{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:VRQMAQ2F43GXLDZPQ4NPLHQ2WX","short_pith_number":"pith:VRQMAQ2F","canonical_record":{"source":{"id":"1904.05750","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2019-04-06T01:57:52Z","cross_cats_sorted":["physics.optics"],"title_canon_sha256":"d7034a25e789c976e71ebc237e56540ea0fc9d04efe2e07e76870dcdff73fe8f","abstract_canon_sha256":"11cd8c229149279698a927a59826508a989e48d9c3a20389a72292836987fffb"},"schema_version":"1.0"},"canonical_sha256":"ac60c04345e6cd758f2f871af59e1ab5fec82fc56fd8dcd691df2be921d4e6be","source":{"kind":"arxiv","id":"1904.05750","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.05750","created_at":"2026-07-04T23:52:35Z"},{"alias_kind":"arxiv_version","alias_value":"1904.05750v2","created_at":"2026-07-04T23:52:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.05750","created_at":"2026-07-04T23:52:35Z"},{"alias_kind":"pith_short_12","alias_value":"VRQMAQ2F43GX","created_at":"2026-07-04T23:52:35Z"},{"alias_kind":"pith_short_16","alias_value":"VRQMAQ2F43GXLDZP","created_at":"2026-07-04T23:52:35Z"},{"alias_kind":"pith_short_8","alias_value":"VRQMAQ2F","created_at":"2026-07-04T23:52:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:VRQMAQ2F43GXLDZPQ4NPLHQ2WX","target":"record","payload":{"canonical_record":{"source":{"id":"1904.05750","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2019-04-06T01:57:52Z","cross_cats_sorted":["physics.optics"],"title_canon_sha256":"d7034a25e789c976e71ebc237e56540ea0fc9d04efe2e07e76870dcdff73fe8f","abstract_canon_sha256":"11cd8c229149279698a927a59826508a989e48d9c3a20389a72292836987fffb"},"schema_version":"1.0"},"canonical_sha256":"ac60c04345e6cd758f2f871af59e1ab5fec82fc56fd8dcd691df2be921d4e6be","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:52:35.513580Z","signature_b64":"M7PIp9GWabm4HxVRyiQ9OOzP/lt83KMyFXq+9TMuSF5JSy1RkJaTMfSPW79ogJEw3er2RFeEnYAZmPsVOJoIDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac60c04345e6cd758f2f871af59e1ab5fec82fc56fd8dcd691df2be921d4e6be","last_reissued_at":"2026-07-04T23:52:35.513143Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:52:35.513143Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.05750","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T23:52:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pi8p5j6jgaFAnEECuaTj7EZJMVw+ZYIM8oIiaPVtaSFPTC6TkJJlSP19shTkuIWhsoOH8bLX9/yc3ciSe3sdCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T20:08:17.673587Z"},"content_sha256":"60ecb2e36d07daba142f5670b033802060002433a68b6b1f1bff610fed518e8a","schema_version":"1.0","event_id":"sha256:60ecb2e36d07daba142f5670b033802060002433a68b6b1f1bff610fed518e8a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:VRQMAQ2F43GXLDZPQ4NPLHQ2WX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Chiral Balls: Knotted Structures with Both Chirality and Three-dimensional Rotational Symmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.optics"],"primary_cat":"physics.class-ph","authors_text":"Chunxu Mao, Douglas H. Werner, Jun Hu, Lei Kang, Wending Mai, Yifan Chen","submitted_at":"2019-04-06T01:57:52Z","abstract_excerpt":"Knots have been put forward to explain various physical phenomena because of their topological stability. Nevertheless, few works have reported on the exotic symmetry properties that certain knots possess. Here we reveal an exceptional form of symmetry for a family of knots that are both chiral and three-dimensional (3-D) rotationally symmetric about every axis of a standard Cartesian coordinate system. We call these unique knotted structures chiral balls. To demonstrate the unprecedented physical characteristics exhibited by these unique structures, we study the electromagnetic scattering pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.05750","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1904.05750/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T23:52:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PL+Z5FRc9/H03hjheOnaDvDmlL911l6OXfQ+eiHk2OugyD/uknQ6BE93FUThW9xMFZY6mRh+yk2HGC3HJWuoCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T20:08:17.674946Z"},"content_sha256":"f17d473a902d6675ce0c589160729b7cb4caa4631f1eed5535ec5d7f2fa3eaff","schema_version":"1.0","event_id":"sha256:f17d473a902d6675ce0c589160729b7cb4caa4631f1eed5535ec5d7f2fa3eaff"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VRQMAQ2F43GXLDZPQ4NPLHQ2WX/bundle.json","state_url":"https://pith.science/pith/VRQMAQ2F43GXLDZPQ4NPLHQ2WX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VRQMAQ2F43GXLDZPQ4NPLHQ2WX/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":"2026-08-10T20:08:17Z","links":{"resolver":"https://pith.science/pith/VRQMAQ2F43GXLDZPQ4NPLHQ2WX","bundle":"https://pith.science/pith/VRQMAQ2F43GXLDZPQ4NPLHQ2WX/bundle.json","state":"https://pith.science/pith/VRQMAQ2F43GXLDZPQ4NPLHQ2WX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VRQMAQ2F43GXLDZPQ4NPLHQ2WX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:VRQMAQ2F43GXLDZPQ4NPLHQ2WX","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":"11cd8c229149279698a927a59826508a989e48d9c3a20389a72292836987fffb","cross_cats_sorted":["physics.optics"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2019-04-06T01:57:52Z","title_canon_sha256":"d7034a25e789c976e71ebc237e56540ea0fc9d04efe2e07e76870dcdff73fe8f"},"schema_version":"1.0","source":{"id":"1904.05750","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.05750","created_at":"2026-07-04T23:52:35Z"},{"alias_kind":"arxiv_version","alias_value":"1904.05750v2","created_at":"2026-07-04T23:52:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.05750","created_at":"2026-07-04T23:52:35Z"},{"alias_kind":"pith_short_12","alias_value":"VRQMAQ2F43GX","created_at":"2026-07-04T23:52:35Z"},{"alias_kind":"pith_short_16","alias_value":"VRQMAQ2F43GXLDZP","created_at":"2026-07-04T23:52:35Z"},{"alias_kind":"pith_short_8","alias_value":"VRQMAQ2F","created_at":"2026-07-04T23:52:35Z"}],"graph_snapshots":[{"event_id":"sha256:f17d473a902d6675ce0c589160729b7cb4caa4631f1eed5535ec5d7f2fa3eaff","target":"graph","created_at":"2026-07-04T23:52:35Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1904.05750/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Knots have been put forward to explain various physical phenomena because of their topological stability. Nevertheless, few works have reported on the exotic symmetry properties that certain knots possess. Here we reveal an exceptional form of symmetry for a family of knots that are both chiral and three-dimensional (3-D) rotationally symmetric about every axis of a standard Cartesian coordinate system. We call these unique knotted structures chiral balls. To demonstrate the unprecedented physical characteristics exhibited by these unique structures, we study the electromagnetic scattering pro","authors_text":"Chunxu Mao, Douglas H. Werner, Jun Hu, Lei Kang, Wending Mai, Yifan Chen","cross_cats":["physics.optics"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2019-04-06T01:57:52Z","title":"Chiral Balls: Knotted Structures with Both Chirality and Three-dimensional Rotational Symmetry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.05750","kind":"arxiv","version":2},"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":"sha256:60ecb2e36d07daba142f5670b033802060002433a68b6b1f1bff610fed518e8a","target":"record","created_at":"2026-07-04T23:52:35Z","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":"11cd8c229149279698a927a59826508a989e48d9c3a20389a72292836987fffb","cross_cats_sorted":["physics.optics"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2019-04-06T01:57:52Z","title_canon_sha256":"d7034a25e789c976e71ebc237e56540ea0fc9d04efe2e07e76870dcdff73fe8f"},"schema_version":"1.0","source":{"id":"1904.05750","kind":"arxiv","version":2}},"canonical_sha256":"ac60c04345e6cd758f2f871af59e1ab5fec82fc56fd8dcd691df2be921d4e6be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac60c04345e6cd758f2f871af59e1ab5fec82fc56fd8dcd691df2be921d4e6be","first_computed_at":"2026-07-04T23:52:35.513143Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:52:35.513143Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M7PIp9GWabm4HxVRyiQ9OOzP/lt83KMyFXq+9TMuSF5JSy1RkJaTMfSPW79ogJEw3er2RFeEnYAZmPsVOJoIDg==","signature_status":"signed_v1","signed_at":"2026-07-04T23:52:35.513580Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.05750","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:60ecb2e36d07daba142f5670b033802060002433a68b6b1f1bff610fed518e8a","sha256:f17d473a902d6675ce0c589160729b7cb4caa4631f1eed5535ec5d7f2fa3eaff"],"state_sha256":"56c01f55ca92701eb569369ed369866c06969b45d3181fea9cd0cf881e85775f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2c3E2THQ7SI/XTahGlR65UaInEhs78Fp5OI3F7m4S3gMLg8smQ14MfawR9JwpTsQEbKqfgcnnmCkacfHJoTpCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T20:08:17.680993Z","bundle_sha256":"d2efc81c9bb1dfbe044c1d695ec4b1f119a39681cbf18cff8dfed22433908255"}}