{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:SEGZLJBN6DZISEWRD3YH7GIWDB","short_pith_number":"pith:SEGZLJBN","canonical_record":{"source":{"id":"1210.5494","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-10-19T18:27:54Z","cross_cats_sorted":["math.DG","math.GR"],"title_canon_sha256":"84034ba70351defeb061e2b2d9c7467fb004abb005043721d33d58bc907ef40a","abstract_canon_sha256":"d319d612dd44c1206ec15f7cfd70d01086d6df229e07ea3fff1f92217603b1a2"},"schema_version":"1.0"},"canonical_sha256":"910d95a42df0f28912d11ef07f991618686b01761b711d18511a63fab9a57806","source":{"kind":"arxiv","id":"1210.5494","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.5494","created_at":"2026-05-18T03:42:45Z"},{"alias_kind":"arxiv_version","alias_value":"1210.5494v1","created_at":"2026-05-18T03:42:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.5494","created_at":"2026-05-18T03:42:45Z"},{"alias_kind":"pith_short_12","alias_value":"SEGZLJBN6DZI","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"SEGZLJBN6DZISEWR","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"SEGZLJBN","created_at":"2026-05-18T12:27:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:SEGZLJBN6DZISEWRD3YH7GIWDB","target":"record","payload":{"canonical_record":{"source":{"id":"1210.5494","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-10-19T18:27:54Z","cross_cats_sorted":["math.DG","math.GR"],"title_canon_sha256":"84034ba70351defeb061e2b2d9c7467fb004abb005043721d33d58bc907ef40a","abstract_canon_sha256":"d319d612dd44c1206ec15f7cfd70d01086d6df229e07ea3fff1f92217603b1a2"},"schema_version":"1.0"},"canonical_sha256":"910d95a42df0f28912d11ef07f991618686b01761b711d18511a63fab9a57806","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:42:45.141934Z","signature_b64":"k4h/iWnqOyWyHJWNCIYx1GDpxKKHWdE0qbrzS4hWEqvV05aHyS6M/Vr8x6x1cek4GWJ72zuCfsZluHPKdYeKBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"910d95a42df0f28912d11ef07f991618686b01761b711d18511a63fab9a57806","last_reissued_at":"2026-05-18T03:42:45.141415Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:42:45.141415Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.5494","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":"2026-05-18T03:42:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aYvEHQlBkpdOFaCP6bdKzUSVgoqvtPo7BO3QrU5t8Etjy5x0Czp1fFgHQmBNmMOfN03Z/DVMQgbyNvarDLNWCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T13:40:44.357198Z"},"content_sha256":"0f2204d66d5c759e63d2ac9996149e172f8cd636b1d7991bcf906c80df246eff","schema_version":"1.0","event_id":"sha256:0f2204d66d5c759e63d2ac9996149e172f8cd636b1d7991bcf906c80df246eff"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:SEGZLJBN6DZISEWRD3YH7GIWDB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Separating Vector Bundle Sections by Invariant Means","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.GR"],"primary_cat":"math.RT","authors_text":"Gestur Olafsson, Joseph A. Wolf","submitted_at":"2012-10-19T18:27:54Z","abstract_excerpt":"We sharpen the construction of representation space in the paper \"Principal Series Representations of Infinite Dimensional Lie Groups II: Construction of Induced Representations\". We show that the principal series representation spaces constructed there, are completions of spaces of sections of Hilbert bundles rather than completions of quotient spaces of sections."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5494","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":"2026-05-18T03:42:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HtyWmRzpq/p/Ld8oDaT+sx2imOVgEKh28WHklllV8Oa/4YZ9psWz+daAJkRMcmFWCaHi9U8gN+PcpPm6ulklCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T13:40:44.357571Z"},"content_sha256":"ce1d47d3a2fb82f976ea82e4e997613ed7ad1ad303aea09fe003ff20fde34ba1","schema_version":"1.0","event_id":"sha256:ce1d47d3a2fb82f976ea82e4e997613ed7ad1ad303aea09fe003ff20fde34ba1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SEGZLJBN6DZISEWRD3YH7GIWDB/bundle.json","state_url":"https://pith.science/pith/SEGZLJBN6DZISEWRD3YH7GIWDB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SEGZLJBN6DZISEWRD3YH7GIWDB/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":"2026-06-26T13:40:44Z","links":{"resolver":"https://pith.science/pith/SEGZLJBN6DZISEWRD3YH7GIWDB","bundle":"https://pith.science/pith/SEGZLJBN6DZISEWRD3YH7GIWDB/bundle.json","state":"https://pith.science/pith/SEGZLJBN6DZISEWRD3YH7GIWDB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SEGZLJBN6DZISEWRD3YH7GIWDB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:SEGZLJBN6DZISEWRD3YH7GIWDB","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":"d319d612dd44c1206ec15f7cfd70d01086d6df229e07ea3fff1f92217603b1a2","cross_cats_sorted":["math.DG","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-10-19T18:27:54Z","title_canon_sha256":"84034ba70351defeb061e2b2d9c7467fb004abb005043721d33d58bc907ef40a"},"schema_version":"1.0","source":{"id":"1210.5494","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.5494","created_at":"2026-05-18T03:42:45Z"},{"alias_kind":"arxiv_version","alias_value":"1210.5494v1","created_at":"2026-05-18T03:42:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.5494","created_at":"2026-05-18T03:42:45Z"},{"alias_kind":"pith_short_12","alias_value":"SEGZLJBN6DZI","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"SEGZLJBN6DZISEWR","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"SEGZLJBN","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:ce1d47d3a2fb82f976ea82e4e997613ed7ad1ad303aea09fe003ff20fde34ba1","target":"graph","created_at":"2026-05-18T03:42:45Z","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":"We sharpen the construction of representation space in the paper \"Principal Series Representations of Infinite Dimensional Lie Groups II: Construction of Induced Representations\". We show that the principal series representation spaces constructed there, are completions of spaces of sections of Hilbert bundles rather than completions of quotient spaces of sections.","authors_text":"Gestur Olafsson, Joseph A. Wolf","cross_cats":["math.DG","math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-10-19T18:27:54Z","title":"Separating Vector Bundle Sections by Invariant Means"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.5494","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":"sha256:0f2204d66d5c759e63d2ac9996149e172f8cd636b1d7991bcf906c80df246eff","target":"record","created_at":"2026-05-18T03:42:45Z","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":"d319d612dd44c1206ec15f7cfd70d01086d6df229e07ea3fff1f92217603b1a2","cross_cats_sorted":["math.DG","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-10-19T18:27:54Z","title_canon_sha256":"84034ba70351defeb061e2b2d9c7467fb004abb005043721d33d58bc907ef40a"},"schema_version":"1.0","source":{"id":"1210.5494","kind":"arxiv","version":1}},"canonical_sha256":"910d95a42df0f28912d11ef07f991618686b01761b711d18511a63fab9a57806","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"910d95a42df0f28912d11ef07f991618686b01761b711d18511a63fab9a57806","first_computed_at":"2026-05-18T03:42:45.141415Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:42:45.141415Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k4h/iWnqOyWyHJWNCIYx1GDpxKKHWdE0qbrzS4hWEqvV05aHyS6M/Vr8x6x1cek4GWJ72zuCfsZluHPKdYeKBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:42:45.141934Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.5494","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f2204d66d5c759e63d2ac9996149e172f8cd636b1d7991bcf906c80df246eff","sha256:ce1d47d3a2fb82f976ea82e4e997613ed7ad1ad303aea09fe003ff20fde34ba1"],"state_sha256":"3304acee4e5c4293d43ce168218f763e159d1a37261dae52988760648743f756"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IBVEo1PGFUPELwyZIhNDWns5WKcATQHIWXxYxGZ2ELq9MHz3i8Y0e6QeymYi2FsgLQoOMIIoXDyiGICxQ1oGAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T13:40:44.359478Z","bundle_sha256":"eff4874d34ba4bff03b931fa7c5dc68cf254506dbc3886b5c2da9f9f1fc1b5f4"}}