{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:JUANHOEKALIIFMWUY2GWE67W55","short_pith_number":"pith:JUANHOEK","canonical_record":{"source":{"id":"1512.08203","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-12-27T11:20:42Z","cross_cats_sorted":["math-ph","math.DG","math.FA","math.MP"],"title_canon_sha256":"4d0229c9a4fbce2e88ccd8a86753f8a1ab6957590ff552de93d040ee15699df7","abstract_canon_sha256":"150954c3f7b298279fd648d8f0f26125c9b7a5228beb3444152b5286009559bf"},"schema_version":"1.0"},"canonical_sha256":"4d00d3b88a02d082b2d4c68d627bf6ef4ed6735c5a35e7cd15b8996cfdce1dae","source":{"kind":"arxiv","id":"1512.08203","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.08203","created_at":"2026-05-18T00:48:20Z"},{"alias_kind":"arxiv_version","alias_value":"1512.08203v3","created_at":"2026-05-18T00:48:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.08203","created_at":"2026-05-18T00:48:20Z"},{"alias_kind":"pith_short_12","alias_value":"JUANHOEKALII","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JUANHOEKALIIFMWU","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JUANHOEK","created_at":"2026-05-18T12:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:JUANHOEKALIIFMWUY2GWE67W55","target":"record","payload":{"canonical_record":{"source":{"id":"1512.08203","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-12-27T11:20:42Z","cross_cats_sorted":["math-ph","math.DG","math.FA","math.MP"],"title_canon_sha256":"4d0229c9a4fbce2e88ccd8a86753f8a1ab6957590ff552de93d040ee15699df7","abstract_canon_sha256":"150954c3f7b298279fd648d8f0f26125c9b7a5228beb3444152b5286009559bf"},"schema_version":"1.0"},"canonical_sha256":"4d00d3b88a02d082b2d4c68d627bf6ef4ed6735c5a35e7cd15b8996cfdce1dae","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:20.345978Z","signature_b64":"FERzkcNZpITIpaCViMoKGyEsORm7TarpSxFgHL9Yy5xTubzUFpSWPuIANpWiOSnn1qHq7KgsXFG7B0kU9b7YBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4d00d3b88a02d082b2d4c68d627bf6ef4ed6735c5a35e7cd15b8996cfdce1dae","last_reissued_at":"2026-05-18T00:48:20.345073Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:20.345073Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.08203","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":"2026-05-18T00:48:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KxFFgI9G1ztyNL7cQBXnoxYn054N2aeuBs/EhtHKi6nfcuc8Tz+a+pOa8Xe1dm8FrUin8v+QDOGtju6ZmVrACA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T07:46:33.242613Z"},"content_sha256":"85bad4ce36cc3f45036133f397e5e1096ee963cb02b4793b2ba00dbb7e169c5c","schema_version":"1.0","event_id":"sha256:85bad4ce36cc3f45036133f397e5e1096ee963cb02b4793b2ba00dbb7e169c5c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:JUANHOEKALIIFMWUY2GWE67W55","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Differential invariants on symplectic spinors in contact projective geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DG","math.FA","math.MP"],"primary_cat":"math.RT","authors_text":"Libor K\\v{r}i\\v{z}ka, Petr Somberg","submitted_at":"2015-12-27T11:20:42Z","abstract_excerpt":"We present a complete classification and the construction of $\\mathrm{Mp}(2n+2,\\mathbb{R})$-equivariant differential operators acting on the principal series representations, associated to the contact projective geometry on $\\mathbb{RP}^{2n+1}$ and induced from the irreducible $\\mathrm{Mp}(2n,\\mathbb{R})$-submodules of the Segal-Shale-Weil representation twisted by a one-parameter family of characters. The proof is based on the classification of homomorphisms of generalized Verma modules for the Segal-Shale-Weil representation twisted by a one-parameter family of characters, together with a ge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08203","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":"2026-05-18T00:48:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YGSAWorXYgbN5DJdL0YCcfDocK44lLnGRWsprlu25uApfhVjpcBrgE594lHl6dBHEvZt1qZ4WgBIt7Oqx+lABA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T07:46:33.242956Z"},"content_sha256":"d9bb5ea0997f1258d65e21f4b1d0a6cd18846eb23cacf6d2a235b252548a4e80","schema_version":"1.0","event_id":"sha256:d9bb5ea0997f1258d65e21f4b1d0a6cd18846eb23cacf6d2a235b252548a4e80"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JUANHOEKALIIFMWUY2GWE67W55/bundle.json","state_url":"https://pith.science/pith/JUANHOEKALIIFMWUY2GWE67W55/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JUANHOEKALIIFMWUY2GWE67W55/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":"2026-06-03T07:46:33Z","links":{"resolver":"https://pith.science/pith/JUANHOEKALIIFMWUY2GWE67W55","bundle":"https://pith.science/pith/JUANHOEKALIIFMWUY2GWE67W55/bundle.json","state":"https://pith.science/pith/JUANHOEKALIIFMWUY2GWE67W55/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JUANHOEKALIIFMWUY2GWE67W55/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:JUANHOEKALIIFMWUY2GWE67W55","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":"150954c3f7b298279fd648d8f0f26125c9b7a5228beb3444152b5286009559bf","cross_cats_sorted":["math-ph","math.DG","math.FA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-12-27T11:20:42Z","title_canon_sha256":"4d0229c9a4fbce2e88ccd8a86753f8a1ab6957590ff552de93d040ee15699df7"},"schema_version":"1.0","source":{"id":"1512.08203","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.08203","created_at":"2026-05-18T00:48:20Z"},{"alias_kind":"arxiv_version","alias_value":"1512.08203v3","created_at":"2026-05-18T00:48:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.08203","created_at":"2026-05-18T00:48:20Z"},{"alias_kind":"pith_short_12","alias_value":"JUANHOEKALII","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JUANHOEKALIIFMWU","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JUANHOEK","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:d9bb5ea0997f1258d65e21f4b1d0a6cd18846eb23cacf6d2a235b252548a4e80","target":"graph","created_at":"2026-05-18T00:48:20Z","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 present a complete classification and the construction of $\\mathrm{Mp}(2n+2,\\mathbb{R})$-equivariant differential operators acting on the principal series representations, associated to the contact projective geometry on $\\mathbb{RP}^{2n+1}$ and induced from the irreducible $\\mathrm{Mp}(2n,\\mathbb{R})$-submodules of the Segal-Shale-Weil representation twisted by a one-parameter family of characters. The proof is based on the classification of homomorphisms of generalized Verma modules for the Segal-Shale-Weil representation twisted by a one-parameter family of characters, together with a ge","authors_text":"Libor K\\v{r}i\\v{z}ka, Petr Somberg","cross_cats":["math-ph","math.DG","math.FA","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-12-27T11:20:42Z","title":"Differential invariants on symplectic spinors in contact projective geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08203","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":"sha256:85bad4ce36cc3f45036133f397e5e1096ee963cb02b4793b2ba00dbb7e169c5c","target":"record","created_at":"2026-05-18T00:48:20Z","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":"150954c3f7b298279fd648d8f0f26125c9b7a5228beb3444152b5286009559bf","cross_cats_sorted":["math-ph","math.DG","math.FA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-12-27T11:20:42Z","title_canon_sha256":"4d0229c9a4fbce2e88ccd8a86753f8a1ab6957590ff552de93d040ee15699df7"},"schema_version":"1.0","source":{"id":"1512.08203","kind":"arxiv","version":3}},"canonical_sha256":"4d00d3b88a02d082b2d4c68d627bf6ef4ed6735c5a35e7cd15b8996cfdce1dae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4d00d3b88a02d082b2d4c68d627bf6ef4ed6735c5a35e7cd15b8996cfdce1dae","first_computed_at":"2026-05-18T00:48:20.345073Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:20.345073Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FERzkcNZpITIpaCViMoKGyEsORm7TarpSxFgHL9Yy5xTubzUFpSWPuIANpWiOSnn1qHq7KgsXFG7B0kU9b7YBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:20.345978Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.08203","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:85bad4ce36cc3f45036133f397e5e1096ee963cb02b4793b2ba00dbb7e169c5c","sha256:d9bb5ea0997f1258d65e21f4b1d0a6cd18846eb23cacf6d2a235b252548a4e80"],"state_sha256":"7d37d5c9da67dd43944a27fa051f8728758ad4e8422f464e3a2db2794ce85624"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tdIDEcPxsQPLiD27RmPY5U7rlmZKaU4iXSn9Kz2ejGAXqFGVITYkBmZArEaF92EFBdupwC7gwwwgYmZNnZRaDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T07:46:33.244891Z","bundle_sha256":"1a9dda87d799ba19141ac981e15a7ed93c5fa8e2f362a7679abde479cff70271"}}