{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:6LKHOIRS7RARQVWDOA32WWZJVJ","short_pith_number":"pith:6LKHOIRS","canonical_record":{"source":{"id":"2405.03778","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2024-05-06T18:19:22Z","cross_cats_sorted":[],"title_canon_sha256":"06fff54baa505144209fa5d9336844d68e8bff9253b3517878bdd66886bc944a","abstract_canon_sha256":"99baa87d4baac37b766efd1f252f7b5b3807ee919dac591354455342041864e9"},"schema_version":"1.0"},"canonical_sha256":"f2d4772232fc411856c37037ab5b29aa4f92ed21d8962dccb15a965ee3e4a3e9","source":{"kind":"arxiv","id":"2405.03778","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.03778","created_at":"2026-07-05T09:09:59Z"},{"alias_kind":"arxiv_version","alias_value":"2405.03778v2","created_at":"2026-07-05T09:09:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.03778","created_at":"2026-07-05T09:09:59Z"},{"alias_kind":"pith_short_12","alias_value":"6LKHOIRS7RAR","created_at":"2026-07-05T09:09:59Z"},{"alias_kind":"pith_short_16","alias_value":"6LKHOIRS7RARQVWD","created_at":"2026-07-05T09:09:59Z"},{"alias_kind":"pith_short_8","alias_value":"6LKHOIRS","created_at":"2026-07-05T09:09:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:6LKHOIRS7RARQVWDOA32WWZJVJ","target":"record","payload":{"canonical_record":{"source":{"id":"2405.03778","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2024-05-06T18:19:22Z","cross_cats_sorted":[],"title_canon_sha256":"06fff54baa505144209fa5d9336844d68e8bff9253b3517878bdd66886bc944a","abstract_canon_sha256":"99baa87d4baac37b766efd1f252f7b5b3807ee919dac591354455342041864e9"},"schema_version":"1.0"},"canonical_sha256":"f2d4772232fc411856c37037ab5b29aa4f92ed21d8962dccb15a965ee3e4a3e9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:09:59.319544Z","signature_b64":"iVvRxIh/fh08iuvOSf5tgF2YNbnB6dNqcofg/WIK2jGW/jisU8czIQxzZ1VIz0jCTcN7YDt+E7KT5GC+b84IBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f2d4772232fc411856c37037ab5b29aa4f92ed21d8962dccb15a965ee3e4a3e9","last_reissued_at":"2026-07-05T09:09:59.319113Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:09:59.319113Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2405.03778","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":"2026-07-05T09:09:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+JhPtzOy2ALZwwvFlZn7IIFgJrEQVn50LWCnxDSK6SvWq2AexGc9d0whQSbxrCEk6Z7j4qpx2N+wftkB2sHzBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T10:46:02.902086Z"},"content_sha256":"b8602b77518ebd4f0573517adef2a1d1f2335138a2b660cc8f10095bbda4bff7","schema_version":"1.0","event_id":"sha256:b8602b77518ebd4f0573517adef2a1d1f2335138a2b660cc8f10095bbda4bff7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:6LKHOIRS7RARQVWDOA32WWZJVJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Autoregressive Model for Time Series of Random Objects","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Helle S{\\o}rensen, Matthieu Bult\\'e","submitted_at":"2024-05-06T18:19:22Z","abstract_excerpt":"Random variables in metric spaces indexed by time and observed at equally spaced time points are receiving increased attention due to their broad applicability. The absence of inherent structure in metric spaces has resulted in a literature that is predominantly non-parametric and model-free. To address this gap in models for time series of random objects, we introduce an adaptation of the classical linear autoregressive model tailored for data lying in a Hadamard space. The parameters of interest in this model are the Fr\\'echet mean and a concentration parameter, both of which we prove can be"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.03778","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/2405.03778/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":"2026-07-05T09:09:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HiNb/5QRceYcBD14hJFcnS1JDRGNfY4s3SQB318ukuQarH94x9cRrkra81/HESkDpay+QPMdw8oOvZkn9D5jBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T10:46:02.902981Z"},"content_sha256":"2b03bf04bb55e1aeae11659a8ec5b627d89cae2154f8cad94684d0e95aa976ce","schema_version":"1.0","event_id":"sha256:2b03bf04bb55e1aeae11659a8ec5b627d89cae2154f8cad94684d0e95aa976ce"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6LKHOIRS7RARQVWDOA32WWZJVJ/bundle.json","state_url":"https://pith.science/pith/6LKHOIRS7RARQVWDOA32WWZJVJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6LKHOIRS7RARQVWDOA32WWZJVJ/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":"2026-08-11T10:46:02Z","links":{"resolver":"https://pith.science/pith/6LKHOIRS7RARQVWDOA32WWZJVJ","bundle":"https://pith.science/pith/6LKHOIRS7RARQVWDOA32WWZJVJ/bundle.json","state":"https://pith.science/pith/6LKHOIRS7RARQVWDOA32WWZJVJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6LKHOIRS7RARQVWDOA32WWZJVJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:6LKHOIRS7RARQVWDOA32WWZJVJ","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":"99baa87d4baac37b766efd1f252f7b5b3807ee919dac591354455342041864e9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2024-05-06T18:19:22Z","title_canon_sha256":"06fff54baa505144209fa5d9336844d68e8bff9253b3517878bdd66886bc944a"},"schema_version":"1.0","source":{"id":"2405.03778","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.03778","created_at":"2026-07-05T09:09:59Z"},{"alias_kind":"arxiv_version","alias_value":"2405.03778v2","created_at":"2026-07-05T09:09:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.03778","created_at":"2026-07-05T09:09:59Z"},{"alias_kind":"pith_short_12","alias_value":"6LKHOIRS7RAR","created_at":"2026-07-05T09:09:59Z"},{"alias_kind":"pith_short_16","alias_value":"6LKHOIRS7RARQVWD","created_at":"2026-07-05T09:09:59Z"},{"alias_kind":"pith_short_8","alias_value":"6LKHOIRS","created_at":"2026-07-05T09:09:59Z"}],"graph_snapshots":[{"event_id":"sha256:2b03bf04bb55e1aeae11659a8ec5b627d89cae2154f8cad94684d0e95aa976ce","target":"graph","created_at":"2026-07-05T09:09:59Z","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/2405.03778/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Random variables in metric spaces indexed by time and observed at equally spaced time points are receiving increased attention due to their broad applicability. The absence of inherent structure in metric spaces has resulted in a literature that is predominantly non-parametric and model-free. To address this gap in models for time series of random objects, we introduce an adaptation of the classical linear autoregressive model tailored for data lying in a Hadamard space. The parameters of interest in this model are the Fr\\'echet mean and a concentration parameter, both of which we prove can be","authors_text":"Helle S{\\o}rensen, Matthieu Bult\\'e","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2024-05-06T18:19:22Z","title":"An Autoregressive Model for Time Series of Random Objects"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.03778","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:b8602b77518ebd4f0573517adef2a1d1f2335138a2b660cc8f10095bbda4bff7","target":"record","created_at":"2026-07-05T09:09:59Z","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":"99baa87d4baac37b766efd1f252f7b5b3807ee919dac591354455342041864e9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2024-05-06T18:19:22Z","title_canon_sha256":"06fff54baa505144209fa5d9336844d68e8bff9253b3517878bdd66886bc944a"},"schema_version":"1.0","source":{"id":"2405.03778","kind":"arxiv","version":2}},"canonical_sha256":"f2d4772232fc411856c37037ab5b29aa4f92ed21d8962dccb15a965ee3e4a3e9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2d4772232fc411856c37037ab5b29aa4f92ed21d8962dccb15a965ee3e4a3e9","first_computed_at":"2026-07-05T09:09:59.319113Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:09:59.319113Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iVvRxIh/fh08iuvOSf5tgF2YNbnB6dNqcofg/WIK2jGW/jisU8czIQxzZ1VIz0jCTcN7YDt+E7KT5GC+b84IBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:09:59.319544Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.03778","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b8602b77518ebd4f0573517adef2a1d1f2335138a2b660cc8f10095bbda4bff7","sha256:2b03bf04bb55e1aeae11659a8ec5b627d89cae2154f8cad94684d0e95aa976ce"],"state_sha256":"cccf8810a1756b34e944f98d0986e2ff2d036d18fb99ef58c000cb4113f8a488"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G+a+RS//FvmYBMpkUuw3bgcxEmgpW8EssKQfWLPp3qeRxx0wJklwi6f7RyPDx8NFrhyWKXlaGJbKXLeOLDPDCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T10:46:02.910979Z","bundle_sha256":"81701308a11472a56aedbacd5c391ca3f05bdd5e8f880ef61cfb4b1a6ae54028"}}