{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:NSI7N7R2RABHNNPQBPFL36I2HY","short_pith_number":"pith:NSI7N7R2","canonical_record":{"source":{"id":"1504.03167","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2015-04-13T13:16:10Z","cross_cats_sorted":["nlin.CD"],"title_canon_sha256":"916229ddf9bd96b92b21a599ae1be33d5183ce6bd50b2eea904265143e24cd0d","abstract_canon_sha256":"1ff334cfd2dfe32f2b615525efaeb5c2ef2650ea398dbbc17a321c2fb01b7fb2"},"schema_version":"1.0"},"canonical_sha256":"6c91f6fe3a880276b5f00bcabdf91a3e1972e578eda77c49c1d81a3ca91dbdff","source":{"kind":"arxiv","id":"1504.03167","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.03167","created_at":"2026-05-18T01:13:30Z"},{"alias_kind":"arxiv_version","alias_value":"1504.03167v1","created_at":"2026-05-18T01:13:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.03167","created_at":"2026-05-18T01:13:30Z"},{"alias_kind":"pith_short_12","alias_value":"NSI7N7R2RABH","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"NSI7N7R2RABHNNPQ","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"NSI7N7R2","created_at":"2026-05-18T12:29:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:NSI7N7R2RABHNNPQBPFL36I2HY","target":"record","payload":{"canonical_record":{"source":{"id":"1504.03167","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2015-04-13T13:16:10Z","cross_cats_sorted":["nlin.CD"],"title_canon_sha256":"916229ddf9bd96b92b21a599ae1be33d5183ce6bd50b2eea904265143e24cd0d","abstract_canon_sha256":"1ff334cfd2dfe32f2b615525efaeb5c2ef2650ea398dbbc17a321c2fb01b7fb2"},"schema_version":"1.0"},"canonical_sha256":"6c91f6fe3a880276b5f00bcabdf91a3e1972e578eda77c49c1d81a3ca91dbdff","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:13:30.988176Z","signature_b64":"Qp9lXc5NV9wu1yK1C92u45UflqVxb2FiC5i1UG2JMxXQR6YH41TMaP6JowFukJ8MQbDTT035iSta0dAEGX+eCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c91f6fe3a880276b5f00bcabdf91a3e1972e578eda77c49c1d81a3ca91dbdff","last_reissued_at":"2026-05-18T01:13:30.987443Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:13:30.987443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.03167","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":"2026-05-18T01:13:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wxilpaihRvAzYMfEvKIyn6yb4Dw1zglETvPMNOcS2XsPyggDZNM9jvp492u95nuieRLwfESHGcK4Ih7M5HgTBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T22:39:51.873373Z"},"content_sha256":"b40beadbf4fec02ed2e3e2eb28947b80c318aa86db118eff925694f600f9ea9e","schema_version":"1.0","event_id":"sha256:b40beadbf4fec02ed2e3e2eb28947b80c318aa86db118eff925694f600f9ea9e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:NSI7N7R2RABHNNPQBPFL36I2HY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A versatile class of prototype dynamical systems for complex bifurcation cascades of limit cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.CD"],"primary_cat":"physics.comp-ph","authors_text":"Bulcs\\'u S\\'andor, Claudius Gros","submitted_at":"2015-04-13T13:16:10Z","abstract_excerpt":"We introduce a versatile class of prototype dynamical systems for the study of complex bifurcation cascades of limit cycles, including bifurcations breaking spontaneously a symmetry of the system, period doubling bifurcations and transitions to chaos induced by sequences of limit cycle bifurcations. The prototype system consist of a $2d$-dimensional dynamical system with friction forces $f(V(\\mathbf{x}))$ functionally dependent exclusively on the mechanical potential $V(\\mathbf{x})$, which is typically characterized, here, by a finite number of local minima. We present examples for $d=1,2$ and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.03167","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":"2026-05-18T01:13:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/rnEpiSDMcr/e3BjpxqdHCY3+oC7mBE7dH+Q1aqIfmTJnTA2B5Po8pGCrzqGQoQIPNlR/6BwtGsUqUFYmlkmDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T22:39:51.874035Z"},"content_sha256":"d3e5aafbd98b9e03d08b1eee799967e58d2525d3d1f4e80758a003927e507bc5","schema_version":"1.0","event_id":"sha256:d3e5aafbd98b9e03d08b1eee799967e58d2525d3d1f4e80758a003927e507bc5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NSI7N7R2RABHNNPQBPFL36I2HY/bundle.json","state_url":"https://pith.science/pith/NSI7N7R2RABHNNPQBPFL36I2HY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NSI7N7R2RABHNNPQBPFL36I2HY/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":"2026-05-26T22:39:51Z","links":{"resolver":"https://pith.science/pith/NSI7N7R2RABHNNPQBPFL36I2HY","bundle":"https://pith.science/pith/NSI7N7R2RABHNNPQBPFL36I2HY/bundle.json","state":"https://pith.science/pith/NSI7N7R2RABHNNPQBPFL36I2HY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NSI7N7R2RABHNNPQBPFL36I2HY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:NSI7N7R2RABHNNPQBPFL36I2HY","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":"1ff334cfd2dfe32f2b615525efaeb5c2ef2650ea398dbbc17a321c2fb01b7fb2","cross_cats_sorted":["nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2015-04-13T13:16:10Z","title_canon_sha256":"916229ddf9bd96b92b21a599ae1be33d5183ce6bd50b2eea904265143e24cd0d"},"schema_version":"1.0","source":{"id":"1504.03167","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.03167","created_at":"2026-05-18T01:13:30Z"},{"alias_kind":"arxiv_version","alias_value":"1504.03167v1","created_at":"2026-05-18T01:13:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.03167","created_at":"2026-05-18T01:13:30Z"},{"alias_kind":"pith_short_12","alias_value":"NSI7N7R2RABH","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"NSI7N7R2RABHNNPQ","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"NSI7N7R2","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:d3e5aafbd98b9e03d08b1eee799967e58d2525d3d1f4e80758a003927e507bc5","target":"graph","created_at":"2026-05-18T01:13:30Z","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 introduce a versatile class of prototype dynamical systems for the study of complex bifurcation cascades of limit cycles, including bifurcations breaking spontaneously a symmetry of the system, period doubling bifurcations and transitions to chaos induced by sequences of limit cycle bifurcations. The prototype system consist of a $2d$-dimensional dynamical system with friction forces $f(V(\\mathbf{x}))$ functionally dependent exclusively on the mechanical potential $V(\\mathbf{x})$, which is typically characterized, here, by a finite number of local minima. We present examples for $d=1,2$ and","authors_text":"Bulcs\\'u S\\'andor, Claudius Gros","cross_cats":["nlin.CD"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2015-04-13T13:16:10Z","title":"A versatile class of prototype dynamical systems for complex bifurcation cascades of limit cycles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.03167","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:b40beadbf4fec02ed2e3e2eb28947b80c318aa86db118eff925694f600f9ea9e","target":"record","created_at":"2026-05-18T01:13:30Z","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":"1ff334cfd2dfe32f2b615525efaeb5c2ef2650ea398dbbc17a321c2fb01b7fb2","cross_cats_sorted":["nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2015-04-13T13:16:10Z","title_canon_sha256":"916229ddf9bd96b92b21a599ae1be33d5183ce6bd50b2eea904265143e24cd0d"},"schema_version":"1.0","source":{"id":"1504.03167","kind":"arxiv","version":1}},"canonical_sha256":"6c91f6fe3a880276b5f00bcabdf91a3e1972e578eda77c49c1d81a3ca91dbdff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6c91f6fe3a880276b5f00bcabdf91a3e1972e578eda77c49c1d81a3ca91dbdff","first_computed_at":"2026-05-18T01:13:30.987443Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:13:30.987443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Qp9lXc5NV9wu1yK1C92u45UflqVxb2FiC5i1UG2JMxXQR6YH41TMaP6JowFukJ8MQbDTT035iSta0dAEGX+eCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:13:30.988176Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.03167","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b40beadbf4fec02ed2e3e2eb28947b80c318aa86db118eff925694f600f9ea9e","sha256:d3e5aafbd98b9e03d08b1eee799967e58d2525d3d1f4e80758a003927e507bc5"],"state_sha256":"f5838fa0b28b27be115a2a8682b750b49ed492b86ac09f000ff269211ca50415"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"alzxx3YAok3BW8i7t2N/+CjaXE4ANmhj1Go2QDuPL0WmZEk/06oeHVh3EmgQ7jEtU6HfddtBkhjma0bvpQLhDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T22:39:51.877670Z","bundle_sha256":"12ac55356f29818f332d1b85b7b0c7a1d2b85d09d86167827597c71e73866833"}}