{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:N6H3MYDE7KWKMUAC72PTLSCCBK","short_pith_number":"pith:N6H3MYDE","canonical_record":{"source":{"id":"1509.01108","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2015-09-03T14:43:34Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"f87d4a7e641f61aa71a1eb836ec6cb90f5c93383bd4e29dac739803638ab7055","abstract_canon_sha256":"480652b26534d5db451877bfcc3c82b90608004cda384504af248738730d699e"},"schema_version":"1.0"},"canonical_sha256":"6f8fb66064faaca65002fe9f35c8420ab9e15b4231e859abab56e06b6bcf6f84","source":{"kind":"arxiv","id":"1509.01108","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.01108","created_at":"2026-05-18T01:34:04Z"},{"alias_kind":"arxiv_version","alias_value":"1509.01108v1","created_at":"2026-05-18T01:34:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.01108","created_at":"2026-05-18T01:34:04Z"},{"alias_kind":"pith_short_12","alias_value":"N6H3MYDE7KWK","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"N6H3MYDE7KWKMUAC","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"N6H3MYDE","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:N6H3MYDE7KWKMUAC72PTLSCCBK","target":"record","payload":{"canonical_record":{"source":{"id":"1509.01108","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2015-09-03T14:43:34Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"f87d4a7e641f61aa71a1eb836ec6cb90f5c93383bd4e29dac739803638ab7055","abstract_canon_sha256":"480652b26534d5db451877bfcc3c82b90608004cda384504af248738730d699e"},"schema_version":"1.0"},"canonical_sha256":"6f8fb66064faaca65002fe9f35c8420ab9e15b4231e859abab56e06b6bcf6f84","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:04.284218Z","signature_b64":"Wh0nsLMoNr46MnS2daHzPiT62bqPC3CmT3bMWBua5kbHfHVFqOYt4Mz2gBERGzaJHrBNWs1/EoI7QDofbMKoDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6f8fb66064faaca65002fe9f35c8420ab9e15b4231e859abab56e06b6bcf6f84","last_reissued_at":"2026-05-18T01:34:04.283604Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:04.283604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.01108","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":"2026-05-18T01:34:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9sKWvngjQAPquxZmsxDMaexrMKqsyYtp+lBjhW2Irk+vc/YE3K8oWhgU4JhD1uZdIXlyBHwqaMtLjruTAFa8Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T12:08:23.268901Z"},"content_sha256":"1e588ccdd3b18376920efc55ae07ac9dce350c31fb12cec0d0875af1daaa16c6","schema_version":"1.0","event_id":"sha256:1e588ccdd3b18376920efc55ae07ac9dce350c31fb12cec0d0875af1daaa16c6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:N6H3MYDE7KWKMUAC72PTLSCCBK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Characterized subgroups of topological abelian groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.GN","authors_text":"Anna Giordano Bruno, Daniele Impieri, Dikran Dikranjan","submitted_at":"2015-09-03T14:43:34Z","abstract_excerpt":"A subgroup $H$ of a topological abelian group $X$ is said to be characterized by a sequence $\\mathbf v =(v_n)$ of characters of $X$ if $H=\\{x\\in X:v_n(x)\\to 0\\ \\text{in}\\ \\mathbb T\\}$. We study the basic properties of characterized subgroups in the general setting, extending results known in the compact case. For a better description, we isolate various types of characterized subgroups. Moreover, we introduce the relevant class of autochacaracterized groups (namely, the groups that are characterized subgroups of themselves by means of a sequence of non-null characters); in the case of locally "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01108","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":"2026-05-18T01:34:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QIn4V8bkRZo1BoZug+HUijGGPfnqVoStZr/rE2KbdgzfZ8cYnyeVEYyxYni05v21iY3QMi7LxmAoIp1nYV3dCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T12:08:23.269250Z"},"content_sha256":"5ef86c2f05860e4246a7d603897aee82842ddee8e78c85a164d0f18a5966ff88","schema_version":"1.0","event_id":"sha256:5ef86c2f05860e4246a7d603897aee82842ddee8e78c85a164d0f18a5966ff88"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N6H3MYDE7KWKMUAC72PTLSCCBK/bundle.json","state_url":"https://pith.science/pith/N6H3MYDE7KWKMUAC72PTLSCCBK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N6H3MYDE7KWKMUAC72PTLSCCBK/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":"2026-06-01T12:08:23Z","links":{"resolver":"https://pith.science/pith/N6H3MYDE7KWKMUAC72PTLSCCBK","bundle":"https://pith.science/pith/N6H3MYDE7KWKMUAC72PTLSCCBK/bundle.json","state":"https://pith.science/pith/N6H3MYDE7KWKMUAC72PTLSCCBK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N6H3MYDE7KWKMUAC72PTLSCCBK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:N6H3MYDE7KWKMUAC72PTLSCCBK","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":"480652b26534d5db451877bfcc3c82b90608004cda384504af248738730d699e","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2015-09-03T14:43:34Z","title_canon_sha256":"f87d4a7e641f61aa71a1eb836ec6cb90f5c93383bd4e29dac739803638ab7055"},"schema_version":"1.0","source":{"id":"1509.01108","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.01108","created_at":"2026-05-18T01:34:04Z"},{"alias_kind":"arxiv_version","alias_value":"1509.01108v1","created_at":"2026-05-18T01:34:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.01108","created_at":"2026-05-18T01:34:04Z"},{"alias_kind":"pith_short_12","alias_value":"N6H3MYDE7KWK","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"N6H3MYDE7KWKMUAC","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"N6H3MYDE","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:5ef86c2f05860e4246a7d603897aee82842ddee8e78c85a164d0f18a5966ff88","target":"graph","created_at":"2026-05-18T01:34:04Z","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":"A subgroup $H$ of a topological abelian group $X$ is said to be characterized by a sequence $\\mathbf v =(v_n)$ of characters of $X$ if $H=\\{x\\in X:v_n(x)\\to 0\\ \\text{in}\\ \\mathbb T\\}$. We study the basic properties of characterized subgroups in the general setting, extending results known in the compact case. For a better description, we isolate various types of characterized subgroups. Moreover, we introduce the relevant class of autochacaracterized groups (namely, the groups that are characterized subgroups of themselves by means of a sequence of non-null characters); in the case of locally ","authors_text":"Anna Giordano Bruno, Daniele Impieri, Dikran Dikranjan","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2015-09-03T14:43:34Z","title":"Characterized subgroups of topological abelian groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01108","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":"sha256:1e588ccdd3b18376920efc55ae07ac9dce350c31fb12cec0d0875af1daaa16c6","target":"record","created_at":"2026-05-18T01:34:04Z","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":"480652b26534d5db451877bfcc3c82b90608004cda384504af248738730d699e","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2015-09-03T14:43:34Z","title_canon_sha256":"f87d4a7e641f61aa71a1eb836ec6cb90f5c93383bd4e29dac739803638ab7055"},"schema_version":"1.0","source":{"id":"1509.01108","kind":"arxiv","version":1}},"canonical_sha256":"6f8fb66064faaca65002fe9f35c8420ab9e15b4231e859abab56e06b6bcf6f84","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6f8fb66064faaca65002fe9f35c8420ab9e15b4231e859abab56e06b6bcf6f84","first_computed_at":"2026-05-18T01:34:04.283604Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:04.283604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Wh0nsLMoNr46MnS2daHzPiT62bqPC3CmT3bMWBua5kbHfHVFqOYt4Mz2gBERGzaJHrBNWs1/EoI7QDofbMKoDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:04.284218Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.01108","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e588ccdd3b18376920efc55ae07ac9dce350c31fb12cec0d0875af1daaa16c6","sha256:5ef86c2f05860e4246a7d603897aee82842ddee8e78c85a164d0f18a5966ff88"],"state_sha256":"3627446578366eee62dccf55f646bbe1239959d7d4817dd2273f5393fd090536"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bRY68rRjPrCDqoLxpTXkxj2h+X+aKWMgY7hFiwE898L3YrtHimTLefR/Pl3IIDkXBbwbC2/QnkyWTT1qDdI5Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T12:08:23.271273Z","bundle_sha256":"eb6b5906afbac6ee270bd931ad657ff2f839a1464317c710fdc6388b556b9bd0"}}