{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:KF5RKBFZYBLVB3Q5MBJVCEQXE2","short_pith_number":"pith:KF5RKBFZ","canonical_record":{"source":{"id":"1612.07372","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-12-21T22:33:06Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"2af3279c24a8125a5359c3e86f95420eb349ff37e8448bdbf65b7e6724c6f5a9","abstract_canon_sha256":"10c053b5cefa372354774de678e1246c0289cda0f7c80f036d4d20e9ad306e48"},"schema_version":"1.0"},"canonical_sha256":"517b1504b9c05750ee1d605351121726ad45c72df3dc99e4db42c2d5d1a601c2","source":{"kind":"arxiv","id":"1612.07372","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.07372","created_at":"2026-05-18T00:54:10Z"},{"alias_kind":"arxiv_version","alias_value":"1612.07372v1","created_at":"2026-05-18T00:54:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.07372","created_at":"2026-05-18T00:54:10Z"},{"alias_kind":"pith_short_12","alias_value":"KF5RKBFZYBLV","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"KF5RKBFZYBLVB3Q5","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"KF5RKBFZ","created_at":"2026-05-18T12:30:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:KF5RKBFZYBLVB3Q5MBJVCEQXE2","target":"record","payload":{"canonical_record":{"source":{"id":"1612.07372","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-12-21T22:33:06Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"2af3279c24a8125a5359c3e86f95420eb349ff37e8448bdbf65b7e6724c6f5a9","abstract_canon_sha256":"10c053b5cefa372354774de678e1246c0289cda0f7c80f036d4d20e9ad306e48"},"schema_version":"1.0"},"canonical_sha256":"517b1504b9c05750ee1d605351121726ad45c72df3dc99e4db42c2d5d1a601c2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:10.166537Z","signature_b64":"O2h+5C5bCyPipq3RQGSZn/4FBOCWCzBaQ6KAxfN1Wo6be6ULjoWnHOIPL5hSEI/JxDGLAXW9z0Om1IUD22JmCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"517b1504b9c05750ee1d605351121726ad45c72df3dc99e4db42c2d5d1a601c2","last_reissued_at":"2026-05-18T00:54:10.166042Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:10.166042Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.07372","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":"2026-05-18T00:54:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4YzmToaqQQHbioi2mvCUX82LUGG8b42853IyQ+c5y7F6X4ikVbrVi8vmFdOmM+Hgrhjnf1Cyj0PDOyM6Tc8VAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T21:51:25.600277Z"},"content_sha256":"ac166a1f90b3453ae99cc16320e8a58604d43effe5d7dce42e7daf8f952d3728","schema_version":"1.0","event_id":"sha256:ac166a1f90b3453ae99cc16320e8a58604d43effe5d7dce42e7daf8f952d3728"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:KF5RKBFZYBLVB3Q5MBJVCEQXE2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An equivariant parametric Oka principle for bundles of homogeneous spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CV","authors_text":"Finnur Larusson, Frank Kutzschebauch, Gerald W. Schwarz","submitted_at":"2016-12-21T22:33:06Z","abstract_excerpt":"We prove a parametric Oka principle for equivariant sections of a holomorphic fibre bundle $E$ with a structure group bundle $\\mathscr G$ on a reduced Stein space $X$, such that the fibre of $E$ is a homogeneous space of the fibre of $\\mathscr G$, with the complexification $K^\\mathbb C$ of a compact real Lie group $K$ acting on $X$, $\\mathscr G$, and $E$. Our main result is that the inclusion of the space of $K^\\mathbb C$-equivariant holomorphic sections of $E$ over $X$ into the space of $K$-equivariant continuous sections is a weak homotopy equivalence. The result has a wide scope; we describ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07372","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":"2026-05-18T00:54:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BgD0PciilGJaFPr86f+78rTErYr+lNfFBqSFVsTbki7EdIqnSffO+Gm4nEgAEQVcCI3N0JfOdq8Do60IYWoPDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T21:51:25.600976Z"},"content_sha256":"5e11a1b7269c55e93895d1396d282a4c3c3d4298a4f5cf625d4a67b1321584f6","schema_version":"1.0","event_id":"sha256:5e11a1b7269c55e93895d1396d282a4c3c3d4298a4f5cf625d4a67b1321584f6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KF5RKBFZYBLVB3Q5MBJVCEQXE2/bundle.json","state_url":"https://pith.science/pith/KF5RKBFZYBLVB3Q5MBJVCEQXE2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KF5RKBFZYBLVB3Q5MBJVCEQXE2/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":"2026-05-27T21:51:25Z","links":{"resolver":"https://pith.science/pith/KF5RKBFZYBLVB3Q5MBJVCEQXE2","bundle":"https://pith.science/pith/KF5RKBFZYBLVB3Q5MBJVCEQXE2/bundle.json","state":"https://pith.science/pith/KF5RKBFZYBLVB3Q5MBJVCEQXE2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KF5RKBFZYBLVB3Q5MBJVCEQXE2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:KF5RKBFZYBLVB3Q5MBJVCEQXE2","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":"10c053b5cefa372354774de678e1246c0289cda0f7c80f036d4d20e9ad306e48","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-12-21T22:33:06Z","title_canon_sha256":"2af3279c24a8125a5359c3e86f95420eb349ff37e8448bdbf65b7e6724c6f5a9"},"schema_version":"1.0","source":{"id":"1612.07372","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.07372","created_at":"2026-05-18T00:54:10Z"},{"alias_kind":"arxiv_version","alias_value":"1612.07372v1","created_at":"2026-05-18T00:54:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.07372","created_at":"2026-05-18T00:54:10Z"},{"alias_kind":"pith_short_12","alias_value":"KF5RKBFZYBLV","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"KF5RKBFZYBLVB3Q5","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"KF5RKBFZ","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:5e11a1b7269c55e93895d1396d282a4c3c3d4298a4f5cf625d4a67b1321584f6","target":"graph","created_at":"2026-05-18T00:54:10Z","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 prove a parametric Oka principle for equivariant sections of a holomorphic fibre bundle $E$ with a structure group bundle $\\mathscr G$ on a reduced Stein space $X$, such that the fibre of $E$ is a homogeneous space of the fibre of $\\mathscr G$, with the complexification $K^\\mathbb C$ of a compact real Lie group $K$ acting on $X$, $\\mathscr G$, and $E$. Our main result is that the inclusion of the space of $K^\\mathbb C$-equivariant holomorphic sections of $E$ over $X$ into the space of $K$-equivariant continuous sections is a weak homotopy equivalence. The result has a wide scope; we describ","authors_text":"Finnur Larusson, Frank Kutzschebauch, Gerald W. Schwarz","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-12-21T22:33:06Z","title":"An equivariant parametric Oka principle for bundles of homogeneous spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07372","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:ac166a1f90b3453ae99cc16320e8a58604d43effe5d7dce42e7daf8f952d3728","target":"record","created_at":"2026-05-18T00:54:10Z","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":"10c053b5cefa372354774de678e1246c0289cda0f7c80f036d4d20e9ad306e48","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-12-21T22:33:06Z","title_canon_sha256":"2af3279c24a8125a5359c3e86f95420eb349ff37e8448bdbf65b7e6724c6f5a9"},"schema_version":"1.0","source":{"id":"1612.07372","kind":"arxiv","version":1}},"canonical_sha256":"517b1504b9c05750ee1d605351121726ad45c72df3dc99e4db42c2d5d1a601c2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"517b1504b9c05750ee1d605351121726ad45c72df3dc99e4db42c2d5d1a601c2","first_computed_at":"2026-05-18T00:54:10.166042Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:10.166042Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O2h+5C5bCyPipq3RQGSZn/4FBOCWCzBaQ6KAxfN1Wo6be6ULjoWnHOIPL5hSEI/JxDGLAXW9z0Om1IUD22JmCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:10.166537Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.07372","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac166a1f90b3453ae99cc16320e8a58604d43effe5d7dce42e7daf8f952d3728","sha256:5e11a1b7269c55e93895d1396d282a4c3c3d4298a4f5cf625d4a67b1321584f6"],"state_sha256":"9c1a574062e9d1195532788063b14ee733af339aa2a96d28aa2f70646b501d4f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nqEMapPw1TvioPrCalVtLc5ub+7R1zY8sJY3RybYfFuwQMqPbcG+Jy0iQuUTTf5RYaYuDrXRsjcqvyTvH1zmDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T21:51:25.604547Z","bundle_sha256":"55278e1889e4daccb29dd00e20e64594dd9673805d992e6f73026f56bc5e1d51"}}