":"1511.02898","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2015-11-09T21:40:36Z","cross_cats_sorted":[],"title_canon_sha256":"a11be667a343f0f7b6cce065fd0a09f8ec66d4ba646a314edaf73d4b9848d692","abstract_canon_sha256":"776131594b8b94502f5657aed210d081116c986b18dc4a81e84df8a643c51672"},"schema_version":"1.0"},"canonical_sha256":"0f354738d81dd1612d20b3357d1c2b9f473cde31581fbe246882a450f2186502","source":{"kind":"arxiv","id":"1511.02898","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.02898","created_at":"2026-05-18T01:27:17Z"},{"alias_kind":"arxiv_version","alias_value":"1511.02898v1","created_at":"2026-05-18T01:27:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.02898","created_at":"2026-05-18T01:27:17Z"},{"alias_kind":"pith_short_12","alias_value":"B42UOOGYDXIW","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"B42UOOGYDXIWCLJA","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"B42UOOGY","created_at":"2026-05-18T12:29:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:B42UOOGYDXIWCLJAWM2X2HBLT5","target":"record","payload":{"canonical_record":{"source":{"id":"1511.02898","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2015-11-09T21:40:36Z","cross_cats_sorted":[],"title_canon_sha256":"a11be667a343f0f7b6cce065fd0a09f8ec66d4ba646a314edaf73d4b9848d692","abstract_canon_sha256":"776131594b8b94502f5657aed210d081116c986b18dc4a81e84df8a643c51672"},"schema_version":"1.0"},"canonical_sha256":"0f354738d81dd1612d20b3357d1c2b9f473cde31581fbe246882a450f2186502","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:17.514987Z","signature_b64":"G5/qJ4i13yp4rNZHEUi6MiS38OOQkonJEsyq5K8aEQ/0aQEuCy0ogPkUQK3LJsr2QmxbadsayH1MRbZ9tCsEBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0f354738d81dd1612d20b3357d1c2b9f473cde31581fbe246882a450f2186502","last_reissued_at":"2026-05-18T01:27:17.514168Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:17.514168Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.02898","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:27:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xT/nFWPzFSno2ZiSyL9am5wXLIoMPanANhHL9G5MQ5xNVinhhntrfou+EZKBVApR5GZGkq4p4bAb0OYTS7gjDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-19T23:41:00.967155Z"},"content_sha256":"67613e461410a4ee14a4dd4395c05d858b7111fe8e55bbef04a294bf3187b74c","schema_version":"1.0","event_id":"sha256:67613e461410a4ee14a4dd4395c05d858b7111fe8e55bbef04a294bf3187b74c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:B42UOOGYDXIWCLJAWM2X2HBLT5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Categorically proper homomorphisms of topological groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Walter Tholen, Wei He","submitted_at":"2015-11-09T21:40:36Z","abstract_excerpt":"We extend the Dikranjan-Uspenskij notions of c-compact and h-complete topological group to the morphism level, study the stability properties of the newly defined types of maps, such as closure under direct products, and compare them with their counterparts in topology. We assume Hausdorffness only when our proofs require us to do so, which leads to new results and the affirmation of some facts that were known in a Hausdorff context."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.02898","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:27:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LdZYICNy3/pNc9HAlydqZaRwnQpky/T5sIHZi1zTJHxdSy+zZBbSyRNucZn8NtxoET2OAnoYtYar82wI22zsDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-19T23:41:00.967513Z"},"content_sha256":"8ead7678ac70be0f52ad927a5032142199c6d49d8d9be9f291c046a418389d35","schema_version":"1.0","event_id":"sha256:8ead7678ac70be0f52ad927a5032142199c6d49d8d9be9f291c046a418389d35"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B42UOOGYDXIWCLJAWM2X2HBLT5/bundle.json","state_url":"https://pith.science/pith/B42UOOGYDXIWCLJAWM2X2HBLT5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B42UOOGYDXIWCLJAWM2X2HBLT5/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":"2026-06-19T23:41:00Z","links":{"resolver":"https://pith.science/pith/B42UOOGYDXIWCLJAWM2X2HBLT5","bundle":"https://pith.science/pith/B42UOOGYDXIWCLJAWM2X2HBLT5/bundle.json","state":"https://pith.science/pith/B42UOOGYDXIWCLJAWM2X2HBLT5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B42UOOGYDXIWCLJAWM2X2HBLT5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:B42UOOGYDXIWCLJAWM2X2HBLT5","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":"776131594b8b94502f5657aed210d081116c986b18dc4a81e84df8a643c51672","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2015-11-09T21:40:36Z","title_canon_sha256":"a11be667a343f0f7b6cce065fd0a09f8ec66d4ba646a314edaf73d4b9848d692"},"schema_version":"1.0","source":{"id":"1511.02898","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.02898","created_at":"2026-05-18T01:27:17Z"},{"alias_kind":"arxiv_version","alias_value":"1511.02898v1","created_at":"2026-05-18T01:27:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.02898","created_at":"2026-05-18T01:27:17Z"},{"alias_kind":"pith_short_12","alias_value":"B42UOOGYDXIW","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"B42UOOGYDXIWCLJA","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"B42UOOGY","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:8ead7678ac70be0f52ad927a5032142199c6d49d8d9be9f291c046a418389d35","target":"graph","created_at":"2026-05-18T01:27:17Z","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":"We extend the Dikranjan-Uspenskij notions of c-compact and h-complete topological group to the morphism level, study the stability properties of the newly defined types of maps, such as closure under direct products, and compare them with their counterparts in topology. We assume Hausdorffness only when our proofs require us to do so, which leads to new results and the affirmation of some facts that were known in a Hausdorff context.","authors_text":"Walter Tholen, Wei He","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2015-11-09T21:40:36Z","title":"Categorically proper homomorphisms of topological groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.02898","kind":"arxiv","version":1},"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":"sha256:67613e461410a4ee14a4dd4395c05d858b7111fe8e55bbef04a294bf3187b74c","target":"record","created_at":"2026-05-18T01:27:17Z","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":"776131594b8b94502f5657aed210d081116c986b18dc4a81e84df8a643c51672","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2015-11-09T21:40:36Z","title_canon_sha256":"a11be667a343f0f7b6cce065fd0a09f8ec66d4ba646a314edaf73d4b9848d692"},"schema_version":"1.0","source":{"id":"1511.02898","kind":"arxiv","version":1}},"canonical_sha256":"0f354738d81dd1612d20b3357d1c2b9f473cde31581fbe246882a450f2186502","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0f354738d81dd1612d20b3357d1c2b9f473cde31581fbe246882a450f2186502","first_computed_at":"2026-05-18T01:27:17.514168Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:27:17.514168Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G5/qJ4i13yp4rNZHEUi6MiS38OOQkonJEsyq5K8aEQ/0aQEuCy0ogPkUQK3LJsr2QmxbadsayH1MRbZ9tCsEBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:27:17.514987Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.02898","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:67613e461410a4ee14a4dd4395c05d858b7111fe8e55bbef04a294bf3187b74c","sha256:8ead7678ac70be0f52ad927a5032142199c6d49d8d9be9f291c046a418389d35"],"state_sha256":"6d02e826c8c654c779e1d58d10759aad8edbfa76267e294bf4945c5adb24a3b4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U6+nJ/tPy1VUqbfb5AxAKB5no6wdBfN47UQ52ugb8oBRAMiTZ0QikLltj2rvb/DEdNMtW9a7uUhIrY8qHybtCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-19T23:41:00.969417Z","bundle_sha256":"195c18f4e248e1798c67834c69f398296b7b7344afe1f75fcc799370b80ea09a"}}