{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:QVO4LQLISXMBTBQHYDXRLBLURQ","short_pith_number":"pith:QVO4LQLI","canonical_record":{"source":{"id":"1507.00454","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-07-02T07:44:04Z","cross_cats_sorted":["math-ph","math.AT","math.MP","math.SG"],"title_canon_sha256":"3da50a0eb6546b3610feadd385b251dd4b0eac32043d049ca69ea9e5281bc078","abstract_canon_sha256":"c74aff45f5261003886386df441ebe00b8382567a43470a4305fb4f6ad1af0b2"},"schema_version":"1.0"},"canonical_sha256":"855dc5c16895d8198607c0ef1585748c23ecad261447348d65a14d094056f1e9","source":{"kind":"arxiv","id":"1507.00454","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.00454","created_at":"2026-05-18T01:11:00Z"},{"alias_kind":"arxiv_version","alias_value":"1507.00454v2","created_at":"2026-05-18T01:11:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.00454","created_at":"2026-05-18T01:11:00Z"},{"alias_kind":"pith_short_12","alias_value":"QVO4LQLISXMB","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"QVO4LQLISXMBTBQH","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"QVO4LQLI","created_at":"2026-05-18T12:29:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:QVO4LQLISXMBTBQHYDXRLBLURQ","target":"record","payload":{"canonical_record":{"source":{"id":"1507.00454","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-07-02T07:44:04Z","cross_cats_sorted":["math-ph","math.AT","math.MP","math.SG"],"title_canon_sha256":"3da50a0eb6546b3610feadd385b251dd4b0eac32043d049ca69ea9e5281bc078","abstract_canon_sha256":"c74aff45f5261003886386df441ebe00b8382567a43470a4305fb4f6ad1af0b2"},"schema_version":"1.0"},"canonical_sha256":"855dc5c16895d8198607c0ef1585748c23ecad261447348d65a14d094056f1e9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:00.038792Z","signature_b64":"ly0JV+bi4EX/+yyesEskmlhtvGKD2jiXj03oaZoeMI7MHMEzna6fwwT7P6DtTKSGgxHaHHobNQzfG1dAh2sBDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"855dc5c16895d8198607c0ef1585748c23ecad261447348d65a14d094056f1e9","last_reissued_at":"2026-05-18T01:11:00.038157Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:00.038157Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.00454","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":"2026-05-18T01:11:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"esUKS7hJo+mQb9hJt16nLeOUHOUMlHhg1nLz8IELK0gxlD2wBXIeQq/CxO3alEhperDOSPhLcerJSuC8bnfVDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T20:30:50.028295Z"},"content_sha256":"455e934cf56b53962655f1dad3da9cb61ffd4065c28d15e0ea4d3c7382d2da1e","schema_version":"1.0","event_id":"sha256:455e934cf56b53962655f1dad3da9cb61ffd4065c28d15e0ea4d3c7382d2da1e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:QVO4LQLISXMBTBQHYDXRLBLURQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Kirillov structures up to homotopy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AT","math.MP","math.SG"],"primary_cat":"math.DG","authors_text":"Alfonso G. Tortorella, Andrew James Bruce","submitted_at":"2015-07-02T07:44:04Z","abstract_excerpt":"We present the notion of higher Kirillov brackets on the sections of an even line bundle over a supermanifold. When the line bundle is trivial we shall speak of higher Jacobi brackets. These brackets are understood furnishing the module of sections with an $L_{\\infty}$-algebra, which we refer to as a homotopy Kirillov algebra. We are then to higher Kirillov algebroids as higher generalisations of Jacobi algebroids. Furthermore, we show how to associate a higher Kirillov algebroid and a homotopy BV-algebra with every higher Kirillov manifold. In short, we construct homotopy versions of some of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.00454","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":"2026-05-18T01:11:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FLJQcLiPU4XtRjJ6iHP8solZ/atu6clxfs81meVZKxZ9O3BF9RozWILK3nv+jbKvombJ2DMhSbZyzd9XVku+DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T20:30:50.028646Z"},"content_sha256":"00dd7586d024d5eb3a06c27054ad698f74a38c358a1687a806fb7be165e3ddf9","schema_version":"1.0","event_id":"sha256:00dd7586d024d5eb3a06c27054ad698f74a38c358a1687a806fb7be165e3ddf9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QVO4LQLISXMBTBQHYDXRLBLURQ/bundle.json","state_url":"https://pith.science/pith/QVO4LQLISXMBTBQHYDXRLBLURQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QVO4LQLISXMBTBQHYDXRLBLURQ/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":"2026-06-25T20:30:50Z","links":{"resolver":"https://pith.science/pith/QVO4LQLISXMBTBQHYDXRLBLURQ","bundle":"https://pith.science/pith/QVO4LQLISXMBTBQHYDXRLBLURQ/bundle.json","state":"https://pith.science/pith/QVO4LQLISXMBTBQHYDXRLBLURQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QVO4LQLISXMBTBQHYDXRLBLURQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:QVO4LQLISXMBTBQHYDXRLBLURQ","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":"c74aff45f5261003886386df441ebe00b8382567a43470a4305fb4f6ad1af0b2","cross_cats_sorted":["math-ph","math.AT","math.MP","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-07-02T07:44:04Z","title_canon_sha256":"3da50a0eb6546b3610feadd385b251dd4b0eac32043d049ca69ea9e5281bc078"},"schema_version":"1.0","source":{"id":"1507.00454","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.00454","created_at":"2026-05-18T01:11:00Z"},{"alias_kind":"arxiv_version","alias_value":"1507.00454v2","created_at":"2026-05-18T01:11:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.00454","created_at":"2026-05-18T01:11:00Z"},{"alias_kind":"pith_short_12","alias_value":"QVO4LQLISXMB","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"QVO4LQLISXMBTBQH","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"QVO4LQLI","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:00dd7586d024d5eb3a06c27054ad698f74a38c358a1687a806fb7be165e3ddf9","target":"graph","created_at":"2026-05-18T01:11:00Z","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 the notion of higher Kirillov brackets on the sections of an even line bundle over a supermanifold. When the line bundle is trivial we shall speak of higher Jacobi brackets. These brackets are understood furnishing the module of sections with an $L_{\\infty}$-algebra, which we refer to as a homotopy Kirillov algebra. We are then to higher Kirillov algebroids as higher generalisations of Jacobi algebroids. Furthermore, we show how to associate a higher Kirillov algebroid and a homotopy BV-algebra with every higher Kirillov manifold. In short, we construct homotopy versions of some of ","authors_text":"Alfonso G. Tortorella, Andrew James Bruce","cross_cats":["math-ph","math.AT","math.MP","math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-07-02T07:44:04Z","title":"Kirillov structures up to homotopy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.00454","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":"sha256:455e934cf56b53962655f1dad3da9cb61ffd4065c28d15e0ea4d3c7382d2da1e","target":"record","created_at":"2026-05-18T01:11:00Z","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":"c74aff45f5261003886386df441ebe00b8382567a43470a4305fb4f6ad1af0b2","cross_cats_sorted":["math-ph","math.AT","math.MP","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-07-02T07:44:04Z","title_canon_sha256":"3da50a0eb6546b3610feadd385b251dd4b0eac32043d049ca69ea9e5281bc078"},"schema_version":"1.0","source":{"id":"1507.00454","kind":"arxiv","version":2}},"canonical_sha256":"855dc5c16895d8198607c0ef1585748c23ecad261447348d65a14d094056f1e9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"855dc5c16895d8198607c0ef1585748c23ecad261447348d65a14d094056f1e9","first_computed_at":"2026-05-18T01:11:00.038157Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:00.038157Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ly0JV+bi4EX/+yyesEskmlhtvGKD2jiXj03oaZoeMI7MHMEzna6fwwT7P6DtTKSGgxHaHHobNQzfG1dAh2sBDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:00.038792Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.00454","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:455e934cf56b53962655f1dad3da9cb61ffd4065c28d15e0ea4d3c7382d2da1e","sha256:00dd7586d024d5eb3a06c27054ad698f74a38c358a1687a806fb7be165e3ddf9"],"state_sha256":"70cfae2f4cb69b8869bcddbd817350a1dcbf0a81ecf8331e4ff4ea3e8effd2b3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U55NL5R/muOE82vxwfv2inrQWUCZbh0vJ69SqjRnsDcAkwIX2Oz3yXo1SNVWJAwAIcJW7lrZObEQJMyXsezjBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T20:30:50.030493Z","bundle_sha256":"f77633ad87a68d3b54d82027302bf7af238d3d29571d9bbf1d3908e206f9dd72"}}