{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:TLKXBMNZGD4FZRNFQRCYQ6BPTY","short_pith_number":"pith:TLKXBMNZ","canonical_record":{"source":{"id":"1703.07497","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-03-22T02:39:23Z","cross_cats_sorted":[],"title_canon_sha256":"3f6a079947a26b6b0ca330019e525d713bcb67830a6426e1420fc6f320c6313e","abstract_canon_sha256":"7d8b8281114ca4395fbb4ff56ba5181566514bb800de832cb02e776f4a0bb6e5"},"schema_version":"1.0"},"canonical_sha256":"9ad570b1b930f85cc5a5844588782f9e1a6c105707076459667092a33d1a1302","source":{"kind":"arxiv","id":"1703.07497","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.07497","created_at":"2026-05-18T00:11:50Z"},{"alias_kind":"arxiv_version","alias_value":"1703.07497v5","created_at":"2026-05-18T00:11:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.07497","created_at":"2026-05-18T00:11:50Z"},{"alias_kind":"pith_short_12","alias_value":"TLKXBMNZGD4F","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"TLKXBMNZGD4FZRNF","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"TLKXBMNZ","created_at":"2026-05-18T12:31:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:TLKXBMNZGD4FZRNFQRCYQ6BPTY","target":"record","payload":{"canonical_record":{"source":{"id":"1703.07497","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-03-22T02:39:23Z","cross_cats_sorted":[],"title_canon_sha256":"3f6a079947a26b6b0ca330019e525d713bcb67830a6426e1420fc6f320c6313e","abstract_canon_sha256":"7d8b8281114ca4395fbb4ff56ba5181566514bb800de832cb02e776f4a0bb6e5"},"schema_version":"1.0"},"canonical_sha256":"9ad570b1b930f85cc5a5844588782f9e1a6c105707076459667092a33d1a1302","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:50.908701Z","signature_b64":"7hh83F1n5WFrlg3vG8BBTHQXx6vi5cBO9SYbh0jFvgrB4uIY2DbKbzYHHv1p576MH7WvY5e0VkO6yWM2FnWcDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9ad570b1b930f85cc5a5844588782f9e1a6c105707076459667092a33d1a1302","last_reissued_at":"2026-05-18T00:11:50.908065Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:50.908065Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.07497","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:11:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cPFmZ3jVeCp1kUgccAf9/VWCVDrx0Hjv0gLWnEEyg9dVwHxYLNZ+HIdVOMSn8cEA/tt+N2kmecNYS2dlxXEkCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T00:04:21.825919Z"},"content_sha256":"b713533f7386f50bf968218ae33cba82f991842ac987a84949992425a8bc6338","schema_version":"1.0","event_id":"sha256:b713533f7386f50bf968218ae33cba82f991842ac987a84949992425a8bc6338"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:TLKXBMNZGD4FZRNFQRCYQ6BPTY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$T$-duality on nilmanifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Leonardo Soriani, Lino Grama, Viviana del Barco","submitted_at":"2017-03-22T02:39:23Z","abstract_excerpt":"We study generalized complex structures and $T$-duality (in the sense of Bouwknegt, Evslin, Hannabuss and Mathai) on Lie algebras and construct the corresponding Cavalcanti and Gualtieri map. Such a construction is called \"Infinitesimal $T$-duality\". As an application we deal with the problem of finding symplectic structures on 2-step nilpotent Lie algebras. We also give a criteria for the intregability of the infinitesimal $T$-duality of Lie algebras to topological $T$-duality of the associated nilmanifolds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.07497","kind":"arxiv","version":5},"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":"2026-05-18T00:11:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rDMWoEyWp1OB6m6Jg+L2ZtXwaPC9sxvm4FTOxNpl4xKoKEDCh3MQqck3EitkqcQl4a8H+zS6ymUOT6IMIV3bDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T00:04:21.826269Z"},"content_sha256":"98a213245eea76f05fd881cc44cc8964ecaf000c5495d043ad63bf454806ed07","schema_version":"1.0","event_id":"sha256:98a213245eea76f05fd881cc44cc8964ecaf000c5495d043ad63bf454806ed07"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TLKXBMNZGD4FZRNFQRCYQ6BPTY/bundle.json","state_url":"https://pith.science/pith/TLKXBMNZGD4FZRNFQRCYQ6BPTY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TLKXBMNZGD4FZRNFQRCYQ6BPTY/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":"2026-06-22T00:04:21Z","links":{"resolver":"https://pith.science/pith/TLKXBMNZGD4FZRNFQRCYQ6BPTY","bundle":"https://pith.science/pith/TLKXBMNZGD4FZRNFQRCYQ6BPTY/bundle.json","state":"https://pith.science/pith/TLKXBMNZGD4FZRNFQRCYQ6BPTY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TLKXBMNZGD4FZRNFQRCYQ6BPTY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:TLKXBMNZGD4FZRNFQRCYQ6BPTY","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":"7d8b8281114ca4395fbb4ff56ba5181566514bb800de832cb02e776f4a0bb6e5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-03-22T02:39:23Z","title_canon_sha256":"3f6a079947a26b6b0ca330019e525d713bcb67830a6426e1420fc6f320c6313e"},"schema_version":"1.0","source":{"id":"1703.07497","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.07497","created_at":"2026-05-18T00:11:50Z"},{"alias_kind":"arxiv_version","alias_value":"1703.07497v5","created_at":"2026-05-18T00:11:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.07497","created_at":"2026-05-18T00:11:50Z"},{"alias_kind":"pith_short_12","alias_value":"TLKXBMNZGD4F","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"TLKXBMNZGD4FZRNF","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"TLKXBMNZ","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:98a213245eea76f05fd881cc44cc8964ecaf000c5495d043ad63bf454806ed07","target":"graph","created_at":"2026-05-18T00:11:50Z","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 study generalized complex structures and $T$-duality (in the sense of Bouwknegt, Evslin, Hannabuss and Mathai) on Lie algebras and construct the corresponding Cavalcanti and Gualtieri map. Such a construction is called \"Infinitesimal $T$-duality\". As an application we deal with the problem of finding symplectic structures on 2-step nilpotent Lie algebras. We also give a criteria for the intregability of the infinitesimal $T$-duality of Lie algebras to topological $T$-duality of the associated nilmanifolds.","authors_text":"Leonardo Soriani, Lino Grama, Viviana del Barco","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-03-22T02:39:23Z","title":"$T$-duality on nilmanifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.07497","kind":"arxiv","version":5},"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:b713533f7386f50bf968218ae33cba82f991842ac987a84949992425a8bc6338","target":"record","created_at":"2026-05-18T00:11:50Z","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":"7d8b8281114ca4395fbb4ff56ba5181566514bb800de832cb02e776f4a0bb6e5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-03-22T02:39:23Z","title_canon_sha256":"3f6a079947a26b6b0ca330019e525d713bcb67830a6426e1420fc6f320c6313e"},"schema_version":"1.0","source":{"id":"1703.07497","kind":"arxiv","version":5}},"canonical_sha256":"9ad570b1b930f85cc5a5844588782f9e1a6c105707076459667092a33d1a1302","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ad570b1b930f85cc5a5844588782f9e1a6c105707076459667092a33d1a1302","first_computed_at":"2026-05-18T00:11:50.908065Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:50.908065Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7hh83F1n5WFrlg3vG8BBTHQXx6vi5cBO9SYbh0jFvgrB4uIY2DbKbzYHHv1p576MH7WvY5e0VkO6yWM2FnWcDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:50.908701Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.07497","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b713533f7386f50bf968218ae33cba82f991842ac987a84949992425a8bc6338","sha256:98a213245eea76f05fd881cc44cc8964ecaf000c5495d043ad63bf454806ed07"],"state_sha256":"05e2b7ea88d929adddc385d64aacfde5bf204e861cb5f011b9638a9b205298a4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/8+oUNRKg7d6AuGy/7USA6nswZsYfCJssLEjbrxd0QRa4m3+RKOXqy5CqNca1nUrSeLSCtNBywOatI2TQHldDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T00:04:21.828129Z","bundle_sha256":"e06a5beb701ccbb0f83c508a9f817391b7fd4031179e322ab43cb159a17acb90"}}