{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:OKFGU4EHZ34LQXZ4KZ35NXRAUZ","short_pith_number":"pith:OKFGU4EH","canonical_record":{"source":{"id":"1811.10406","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2018-11-21T13:56:50Z","cross_cats_sorted":[],"title_canon_sha256":"e01bdcc5939ed1f3dd11abbed746fed22572feb4acdb209aa6b87506ad1c633f","abstract_canon_sha256":"88a6863f1ad29b5e8ce013dd8defa53709348968b13e60e245e866e1a79320cd"},"schema_version":"1.0"},"canonical_sha256":"728a6a7087cef8b85f3c5677d6de20a679c823c56c2fc9aff861bea1a9bb9278","source":{"kind":"arxiv","id":"1811.10406","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.10406","created_at":"2026-07-05T11:46:31Z"},{"alias_kind":"arxiv_version","alias_value":"1811.10406v2","created_at":"2026-07-05T11:46:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.10406","created_at":"2026-07-05T11:46:31Z"},{"alias_kind":"pith_short_12","alias_value":"OKFGU4EHZ34L","created_at":"2026-07-05T11:46:31Z"},{"alias_kind":"pith_short_16","alias_value":"OKFGU4EHZ34LQXZ4","created_at":"2026-07-05T11:46:31Z"},{"alias_kind":"pith_short_8","alias_value":"OKFGU4EH","created_at":"2026-07-05T11:46:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:OKFGU4EHZ34LQXZ4KZ35NXRAUZ","target":"record","payload":{"canonical_record":{"source":{"id":"1811.10406","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2018-11-21T13:56:50Z","cross_cats_sorted":[],"title_canon_sha256":"e01bdcc5939ed1f3dd11abbed746fed22572feb4acdb209aa6b87506ad1c633f","abstract_canon_sha256":"88a6863f1ad29b5e8ce013dd8defa53709348968b13e60e245e866e1a79320cd"},"schema_version":"1.0"},"canonical_sha256":"728a6a7087cef8b85f3c5677d6de20a679c823c56c2fc9aff861bea1a9bb9278","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:46:31.575757Z","signature_b64":"+ak6fbOpv9P0OK7/duKgk22u/th89nsgqIc/BT1yhrtNL3d5Y3hMROQ8fbp+N8BiK/3VAv5ILdqt1LMasCcOBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"728a6a7087cef8b85f3c5677d6de20a679c823c56c2fc9aff861bea1a9bb9278","last_reissued_at":"2026-07-05T11:46:31.575213Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:46:31.575213Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.10406","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":"2026-07-05T11:46:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iwVeYpCbnByBTRCkUawFz8RUc5x8oo+7tMWTeIWyhLErygOFTNM1/25i2Sr7VAOrGEIcNUTWBg6XfTMvrs72CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T00:21:00.267770Z"},"content_sha256":"fb497140dfd80355708d9df9898c7a48797c472307d94623aa41e7510f4d0099","schema_version":"1.0","event_id":"sha256:fb497140dfd80355708d9df9898c7a48797c472307d94623aa41e7510f4d0099"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:OKFGU4EHZ34LQXZ4KZ35NXRAUZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the geometry of metallic pseudo-Riemannian structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Adara M. Blaga, Antonella Nannicini","submitted_at":"2018-11-21T13:56:50Z","abstract_excerpt":"We generalize the notion of metallic structure in the pseudo-Riemannian setting, define the metallic Norden structure and study its integrability. We consider metallic maps between metallic manifolds and give conditions under which they are constant. We also construct a metallic natural connection recovering as particular case the Ganchev and Mihova connection, which we extend to a metallic natural connection on the generalized tangent bundle. Moreover, we construct metallic pseudo-Riemannian structures on the tangent and cotangent bundles."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.10406","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/1811.10406/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":"2026-07-05T11:46:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/TTKakeXyQxhFjJzgLGat475qphlPW7ZbVmc2DQtAKM/1jgJY+cHV4v6cZd8ma0/ZFeAEEzNmC7yhHvXxE1EDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T00:21:00.269855Z"},"content_sha256":"832187d33f6cd77f362e388aa0d191e3f74c750790614e8ff4ee88df8baed86b","schema_version":"1.0","event_id":"sha256:832187d33f6cd77f362e388aa0d191e3f74c750790614e8ff4ee88df8baed86b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OKFGU4EHZ34LQXZ4KZ35NXRAUZ/bundle.json","state_url":"https://pith.science/pith/OKFGU4EHZ34LQXZ4KZ35NXRAUZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OKFGU4EHZ34LQXZ4KZ35NXRAUZ/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":"2026-08-17T00:21:00Z","links":{"resolver":"https://pith.science/pith/OKFGU4EHZ34LQXZ4KZ35NXRAUZ","bundle":"https://pith.science/pith/OKFGU4EHZ34LQXZ4KZ35NXRAUZ/bundle.json","state":"https://pith.science/pith/OKFGU4EHZ34LQXZ4KZ35NXRAUZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OKFGU4EHZ34LQXZ4KZ35NXRAUZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:OKFGU4EHZ34LQXZ4KZ35NXRAUZ","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":"88a6863f1ad29b5e8ce013dd8defa53709348968b13e60e245e866e1a79320cd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2018-11-21T13:56:50Z","title_canon_sha256":"e01bdcc5939ed1f3dd11abbed746fed22572feb4acdb209aa6b87506ad1c633f"},"schema_version":"1.0","source":{"id":"1811.10406","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.10406","created_at":"2026-07-05T11:46:31Z"},{"alias_kind":"arxiv_version","alias_value":"1811.10406v2","created_at":"2026-07-05T11:46:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.10406","created_at":"2026-07-05T11:46:31Z"},{"alias_kind":"pith_short_12","alias_value":"OKFGU4EHZ34L","created_at":"2026-07-05T11:46:31Z"},{"alias_kind":"pith_short_16","alias_value":"OKFGU4EHZ34LQXZ4","created_at":"2026-07-05T11:46:31Z"},{"alias_kind":"pith_short_8","alias_value":"OKFGU4EH","created_at":"2026-07-05T11:46:31Z"}],"graph_snapshots":[{"event_id":"sha256:832187d33f6cd77f362e388aa0d191e3f74c750790614e8ff4ee88df8baed86b","target":"graph","created_at":"2026-07-05T11:46:31Z","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/1811.10406/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We generalize the notion of metallic structure in the pseudo-Riemannian setting, define the metallic Norden structure and study its integrability. We consider metallic maps between metallic manifolds and give conditions under which they are constant. We also construct a metallic natural connection recovering as particular case the Ganchev and Mihova connection, which we extend to a metallic natural connection on the generalized tangent bundle. Moreover, we construct metallic pseudo-Riemannian structures on the tangent and cotangent bundles.","authors_text":"Adara M. Blaga, Antonella Nannicini","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2018-11-21T13:56:50Z","title":"On the geometry of metallic pseudo-Riemannian structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.10406","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:fb497140dfd80355708d9df9898c7a48797c472307d94623aa41e7510f4d0099","target":"record","created_at":"2026-07-05T11:46:31Z","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":"88a6863f1ad29b5e8ce013dd8defa53709348968b13e60e245e866e1a79320cd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GM","submitted_at":"2018-11-21T13:56:50Z","title_canon_sha256":"e01bdcc5939ed1f3dd11abbed746fed22572feb4acdb209aa6b87506ad1c633f"},"schema_version":"1.0","source":{"id":"1811.10406","kind":"arxiv","version":2}},"canonical_sha256":"728a6a7087cef8b85f3c5677d6de20a679c823c56c2fc9aff861bea1a9bb9278","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"728a6a7087cef8b85f3c5677d6de20a679c823c56c2fc9aff861bea1a9bb9278","first_computed_at":"2026-07-05T11:46:31.575213Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:46:31.575213Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+ak6fbOpv9P0OK7/duKgk22u/th89nsgqIc/BT1yhrtNL3d5Y3hMROQ8fbp+N8BiK/3VAv5ILdqt1LMasCcOBA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:46:31.575757Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.10406","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fb497140dfd80355708d9df9898c7a48797c472307d94623aa41e7510f4d0099","sha256:832187d33f6cd77f362e388aa0d191e3f74c750790614e8ff4ee88df8baed86b"],"state_sha256":"8a3554f518b1a46c996f41763a3e70a68fa616befd0a6800d0f78b0539167508"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qShyDFXTdtNLHnV+/SkYS3sb91KPMg24e2K4jdtZmFfFSUP5925AegN/3nM/orE0UzL0guO59q1Ia7+a6EeSBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T00:21:00.277228Z","bundle_sha256":"f456b8b8154cc80ea1da69ca954caf986943912d090a46ad31a1ad6246601e25"}}