{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:QFS7GNSV724KYYRFRT65RVFNLZ","short_pith_number":"pith:QFS7GNSV","canonical_record":{"source":{"id":"2512.23543","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-12-29T15:31:42Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"62c8a92dc0931795c8367c08ef9b5ab75cd51f4666ae006440128996579eca4b","abstract_canon_sha256":"e5e2e893741d61e0876a57579732f7b6877d50f667ccbc82a361337b3d1408a2"},"schema_version":"1.0"},"canonical_sha256":"8165f33655feb8ac62258cfdd8d4ad5e66509e92b5044accca9f139460e8e72b","source":{"kind":"arxiv","id":"2512.23543","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2512.23543","created_at":"2026-06-09T01:04:40Z"},{"alias_kind":"arxiv_version","alias_value":"2512.23543v2","created_at":"2026-06-09T01:04:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.23543","created_at":"2026-06-09T01:04:40Z"},{"alias_kind":"pith_short_12","alias_value":"QFS7GNSV724K","created_at":"2026-06-09T01:04:40Z"},{"alias_kind":"pith_short_16","alias_value":"QFS7GNSV724KYYRF","created_at":"2026-06-09T01:04:40Z"},{"alias_kind":"pith_short_8","alias_value":"QFS7GNSV","created_at":"2026-06-09T01:04:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:QFS7GNSV724KYYRFRT65RVFNLZ","target":"record","payload":{"canonical_record":{"source":{"id":"2512.23543","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-12-29T15:31:42Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"62c8a92dc0931795c8367c08ef9b5ab75cd51f4666ae006440128996579eca4b","abstract_canon_sha256":"e5e2e893741d61e0876a57579732f7b6877d50f667ccbc82a361337b3d1408a2"},"schema_version":"1.0"},"canonical_sha256":"8165f33655feb8ac62258cfdd8d4ad5e66509e92b5044accca9f139460e8e72b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T01:04:40.639368Z","signature_b64":"/p/cbRjR8skdQHi3b2M3FHm9ZGA+u42ONL0dEXLKInJ2zfRm1E/V3CETXdEY4CWDU1wMV+sCG7avx1YAGcb7Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8165f33655feb8ac62258cfdd8d4ad5e66509e92b5044accca9f139460e8e72b","last_reissued_at":"2026-06-09T01:04:40.638899Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T01:04:40.638899Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2512.23543","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":"2026-06-09T01:04:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2/umL6BtrjKyrlwietiWVajhjsQT7XK3Afxpwbszb0n1doGbxPUgeC87kRR3KlOF3uN9jormsJTSznD25dqwAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T20:32:48.536382Z"},"content_sha256":"a8f853d0a8f887cfbc63c47936c486bcf2ca45942c1bab7c083536b68599d89a","schema_version":"1.0","event_id":"sha256:a8f853d0a8f887cfbc63c47936c486bcf2ca45942c1bab7c083536b68599d89a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:QFS7GNSV724KYYRFRT65RVFNLZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Complex structures on 2-step nilpotent Lie algebras arising from graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.DG","authors_text":"Adri\\'an Andrada, Sonia Vera","submitted_at":"2025-12-29T15:31:42Z","abstract_excerpt":"This work investigates the existence of complex structures on 2-step nilpotent Lie algebras arising from finite graphs. We introduce the notion of adapted complex structure, namely a complex structure that maps vertices and edges of the graph to vertices and edges, and we analyze in depth the restrictions imposed by the integrability condition. We completely characterize the graphs that admit abelian adapted complex structures, showing that they belong to a small family of graphs that we call basic. We prove that any graph endowed with an adapted complex structure $J$ contains a unique $J$-inv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.23543","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2512.23543/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-09T01:04:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RJqMuSf/pMyn/miRg4aoXOv4JNAxiud39YNRgivNVSKR83PTkapBH5JXkgMxdhHAiVt1vziYKXemaxzdQIb1Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T20:32:48.536753Z"},"content_sha256":"73f5dc059becd5ba9d023164e30285ef25cac55b3a8b70467def0fd11055b700","schema_version":"1.0","event_id":"sha256:73f5dc059becd5ba9d023164e30285ef25cac55b3a8b70467def0fd11055b700"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QFS7GNSV724KYYRFRT65RVFNLZ/bundle.json","state_url":"https://pith.science/pith/QFS7GNSV724KYYRFRT65RVFNLZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QFS7GNSV724KYYRFRT65RVFNLZ/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":"2026-06-10T20:32:48Z","links":{"resolver":"https://pith.science/pith/QFS7GNSV724KYYRFRT65RVFNLZ","bundle":"https://pith.science/pith/QFS7GNSV724KYYRFRT65RVFNLZ/bundle.json","state":"https://pith.science/pith/QFS7GNSV724KYYRFRT65RVFNLZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QFS7GNSV724KYYRFRT65RVFNLZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:QFS7GNSV724KYYRFRT65RVFNLZ","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":"e5e2e893741d61e0876a57579732f7b6877d50f667ccbc82a361337b3d1408a2","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-12-29T15:31:42Z","title_canon_sha256":"62c8a92dc0931795c8367c08ef9b5ab75cd51f4666ae006440128996579eca4b"},"schema_version":"1.0","source":{"id":"2512.23543","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2512.23543","created_at":"2026-06-09T01:04:40Z"},{"alias_kind":"arxiv_version","alias_value":"2512.23543v2","created_at":"2026-06-09T01:04:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.23543","created_at":"2026-06-09T01:04:40Z"},{"alias_kind":"pith_short_12","alias_value":"QFS7GNSV724K","created_at":"2026-06-09T01:04:40Z"},{"alias_kind":"pith_short_16","alias_value":"QFS7GNSV724KYYRF","created_at":"2026-06-09T01:04:40Z"},{"alias_kind":"pith_short_8","alias_value":"QFS7GNSV","created_at":"2026-06-09T01:04:40Z"}],"graph_snapshots":[{"event_id":"sha256:73f5dc059becd5ba9d023164e30285ef25cac55b3a8b70467def0fd11055b700","target":"graph","created_at":"2026-06-09T01:04:40Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2512.23543/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This work investigates the existence of complex structures on 2-step nilpotent Lie algebras arising from finite graphs. We introduce the notion of adapted complex structure, namely a complex structure that maps vertices and edges of the graph to vertices and edges, and we analyze in depth the restrictions imposed by the integrability condition. We completely characterize the graphs that admit abelian adapted complex structures, showing that they belong to a small family of graphs that we call basic. We prove that any graph endowed with an adapted complex structure $J$ contains a unique $J$-inv","authors_text":"Adri\\'an Andrada, Sonia Vera","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-12-29T15:31:42Z","title":"Complex structures on 2-step nilpotent Lie algebras arising from graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.23543","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:a8f853d0a8f887cfbc63c47936c486bcf2ca45942c1bab7c083536b68599d89a","target":"record","created_at":"2026-06-09T01:04:40Z","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":"e5e2e893741d61e0876a57579732f7b6877d50f667ccbc82a361337b3d1408a2","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-12-29T15:31:42Z","title_canon_sha256":"62c8a92dc0931795c8367c08ef9b5ab75cd51f4666ae006440128996579eca4b"},"schema_version":"1.0","source":{"id":"2512.23543","kind":"arxiv","version":2}},"canonical_sha256":"8165f33655feb8ac62258cfdd8d4ad5e66509e92b5044accca9f139460e8e72b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8165f33655feb8ac62258cfdd8d4ad5e66509e92b5044accca9f139460e8e72b","first_computed_at":"2026-06-09T01:04:40.638899Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T01:04:40.638899Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/p/cbRjR8skdQHi3b2M3FHm9ZGA+u42ONL0dEXLKInJ2zfRm1E/V3CETXdEY4CWDU1wMV+sCG7avx1YAGcb7Cg==","signature_status":"signed_v1","signed_at":"2026-06-09T01:04:40.639368Z","signed_message":"canonical_sha256_bytes"},"source_id":"2512.23543","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a8f853d0a8f887cfbc63c47936c486bcf2ca45942c1bab7c083536b68599d89a","sha256:73f5dc059becd5ba9d023164e30285ef25cac55b3a8b70467def0fd11055b700"],"state_sha256":"af9cc0fee1f9432f4fec69a0de800129abd8d1ed27b2e1a6a8ba47e421ef7439"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k/VigAzFs0DiGLFTklWgq0RM6EOxhKfZbkvfjj8tYTDDlvTGHe/YdT2MqS8/Y0a3rkMAqGUIHDVFJHHYBkj/BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T20:32:48.538768Z","bundle_sha256":"db28b8bb66b75b7c36e285b323e2bacbe789c1966e64db64f87a74314babc910"}}