{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:AFUBO4P4AKTQYWAEESGY5YXFSG","short_pith_number":"pith:AFUBO4P4","canonical_record":{"source":{"id":"1703.02909","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-03-08T16:48:00Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"e1c66eb5c2b6ec931c8129a6a9ec41e265b716779852a5250bb28ce5d28b5d6b","abstract_canon_sha256":"46186479934e6ef3d41f0ff5e30942ea6f3738e7be741cb49b4aeb0c2f01b190"},"schema_version":"1.0"},"canonical_sha256":"01681771fc02a70c5804248d8ee2e591a7d28b2191e98dd70a8de1be01bcfb33","source":{"kind":"arxiv","id":"1703.02909","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.02909","created_at":"2026-05-18T00:49:05Z"},{"alias_kind":"arxiv_version","alias_value":"1703.02909v1","created_at":"2026-05-18T00:49:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.02909","created_at":"2026-05-18T00:49:05Z"},{"alias_kind":"pith_short_12","alias_value":"AFUBO4P4AKTQ","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"AFUBO4P4AKTQYWAE","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"AFUBO4P4","created_at":"2026-05-18T12:31:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:AFUBO4P4AKTQYWAEESGY5YXFSG","target":"record","payload":{"canonical_record":{"source":{"id":"1703.02909","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-03-08T16:48:00Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"e1c66eb5c2b6ec931c8129a6a9ec41e265b716779852a5250bb28ce5d28b5d6b","abstract_canon_sha256":"46186479934e6ef3d41f0ff5e30942ea6f3738e7be741cb49b4aeb0c2f01b190"},"schema_version":"1.0"},"canonical_sha256":"01681771fc02a70c5804248d8ee2e591a7d28b2191e98dd70a8de1be01bcfb33","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:05.340341Z","signature_b64":"1vOxQ4hLBXjCvq/wdI0AjQMrL95OWL14J0R3kfMS8OrBQ+AlPM9Xndj81sXy4xnjwSFR3p4RvUOJ0c9llvnEBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"01681771fc02a70c5804248d8ee2e591a7d28b2191e98dd70a8de1be01bcfb33","last_reissued_at":"2026-05-18T00:49:05.339767Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:05.339767Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.02909","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":"2026-05-18T00:49:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hbVDWJy+X7LoWh99EgJcJ0RtDzTzId/Pg8pqlQCR6sG+1e4peeKQ2JOub4Rv21838yEyOo0jzLpVL5LrUsYRAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T04:05:06.641713Z"},"content_sha256":"dc3dfc6fbaeac6576dc6a1ae0fb0b9760c1342d5e339e31e3dd5a562791438bb","schema_version":"1.0","event_id":"sha256:dc3dfc6fbaeac6576dc6a1ae0fb0b9760c1342d5e339e31e3dd5a562791438bb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:AFUBO4P4AKTQYWAEESGY5YXFSG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Weak separation properties for closed subgroups of locally compact groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Zsolt Tanko","submitted_at":"2017-03-08T16:48:00Z","abstract_excerpt":"Three separation properties for a closed subgroup $H$ of a locally compact group $G$ are studied: (1) the existence of a bounded approximate indicator for $H$, (2) the existence of a completely bounded invariant projection of $VN\\left(G\\right)$ onto $VN_{H}\\left(G\\right)$, and (3) the approximability of the characteristic function $\\chi_{H}$ by functions in $M_{cb}A\\left(G\\right)$ with respect to the weak$^{*}$ topology of $M_{cb}A\\left(G_{d}\\right)$. We show that the $H$-separation property of Kaniuth and Lau is characterized by the existence of certain bounded approximate indicators for $H$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.02909","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":"2026-05-18T00:49:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K+trIYKTkHa+RHBpRaWz1zff55L5qah4OUnA56ABhsG0J1PHwyuM1WaYSg3qkn9mAo2oJ3OAxcx3GwQd35quDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T04:05:06.642061Z"},"content_sha256":"5c00b9dc12339b4512dc8d43bcfa3d79fba69adf36fb748295b990314f5d4e07","schema_version":"1.0","event_id":"sha256:5c00b9dc12339b4512dc8d43bcfa3d79fba69adf36fb748295b990314f5d4e07"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AFUBO4P4AKTQYWAEESGY5YXFSG/bundle.json","state_url":"https://pith.science/pith/AFUBO4P4AKTQYWAEESGY5YXFSG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AFUBO4P4AKTQYWAEESGY5YXFSG/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":"2026-06-24T04:05:06Z","links":{"resolver":"https://pith.science/pith/AFUBO4P4AKTQYWAEESGY5YXFSG","bundle":"https://pith.science/pith/AFUBO4P4AKTQYWAEESGY5YXFSG/bundle.json","state":"https://pith.science/pith/AFUBO4P4AKTQYWAEESGY5YXFSG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AFUBO4P4AKTQYWAEESGY5YXFSG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:AFUBO4P4AKTQYWAEESGY5YXFSG","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":"46186479934e6ef3d41f0ff5e30942ea6f3738e7be741cb49b4aeb0c2f01b190","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-03-08T16:48:00Z","title_canon_sha256":"e1c66eb5c2b6ec931c8129a6a9ec41e265b716779852a5250bb28ce5d28b5d6b"},"schema_version":"1.0","source":{"id":"1703.02909","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.02909","created_at":"2026-05-18T00:49:05Z"},{"alias_kind":"arxiv_version","alias_value":"1703.02909v1","created_at":"2026-05-18T00:49:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.02909","created_at":"2026-05-18T00:49:05Z"},{"alias_kind":"pith_short_12","alias_value":"AFUBO4P4AKTQ","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"AFUBO4P4AKTQYWAE","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"AFUBO4P4","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:5c00b9dc12339b4512dc8d43bcfa3d79fba69adf36fb748295b990314f5d4e07","target":"graph","created_at":"2026-05-18T00:49:05Z","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":"Three separation properties for a closed subgroup $H$ of a locally compact group $G$ are studied: (1) the existence of a bounded approximate indicator for $H$, (2) the existence of a completely bounded invariant projection of $VN\\left(G\\right)$ onto $VN_{H}\\left(G\\right)$, and (3) the approximability of the characteristic function $\\chi_{H}$ by functions in $M_{cb}A\\left(G\\right)$ with respect to the weak$^{*}$ topology of $M_{cb}A\\left(G_{d}\\right)$. We show that the $H$-separation property of Kaniuth and Lau is characterized by the existence of certain bounded approximate indicators for $H$ ","authors_text":"Zsolt Tanko","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-03-08T16:48:00Z","title":"Weak separation properties for closed subgroups of locally compact groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.02909","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:dc3dfc6fbaeac6576dc6a1ae0fb0b9760c1342d5e339e31e3dd5a562791438bb","target":"record","created_at":"2026-05-18T00:49:05Z","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":"46186479934e6ef3d41f0ff5e30942ea6f3738e7be741cb49b4aeb0c2f01b190","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-03-08T16:48:00Z","title_canon_sha256":"e1c66eb5c2b6ec931c8129a6a9ec41e265b716779852a5250bb28ce5d28b5d6b"},"schema_version":"1.0","source":{"id":"1703.02909","kind":"arxiv","version":1}},"canonical_sha256":"01681771fc02a70c5804248d8ee2e591a7d28b2191e98dd70a8de1be01bcfb33","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"01681771fc02a70c5804248d8ee2e591a7d28b2191e98dd70a8de1be01bcfb33","first_computed_at":"2026-05-18T00:49:05.339767Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:05.339767Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1vOxQ4hLBXjCvq/wdI0AjQMrL95OWL14J0R3kfMS8OrBQ+AlPM9Xndj81sXy4xnjwSFR3p4RvUOJ0c9llvnEBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:05.340341Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.02909","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dc3dfc6fbaeac6576dc6a1ae0fb0b9760c1342d5e339e31e3dd5a562791438bb","sha256:5c00b9dc12339b4512dc8d43bcfa3d79fba69adf36fb748295b990314f5d4e07"],"state_sha256":"e9b6c5c629624a92cfc13e6a629e4155a8b51536f42634a0855b73680a937db6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sj2PLDlrsMDYAGGe810P+rj9jskCmSfyZw24hRppoU4hKFnpUi1DOapUfOrgJAGzFOsRi5XO1CgabpigzQlADw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T04:05:06.643959Z","bundle_sha256":"2318c182c1f41c1c8e5697c7e661e6eeb67b9992c8d8ef4e0a68ca8edde5e5ba"}}