{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:646HOQG6Y4K7QH7UCYLR3WDPVV","short_pith_number":"pith:646HOQG6","canonical_record":{"source":{"id":"1406.5867","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2014-06-23T11:07:37Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"c956302762c887b52f99cfb14a187d71e9e64821055781c84aabfaaf18f93e0e","abstract_canon_sha256":"50ff0e07790d6de386208d68c690dc26c4704630eda5faa5301c367d39904baf"},"schema_version":"1.0"},"canonical_sha256":"f73c7740dec715f81ff416171dd86fad64b78b3dcacf51fd7a991c9cf44783cc","source":{"kind":"arxiv","id":"1406.5867","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.5867","created_at":"2026-05-18T02:49:10Z"},{"alias_kind":"arxiv_version","alias_value":"1406.5867v1","created_at":"2026-05-18T02:49:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.5867","created_at":"2026-05-18T02:49:10Z"},{"alias_kind":"pith_short_12","alias_value":"646HOQG6Y4K7","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"646HOQG6Y4K7QH7U","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"646HOQG6","created_at":"2026-05-18T12:28:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:646HOQG6Y4K7QH7UCYLR3WDPVV","target":"record","payload":{"canonical_record":{"source":{"id":"1406.5867","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2014-06-23T11:07:37Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"c956302762c887b52f99cfb14a187d71e9e64821055781c84aabfaaf18f93e0e","abstract_canon_sha256":"50ff0e07790d6de386208d68c690dc26c4704630eda5faa5301c367d39904baf"},"schema_version":"1.0"},"canonical_sha256":"f73c7740dec715f81ff416171dd86fad64b78b3dcacf51fd7a991c9cf44783cc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:10.583375Z","signature_b64":"ZF5KztNKyeca1ZhvPRFmycupOoFpNPfR+yvilWDGZqqY3aG0dl6jJtkFDxclhhsFdVd5uFpwv610AUJSv4HnAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f73c7740dec715f81ff416171dd86fad64b78b3dcacf51fd7a991c9cf44783cc","last_reissued_at":"2026-05-18T02:49:10.582787Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:10.582787Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.5867","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":"2026-05-18T02:49:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yCh+zZMEZNigMLWVcLdvgMjHCo/gs7twd/a7KifKucTtGd9nt3NwD56PVEa3+24yxEny2D/juxZEB7/ZVVuFCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T06:32:04.045303Z"},"content_sha256":"070fa27284e4daaece13d20be322f8024162d1c8ea7e029b53b37b67475080d8","schema_version":"1.0","event_id":"sha256:070fa27284e4daaece13d20be322f8024162d1c8ea7e029b53b37b67475080d8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:646HOQG6Y4K7QH7UCYLR3WDPVV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Effects of complex parameters on classical trajectories of Hamiltonian systems","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Asiri Nanayakkara, Thilagarajah Mathanaranjan","submitted_at":"2014-06-23T11:07:37Z","abstract_excerpt":"Anderson $\\textit{et al}$ have shown that for complex energies, the classical trajectories of $\\textit{real}$ quartic potentials are closed and periodic only on a discrete set of eigencurves. Moreover, recently it was revealed that, when time is complex $t$ $(t=t_{r}e^{i\\theta _{\\tau }}),$ certain real hermitian systems possess close periodic trajectories only for a discrete set of values of $\\theta _{\\tau }$. On the other hand it is generally true that even for real energies, classical trajectories of non $\\mathcal{PT}$- symmetric Hamiltonians with complex parameters are mostly non-periodic a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5867","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":"2026-05-18T02:49:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LO7vMlh3kFRcsCjnW3YNLXW/ch2UAGYcuhyFCVJqvlXSntBSrSFzzNQePwYMa5I+CuZxtH65tc3ELUI3GSaLAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T06:32:04.046061Z"},"content_sha256":"2243fae2701c3425a2ff4ceb5fe960799060228acead9b3c47f01eb87b8acc83","schema_version":"1.0","event_id":"sha256:2243fae2701c3425a2ff4ceb5fe960799060228acead9b3c47f01eb87b8acc83"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/646HOQG6Y4K7QH7UCYLR3WDPVV/bundle.json","state_url":"https://pith.science/pith/646HOQG6Y4K7QH7UCYLR3WDPVV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/646HOQG6Y4K7QH7UCYLR3WDPVV/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":"2026-06-08T06:32:04Z","links":{"resolver":"https://pith.science/pith/646HOQG6Y4K7QH7UCYLR3WDPVV","bundle":"https://pith.science/pith/646HOQG6Y4K7QH7UCYLR3WDPVV/bundle.json","state":"https://pith.science/pith/646HOQG6Y4K7QH7UCYLR3WDPVV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/646HOQG6Y4K7QH7UCYLR3WDPVV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:646HOQG6Y4K7QH7UCYLR3WDPVV","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":"50ff0e07790d6de386208d68c690dc26c4704630eda5faa5301c367d39904baf","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2014-06-23T11:07:37Z","title_canon_sha256":"c956302762c887b52f99cfb14a187d71e9e64821055781c84aabfaaf18f93e0e"},"schema_version":"1.0","source":{"id":"1406.5867","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.5867","created_at":"2026-05-18T02:49:10Z"},{"alias_kind":"arxiv_version","alias_value":"1406.5867v1","created_at":"2026-05-18T02:49:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.5867","created_at":"2026-05-18T02:49:10Z"},{"alias_kind":"pith_short_12","alias_value":"646HOQG6Y4K7","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"646HOQG6Y4K7QH7U","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"646HOQG6","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:2243fae2701c3425a2ff4ceb5fe960799060228acead9b3c47f01eb87b8acc83","target":"graph","created_at":"2026-05-18T02:49:10Z","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":"Anderson $\\textit{et al}$ have shown that for complex energies, the classical trajectories of $\\textit{real}$ quartic potentials are closed and periodic only on a discrete set of eigencurves. Moreover, recently it was revealed that, when time is complex $t$ $(t=t_{r}e^{i\\theta _{\\tau }}),$ certain real hermitian systems possess close periodic trajectories only for a discrete set of values of $\\theta _{\\tau }$. On the other hand it is generally true that even for real energies, classical trajectories of non $\\mathcal{PT}$- symmetric Hamiltonians with complex parameters are mostly non-periodic a","authors_text":"Asiri Nanayakkara, Thilagarajah Mathanaranjan","cross_cats":["math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2014-06-23T11:07:37Z","title":"Effects of complex parameters on classical trajectories of Hamiltonian systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5867","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":"sha256:070fa27284e4daaece13d20be322f8024162d1c8ea7e029b53b37b67475080d8","target":"record","created_at":"2026-05-18T02:49:10Z","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":"50ff0e07790d6de386208d68c690dc26c4704630eda5faa5301c367d39904baf","cross_cats_sorted":["math.MP"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2014-06-23T11:07:37Z","title_canon_sha256":"c956302762c887b52f99cfb14a187d71e9e64821055781c84aabfaaf18f93e0e"},"schema_version":"1.0","source":{"id":"1406.5867","kind":"arxiv","version":1}},"canonical_sha256":"f73c7740dec715f81ff416171dd86fad64b78b3dcacf51fd7a991c9cf44783cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f73c7740dec715f81ff416171dd86fad64b78b3dcacf51fd7a991c9cf44783cc","first_computed_at":"2026-05-18T02:49:10.582787Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:10.582787Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZF5KztNKyeca1ZhvPRFmycupOoFpNPfR+yvilWDGZqqY3aG0dl6jJtkFDxclhhsFdVd5uFpwv610AUJSv4HnAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:10.583375Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.5867","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:070fa27284e4daaece13d20be322f8024162d1c8ea7e029b53b37b67475080d8","sha256:2243fae2701c3425a2ff4ceb5fe960799060228acead9b3c47f01eb87b8acc83"],"state_sha256":"9ffc3bd7dececf6d71f899626a2be8a481c1d7f914e11c661a23570ec46578ba"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nqPqgCf5h1CS2IJfOYAqBNvU2jdH7hN2NbobiKCJXlYG33SVGKQChs4osogH+gJ9ldKj3Qtav1mKmkMtaXzKAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T06:32:04.049548Z","bundle_sha256":"f9721a20a6f4b4fdf77f9a377add104d5c487fe09eb9230800a206c1f789453d"}}