{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:55LQX5SBCTIEQOECFTT2U6ITH6","short_pith_number":"pith:55LQX5SB","canonical_record":{"source":{"id":"1109.0482","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-09-02T15:37:14Z","cross_cats_sorted":[],"title_canon_sha256":"1fb4a8555bde53cb6963235c74717cfe2f66271ac0c4fad78034fd0820148e11","abstract_canon_sha256":"67fe730d4d11f10ab11b164196180229257b7ce620127b85aacac6d81158b800"},"schema_version":"1.0"},"canonical_sha256":"ef570bf64114d04838822ce7aa79133fbac9d74a09cd68f513e3c55aa146ac76","source":{"kind":"arxiv","id":"1109.0482","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.0482","created_at":"2026-05-18T03:54:15Z"},{"alias_kind":"arxiv_version","alias_value":"1109.0482v3","created_at":"2026-05-18T03:54:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.0482","created_at":"2026-05-18T03:54:15Z"},{"alias_kind":"pith_short_12","alias_value":"55LQX5SBCTIE","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"55LQX5SBCTIEQOEC","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"55LQX5SB","created_at":"2026-05-18T12:26:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:55LQX5SBCTIEQOECFTT2U6ITH6","target":"record","payload":{"canonical_record":{"source":{"id":"1109.0482","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-09-02T15:37:14Z","cross_cats_sorted":[],"title_canon_sha256":"1fb4a8555bde53cb6963235c74717cfe2f66271ac0c4fad78034fd0820148e11","abstract_canon_sha256":"67fe730d4d11f10ab11b164196180229257b7ce620127b85aacac6d81158b800"},"schema_version":"1.0"},"canonical_sha256":"ef570bf64114d04838822ce7aa79133fbac9d74a09cd68f513e3c55aa146ac76","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:54:15.956505Z","signature_b64":"rcwU5pIBN3PNiEGu/zPLeL4uoPLLPi6y80QVDXzvtt7n18Zmk2FtivgXGOTk/0slaWwPUBBc60MoqCZXUe3NAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ef570bf64114d04838822ce7aa79133fbac9d74a09cd68f513e3c55aa146ac76","last_reissued_at":"2026-05-18T03:54:15.955975Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:54:15.955975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.0482","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:54:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qzMzFNb1OmP6D1jBX1Mcd5VN0xgWIAKma7XueMaa5+NnxwgGYgKsYCRNDrjlOyeRebaM2i1kpeWQ2hzPe8JADw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T23:14:59.053494Z"},"content_sha256":"8c09573b27833c0ed4279b3e247d448227d3ae1d2cff72095888721ea69b2356","schema_version":"1.0","event_id":"sha256:8c09573b27833c0ed4279b3e247d448227d3ae1d2cff72095888721ea69b2356"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:55LQX5SBCTIEQOECFTT2U6ITH6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Shift-modulation invariant spaces on LCA groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Carlos Cabrelli, Victoria Paternostro","submitted_at":"2011-09-02T15:37:14Z","abstract_excerpt":"A $(K,\\Lambda)$ shift-modulation invariant space is a subspace of $L^2(G)$, that is invariant by translations along elements in $K$ and modulations by elements in $\\Lambda$. Here $G$ is a locally compact abelian group, and $K$ and $\\Lambda$ are closed subgroups of $G$ and the dual group $\\hat G$, respectively. In this article we provide a characterization of shift-modulation invariant spaces in this general context when $K$ and $\\Lambda$ are uniform lattices. This extends previous results known for $L^2(\\R^d)$. We develop fiberization techniques and suitable range functions adapted to LCA grou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.0482","kind":"arxiv","version":3},"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":"2026-05-18T03:54:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WjlkbVNmBoVBSsBj2Jmt+08V7dzD+hu5zAf5Ep0OWfqNy8yx8IfCfJZ+aOFqoTwoXm5WFVAb3K6PQv5ln4hqDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T23:14:59.053855Z"},"content_sha256":"ef049d684ddce4ca30b2b83faab4b008dceefe929bf1a56d6ade0fd76c4ed022","schema_version":"1.0","event_id":"sha256:ef049d684ddce4ca30b2b83faab4b008dceefe929bf1a56d6ade0fd76c4ed022"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/55LQX5SBCTIEQOECFTT2U6ITH6/bundle.json","state_url":"https://pith.science/pith/55LQX5SBCTIEQOECFTT2U6ITH6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/55LQX5SBCTIEQOECFTT2U6ITH6/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":"2026-05-27T23:14:59Z","links":{"resolver":"https://pith.science/pith/55LQX5SBCTIEQOECFTT2U6ITH6","bundle":"https://pith.science/pith/55LQX5SBCTIEQOECFTT2U6ITH6/bundle.json","state":"https://pith.science/pith/55LQX5SBCTIEQOECFTT2U6ITH6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/55LQX5SBCTIEQOECFTT2U6ITH6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:55LQX5SBCTIEQOECFTT2U6ITH6","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":"67fe730d4d11f10ab11b164196180229257b7ce620127b85aacac6d81158b800","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-09-02T15:37:14Z","title_canon_sha256":"1fb4a8555bde53cb6963235c74717cfe2f66271ac0c4fad78034fd0820148e11"},"schema_version":"1.0","source":{"id":"1109.0482","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.0482","created_at":"2026-05-18T03:54:15Z"},{"alias_kind":"arxiv_version","alias_value":"1109.0482v3","created_at":"2026-05-18T03:54:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.0482","created_at":"2026-05-18T03:54:15Z"},{"alias_kind":"pith_short_12","alias_value":"55LQX5SBCTIE","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"55LQX5SBCTIEQOEC","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"55LQX5SB","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:ef049d684ddce4ca30b2b83faab4b008dceefe929bf1a56d6ade0fd76c4ed022","target":"graph","created_at":"2026-05-18T03:54:15Z","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 $(K,\\Lambda)$ shift-modulation invariant space is a subspace of $L^2(G)$, that is invariant by translations along elements in $K$ and modulations by elements in $\\Lambda$. Here $G$ is a locally compact abelian group, and $K$ and $\\Lambda$ are closed subgroups of $G$ and the dual group $\\hat G$, respectively. In this article we provide a characterization of shift-modulation invariant spaces in this general context when $K$ and $\\Lambda$ are uniform lattices. This extends previous results known for $L^2(\\R^d)$. We develop fiberization techniques and suitable range functions adapted to LCA grou","authors_text":"Carlos Cabrelli, Victoria Paternostro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-09-02T15:37:14Z","title":"Shift-modulation invariant spaces on LCA groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.0482","kind":"arxiv","version":3},"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":"sha256:8c09573b27833c0ed4279b3e247d448227d3ae1d2cff72095888721ea69b2356","target":"record","created_at":"2026-05-18T03:54:15Z","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":"67fe730d4d11f10ab11b164196180229257b7ce620127b85aacac6d81158b800","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-09-02T15:37:14Z","title_canon_sha256":"1fb4a8555bde53cb6963235c74717cfe2f66271ac0c4fad78034fd0820148e11"},"schema_version":"1.0","source":{"id":"1109.0482","kind":"arxiv","version":3}},"canonical_sha256":"ef570bf64114d04838822ce7aa79133fbac9d74a09cd68f513e3c55aa146ac76","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ef570bf64114d04838822ce7aa79133fbac9d74a09cd68f513e3c55aa146ac76","first_computed_at":"2026-05-18T03:54:15.955975Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:54:15.955975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rcwU5pIBN3PNiEGu/zPLeL4uoPLLPi6y80QVDXzvtt7n18Zmk2FtivgXGOTk/0slaWwPUBBc60MoqCZXUe3NAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:54:15.956505Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.0482","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8c09573b27833c0ed4279b3e247d448227d3ae1d2cff72095888721ea69b2356","sha256:ef049d684ddce4ca30b2b83faab4b008dceefe929bf1a56d6ade0fd76c4ed022"],"state_sha256":"f010ec9f36a6405456db3b0cb707f63a0f2e99dbf490a1be68a7a66bdedaaecd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LZI2NJuSaC80XMmb2WpdHWFm0yjFNdrBrDO3uW1e1t7CB/OO0jpaHxzftkSSw2jNBfiDNvxiZgYOe7Lc5kMNCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T23:14:59.056356Z","bundle_sha256":"904714ca397dad024f547990aa4f23ffdc90e1fae9191982bf4c0e72ad3d956e"}}