{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:DHDZAGXHK7VOCSEKZMKBDQFBQR","short_pith_number":"pith:DHDZAGXH","canonical_record":{"source":{"id":"1006.1845","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-06-09T16:15:36Z","cross_cats_sorted":[],"title_canon_sha256":"c6a19941d4c31acda4e9c7e52eb07c969ba0b2fd60bb4264e12ab0da8cdb84d5","abstract_canon_sha256":"86b4b68d9423ba832fa9b481ea37797cadff70f4ec38194f5266f5249d044d9d"},"schema_version":"1.0"},"canonical_sha256":"19c7901ae757eae1488acb1411c0a184574f4e4b60280d8710b40223d2241686","source":{"kind":"arxiv","id":"1006.1845","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.1845","created_at":"2026-05-18T02:54:13Z"},{"alias_kind":"arxiv_version","alias_value":"1006.1845v2","created_at":"2026-05-18T02:54:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.1845","created_at":"2026-05-18T02:54:13Z"},{"alias_kind":"pith_short_12","alias_value":"DHDZAGXHK7VO","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"DHDZAGXHK7VOCSEK","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"DHDZAGXH","created_at":"2026-05-18T12:26:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:DHDZAGXHK7VOCSEKZMKBDQFBQR","target":"record","payload":{"canonical_record":{"source":{"id":"1006.1845","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-06-09T16:15:36Z","cross_cats_sorted":[],"title_canon_sha256":"c6a19941d4c31acda4e9c7e52eb07c969ba0b2fd60bb4264e12ab0da8cdb84d5","abstract_canon_sha256":"86b4b68d9423ba832fa9b481ea37797cadff70f4ec38194f5266f5249d044d9d"},"schema_version":"1.0"},"canonical_sha256":"19c7901ae757eae1488acb1411c0a184574f4e4b60280d8710b40223d2241686","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:13.071648Z","signature_b64":"VylDXXcnHSy3YP2yeQZtv+8hNzCMasbjzIjMFVa8cIWHaw9wA55vC/T6ACEBJge5qJYlzIRRtc+J1I1MzxSYCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"19c7901ae757eae1488acb1411c0a184574f4e4b60280d8710b40223d2241686","last_reissued_at":"2026-05-18T02:54:13.071095Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:13.071095Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1006.1845","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:54:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kpDz2+4r1IIlYShAE8X6NX89BiF9PwoaCjJ6CDeg9f3MOj9sX47OEFJS7RR7ymCsgXNlGAfSm61Vet6YfczlCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T22:23:22.029962Z"},"content_sha256":"94194cf5910d188bc4e67d146795f29561b055d769e3b547e686e07922cbf4b1","schema_version":"1.0","event_id":"sha256:94194cf5910d188bc4e67d146795f29561b055d769e3b547e686e07922cbf4b1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:DHDZAGXHK7VOCSEKZMKBDQFBQR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Irreducibility of some representations of the groups of symplectomorphisms and contactomorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"{\\L}ukasz Garncarek","submitted_at":"2010-06-09T16:15:36Z","abstract_excerpt":"We show the irreducibility of some unitary representations of the group of symplectomorphisms and the group of contactomorphisms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.1845","kind":"arxiv","version":2},"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":"2026-05-18T02:54:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4vsoAurn/GBFQiADnmQBA9HA/+DH9A26+rX0J6kV5w51FHWFRrcz3GUyYWAjfYSYKBtMcipSrbFhmY6I9RM+DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T22:23:22.030433Z"},"content_sha256":"9b7402f667b3027b7aed931acd345cabe9e02d1de28fe884de0ec7782718e61f","schema_version":"1.0","event_id":"sha256:9b7402f667b3027b7aed931acd345cabe9e02d1de28fe884de0ec7782718e61f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DHDZAGXHK7VOCSEKZMKBDQFBQR/bundle.json","state_url":"https://pith.science/pith/DHDZAGXHK7VOCSEKZMKBDQFBQR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DHDZAGXHK7VOCSEKZMKBDQFBQR/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":"2026-06-22T22:23:22Z","links":{"resolver":"https://pith.science/pith/DHDZAGXHK7VOCSEKZMKBDQFBQR","bundle":"https://pith.science/pith/DHDZAGXHK7VOCSEKZMKBDQFBQR/bundle.json","state":"https://pith.science/pith/DHDZAGXHK7VOCSEKZMKBDQFBQR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DHDZAGXHK7VOCSEKZMKBDQFBQR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:DHDZAGXHK7VOCSEKZMKBDQFBQR","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":"86b4b68d9423ba832fa9b481ea37797cadff70f4ec38194f5266f5249d044d9d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-06-09T16:15:36Z","title_canon_sha256":"c6a19941d4c31acda4e9c7e52eb07c969ba0b2fd60bb4264e12ab0da8cdb84d5"},"schema_version":"1.0","source":{"id":"1006.1845","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.1845","created_at":"2026-05-18T02:54:13Z"},{"alias_kind":"arxiv_version","alias_value":"1006.1845v2","created_at":"2026-05-18T02:54:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.1845","created_at":"2026-05-18T02:54:13Z"},{"alias_kind":"pith_short_12","alias_value":"DHDZAGXHK7VO","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"DHDZAGXHK7VOCSEK","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"DHDZAGXH","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:9b7402f667b3027b7aed931acd345cabe9e02d1de28fe884de0ec7782718e61f","target":"graph","created_at":"2026-05-18T02:54:13Z","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 show the irreducibility of some unitary representations of the group of symplectomorphisms and the group of contactomorphisms.","authors_text":"{\\L}ukasz Garncarek","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-06-09T16:15:36Z","title":"Irreducibility of some representations of the groups of symplectomorphisms and contactomorphisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.1845","kind":"arxiv","version":2},"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":"sha256:94194cf5910d188bc4e67d146795f29561b055d769e3b547e686e07922cbf4b1","target":"record","created_at":"2026-05-18T02:54:13Z","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":"86b4b68d9423ba832fa9b481ea37797cadff70f4ec38194f5266f5249d044d9d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-06-09T16:15:36Z","title_canon_sha256":"c6a19941d4c31acda4e9c7e52eb07c969ba0b2fd60bb4264e12ab0da8cdb84d5"},"schema_version":"1.0","source":{"id":"1006.1845","kind":"arxiv","version":2}},"canonical_sha256":"19c7901ae757eae1488acb1411c0a184574f4e4b60280d8710b40223d2241686","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"19c7901ae757eae1488acb1411c0a184574f4e4b60280d8710b40223d2241686","first_computed_at":"2026-05-18T02:54:13.071095Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:13.071095Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VylDXXcnHSy3YP2yeQZtv+8hNzCMasbjzIjMFVa8cIWHaw9wA55vC/T6ACEBJge5qJYlzIRRtc+J1I1MzxSYCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:13.071648Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.1845","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:94194cf5910d188bc4e67d146795f29561b055d769e3b547e686e07922cbf4b1","sha256:9b7402f667b3027b7aed931acd345cabe9e02d1de28fe884de0ec7782718e61f"],"state_sha256":"33042ba638ef6e50a2116cc5b02dc42e04e3b835b587dca1e6adf317661ed905"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BmRLYK4oh9SQyvEb/yhFkamrIvJ9593cckfP8gy3deMLnfGPqVsHHIVv+rfuzLYJoBRtbhc4AbEfWnI8W7pGAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T22:23:22.033041Z","bundle_sha256":"6e4daebea1da2cf792e55139b4f71f6875f33d7f4619b675316dc7b046a343ed"}}