{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:IPBREO6DVKYFDZZG4FF34G7MBE","short_pith_number":"pith:IPBREO6D","canonical_record":{"source":{"id":"1208.4021","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-08-20T14:26:52Z","cross_cats_sorted":[],"title_canon_sha256":"462f2914ba2737056794b8d8dd95f0e8720829a25efa74c27b96236d0150fed9","abstract_canon_sha256":"123cc4d809da762203a5910f7ce071edd2427864e90faa42ca479f4744b5ae28"},"schema_version":"1.0"},"canonical_sha256":"43c3123bc3aab051e726e14bbe1bec09170150e343bd2cd338cb66efcd76e536","source":{"kind":"arxiv","id":"1208.4021","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.4021","created_at":"2026-05-18T03:48:24Z"},{"alias_kind":"arxiv_version","alias_value":"1208.4021v2","created_at":"2026-05-18T03:48:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.4021","created_at":"2026-05-18T03:48:24Z"},{"alias_kind":"pith_short_12","alias_value":"IPBREO6DVKYF","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"IPBREO6DVKYFDZZG","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"IPBREO6D","created_at":"2026-05-18T12:27:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:IPBREO6DVKYFDZZG4FF34G7MBE","target":"record","payload":{"canonical_record":{"source":{"id":"1208.4021","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-08-20T14:26:52Z","cross_cats_sorted":[],"title_canon_sha256":"462f2914ba2737056794b8d8dd95f0e8720829a25efa74c27b96236d0150fed9","abstract_canon_sha256":"123cc4d809da762203a5910f7ce071edd2427864e90faa42ca479f4744b5ae28"},"schema_version":"1.0"},"canonical_sha256":"43c3123bc3aab051e726e14bbe1bec09170150e343bd2cd338cb66efcd76e536","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:48:24.092619Z","signature_b64":"Lafwj2N/tAsA+l72cI7RVEq9OzMFlQB4FhCuCEkgEXRNq/eFrNGORXJ1JoDux7hrWTiJZKIlOhKOSDNiHSX2AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"43c3123bc3aab051e726e14bbe1bec09170150e343bd2cd338cb66efcd76e536","last_reissued_at":"2026-05-18T03:48:24.092017Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:48:24.092017Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.4021","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":"2026-05-18T03:48:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JSO59Lpq3+M0mH11xP0KBpB+wJBtuRlr7m1WaH2/rue421argGJJlvZqXOJsG/MGo56rSk1YoxyUWCmfm+nkAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T15:39:15.665927Z"},"content_sha256":"da1b86f954a20eae1b2cc10ed7f7f0b95f3ffc8ac30180081c739f8b66b82229","schema_version":"1.0","event_id":"sha256:da1b86f954a20eae1b2cc10ed7f7f0b95f3ffc8ac30180081c739f8b66b82229"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:IPBREO6DVKYFDZZG4FF34G7MBE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the metric structure of some non-K\\\"ahler complex threefolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Florin Belgun","submitted_at":"2012-08-20T14:26:52Z","abstract_excerpt":"We introduce a class of hermitian metrics with {\\em Lee potential}, that generalize the notion of l.c.K. metrics with potential introduced in \\cite{ov} and show that in the classical examples of Calabi and Eckmann of complex structures on $S^{2p+1}\\x S^{2q+1}$, the corresponding hermitian metrics are of this type. These examples satisfy, actually, a stronger differential condition, that we call {\\em generalized Calabi-Eckmann}, condition that is satisfied also by the {\\em Vaisman} metrics (previously also refered to as {\\em generalized Hopf manifolds}). This condition means that, in addition t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.4021","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":"2026-05-18T03:48:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GS8ZYi4CZ/WeG0zO3dU494CWKl22zQPA3PpkJvt5GLsiVQ+WkPLheIId5QIJhlTEPekDmqzSsjHBfnD233jHAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T15:39:15.666278Z"},"content_sha256":"80259ce125a27c8293a7fe272385796d0ee80ffdc25d97fbe501900d12c90262","schema_version":"1.0","event_id":"sha256:80259ce125a27c8293a7fe272385796d0ee80ffdc25d97fbe501900d12c90262"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IPBREO6DVKYFDZZG4FF34G7MBE/bundle.json","state_url":"https://pith.science/pith/IPBREO6DVKYFDZZG4FF34G7MBE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IPBREO6DVKYFDZZG4FF34G7MBE/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":"2026-06-20T15:39:15Z","links":{"resolver":"https://pith.science/pith/IPBREO6DVKYFDZZG4FF34G7MBE","bundle":"https://pith.science/pith/IPBREO6DVKYFDZZG4FF34G7MBE/bundle.json","state":"https://pith.science/pith/IPBREO6DVKYFDZZG4FF34G7MBE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IPBREO6DVKYFDZZG4FF34G7MBE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:IPBREO6DVKYFDZZG4FF34G7MBE","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":"123cc4d809da762203a5910f7ce071edd2427864e90faa42ca479f4744b5ae28","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-08-20T14:26:52Z","title_canon_sha256":"462f2914ba2737056794b8d8dd95f0e8720829a25efa74c27b96236d0150fed9"},"schema_version":"1.0","source":{"id":"1208.4021","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.4021","created_at":"2026-05-18T03:48:24Z"},{"alias_kind":"arxiv_version","alias_value":"1208.4021v2","created_at":"2026-05-18T03:48:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.4021","created_at":"2026-05-18T03:48:24Z"},{"alias_kind":"pith_short_12","alias_value":"IPBREO6DVKYF","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"IPBREO6DVKYFDZZG","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"IPBREO6D","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:80259ce125a27c8293a7fe272385796d0ee80ffdc25d97fbe501900d12c90262","target":"graph","created_at":"2026-05-18T03:48:24Z","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 introduce a class of hermitian metrics with {\\em Lee potential}, that generalize the notion of l.c.K. metrics with potential introduced in \\cite{ov} and show that in the classical examples of Calabi and Eckmann of complex structures on $S^{2p+1}\\x S^{2q+1}$, the corresponding hermitian metrics are of this type. These examples satisfy, actually, a stronger differential condition, that we call {\\em generalized Calabi-Eckmann}, condition that is satisfied also by the {\\em Vaisman} metrics (previously also refered to as {\\em generalized Hopf manifolds}). This condition means that, in addition t","authors_text":"Florin Belgun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-08-20T14:26:52Z","title":"On the metric structure of some non-K\\\"ahler complex threefolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.4021","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:da1b86f954a20eae1b2cc10ed7f7f0b95f3ffc8ac30180081c739f8b66b82229","target":"record","created_at":"2026-05-18T03:48:24Z","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":"123cc4d809da762203a5910f7ce071edd2427864e90faa42ca479f4744b5ae28","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-08-20T14:26:52Z","title_canon_sha256":"462f2914ba2737056794b8d8dd95f0e8720829a25efa74c27b96236d0150fed9"},"schema_version":"1.0","source":{"id":"1208.4021","kind":"arxiv","version":2}},"canonical_sha256":"43c3123bc3aab051e726e14bbe1bec09170150e343bd2cd338cb66efcd76e536","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"43c3123bc3aab051e726e14bbe1bec09170150e343bd2cd338cb66efcd76e536","first_computed_at":"2026-05-18T03:48:24.092017Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:48:24.092017Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Lafwj2N/tAsA+l72cI7RVEq9OzMFlQB4FhCuCEkgEXRNq/eFrNGORXJ1JoDux7hrWTiJZKIlOhKOSDNiHSX2AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:48:24.092619Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.4021","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:da1b86f954a20eae1b2cc10ed7f7f0b95f3ffc8ac30180081c739f8b66b82229","sha256:80259ce125a27c8293a7fe272385796d0ee80ffdc25d97fbe501900d12c90262"],"state_sha256":"42095b21e5669de6ed73518613c863ce9305399d9462350a83cb846a264c18a3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jyt1JWuogVaFP43/Dn8kw8GgkFzJHHOFXtl/6VpWWua/+bCJ5LkJ0JhxkJLsvi+OuQ8Jh6LZUkQjbo8BsL76Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T15:39:15.668296Z","bundle_sha256":"442508ebcf8bb680f6173f0cc2851e5f4e103b6c94f3bf1b28a424dcb0d239a2"}}