{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:QU2LNTOT4R64SCRPPEXDBB2BTO","short_pith_number":"pith:QU2LNTOT","canonical_record":{"source":{"id":"1411.5952","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-11-21T16:49:45Z","cross_cats_sorted":[],"title_canon_sha256":"8bccdb2d62ddd83b334ea0cbe80e2e4f35f50460209075f8b8ca307eb268a714","abstract_canon_sha256":"763a4e46cdb8b83f2124a1e6aa027fab12856e33e63197962cb9100b9ac76a6d"},"schema_version":"1.0"},"canonical_sha256":"8534b6cdd3e47dc90a2f792e3087419b8a576b1ed0dd942f9af4255d8ce2f832","source":{"kind":"arxiv","id":"1411.5952","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.5952","created_at":"2026-05-18T00:50:02Z"},{"alias_kind":"arxiv_version","alias_value":"1411.5952v2","created_at":"2026-05-18T00:50:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.5952","created_at":"2026-05-18T00:50:02Z"},{"alias_kind":"pith_short_12","alias_value":"QU2LNTOT4R64","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"QU2LNTOT4R64SCRP","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"QU2LNTOT","created_at":"2026-05-18T12:28:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:QU2LNTOT4R64SCRPPEXDBB2BTO","target":"record","payload":{"canonical_record":{"source":{"id":"1411.5952","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-11-21T16:49:45Z","cross_cats_sorted":[],"title_canon_sha256":"8bccdb2d62ddd83b334ea0cbe80e2e4f35f50460209075f8b8ca307eb268a714","abstract_canon_sha256":"763a4e46cdb8b83f2124a1e6aa027fab12856e33e63197962cb9100b9ac76a6d"},"schema_version":"1.0"},"canonical_sha256":"8534b6cdd3e47dc90a2f792e3087419b8a576b1ed0dd942f9af4255d8ce2f832","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:02.199743Z","signature_b64":"oXonCTgDoMThBfqomj8/CvJWQe9SEml8t+O8RG6YdgT6CEdbGtsnR/1H/y+6VgKwIsuLQSgukZ1ISP7fOXT4Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8534b6cdd3e47dc90a2f792e3087419b8a576b1ed0dd942f9af4255d8ce2f832","last_reissued_at":"2026-05-18T00:50:02.199041Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:02.199041Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.5952","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":"2026-05-18T00:50:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uPwWDoQfi2cJZObdhe3RJBANM+Gj2gldGx3GsBjKmotaj16AqZ+p3hk9AB7nVVZS0ZIT1W5BySgbJtN/Q7SoDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T14:22:25.099312Z"},"content_sha256":"bc88cd1c6f685adb13cc0763ad70110e7313854fc2819b30a4f114ffee35723e","schema_version":"1.0","event_id":"sha256:bc88cd1c6f685adb13cc0763ad70110e7313854fc2819b30a4f114ffee35723e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:QU2LNTOT4R64SCRPPEXDBB2BTO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On vector bundle manifolds with spherically symmetric metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Rui Albuquerque","submitted_at":"2014-11-21T16:49:45Z","abstract_excerpt":"We give a general description of the construction of weighted spherically symmetric metrics on vector bundle manifolds, i.e. the total space of a vector bundle $E\\rightarrow M$, over a Riemannian manifold $M$, when $E$ is endowed with a metric connection. The tangent bundle of $E$ admits a canonical decomposition and thus it is possible to define an interesting class of two-weights metrics with the weight functions depending on the fibre norm of $E$; hence the generalized concept of spherically symmetric metrics. We study its main properties and curvature equations. Finally we focus on a few a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.5952","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":"2026-05-18T00:50:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dw/QQqEvozAcr0Fx+48vxiiByypCUjj9I08mvmXGgfy7A/ogNPn6G5YLIKaTdLJDFKmaDB8a/HhWhuo+lPFVCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T14:22:25.099810Z"},"content_sha256":"ce4671c1dc8d241c0c873c05399d732fa34cf3d1839a47fecc13ac1bfd6d24d0","schema_version":"1.0","event_id":"sha256:ce4671c1dc8d241c0c873c05399d732fa34cf3d1839a47fecc13ac1bfd6d24d0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QU2LNTOT4R64SCRPPEXDBB2BTO/bundle.json","state_url":"https://pith.science/pith/QU2LNTOT4R64SCRPPEXDBB2BTO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QU2LNTOT4R64SCRPPEXDBB2BTO/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":"2026-07-04T14:22:25Z","links":{"resolver":"https://pith.science/pith/QU2LNTOT4R64SCRPPEXDBB2BTO","bundle":"https://pith.science/pith/QU2LNTOT4R64SCRPPEXDBB2BTO/bundle.json","state":"https://pith.science/pith/QU2LNTOT4R64SCRPPEXDBB2BTO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QU2LNTOT4R64SCRPPEXDBB2BTO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:QU2LNTOT4R64SCRPPEXDBB2BTO","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":"763a4e46cdb8b83f2124a1e6aa027fab12856e33e63197962cb9100b9ac76a6d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-11-21T16:49:45Z","title_canon_sha256":"8bccdb2d62ddd83b334ea0cbe80e2e4f35f50460209075f8b8ca307eb268a714"},"schema_version":"1.0","source":{"id":"1411.5952","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.5952","created_at":"2026-05-18T00:50:02Z"},{"alias_kind":"arxiv_version","alias_value":"1411.5952v2","created_at":"2026-05-18T00:50:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.5952","created_at":"2026-05-18T00:50:02Z"},{"alias_kind":"pith_short_12","alias_value":"QU2LNTOT4R64","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"QU2LNTOT4R64SCRP","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"QU2LNTOT","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:ce4671c1dc8d241c0c873c05399d732fa34cf3d1839a47fecc13ac1bfd6d24d0","target":"graph","created_at":"2026-05-18T00:50:02Z","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 give a general description of the construction of weighted spherically symmetric metrics on vector bundle manifolds, i.e. the total space of a vector bundle $E\\rightarrow M$, over a Riemannian manifold $M$, when $E$ is endowed with a metric connection. The tangent bundle of $E$ admits a canonical decomposition and thus it is possible to define an interesting class of two-weights metrics with the weight functions depending on the fibre norm of $E$; hence the generalized concept of spherically symmetric metrics. We study its main properties and curvature equations. Finally we focus on a few a","authors_text":"Rui Albuquerque","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-11-21T16:49:45Z","title":"On vector bundle manifolds with spherically symmetric metrics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.5952","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:bc88cd1c6f685adb13cc0763ad70110e7313854fc2819b30a4f114ffee35723e","target":"record","created_at":"2026-05-18T00:50:02Z","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":"763a4e46cdb8b83f2124a1e6aa027fab12856e33e63197962cb9100b9ac76a6d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-11-21T16:49:45Z","title_canon_sha256":"8bccdb2d62ddd83b334ea0cbe80e2e4f35f50460209075f8b8ca307eb268a714"},"schema_version":"1.0","source":{"id":"1411.5952","kind":"arxiv","version":2}},"canonical_sha256":"8534b6cdd3e47dc90a2f792e3087419b8a576b1ed0dd942f9af4255d8ce2f832","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8534b6cdd3e47dc90a2f792e3087419b8a576b1ed0dd942f9af4255d8ce2f832","first_computed_at":"2026-05-18T00:50:02.199041Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:02.199041Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oXonCTgDoMThBfqomj8/CvJWQe9SEml8t+O8RG6YdgT6CEdbGtsnR/1H/y+6VgKwIsuLQSgukZ1ISP7fOXT4Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:02.199743Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.5952","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bc88cd1c6f685adb13cc0763ad70110e7313854fc2819b30a4f114ffee35723e","sha256:ce4671c1dc8d241c0c873c05399d732fa34cf3d1839a47fecc13ac1bfd6d24d0"],"state_sha256":"9f50a08363d911b547f82b6f6f3760e4c55f78a975bdf80b0b8eb0e447600138"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hz7npWtawY1p5pa+mpm3TTtdW92u3ua9MfCFot68IpZQpJlzrjsQpcMbXt8fBjsIpaw8G5Z4eLSgl7VMN3FXCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T14:22:25.101833Z","bundle_sha256":"456b54140631d9c9607cc8513a08f4dc0d17e597afa52da8ab0baa173b384ee6"}}