{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:MSHIDO55VDSRGXXNBDQ533RBPV","short_pith_number":"pith:MSHIDO55","canonical_record":{"source":{"id":"1412.7659","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2014-12-24T13:19:20Z","cross_cats_sorted":["cs.CV","cs.NE"],"title_canon_sha256":"416c1e0fa8eb098f00ce6cbb0307aaac0a9ccf046ec5f21ad7f83e9b831db244","abstract_canon_sha256":"b1a8f7b2b8eb46b817a3bffe0c63e88dbda33042dfa25a34a8fd2d98194d4c60"},"schema_version":"1.0"},"canonical_sha256":"648e81bbbda8e5135eed08e1ddee217d7df36660da79025cd90a88752ef814e1","source":{"kind":"arxiv","id":"1412.7659","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.7659","created_at":"2026-05-17T23:48:07Z"},{"alias_kind":"arxiv_version","alias_value":"1412.7659v3","created_at":"2026-05-17T23:48:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.7659","created_at":"2026-05-17T23:48:07Z"},{"alias_kind":"pith_short_12","alias_value":"MSHIDO55VDSR","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MSHIDO55VDSRGXXN","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MSHIDO55","created_at":"2026-05-18T12:28:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:MSHIDO55VDSRGXXNBDQ533RBPV","target":"record","payload":{"canonical_record":{"source":{"id":"1412.7659","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2014-12-24T13:19:20Z","cross_cats_sorted":["cs.CV","cs.NE"],"title_canon_sha256":"416c1e0fa8eb098f00ce6cbb0307aaac0a9ccf046ec5f21ad7f83e9b831db244","abstract_canon_sha256":"b1a8f7b2b8eb46b817a3bffe0c63e88dbda33042dfa25a34a8fd2d98194d4c60"},"schema_version":"1.0"},"canonical_sha256":"648e81bbbda8e5135eed08e1ddee217d7df36660da79025cd90a88752ef814e1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:07.138292Z","signature_b64":"JsC6vTMBo1dIpvyISWxyfBG5zzeSbJ0wEiF+wWIBK52PWC6fRZJ55bGyIjx6hKMHo2jEtTD4RNdivFpafrMrBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"648e81bbbda8e5135eed08e1ddee217d7df36660da79025cd90a88752ef814e1","last_reissued_at":"2026-05-17T23:48:07.137888Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:07.137888Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.7659","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:48:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OHgoxs/DC+qPV3sbPUMyOlH1uAQwnDFX9nNbXFYruFBYFRAkb4TED+vBvD6NPBMvv/fCp3vZS2f0uxoePXJKBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T23:22:54.761283Z"},"content_sha256":"2778f7a19c501e801218ae9bece49e883981117cd5db189875986eeb8b8d2db9","schema_version":"1.0","event_id":"sha256:2778f7a19c501e801218ae9bece49e883981117cd5db189875986eeb8b8d2db9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:MSHIDO55VDSRGXXNBDQ533RBPV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Transformation Properties of Learned Visual Representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CV","cs.NE"],"primary_cat":"cs.LG","authors_text":"Max Welling, Taco S. Cohen","submitted_at":"2014-12-24T13:19:20Z","abstract_excerpt":"When a three-dimensional object moves relative to an observer, a change occurs on the observer's image plane and in the visual representation computed by a learned model. Starting with the idea that a good visual representation is one that transforms linearly under scene motions, we show, using the theory of group representations, that any such representation is equivalent to a combination of the elementary irreducible representations. We derive a striking relationship between irreducibility and the statistical dependency structure of the representation, by showing that under restricted condit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7659","kind":"arxiv","version":3},"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":"2026-05-17T23:48:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NjMdIaOLVHxZFRoGPKA1N9xH0kYXunvFDM6pTCM8OQHcNJipbeJjrkjPExhaFj4jG8hwDd51/YlUidChNhGSDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T23:22:54.761665Z"},"content_sha256":"58ee121fa91b0f46896a794e4938fb5a73dcad9e1dd099e47fba35c31526481d","schema_version":"1.0","event_id":"sha256:58ee121fa91b0f46896a794e4938fb5a73dcad9e1dd099e47fba35c31526481d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MSHIDO55VDSRGXXNBDQ533RBPV/bundle.json","state_url":"https://pith.science/pith/MSHIDO55VDSRGXXNBDQ533RBPV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MSHIDO55VDSRGXXNBDQ533RBPV/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":"2026-05-25T23:22:54Z","links":{"resolver":"https://pith.science/pith/MSHIDO55VDSRGXXNBDQ533RBPV","bundle":"https://pith.science/pith/MSHIDO55VDSRGXXNBDQ533RBPV/bundle.json","state":"https://pith.science/pith/MSHIDO55VDSRGXXNBDQ533RBPV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MSHIDO55VDSRGXXNBDQ533RBPV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:MSHIDO55VDSRGXXNBDQ533RBPV","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":"b1a8f7b2b8eb46b817a3bffe0c63e88dbda33042dfa25a34a8fd2d98194d4c60","cross_cats_sorted":["cs.CV","cs.NE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2014-12-24T13:19:20Z","title_canon_sha256":"416c1e0fa8eb098f00ce6cbb0307aaac0a9ccf046ec5f21ad7f83e9b831db244"},"schema_version":"1.0","source":{"id":"1412.7659","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.7659","created_at":"2026-05-17T23:48:07Z"},{"alias_kind":"arxiv_version","alias_value":"1412.7659v3","created_at":"2026-05-17T23:48:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.7659","created_at":"2026-05-17T23:48:07Z"},{"alias_kind":"pith_short_12","alias_value":"MSHIDO55VDSR","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MSHIDO55VDSRGXXN","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MSHIDO55","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:58ee121fa91b0f46896a794e4938fb5a73dcad9e1dd099e47fba35c31526481d","target":"graph","created_at":"2026-05-17T23:48:07Z","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":"When a three-dimensional object moves relative to an observer, a change occurs on the observer's image plane and in the visual representation computed by a learned model. Starting with the idea that a good visual representation is one that transforms linearly under scene motions, we show, using the theory of group representations, that any such representation is equivalent to a combination of the elementary irreducible representations. We derive a striking relationship between irreducibility and the statistical dependency structure of the representation, by showing that under restricted condit","authors_text":"Max Welling, Taco S. Cohen","cross_cats":["cs.CV","cs.NE"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2014-12-24T13:19:20Z","title":"Transformation Properties of Learned Visual Representations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7659","kind":"arxiv","version":3},"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":"sha256:2778f7a19c501e801218ae9bece49e883981117cd5db189875986eeb8b8d2db9","target":"record","created_at":"2026-05-17T23:48:07Z","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":"b1a8f7b2b8eb46b817a3bffe0c63e88dbda33042dfa25a34a8fd2d98194d4c60","cross_cats_sorted":["cs.CV","cs.NE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2014-12-24T13:19:20Z","title_canon_sha256":"416c1e0fa8eb098f00ce6cbb0307aaac0a9ccf046ec5f21ad7f83e9b831db244"},"schema_version":"1.0","source":{"id":"1412.7659","kind":"arxiv","version":3}},"canonical_sha256":"648e81bbbda8e5135eed08e1ddee217d7df36660da79025cd90a88752ef814e1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"648e81bbbda8e5135eed08e1ddee217d7df36660da79025cd90a88752ef814e1","first_computed_at":"2026-05-17T23:48:07.137888Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:07.137888Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JsC6vTMBo1dIpvyISWxyfBG5zzeSbJ0wEiF+wWIBK52PWC6fRZJ55bGyIjx6hKMHo2jEtTD4RNdivFpafrMrBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:07.138292Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.7659","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2778f7a19c501e801218ae9bece49e883981117cd5db189875986eeb8b8d2db9","sha256:58ee121fa91b0f46896a794e4938fb5a73dcad9e1dd099e47fba35c31526481d"],"state_sha256":"f1ea28aef73c7f9bdeecdd287727fe9911fc5ab51a402fa22304bb2cc7b9af6b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WTCEXUOsEdsMcWkxEQV4edMvI/TJLp3bAgGbnl51hsbnUqG2RiJE/VM6acSkdF1I9xfi4ttIZbo8LZc8iF69Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T23:22:54.764219Z","bundle_sha256":"f0b2a44e6360f8b7f9a3e2554c06f9b8fc63a9386115bc7f04db33b78565dfe1"}}