{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:75NUAUHNPOFD2YCYLVQHQR7SGH","short_pith_number":"pith:75NUAUHN","canonical_record":{"source":{"id":"1309.3196","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-09-12T15:32:19Z","cross_cats_sorted":[],"title_canon_sha256":"a17ae79223922ce719800926ed78698065d7a0924333127c0de7eb037b52c2af","abstract_canon_sha256":"7270f5cc805b9ad1abfa9221793fd8002bd7d53a4ebd56b3d2361efcc2cd5c62"},"schema_version":"1.0"},"canonical_sha256":"ff5b4050ed7b8a3d60585d607847f231cae74c3bc595ea63ad51d5bd1c7c759c","source":{"kind":"arxiv","id":"1309.3196","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.3196","created_at":"2026-05-18T03:13:32Z"},{"alias_kind":"arxiv_version","alias_value":"1309.3196v1","created_at":"2026-05-18T03:13:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.3196","created_at":"2026-05-18T03:13:32Z"},{"alias_kind":"pith_short_12","alias_value":"75NUAUHNPOFD","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"75NUAUHNPOFD2YCY","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"75NUAUHN","created_at":"2026-05-18T12:27:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:75NUAUHNPOFD2YCYLVQHQR7SGH","target":"record","payload":{"canonical_record":{"source":{"id":"1309.3196","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-09-12T15:32:19Z","cross_cats_sorted":[],"title_canon_sha256":"a17ae79223922ce719800926ed78698065d7a0924333127c0de7eb037b52c2af","abstract_canon_sha256":"7270f5cc805b9ad1abfa9221793fd8002bd7d53a4ebd56b3d2361efcc2cd5c62"},"schema_version":"1.0"},"canonical_sha256":"ff5b4050ed7b8a3d60585d607847f231cae74c3bc595ea63ad51d5bd1c7c759c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:13:32.565558Z","signature_b64":"+nvyRxM/qa0CykNzuJSgKxkemuh/TiJxTmsaXVAfM+WQza9m0sEP9IMBPBsV5JiIySxzZ4NY2IqMXhfGv7SIAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ff5b4050ed7b8a3d60585d607847f231cae74c3bc595ea63ad51d5bd1c7c759c","last_reissued_at":"2026-05-18T03:13:32.564660Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:13:32.564660Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.3196","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":"2026-05-18T03:13:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GfElBufa3bzmlUazOTtgXfTiERAxXsl9yVkKZWT9qSqUsVvjczIdj12+1EYiT7EXFj6ipvsMIcLBD24UPoKtBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T19:30:27.597897Z"},"content_sha256":"332c218d9ad9109128507c412aff9c7d0eedabf167b466c75dfde6be471e34a1","schema_version":"1.0","event_id":"sha256:332c218d9ad9109128507c412aff9c7d0eedabf167b466c75dfde6be471e34a1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:75NUAUHNPOFD2YCYLVQHQR7SGH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dn Symmetric Hamiltonian System: A Network of Coupled Gyroscopes as a Case Study","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Antonio Palacios, Bernard S. Chan, Pietro Luciano Buono, Visarath In","submitted_at":"2013-09-12T15:32:19Z","abstract_excerpt":"The evolution of a large class of biological, physical and engineering systems can be studied through both dynamical systems theory and Hamiltonian mechanics. The former theory, in particular its specialization to study systems with symmetry, is already well developed and has been used extensively on a wide variety of spatio-temporal systems. There are, however, fewer results on higher-dimensional Hamiltonian systems with symmetry. This lack of results has lead us to investigate the role of symmetry, in particular dihedral symmetry, on high-dimensional coupled Hamiltonian systems. As a represe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.3196","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":"2026-05-18T03:13:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4xD50laECAe8OHyrqp7DFVSvk/KNA4QeE4dBM4L2iqVIV8WS1ZsnFMoJWyGFn1hrggbAMi8ZsV3PhFBolkzkAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T19:30:27.598626Z"},"content_sha256":"0cb47bd153d243d34008f9af25cced030d4a009c66fe4f0a37a8230c98de9942","schema_version":"1.0","event_id":"sha256:0cb47bd153d243d34008f9af25cced030d4a009c66fe4f0a37a8230c98de9942"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/75NUAUHNPOFD2YCYLVQHQR7SGH/bundle.json","state_url":"https://pith.science/pith/75NUAUHNPOFD2YCYLVQHQR7SGH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/75NUAUHNPOFD2YCYLVQHQR7SGH/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":"2026-06-06T19:30:27Z","links":{"resolver":"https://pith.science/pith/75NUAUHNPOFD2YCYLVQHQR7SGH","bundle":"https://pith.science/pith/75NUAUHNPOFD2YCYLVQHQR7SGH/bundle.json","state":"https://pith.science/pith/75NUAUHNPOFD2YCYLVQHQR7SGH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/75NUAUHNPOFD2YCYLVQHQR7SGH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:75NUAUHNPOFD2YCYLVQHQR7SGH","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":"7270f5cc805b9ad1abfa9221793fd8002bd7d53a4ebd56b3d2361efcc2cd5c62","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-09-12T15:32:19Z","title_canon_sha256":"a17ae79223922ce719800926ed78698065d7a0924333127c0de7eb037b52c2af"},"schema_version":"1.0","source":{"id":"1309.3196","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.3196","created_at":"2026-05-18T03:13:32Z"},{"alias_kind":"arxiv_version","alias_value":"1309.3196v1","created_at":"2026-05-18T03:13:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.3196","created_at":"2026-05-18T03:13:32Z"},{"alias_kind":"pith_short_12","alias_value":"75NUAUHNPOFD","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"75NUAUHNPOFD2YCY","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"75NUAUHN","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:0cb47bd153d243d34008f9af25cced030d4a009c66fe4f0a37a8230c98de9942","target":"graph","created_at":"2026-05-18T03:13:32Z","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":"The evolution of a large class of biological, physical and engineering systems can be studied through both dynamical systems theory and Hamiltonian mechanics. The former theory, in particular its specialization to study systems with symmetry, is already well developed and has been used extensively on a wide variety of spatio-temporal systems. There are, however, fewer results on higher-dimensional Hamiltonian systems with symmetry. This lack of results has lead us to investigate the role of symmetry, in particular dihedral symmetry, on high-dimensional coupled Hamiltonian systems. As a represe","authors_text":"Antonio Palacios, Bernard S. Chan, Pietro Luciano Buono, Visarath In","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-09-12T15:32:19Z","title":"Dn Symmetric Hamiltonian System: A Network of Coupled Gyroscopes as a Case Study"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.3196","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":"sha256:332c218d9ad9109128507c412aff9c7d0eedabf167b466c75dfde6be471e34a1","target":"record","created_at":"2026-05-18T03:13:32Z","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":"7270f5cc805b9ad1abfa9221793fd8002bd7d53a4ebd56b3d2361efcc2cd5c62","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-09-12T15:32:19Z","title_canon_sha256":"a17ae79223922ce719800926ed78698065d7a0924333127c0de7eb037b52c2af"},"schema_version":"1.0","source":{"id":"1309.3196","kind":"arxiv","version":1}},"canonical_sha256":"ff5b4050ed7b8a3d60585d607847f231cae74c3bc595ea63ad51d5bd1c7c759c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ff5b4050ed7b8a3d60585d607847f231cae74c3bc595ea63ad51d5bd1c7c759c","first_computed_at":"2026-05-18T03:13:32.564660Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:13:32.564660Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+nvyRxM/qa0CykNzuJSgKxkemuh/TiJxTmsaXVAfM+WQza9m0sEP9IMBPBsV5JiIySxzZ4NY2IqMXhfGv7SIAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:13:32.565558Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.3196","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:332c218d9ad9109128507c412aff9c7d0eedabf167b466c75dfde6be471e34a1","sha256:0cb47bd153d243d34008f9af25cced030d4a009c66fe4f0a37a8230c98de9942"],"state_sha256":"7a08f0151fe5585c3cc3254c1340b78f7d4330c6b395743fa7eadfb0d3696d7f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0Y2ipYuPFitqCwnzUJv8fNcyMPJBN6WiSkszIgHaapdellvAXOLkCNlVzZvXPOHAGY5oRzz5dRnoNFy01b2ZDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T19:30:27.602578Z","bundle_sha256":"63ccd4d7e4758000156c295830d66b8cb406fd5dbe287dc8803661b6bc79c95b"}}