{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:TWK5RT2TAB7SLD6VEA43JUSWB5","short_pith_number":"pith:TWK5RT2T","canonical_record":{"source":{"id":"1503.05963","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-03-19T22:58:57Z","cross_cats_sorted":[],"title_canon_sha256":"dcca97d1393cdcca3e5567e9b773712887f730ebfd0cdfe7b9410f9cf6a44db9","abstract_canon_sha256":"c3173031ed799c5285563e20eafea6c8263b86b89d9dc84c9613009cc9e92278"},"schema_version":"1.0"},"canonical_sha256":"9d95d8cf53007f258fd52039b4d2560f68ce216628a979346cbe7eb4ee57a7e5","source":{"kind":"arxiv","id":"1503.05963","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.05963","created_at":"2026-05-18T01:25:01Z"},{"alias_kind":"arxiv_version","alias_value":"1503.05963v1","created_at":"2026-05-18T01:25:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.05963","created_at":"2026-05-18T01:25:01Z"},{"alias_kind":"pith_short_12","alias_value":"TWK5RT2TAB7S","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TWK5RT2TAB7SLD6V","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TWK5RT2T","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:TWK5RT2TAB7SLD6VEA43JUSWB5","target":"record","payload":{"canonical_record":{"source":{"id":"1503.05963","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-03-19T22:58:57Z","cross_cats_sorted":[],"title_canon_sha256":"dcca97d1393cdcca3e5567e9b773712887f730ebfd0cdfe7b9410f9cf6a44db9","abstract_canon_sha256":"c3173031ed799c5285563e20eafea6c8263b86b89d9dc84c9613009cc9e92278"},"schema_version":"1.0"},"canonical_sha256":"9d95d8cf53007f258fd52039b4d2560f68ce216628a979346cbe7eb4ee57a7e5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:01.375728Z","signature_b64":"qPosv6lVCui3sxQnpYQPq4Bf4qF46mn3rbK2wlpOAP01HIn+RzMrRjLp9iFSdj/aNzw9YmRLel3AezaYSqndCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d95d8cf53007f258fd52039b4d2560f68ce216628a979346cbe7eb4ee57a7e5","last_reissued_at":"2026-05-18T01:25:01.375022Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:01.375022Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.05963","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":"2026-05-18T01:25:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"40XelzWF0nt1aw8I1BAQmdWYz9wgS4tl25afBJuqonQ0yOGdaSJnaLP1Vp78yb86oNAj7vcIVWAwJ4Qw8/6uCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T15:29:45.540575Z"},"content_sha256":"ae19124bc7712ae1276ac8efcba6bf3c464bf6c89939f78e9759bc0d0126db53","schema_version":"1.0","event_id":"sha256:ae19124bc7712ae1276ac8efcba6bf3c464bf6c89939f78e9759bc0d0126db53"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:TWK5RT2TAB7SLD6VEA43JUSWB5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on tame/compatible almost complex structures on four-dimensional Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Andres Cubas, Tedi Draghici","submitted_at":"2015-03-19T22:58:57Z","abstract_excerpt":"Four-dimensional, oriented Lie algebras $\\mathfrak{g}$ which satisfy the tame-compatible question of Donaldson for all almost complex structures $J$ on $\\mathfrak{g}$ are completely described. As a consequence, examples are given of (non-unimodular) four-dimensional Lie algebras with almost complex structures which are tamed but not compatible with symplectic forms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05963","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":"2026-05-18T01:25:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wpbR6VrAPSz45HHAYdexzP/88t6vbFj+FgWsZstcpBfNXf7RWrh+s8sghPzmEYQWPTwUDBzyO/WRva5ucCuLAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T15:29:45.540926Z"},"content_sha256":"333e86046052afc9b039927c1245d0989e6992408cc466a2b0b8512c1f5760e4","schema_version":"1.0","event_id":"sha256:333e86046052afc9b039927c1245d0989e6992408cc466a2b0b8512c1f5760e4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TWK5RT2TAB7SLD6VEA43JUSWB5/bundle.json","state_url":"https://pith.science/pith/TWK5RT2TAB7SLD6VEA43JUSWB5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TWK5RT2TAB7SLD6VEA43JUSWB5/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":"2026-07-02T15:29:45Z","links":{"resolver":"https://pith.science/pith/TWK5RT2TAB7SLD6VEA43JUSWB5","bundle":"https://pith.science/pith/TWK5RT2TAB7SLD6VEA43JUSWB5/bundle.json","state":"https://pith.science/pith/TWK5RT2TAB7SLD6VEA43JUSWB5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TWK5RT2TAB7SLD6VEA43JUSWB5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:TWK5RT2TAB7SLD6VEA43JUSWB5","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":"c3173031ed799c5285563e20eafea6c8263b86b89d9dc84c9613009cc9e92278","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-03-19T22:58:57Z","title_canon_sha256":"dcca97d1393cdcca3e5567e9b773712887f730ebfd0cdfe7b9410f9cf6a44db9"},"schema_version":"1.0","source":{"id":"1503.05963","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.05963","created_at":"2026-05-18T01:25:01Z"},{"alias_kind":"arxiv_version","alias_value":"1503.05963v1","created_at":"2026-05-18T01:25:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.05963","created_at":"2026-05-18T01:25:01Z"},{"alias_kind":"pith_short_12","alias_value":"TWK5RT2TAB7S","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TWK5RT2TAB7SLD6V","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TWK5RT2T","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:333e86046052afc9b039927c1245d0989e6992408cc466a2b0b8512c1f5760e4","target":"graph","created_at":"2026-05-18T01:25:01Z","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":"Four-dimensional, oriented Lie algebras $\\mathfrak{g}$ which satisfy the tame-compatible question of Donaldson for all almost complex structures $J$ on $\\mathfrak{g}$ are completely described. As a consequence, examples are given of (non-unimodular) four-dimensional Lie algebras with almost complex structures which are tamed but not compatible with symplectic forms.","authors_text":"Andres Cubas, Tedi Draghici","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-03-19T22:58:57Z","title":"A note on tame/compatible almost complex structures on four-dimensional Lie algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05963","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:ae19124bc7712ae1276ac8efcba6bf3c464bf6c89939f78e9759bc0d0126db53","target":"record","created_at":"2026-05-18T01:25:01Z","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":"c3173031ed799c5285563e20eafea6c8263b86b89d9dc84c9613009cc9e92278","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-03-19T22:58:57Z","title_canon_sha256":"dcca97d1393cdcca3e5567e9b773712887f730ebfd0cdfe7b9410f9cf6a44db9"},"schema_version":"1.0","source":{"id":"1503.05963","kind":"arxiv","version":1}},"canonical_sha256":"9d95d8cf53007f258fd52039b4d2560f68ce216628a979346cbe7eb4ee57a7e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9d95d8cf53007f258fd52039b4d2560f68ce216628a979346cbe7eb4ee57a7e5","first_computed_at":"2026-05-18T01:25:01.375022Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:01.375022Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qPosv6lVCui3sxQnpYQPq4Bf4qF46mn3rbK2wlpOAP01HIn+RzMrRjLp9iFSdj/aNzw9YmRLel3AezaYSqndCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:01.375728Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.05963","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae19124bc7712ae1276ac8efcba6bf3c464bf6c89939f78e9759bc0d0126db53","sha256:333e86046052afc9b039927c1245d0989e6992408cc466a2b0b8512c1f5760e4"],"state_sha256":"18e807d2f74a7937e0255df718bda48b1d937395d8f8a7be3c455aa9f981a71a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sUvU4DEy0lQAgZB8G2pv+ia5DHbVurZ4xW3+8TxC0Xw3u3N88AibbFj78slfcJwcFE7p6pO52aS+rOYUGA2WDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T15:29:45.542855Z","bundle_sha256":"28af00c05eb64e6bc51433aa6b6fa7f5f60d95f64061e6ab3cc0f257e935ff68"}}