{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:UUK2YLIT3YMSM4DBVQY3EY7NNT","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":"85c80c456fc94035cc52f4f1c26dcae35c637d74e3e7a1e86291bda977bdf3c2","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-14T16:34:50Z","title_canon_sha256":"55ddab563a4a3aad05e7647a0cf59057a07ff5b34c02a15cb3faf0e5844fc40c"},"schema_version":"1.0","source":{"id":"1212.3519","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.3519","created_at":"2026-05-18T03:38:24Z"},{"alias_kind":"arxiv_version","alias_value":"1212.3519v1","created_at":"2026-05-18T03:38:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.3519","created_at":"2026-05-18T03:38:24Z"},{"alias_kind":"pith_short_12","alias_value":"UUK2YLIT3YMS","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"UUK2YLIT3YMSM4DB","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"UUK2YLIT","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:65ba0229f58b2c8dac4abd8eece2d0e9c5b39e5d2231d802a72936b40712f67f","target":"graph","created_at":"2026-05-18T03:38:24Z","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 derive transformation formulas for the generalized polarization tensors under rigid motions and scaling in three dimensions, and use them to construct an infinite number of invariants under those transformations. These invariants can be used as shape descriptors for dictionary matching.","authors_text":"Daewon Chung, Habib Ammari, Han Wang, Hyeonbae Kang","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-14T16:34:50Z","title":"Invariance Properties of Generalized Polarization Tensors and Design of Shape Descriptors in Three Dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.3519","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":"sha256:0b20f7d1e3ba65e639f23d5e61835e0eadffe55571075c44c4bbf7a70c893a32","target":"record","created_at":"2026-05-18T03:38:24Z","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":"85c80c456fc94035cc52f4f1c26dcae35c637d74e3e7a1e86291bda977bdf3c2","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-14T16:34:50Z","title_canon_sha256":"55ddab563a4a3aad05e7647a0cf59057a07ff5b34c02a15cb3faf0e5844fc40c"},"schema_version":"1.0","source":{"id":"1212.3519","kind":"arxiv","version":1}},"canonical_sha256":"a515ac2d13de19267061ac31b263ed6cfc647f8c221a1205f043a0f390a140b8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a515ac2d13de19267061ac31b263ed6cfc647f8c221a1205f043a0f390a140b8","first_computed_at":"2026-05-18T03:38:24.405987Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:24.405987Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WpUh4P0QyEzWJcxk5duQDIyReQI5ri9U+cVOrBbqeFV67PZuOIVKv92DdBrid40pvDzjQwNmq+Xd6acrMFLlCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:24.406539Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.3519","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b20f7d1e3ba65e639f23d5e61835e0eadffe55571075c44c4bbf7a70c893a32","sha256:65ba0229f58b2c8dac4abd8eece2d0e9c5b39e5d2231d802a72936b40712f67f"],"state_sha256":"6dd391751249af39230142b87a5d56fb69fb895d50d829719628e30ab3821cdf"}