{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:3WWU32OINJK7QRCFOM2YFQ6XUY","short_pith_number":"pith:3WWU32OI","canonical_record":{"source":{"id":"1110.3222","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-10-14T14:39:10Z","cross_cats_sorted":[],"title_canon_sha256":"80b8ed1a4b889fe674ac3a80c126d4cf82720ff40fd7d5afd09a44217c59c664","abstract_canon_sha256":"33efc04bbb5d9ca84b8c98f1f7cd31d70760bc8fbc57ff076fd83cada4554b6e"},"schema_version":"1.0"},"canonical_sha256":"ddad4de9c86a55f84445733582c3d7a6283fa182a8d6b5b7d3959c93c41e0199","source":{"kind":"arxiv","id":"1110.3222","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.3222","created_at":"2026-05-18T04:10:57Z"},{"alias_kind":"arxiv_version","alias_value":"1110.3222v1","created_at":"2026-05-18T04:10:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.3222","created_at":"2026-05-18T04:10:57Z"},{"alias_kind":"pith_short_12","alias_value":"3WWU32OINJK7","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"3WWU32OINJK7QRCF","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"3WWU32OI","created_at":"2026-05-18T12:26:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:3WWU32OINJK7QRCFOM2YFQ6XUY","target":"record","payload":{"canonical_record":{"source":{"id":"1110.3222","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-10-14T14:39:10Z","cross_cats_sorted":[],"title_canon_sha256":"80b8ed1a4b889fe674ac3a80c126d4cf82720ff40fd7d5afd09a44217c59c664","abstract_canon_sha256":"33efc04bbb5d9ca84b8c98f1f7cd31d70760bc8fbc57ff076fd83cada4554b6e"},"schema_version":"1.0"},"canonical_sha256":"ddad4de9c86a55f84445733582c3d7a6283fa182a8d6b5b7d3959c93c41e0199","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:10:57.723635Z","signature_b64":"5dvoRBA1/aLQdcwxF9+OpgFU4w6fHaj5+AOQuP7IBWHtEG/oj6J2dgGKTq2ZPASfD3kb4xSDG/jC2jA3Fo4VAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ddad4de9c86a55f84445733582c3d7a6283fa182a8d6b5b7d3959c93c41e0199","last_reissued_at":"2026-05-18T04:10:57.723150Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:10:57.723150Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.3222","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":"2026-05-18T04:10:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bl5ibGq3T8OuxPug41/aGO2fWcFzGFa/v84P7ybwBLKFdWn0QF5X76AMnmf7baeBbR57DDQ3L2KTC7/ttPOwDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T23:01:57.307190Z"},"content_sha256":"da6b7c868187ca8441b08e2a068fee14bd51fe4a59ec5634920acc762e5e7900","schema_version":"1.0","event_id":"sha256:da6b7c868187ca8441b08e2a068fee14bd51fe4a59ec5634920acc762e5e7900"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:3WWU32OINJK7QRCFOM2YFQ6XUY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A characterisation of the Fourier transform on the Heisenberg group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"R. Lakshmi Lavanya, S. Thangavelu","submitted_at":"2011-10-14T14:39:10Z","abstract_excerpt":"The aim of this paper is to show that any continuous *-homomorphism of L1(Cn)(with twisted convolution as multipli- cation) into B(L2(Rn)) is essentially a Weyl transform. From this we deduce a similar characterisation for the group Fourier transform on the Heisenberg group, in terms of convolution."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3222","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":"2026-05-18T04:10:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"17/XLTXerFfusxIqZ6+w8pdfrHGgZlse468QJfWHEHJEWpDm2Cp9a1iUCpAIwjs+67uaHXFzwEjGBv2MpG31Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T23:01:57.307546Z"},"content_sha256":"d001f81ca7e3c26781d831b022619c869d9adf001c130bb264ef27fa4727e0d2","schema_version":"1.0","event_id":"sha256:d001f81ca7e3c26781d831b022619c869d9adf001c130bb264ef27fa4727e0d2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3WWU32OINJK7QRCFOM2YFQ6XUY/bundle.json","state_url":"https://pith.science/pith/3WWU32OINJK7QRCFOM2YFQ6XUY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3WWU32OINJK7QRCFOM2YFQ6XUY/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":"2026-06-24T23:01:57Z","links":{"resolver":"https://pith.science/pith/3WWU32OINJK7QRCFOM2YFQ6XUY","bundle":"https://pith.science/pith/3WWU32OINJK7QRCFOM2YFQ6XUY/bundle.json","state":"https://pith.science/pith/3WWU32OINJK7QRCFOM2YFQ6XUY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3WWU32OINJK7QRCFOM2YFQ6XUY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:3WWU32OINJK7QRCFOM2YFQ6XUY","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":"33efc04bbb5d9ca84b8c98f1f7cd31d70760bc8fbc57ff076fd83cada4554b6e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-10-14T14:39:10Z","title_canon_sha256":"80b8ed1a4b889fe674ac3a80c126d4cf82720ff40fd7d5afd09a44217c59c664"},"schema_version":"1.0","source":{"id":"1110.3222","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.3222","created_at":"2026-05-18T04:10:57Z"},{"alias_kind":"arxiv_version","alias_value":"1110.3222v1","created_at":"2026-05-18T04:10:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.3222","created_at":"2026-05-18T04:10:57Z"},{"alias_kind":"pith_short_12","alias_value":"3WWU32OINJK7","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"3WWU32OINJK7QRCF","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"3WWU32OI","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:d001f81ca7e3c26781d831b022619c869d9adf001c130bb264ef27fa4727e0d2","target":"graph","created_at":"2026-05-18T04:10:57Z","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":"The aim of this paper is to show that any continuous *-homomorphism of L1(Cn)(with twisted convolution as multipli- cation) into B(L2(Rn)) is essentially a Weyl transform. From this we deduce a similar characterisation for the group Fourier transform on the Heisenberg group, in terms of convolution.","authors_text":"R. Lakshmi Lavanya, S. Thangavelu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-10-14T14:39:10Z","title":"A characterisation of the Fourier transform on the Heisenberg group"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3222","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:da6b7c868187ca8441b08e2a068fee14bd51fe4a59ec5634920acc762e5e7900","target":"record","created_at":"2026-05-18T04:10:57Z","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":"33efc04bbb5d9ca84b8c98f1f7cd31d70760bc8fbc57ff076fd83cada4554b6e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-10-14T14:39:10Z","title_canon_sha256":"80b8ed1a4b889fe674ac3a80c126d4cf82720ff40fd7d5afd09a44217c59c664"},"schema_version":"1.0","source":{"id":"1110.3222","kind":"arxiv","version":1}},"canonical_sha256":"ddad4de9c86a55f84445733582c3d7a6283fa182a8d6b5b7d3959c93c41e0199","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ddad4de9c86a55f84445733582c3d7a6283fa182a8d6b5b7d3959c93c41e0199","first_computed_at":"2026-05-18T04:10:57.723150Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:10:57.723150Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5dvoRBA1/aLQdcwxF9+OpgFU4w6fHaj5+AOQuP7IBWHtEG/oj6J2dgGKTq2ZPASfD3kb4xSDG/jC2jA3Fo4VAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:10:57.723635Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.3222","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:da6b7c868187ca8441b08e2a068fee14bd51fe4a59ec5634920acc762e5e7900","sha256:d001f81ca7e3c26781d831b022619c869d9adf001c130bb264ef27fa4727e0d2"],"state_sha256":"570c72a186e116f1cb33e94eb9d7d5afd905f2957679fbe1b962cafd32ab7470"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PmmUzZ5c46kZNeBUT53fzDhPdrTJW7BBRPb7gs1WN5AcqAwKmyPlrXTbzoD1yL5WKTAngqf2sIaRleBe/pLXBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T23:01:57.309537Z","bundle_sha256":"728eb5b2b021efa029f6f1eff6fb141142983818e55b540e307ccf06ebe0a604"}}