{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:TRT6ZUA5BAAKQMXOWIO3DKAJU2","short_pith_number":"pith:TRT6ZUA5","canonical_record":{"source":{"id":"1508.06946","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2015-08-27T17:26:50Z","cross_cats_sorted":["physics.class-ph"],"title_canon_sha256":"b54a90c412b969a9e62085912ea64c5a9851e8b3954fbe0ec275638eea056d5d","abstract_canon_sha256":"99dc5cbc5b13ec9b329383cdfb1931a557f043660867bb03831a0602f9b2f212"},"schema_version":"1.0"},"canonical_sha256":"9c67ecd01d0800a832eeb21db1a809a6a49edad2817fb42d48dabadb32812160","source":{"kind":"arxiv","id":"1508.06946","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.06946","created_at":"2026-05-18T01:17:59Z"},{"alias_kind":"arxiv_version","alias_value":"1508.06946v1","created_at":"2026-05-18T01:17:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.06946","created_at":"2026-05-18T01:17:59Z"},{"alias_kind":"pith_short_12","alias_value":"TRT6ZUA5BAAK","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TRT6ZUA5BAAKQMXO","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TRT6ZUA5","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:TRT6ZUA5BAAKQMXOWIO3DKAJU2","target":"record","payload":{"canonical_record":{"source":{"id":"1508.06946","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2015-08-27T17:26:50Z","cross_cats_sorted":["physics.class-ph"],"title_canon_sha256":"b54a90c412b969a9e62085912ea64c5a9851e8b3954fbe0ec275638eea056d5d","abstract_canon_sha256":"99dc5cbc5b13ec9b329383cdfb1931a557f043660867bb03831a0602f9b2f212"},"schema_version":"1.0"},"canonical_sha256":"9c67ecd01d0800a832eeb21db1a809a6a49edad2817fb42d48dabadb32812160","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:59.743720Z","signature_b64":"cZatuNFfYzpOzYfm3m+NZqZkpschyKMqtueRWiEZCiE4xelMfwU5kJgyZNGIyT6Hr+RmC9zgmsdJlNVO7jUBBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c67ecd01d0800a832eeb21db1a809a6a49edad2817fb42d48dabadb32812160","last_reissued_at":"2026-05-18T01:17:59.742995Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:59.742995Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.06946","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":"2026-05-18T01:17:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k/s9PlICTWK3tn+gEDU4CSIQKhP6iq3pCyehbnadzoaMacqQyacDTBbF8N38kYZZ3LGj0NfmvxuFkn/3qFO+Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T02:07:56.770675Z"},"content_sha256":"1bb1b8fd3031e0ca06f5af81a98cdb69054fd9474ceff1ca03f6ea46007d6181","schema_version":"1.0","event_id":"sha256:1bb1b8fd3031e0ca06f5af81a98cdb69054fd9474ceff1ca03f6ea46007d6181"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:TRT6ZUA5BAAKQMXOWIO3DKAJU2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hannay Angle: Yet Another Symmetry Protected Topological Order Parameter in Classical Mechanics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.class-ph"],"primary_cat":"cond-mat.mes-hall","authors_text":"Toshikaze Kariyado, Yasuhiro Hatsugai","submitted_at":"2015-08-27T17:26:50Z","abstract_excerpt":"Topological way of thinking now goes beyond conventional solid materials, and topological characterization of classical mechanical systems governed by Newton's equation of motion begins to attract much attention. To have a deeper insight on physical meaning of topological numbers in mechanical systems, we demonstrate the use of the Hannay angle, a classical counterpart of the Berry phase, as a symmetry protected topological order parameter. We first derive the Hannay angle using a canonical transformation that maps the Newton's equation to the Schr\\\"{o}dinger type equation. The Hannay angle is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.06946","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":"2026-05-18T01:17:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IzMCNXxikZAwr269Qhqh2A07N3nfgB0r15ijAmMDM2/pH8EOmV+GIesMvHCUoy/15/GVuNePqYi2KIQJNZLtCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T02:07:56.771011Z"},"content_sha256":"db797c2c66c0bb34792d618bcb3d344486d7384302a6eb406786e43de40f74ff","schema_version":"1.0","event_id":"sha256:db797c2c66c0bb34792d618bcb3d344486d7384302a6eb406786e43de40f74ff"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TRT6ZUA5BAAKQMXOWIO3DKAJU2/bundle.json","state_url":"https://pith.science/pith/TRT6ZUA5BAAKQMXOWIO3DKAJU2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TRT6ZUA5BAAKQMXOWIO3DKAJU2/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":"2026-06-02T02:07:56Z","links":{"resolver":"https://pith.science/pith/TRT6ZUA5BAAKQMXOWIO3DKAJU2","bundle":"https://pith.science/pith/TRT6ZUA5BAAKQMXOWIO3DKAJU2/bundle.json","state":"https://pith.science/pith/TRT6ZUA5BAAKQMXOWIO3DKAJU2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TRT6ZUA5BAAKQMXOWIO3DKAJU2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:TRT6ZUA5BAAKQMXOWIO3DKAJU2","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":"99dc5cbc5b13ec9b329383cdfb1931a557f043660867bb03831a0602f9b2f212","cross_cats_sorted":["physics.class-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2015-08-27T17:26:50Z","title_canon_sha256":"b54a90c412b969a9e62085912ea64c5a9851e8b3954fbe0ec275638eea056d5d"},"schema_version":"1.0","source":{"id":"1508.06946","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.06946","created_at":"2026-05-18T01:17:59Z"},{"alias_kind":"arxiv_version","alias_value":"1508.06946v1","created_at":"2026-05-18T01:17:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.06946","created_at":"2026-05-18T01:17:59Z"},{"alias_kind":"pith_short_12","alias_value":"TRT6ZUA5BAAK","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TRT6ZUA5BAAKQMXO","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TRT6ZUA5","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:db797c2c66c0bb34792d618bcb3d344486d7384302a6eb406786e43de40f74ff","target":"graph","created_at":"2026-05-18T01:17:59Z","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":"Topological way of thinking now goes beyond conventional solid materials, and topological characterization of classical mechanical systems governed by Newton's equation of motion begins to attract much attention. To have a deeper insight on physical meaning of topological numbers in mechanical systems, we demonstrate the use of the Hannay angle, a classical counterpart of the Berry phase, as a symmetry protected topological order parameter. We first derive the Hannay angle using a canonical transformation that maps the Newton's equation to the Schr\\\"{o}dinger type equation. The Hannay angle is","authors_text":"Toshikaze Kariyado, Yasuhiro Hatsugai","cross_cats":["physics.class-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2015-08-27T17:26:50Z","title":"Hannay Angle: Yet Another Symmetry Protected Topological Order Parameter in Classical Mechanics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.06946","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":"sha256:1bb1b8fd3031e0ca06f5af81a98cdb69054fd9474ceff1ca03f6ea46007d6181","target":"record","created_at":"2026-05-18T01:17:59Z","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":"99dc5cbc5b13ec9b329383cdfb1931a557f043660867bb03831a0602f9b2f212","cross_cats_sorted":["physics.class-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mes-hall","submitted_at":"2015-08-27T17:26:50Z","title_canon_sha256":"b54a90c412b969a9e62085912ea64c5a9851e8b3954fbe0ec275638eea056d5d"},"schema_version":"1.0","source":{"id":"1508.06946","kind":"arxiv","version":1}},"canonical_sha256":"9c67ecd01d0800a832eeb21db1a809a6a49edad2817fb42d48dabadb32812160","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c67ecd01d0800a832eeb21db1a809a6a49edad2817fb42d48dabadb32812160","first_computed_at":"2026-05-18T01:17:59.742995Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:59.742995Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cZatuNFfYzpOzYfm3m+NZqZkpschyKMqtueRWiEZCiE4xelMfwU5kJgyZNGIyT6Hr+RmC9zgmsdJlNVO7jUBBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:59.743720Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.06946","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1bb1b8fd3031e0ca06f5af81a98cdb69054fd9474ceff1ca03f6ea46007d6181","sha256:db797c2c66c0bb34792d618bcb3d344486d7384302a6eb406786e43de40f74ff"],"state_sha256":"0a378e2478d8252f659ee98429c684674dbfd58d431e590ed468ef97b36734ce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nyIuLl2iXPmPcbVTA5jv8tM08GPfFh7u7hNNOH+tEfA/etTZQYp++jkI0B+CLWuqFbLmBrKEpOLbxctEOT2kDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T02:07:56.772876Z","bundle_sha256":"44514db8382eefe72cea96a4388b66ec1606d8aeaa8778fa00c6e1a296c96e81"}}