{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:PK6DF6KB2GH4JHHRJM2T4BQ5XC","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":"8b014886f9d0d4acfc3aacfaac10de8fafe47cc4fb9d4217b1e169751a1fb44b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-01-22T20:04:51Z","title_canon_sha256":"2517b40bd77a914d7eed8a8c72d392c0f5cec86b379a78b6f2e180bd1661de13"},"schema_version":"1.0","source":{"id":"1101.4318","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.4318","created_at":"2026-05-18T04:28:47Z"},{"alias_kind":"arxiv_version","alias_value":"1101.4318v2","created_at":"2026-05-18T04:28:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.4318","created_at":"2026-05-18T04:28:47Z"},{"alias_kind":"pith_short_12","alias_value":"PK6DF6KB2GH4","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PK6DF6KB2GH4JHHR","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PK6DF6KB","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:38f84bd5d87e9d8a210ceeecf18b88c7275c5c69f5a12c9ece30de5be5f41cc2","target":"graph","created_at":"2026-05-18T04:28:47Z","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 propose in this paper a framework dedicated to the construction of what we call time elastic inner products that allows embedding sets of non-uniformly sampled multivariate time series of varying lengths into vector space structures. This framework is based on a recursive definition that covers the case of multiple embedded time elastic dimensions. We prove that such inner products exist in our framework and show how a simple instance of this inner product class operates on some toy applications, while generalizing the Euclidean inner product.","authors_text":"Pierre-Fran\\c{c}ois Marteau (VALORIA)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-01-22T20:04:51Z","title":"Discrete Time Elastic Vector Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4318","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":"sha256:3bfa798a55dc58d84a3e3e569b952a8c54d7b32d3f67dd46d595930e1097d303","target":"record","created_at":"2026-05-18T04:28:47Z","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":"8b014886f9d0d4acfc3aacfaac10de8fafe47cc4fb9d4217b1e169751a1fb44b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-01-22T20:04:51Z","title_canon_sha256":"2517b40bd77a914d7eed8a8c72d392c0f5cec86b379a78b6f2e180bd1661de13"},"schema_version":"1.0","source":{"id":"1101.4318","kind":"arxiv","version":2}},"canonical_sha256":"7abc32f941d18fc49cf14b353e061db8a3a327652879fa97a2ac662f07edeb89","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7abc32f941d18fc49cf14b353e061db8a3a327652879fa97a2ac662f07edeb89","first_computed_at":"2026-05-18T04:28:47.522495Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:28:47.522495Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CRYez/qHIlvWQ4SjxZTWBYyVdiWBxojG4ARKNr70rulju+/Sa379eXIblp8MHJg6dxbDREmdl7N2ri/5Zcx9AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:28:47.523222Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.4318","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3bfa798a55dc58d84a3e3e569b952a8c54d7b32d3f67dd46d595930e1097d303","sha256:38f84bd5d87e9d8a210ceeecf18b88c7275c5c69f5a12c9ece30de5be5f41cc2"],"state_sha256":"dba225f55b3a3b9a6c5170c1d4f098821dba408b129f0757873c5d36bc9219bc"}