{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:63TXMVAWE2EPC3F447YGJWYW6R","short_pith_number":"pith:63TXMVAW","canonical_record":{"source":{"id":"1110.1923","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.GN","submitted_at":"2011-10-10T04:32:07Z","cross_cats_sorted":["math.CT","math.GR"],"title_canon_sha256":"6e99feaabb65461e8d2b132ee7787c3444d7ec8f8b24852be203603b6fbc2e68","abstract_canon_sha256":"25d9d51209d7b3696612f00e8224f625d8e6c7394894d2dc4bc0246501e144b2"},"schema_version":"1.0"},"canonical_sha256":"f6e77654162688f16cbce7f064db16f4711849b3facb47690a9baf1a894f47e6","source":{"kind":"arxiv","id":"1110.1923","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.1923","created_at":"2026-05-18T04:11:19Z"},{"alias_kind":"arxiv_version","alias_value":"1110.1923v1","created_at":"2026-05-18T04:11:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.1923","created_at":"2026-05-18T04:11:19Z"},{"alias_kind":"pith_short_12","alias_value":"63TXMVAWE2EP","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"63TXMVAWE2EPC3F4","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"63TXMVAW","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:63TXMVAWE2EPC3F447YGJWYW6R","target":"record","payload":{"canonical_record":{"source":{"id":"1110.1923","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.GN","submitted_at":"2011-10-10T04:32:07Z","cross_cats_sorted":["math.CT","math.GR"],"title_canon_sha256":"6e99feaabb65461e8d2b132ee7787c3444d7ec8f8b24852be203603b6fbc2e68","abstract_canon_sha256":"25d9d51209d7b3696612f00e8224f625d8e6c7394894d2dc4bc0246501e144b2"},"schema_version":"1.0"},"canonical_sha256":"f6e77654162688f16cbce7f064db16f4711849b3facb47690a9baf1a894f47e6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:11:19.306983Z","signature_b64":"SbSkBWEdw1oWTkjiR8KkPUBVddeZEw2bly6droGjQo9gZJYU8BgXzB3J426Fplwbd/tb4us8HGa+Bji2xWoVBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6e77654162688f16cbce7f064db16f4711849b3facb47690a9baf1a894f47e6","last_reissued_at":"2026-05-18T04:11:19.306515Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:11:19.306515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.1923","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":"2026-05-18T04:11:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I7pRfWqLSVEMu7AXtbqIwM0PzFB8HyI21dmh7lNs70r5UIB7myikMcK66P6w3GjLSwyAZZxefjo1lzt5ZxFRCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T22:56:30.539016Z"},"content_sha256":"fd1998a120b65b43a10977ce422a7828b73979f213e65ceae264c7ca6f751e2f","schema_version":"1.0","event_id":"sha256:fd1998a120b65b43a10977ce422a7828b73979f213e65ceae264c7ca6f751e2f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:63TXMVAWE2EPC3F447YGJWYW6R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Decompositions of the automorphism group of a locally compact abelian group","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.CT","math.GR"],"primary_cat":"math.GN","authors_text":"Iian B. Smythe","submitted_at":"2011-10-10T04:32:07Z","abstract_excerpt":"It is well known that every locally compact abelian group L can be decomposed as L_1 \\oplus R^n, where L_1 contains a compact-open subgroup. In this paper, we use this decomposition to study the topological group Aut(L) of automorphisms of L, equipped with the g-topology. We show that Aut(L) is topologically isomorphic to a matrix group with entries from Aut(L_1), Hom(L_1, R^n), Hom(R^n, L_1), and GL_n(R), respectively. It is also shown that the algebraic portion of the decomposition is not specific to locally compact abelian groups, but is also true for objects with a well-behaved decompositi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1923","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":"2026-05-18T04:11:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iPUZDRbqutTijsqVcnc7NRlIr18Bn6lvNgGPGY18cWYJc9QeXOgxfC8Vl5iCAWauE2ahivMYPFglCr06S+hrAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T22:56:30.539763Z"},"content_sha256":"f22f81adaa3f8b3021efe6cf9c2eabf0391302447ca9c16b47e55f1041db6ef2","schema_version":"1.0","event_id":"sha256:f22f81adaa3f8b3021efe6cf9c2eabf0391302447ca9c16b47e55f1041db6ef2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/63TXMVAWE2EPC3F447YGJWYW6R/bundle.json","state_url":"https://pith.science/pith/63TXMVAWE2EPC3F447YGJWYW6R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/63TXMVAWE2EPC3F447YGJWYW6R/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":"2026-06-11T22:56:30Z","links":{"resolver":"https://pith.science/pith/63TXMVAWE2EPC3F447YGJWYW6R","bundle":"https://pith.science/pith/63TXMVAWE2EPC3F447YGJWYW6R/bundle.json","state":"https://pith.science/pith/63TXMVAWE2EPC3F447YGJWYW6R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/63TXMVAWE2EPC3F447YGJWYW6R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:63TXMVAWE2EPC3F447YGJWYW6R","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":"25d9d51209d7b3696612f00e8224f625d8e6c7394894d2dc4bc0246501e144b2","cross_cats_sorted":["math.CT","math.GR"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.GN","submitted_at":"2011-10-10T04:32:07Z","title_canon_sha256":"6e99feaabb65461e8d2b132ee7787c3444d7ec8f8b24852be203603b6fbc2e68"},"schema_version":"1.0","source":{"id":"1110.1923","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.1923","created_at":"2026-05-18T04:11:19Z"},{"alias_kind":"arxiv_version","alias_value":"1110.1923v1","created_at":"2026-05-18T04:11:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.1923","created_at":"2026-05-18T04:11:19Z"},{"alias_kind":"pith_short_12","alias_value":"63TXMVAWE2EP","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"63TXMVAWE2EPC3F4","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"63TXMVAW","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:f22f81adaa3f8b3021efe6cf9c2eabf0391302447ca9c16b47e55f1041db6ef2","target":"graph","created_at":"2026-05-18T04:11:19Z","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":"It is well known that every locally compact abelian group L can be decomposed as L_1 \\oplus R^n, where L_1 contains a compact-open subgroup. In this paper, we use this decomposition to study the topological group Aut(L) of automorphisms of L, equipped with the g-topology. We show that Aut(L) is topologically isomorphic to a matrix group with entries from Aut(L_1), Hom(L_1, R^n), Hom(R^n, L_1), and GL_n(R), respectively. It is also shown that the algebraic portion of the decomposition is not specific to locally compact abelian groups, but is also true for objects with a well-behaved decompositi","authors_text":"Iian B. Smythe","cross_cats":["math.CT","math.GR"],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.GN","submitted_at":"2011-10-10T04:32:07Z","title":"Decompositions of the automorphism group of a locally compact abelian group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1923","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:fd1998a120b65b43a10977ce422a7828b73979f213e65ceae264c7ca6f751e2f","target":"record","created_at":"2026-05-18T04:11:19Z","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":"25d9d51209d7b3696612f00e8224f625d8e6c7394894d2dc4bc0246501e144b2","cross_cats_sorted":["math.CT","math.GR"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.GN","submitted_at":"2011-10-10T04:32:07Z","title_canon_sha256":"6e99feaabb65461e8d2b132ee7787c3444d7ec8f8b24852be203603b6fbc2e68"},"schema_version":"1.0","source":{"id":"1110.1923","kind":"arxiv","version":1}},"canonical_sha256":"f6e77654162688f16cbce7f064db16f4711849b3facb47690a9baf1a894f47e6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f6e77654162688f16cbce7f064db16f4711849b3facb47690a9baf1a894f47e6","first_computed_at":"2026-05-18T04:11:19.306515Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:11:19.306515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SbSkBWEdw1oWTkjiR8KkPUBVddeZEw2bly6droGjQo9gZJYU8BgXzB3J426Fplwbd/tb4us8HGa+Bji2xWoVBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:11:19.306983Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.1923","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd1998a120b65b43a10977ce422a7828b73979f213e65ceae264c7ca6f751e2f","sha256:f22f81adaa3f8b3021efe6cf9c2eabf0391302447ca9c16b47e55f1041db6ef2"],"state_sha256":"1cbc0945b9506335fea2496d44959eb9781125e5c93842145521689ef3592a33"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EDsByuTmsiBB+6CyZpQVzHKFWaZUzsuFe+kBzZotSp/QQ4L5QC0Og0IZfD8Z1OM3eoEBOFoUruBX3EvSURzvAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T22:56:30.547973Z","bundle_sha256":"770e03f29f3fd2f7899a5271c259de717d57bb979e7da83c95b662f9f98aeac4"}}