{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:ZNQCSPGLBSPPMRGD43KGB5WXJ6","short_pith_number":"pith:ZNQCSPGL","canonical_record":{"source":{"id":"1806.03636","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2018-06-10T11:16:36Z","cross_cats_sorted":[],"title_canon_sha256":"b204507d4aca367b86dd18126a2fff809b717caa43f1394355eea8d204eba66b","abstract_canon_sha256":"2b392438257dcb7fe54968fb7cc7576d254ad5f634eb3ad14a47ba70aefd94ed"},"schema_version":"1.0"},"canonical_sha256":"cb60293ccb0c9ef644c3e6d460f6d74f87da0a65620ee4bace3764db351cc713","source":{"kind":"arxiv","id":"1806.03636","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.03636","created_at":"2026-05-18T00:10:59Z"},{"alias_kind":"arxiv_version","alias_value":"1806.03636v3","created_at":"2026-05-18T00:10:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.03636","created_at":"2026-05-18T00:10:59Z"},{"alias_kind":"pith_short_12","alias_value":"ZNQCSPGLBSPP","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"ZNQCSPGLBSPPMRGD","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"ZNQCSPGL","created_at":"2026-05-18T12:33:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:ZNQCSPGLBSPPMRGD43KGB5WXJ6","target":"record","payload":{"canonical_record":{"source":{"id":"1806.03636","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2018-06-10T11:16:36Z","cross_cats_sorted":[],"title_canon_sha256":"b204507d4aca367b86dd18126a2fff809b717caa43f1394355eea8d204eba66b","abstract_canon_sha256":"2b392438257dcb7fe54968fb7cc7576d254ad5f634eb3ad14a47ba70aefd94ed"},"schema_version":"1.0"},"canonical_sha256":"cb60293ccb0c9ef644c3e6d460f6d74f87da0a65620ee4bace3764db351cc713","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:59.448760Z","signature_b64":"lK4Rb5IU/L+NYvBi2Q3V+pj/JDXeQ2tnoiEGUGL07LZJn+U0WFK6LQ8AFKEd2K4/e6bAoFuIYNWXxf8TmiAYCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb60293ccb0c9ef644c3e6d460f6d74f87da0a65620ee4bace3764db351cc713","last_reissued_at":"2026-05-18T00:10:59.448169Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:59.448169Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.03636","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":"2026-05-18T00:10:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YyqdCiwUs/6/2E9Cip07xgC7f/FWfyitabZRZiPuh2aCGnSaX38+43mCHDOAb+kntP1DG0QNqBXnYtDA8jJIDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T16:53:37.255286Z"},"content_sha256":"4254f562f0fd59b1d0147d1449bf6481d3a1db73a9f3e0e9f3ffd9ee25eaf735","schema_version":"1.0","event_id":"sha256:4254f562f0fd59b1d0147d1449bf6481d3a1db73a9f3e0e9f3ffd9ee25eaf735"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:ZNQCSPGLBSPPMRGD43KGB5WXJ6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Transformationally Identical and Invariant Convolutional Neural Networks through Symmetric Element Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CV","authors_text":"Matthew T. Freedman, Seong K. Mun, Shih Chung B. Lo, Shuo Gu","submitted_at":"2018-06-10T11:16:36Z","abstract_excerpt":"Mathematically speaking, a transformationally invariant operator, such as a transformationally identical (TI) matrix kernel (i.e., K= T{K}), commutes with the transformation (T{.}) itself when they operate on the first operand matrix. We found that by consistently applying the same type of TI kernels in a convolutional neural networks (CNN) system, the commutative property holds throughout all layers of convolution processes with and without involving an activation function and/or a 1D convolution across channels within a layer. We further found that any CNN possessing the same TI kernel prope"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.03636","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":"2026-05-18T00:10:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v8fv57ShZqYwWXpxMp3GL1Z5FahsIyiaOzgzP4Gn0aUon9hOV84zSdT2dGLiPDqjy7Wb/F4TiXhsZ0wFqxmRBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T16:53:37.255645Z"},"content_sha256":"687b5fa7ace6a6885491a9adb8225f3c68002cb5314a8dfd5190ace953b86f8b","schema_version":"1.0","event_id":"sha256:687b5fa7ace6a6885491a9adb8225f3c68002cb5314a8dfd5190ace953b86f8b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZNQCSPGLBSPPMRGD43KGB5WXJ6/bundle.json","state_url":"https://pith.science/pith/ZNQCSPGLBSPPMRGD43KGB5WXJ6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZNQCSPGLBSPPMRGD43KGB5WXJ6/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":"2026-06-02T16:53:37Z","links":{"resolver":"https://pith.science/pith/ZNQCSPGLBSPPMRGD43KGB5WXJ6","bundle":"https://pith.science/pith/ZNQCSPGLBSPPMRGD43KGB5WXJ6/bundle.json","state":"https://pith.science/pith/ZNQCSPGLBSPPMRGD43KGB5WXJ6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZNQCSPGLBSPPMRGD43KGB5WXJ6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ZNQCSPGLBSPPMRGD43KGB5WXJ6","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":"2b392438257dcb7fe54968fb7cc7576d254ad5f634eb3ad14a47ba70aefd94ed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2018-06-10T11:16:36Z","title_canon_sha256":"b204507d4aca367b86dd18126a2fff809b717caa43f1394355eea8d204eba66b"},"schema_version":"1.0","source":{"id":"1806.03636","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.03636","created_at":"2026-05-18T00:10:59Z"},{"alias_kind":"arxiv_version","alias_value":"1806.03636v3","created_at":"2026-05-18T00:10:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.03636","created_at":"2026-05-18T00:10:59Z"},{"alias_kind":"pith_short_12","alias_value":"ZNQCSPGLBSPP","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"ZNQCSPGLBSPPMRGD","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"ZNQCSPGL","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:687b5fa7ace6a6885491a9adb8225f3c68002cb5314a8dfd5190ace953b86f8b","target":"graph","created_at":"2026-05-18T00:10:59Z","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"},"paper":{"abstract_excerpt":"Mathematically speaking, a transformationally invariant operator, such as a transformationally identical (TI) matrix kernel (i.e., K= T{K}), commutes with the transformation (T{.}) itself when they operate on the first operand matrix. We found that by consistently applying the same type of TI kernels in a convolutional neural networks (CNN) system, the commutative property holds throughout all layers of convolution processes with and without involving an activation function and/or a 1D convolution across channels within a layer. We further found that any CNN possessing the same TI kernel prope","authors_text":"Matthew T. Freedman, Seong K. Mun, Shih Chung B. Lo, Shuo Gu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2018-06-10T11:16:36Z","title":"Transformationally Identical and Invariant Convolutional Neural Networks through Symmetric Element Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.03636","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":"sha256:4254f562f0fd59b1d0147d1449bf6481d3a1db73a9f3e0e9f3ffd9ee25eaf735","target":"record","created_at":"2026-05-18T00:10:59Z","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":"2b392438257dcb7fe54968fb7cc7576d254ad5f634eb3ad14a47ba70aefd94ed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CV","submitted_at":"2018-06-10T11:16:36Z","title_canon_sha256":"b204507d4aca367b86dd18126a2fff809b717caa43f1394355eea8d204eba66b"},"schema_version":"1.0","source":{"id":"1806.03636","kind":"arxiv","version":3}},"canonical_sha256":"cb60293ccb0c9ef644c3e6d460f6d74f87da0a65620ee4bace3764db351cc713","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cb60293ccb0c9ef644c3e6d460f6d74f87da0a65620ee4bace3764db351cc713","first_computed_at":"2026-05-18T00:10:59.448169Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:59.448169Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lK4Rb5IU/L+NYvBi2Q3V+pj/JDXeQ2tnoiEGUGL07LZJn+U0WFK6LQ8AFKEd2K4/e6bAoFuIYNWXxf8TmiAYCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:59.448760Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.03636","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4254f562f0fd59b1d0147d1449bf6481d3a1db73a9f3e0e9f3ffd9ee25eaf735","sha256:687b5fa7ace6a6885491a9adb8225f3c68002cb5314a8dfd5190ace953b86f8b"],"state_sha256":"e42f9988c7ea898c7e2171016c0742d3966b0830c933884c57ad69e0a1aad9a0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K57inIdpgscMG1h9nVlAhA/RrGEa9qAMz3iReTzlJgv2sIEYUHS26qqr6ZWfJi5DxC0w+zwbWzS0b0Gu4U5iDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T16:53:37.257573Z","bundle_sha256":"a3761953069defdec60191fd55f8b8df2df5a25e86f11bf4bd75c00ce0378538"}}