{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:IPC2KBQZ57F2I3IVFHV3E2KZWK","short_pith_number":"pith:IPC2KBQZ","canonical_record":{"source":{"id":"1510.04356","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-10-15T00:05:21Z","cross_cats_sorted":["cs.LG","math.IT","stat.ML"],"title_canon_sha256":"748e1a3f8cbba56eefb8a533eac792ebb1feeca9a07ef7b7f1e63a3b0f9fd16a","abstract_canon_sha256":"073cef806360e20edc533d03851e0f3a41a5ab55924ea480acc16066c83e760b"},"schema_version":"1.0"},"canonical_sha256":"43c5a50619efcba46d1529ebb26959b2b212d2f1f92df27373b3a37bf90d3737","source":{"kind":"arxiv","id":"1510.04356","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.04356","created_at":"2026-05-18T01:30:07Z"},{"alias_kind":"arxiv_version","alias_value":"1510.04356v1","created_at":"2026-05-18T01:30:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.04356","created_at":"2026-05-18T01:30:07Z"},{"alias_kind":"pith_short_12","alias_value":"IPC2KBQZ57F2","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"IPC2KBQZ57F2I3IV","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"IPC2KBQZ","created_at":"2026-05-18T12:29:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:IPC2KBQZ57F2I3IVFHV3E2KZWK","target":"record","payload":{"canonical_record":{"source":{"id":"1510.04356","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-10-15T00:05:21Z","cross_cats_sorted":["cs.LG","math.IT","stat.ML"],"title_canon_sha256":"748e1a3f8cbba56eefb8a533eac792ebb1feeca9a07ef7b7f1e63a3b0f9fd16a","abstract_canon_sha256":"073cef806360e20edc533d03851e0f3a41a5ab55924ea480acc16066c83e760b"},"schema_version":"1.0"},"canonical_sha256":"43c5a50619efcba46d1529ebb26959b2b212d2f1f92df27373b3a37bf90d3737","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:07.409766Z","signature_b64":"micBLQ9SYX0tfrmej7+8odLJ9lFxHa8kLBZpqS7KgjMHQGsTctKfjPoOR3i2KVCtVWFLzTVoaoW0SwKU+dc6AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"43c5a50619efcba46d1529ebb26959b2b212d2f1f92df27373b3a37bf90d3737","last_reissued_at":"2026-05-18T01:30:07.409196Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:07.409196Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.04356","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":"2026-05-18T01:30:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ek9p+F0BzIhfcFvqtL3YPyC6S9XhSJGFpq3Hv9DlWC5DIO3kthoW2NwrJiEA18kXnEOi3gCvapaHyvlDwfTIAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T16:15:30.575308Z"},"content_sha256":"6620a11d3fcef095209a0ace2c43408b01d3849a0d0fad20b0d3810a123dc6df","schema_version":"1.0","event_id":"sha256:6620a11d3fcef095209a0ace2c43408b01d3849a0d0fad20b0d3810a123dc6df"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:IPC2KBQZ57F2I3IVFHV3E2KZWK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Group-Invariant Subspace Clustering","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.IT","stat.ML"],"primary_cat":"cs.IT","authors_text":"Eric Kernfeld, Shuchin Aeron","submitted_at":"2015-10-15T00:05:21Z","abstract_excerpt":"In this paper we consider the problem of group invariant subspace clustering where the data is assumed to come from a union of group-invariant subspaces of a vector space, i.e. subspaces which are invariant with respect to action of a given group. Algebraically, such group-invariant subspaces are also referred to as submodules. Similar to the well known Sparse Subspace Clustering approach where the data is assumed to come from a union of subspaces, we analyze an algorithm which, following a recent work [1], we refer to as Sparse Sub-module Clustering (SSmC). The method is based on finding grou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04356","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":"2026-05-18T01:30:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wqbiojNk8KZN4VQvjPbfrB7EnY8vlTkcQSUzBQZW3ASpEVPXQc605PtWQ0+U9TD3ky0cQK7uLj2ZyZrNAZhTAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T16:15:30.575942Z"},"content_sha256":"4e7e99968bc6b194ad999016b8e0ee06257b54264d6e8c2ffcda92902baaf116","schema_version":"1.0","event_id":"sha256:4e7e99968bc6b194ad999016b8e0ee06257b54264d6e8c2ffcda92902baaf116"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IPC2KBQZ57F2I3IVFHV3E2KZWK/bundle.json","state_url":"https://pith.science/pith/IPC2KBQZ57F2I3IVFHV3E2KZWK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IPC2KBQZ57F2I3IVFHV3E2KZWK/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":"2026-06-07T16:15:30Z","links":{"resolver":"https://pith.science/pith/IPC2KBQZ57F2I3IVFHV3E2KZWK","bundle":"https://pith.science/pith/IPC2KBQZ57F2I3IVFHV3E2KZWK/bundle.json","state":"https://pith.science/pith/IPC2KBQZ57F2I3IVFHV3E2KZWK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IPC2KBQZ57F2I3IVFHV3E2KZWK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:IPC2KBQZ57F2I3IVFHV3E2KZWK","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":"073cef806360e20edc533d03851e0f3a41a5ab55924ea480acc16066c83e760b","cross_cats_sorted":["cs.LG","math.IT","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-10-15T00:05:21Z","title_canon_sha256":"748e1a3f8cbba56eefb8a533eac792ebb1feeca9a07ef7b7f1e63a3b0f9fd16a"},"schema_version":"1.0","source":{"id":"1510.04356","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.04356","created_at":"2026-05-18T01:30:07Z"},{"alias_kind":"arxiv_version","alias_value":"1510.04356v1","created_at":"2026-05-18T01:30:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.04356","created_at":"2026-05-18T01:30:07Z"},{"alias_kind":"pith_short_12","alias_value":"IPC2KBQZ57F2","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"IPC2KBQZ57F2I3IV","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"IPC2KBQZ","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:4e7e99968bc6b194ad999016b8e0ee06257b54264d6e8c2ffcda92902baaf116","target":"graph","created_at":"2026-05-18T01:30:07Z","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":"In this paper we consider the problem of group invariant subspace clustering where the data is assumed to come from a union of group-invariant subspaces of a vector space, i.e. subspaces which are invariant with respect to action of a given group. Algebraically, such group-invariant subspaces are also referred to as submodules. Similar to the well known Sparse Subspace Clustering approach where the data is assumed to come from a union of subspaces, we analyze an algorithm which, following a recent work [1], we refer to as Sparse Sub-module Clustering (SSmC). The method is based on finding grou","authors_text":"Eric Kernfeld, Shuchin Aeron","cross_cats":["cs.LG","math.IT","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-10-15T00:05:21Z","title":"Group-Invariant Subspace Clustering"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04356","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":"sha256:6620a11d3fcef095209a0ace2c43408b01d3849a0d0fad20b0d3810a123dc6df","target":"record","created_at":"2026-05-18T01:30:07Z","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":"073cef806360e20edc533d03851e0f3a41a5ab55924ea480acc16066c83e760b","cross_cats_sorted":["cs.LG","math.IT","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-10-15T00:05:21Z","title_canon_sha256":"748e1a3f8cbba56eefb8a533eac792ebb1feeca9a07ef7b7f1e63a3b0f9fd16a"},"schema_version":"1.0","source":{"id":"1510.04356","kind":"arxiv","version":1}},"canonical_sha256":"43c5a50619efcba46d1529ebb26959b2b212d2f1f92df27373b3a37bf90d3737","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"43c5a50619efcba46d1529ebb26959b2b212d2f1f92df27373b3a37bf90d3737","first_computed_at":"2026-05-18T01:30:07.409196Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:07.409196Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"micBLQ9SYX0tfrmej7+8odLJ9lFxHa8kLBZpqS7KgjMHQGsTctKfjPoOR3i2KVCtVWFLzTVoaoW0SwKU+dc6AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:07.409766Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.04356","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6620a11d3fcef095209a0ace2c43408b01d3849a0d0fad20b0d3810a123dc6df","sha256:4e7e99968bc6b194ad999016b8e0ee06257b54264d6e8c2ffcda92902baaf116"],"state_sha256":"196d37e2c6bb16b71b2ee038d98a49b0882a301cbc0843ae6083d9016a933284"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b0pn4gaimwomvd/wfbUGz6kt0MmdlCzBD310V+esEpMTBAkT4ElvW6XcodB+zeSOc6Xptc4msd/HYK39f4tCCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T16:15:30.579628Z","bundle_sha256":"69960a29efe084d3382cc1bba2f76c4796dbf504413ab29d54353747f72679d0"}}