{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:IELJ52UUVGYHM27UKI7CZLWOWN","short_pith_number":"pith:IELJ52UU","canonical_record":{"source":{"id":"1407.1123","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2014-07-04T05:34:38Z","cross_cats_sorted":["cs.LG","stat.ML"],"title_canon_sha256":"2cf0e1aa03b563f161b9234697d4d63640dbd660e21c22f883bda04656bc12d9","abstract_canon_sha256":"872613340c5dbb6f1ed56878e9e4c8ada2dafe8798d5bc48ba527969e67330aa"},"schema_version":"1.0"},"canonical_sha256":"41169eea94a9b0766bf4523e2caeceb34e42fb29ee0c35ebdf2b8a544ffbd96f","source":{"kind":"arxiv","id":"1407.1123","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.1123","created_at":"2026-05-18T02:48:18Z"},{"alias_kind":"arxiv_version","alias_value":"1407.1123v1","created_at":"2026-05-18T02:48:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.1123","created_at":"2026-05-18T02:48:18Z"},{"alias_kind":"pith_short_12","alias_value":"IELJ52UUVGYH","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"IELJ52UUVGYHM27U","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"IELJ52UU","created_at":"2026-05-18T12:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:IELJ52UUVGYHM27UKI7CZLWOWN","target":"record","payload":{"canonical_record":{"source":{"id":"1407.1123","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2014-07-04T05:34:38Z","cross_cats_sorted":["cs.LG","stat.ML"],"title_canon_sha256":"2cf0e1aa03b563f161b9234697d4d63640dbd660e21c22f883bda04656bc12d9","abstract_canon_sha256":"872613340c5dbb6f1ed56878e9e4c8ada2dafe8798d5bc48ba527969e67330aa"},"schema_version":"1.0"},"canonical_sha256":"41169eea94a9b0766bf4523e2caeceb34e42fb29ee0c35ebdf2b8a544ffbd96f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:18.687329Z","signature_b64":"vNQJ05o9+BL6gXGxL+7pxWHM59blcIzrJutI38HN5/DamY6okKp0UFR4DVukVXxm1XHC/u8dImkctQbZobcXAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"41169eea94a9b0766bf4523e2caeceb34e42fb29ee0c35ebdf2b8a544ffbd96f","last_reissued_at":"2026-05-18T02:48:18.686779Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:18.686779Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.1123","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:48:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A8NfjrfPXvy4a5LlEvUWcOAqGLgg9ekCngH+zeszz2zNobTz4hlBZu5LdnmUglbET8D+7eZPoarlrornRYRvCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T18:22:22.962619Z"},"content_sha256":"428be25522c1d2624271737c403bc940799f625e0ef73fe194bdb7068468993e","schema_version":"1.0","event_id":"sha256:428be25522c1d2624271737c403bc940799f625e0ef73fe194bdb7068468993e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:IELJ52UUVGYHM27UKI7CZLWOWN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Expanding the Family of Grassmannian Kernels: An Embedding Perspective","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"cs.CV","authors_text":"Hongdong Li, Mathieu Salzmann, Mehrtash T. Harandi, Richard Hartley, Sadeep Jayasumana","submitted_at":"2014-07-04T05:34:38Z","abstract_excerpt":"Modeling videos and image-sets as linear subspaces has proven beneficial for many visual recognition tasks. However, it also incurs challenges arising from the fact that linear subspaces do not obey Euclidean geometry, but lie on a special type of Riemannian manifolds known as Grassmannian. To leverage the techniques developed for Euclidean spaces (e.g, support vector machines) with subspaces, several recent studies have proposed to embed the Grassmannian into a Hilbert space by making use of a positive definite kernel. Unfortunately, only two Grassmannian kernels are known, none of which -as "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1123","kind":"arxiv","version":1},"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":"2026-05-18T02:48:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sRWe34oGE5DdbKhHPqgVtr9VeCXfVXSEdGzloZg9JPrxYSBbW+nrhg/dT7fYn82szytycuSuh8ah1lxsDVGoDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T18:22:22.963287Z"},"content_sha256":"6eb37e5c3dac9996fc86a4110d455b3247048c2877084a7020258cadf6e2ae3c","schema_version":"1.0","event_id":"sha256:6eb37e5c3dac9996fc86a4110d455b3247048c2877084a7020258cadf6e2ae3c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IELJ52UUVGYHM27UKI7CZLWOWN/bundle.json","state_url":"https://pith.science/pith/IELJ52UUVGYHM27UKI7CZLWOWN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IELJ52UUVGYHM27UKI7CZLWOWN/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":"2026-05-30T18:22:22Z","links":{"resolver":"https://pith.science/pith/IELJ52UUVGYHM27UKI7CZLWOWN","bundle":"https://pith.science/pith/IELJ52UUVGYHM27UKI7CZLWOWN/bundle.json","state":"https://pith.science/pith/IELJ52UUVGYHM27UKI7CZLWOWN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IELJ52UUVGYHM27UKI7CZLWOWN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:IELJ52UUVGYHM27UKI7CZLWOWN","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":"872613340c5dbb6f1ed56878e9e4c8ada2dafe8798d5bc48ba527969e67330aa","cross_cats_sorted":["cs.LG","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2014-07-04T05:34:38Z","title_canon_sha256":"2cf0e1aa03b563f161b9234697d4d63640dbd660e21c22f883bda04656bc12d9"},"schema_version":"1.0","source":{"id":"1407.1123","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.1123","created_at":"2026-05-18T02:48:18Z"},{"alias_kind":"arxiv_version","alias_value":"1407.1123v1","created_at":"2026-05-18T02:48:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.1123","created_at":"2026-05-18T02:48:18Z"},{"alias_kind":"pith_short_12","alias_value":"IELJ52UUVGYH","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"IELJ52UUVGYHM27U","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"IELJ52UU","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:6eb37e5c3dac9996fc86a4110d455b3247048c2877084a7020258cadf6e2ae3c","target":"graph","created_at":"2026-05-18T02:48:18Z","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":"Modeling videos and image-sets as linear subspaces has proven beneficial for many visual recognition tasks. However, it also incurs challenges arising from the fact that linear subspaces do not obey Euclidean geometry, but lie on a special type of Riemannian manifolds known as Grassmannian. To leverage the techniques developed for Euclidean spaces (e.g, support vector machines) with subspaces, several recent studies have proposed to embed the Grassmannian into a Hilbert space by making use of a positive definite kernel. Unfortunately, only two Grassmannian kernels are known, none of which -as ","authors_text":"Hongdong Li, Mathieu Salzmann, Mehrtash T. Harandi, Richard Hartley, Sadeep Jayasumana","cross_cats":["cs.LG","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2014-07-04T05:34:38Z","title":"Expanding the Family of Grassmannian Kernels: An Embedding Perspective"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1123","kind":"arxiv","version":1},"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":"sha256:428be25522c1d2624271737c403bc940799f625e0ef73fe194bdb7068468993e","target":"record","created_at":"2026-05-18T02:48:18Z","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":"872613340c5dbb6f1ed56878e9e4c8ada2dafe8798d5bc48ba527969e67330aa","cross_cats_sorted":["cs.LG","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2014-07-04T05:34:38Z","title_canon_sha256":"2cf0e1aa03b563f161b9234697d4d63640dbd660e21c22f883bda04656bc12d9"},"schema_version":"1.0","source":{"id":"1407.1123","kind":"arxiv","version":1}},"canonical_sha256":"41169eea94a9b0766bf4523e2caeceb34e42fb29ee0c35ebdf2b8a544ffbd96f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"41169eea94a9b0766bf4523e2caeceb34e42fb29ee0c35ebdf2b8a544ffbd96f","first_computed_at":"2026-05-18T02:48:18.686779Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:18.686779Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vNQJ05o9+BL6gXGxL+7pxWHM59blcIzrJutI38HN5/DamY6okKp0UFR4DVukVXxm1XHC/u8dImkctQbZobcXAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:18.687329Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.1123","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:428be25522c1d2624271737c403bc940799f625e0ef73fe194bdb7068468993e","sha256:6eb37e5c3dac9996fc86a4110d455b3247048c2877084a7020258cadf6e2ae3c"],"state_sha256":"d1e1972ec5b2afba13eb85e0f7e9a518dd82a2be62e33a3ee3f2ff792ba27117"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AYfkwdDFxxas5kSwJrScuFyNamq5xCdLyXiQdOXMpgUtJDkZ3igNTleRF2UPYnbLbZDl1zHKHQXdME+HSwpYDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T18:22:22.966927Z","bundle_sha256":"b3693183a328ff191a5d9e67bb1505bc485a76be9bb3dc5ae22034f85236da70"}}