{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:M2GKYXRN7TVGCXQ7ZAHY5WBP6J","short_pith_number":"pith:M2GKYXRN","canonical_record":{"source":{"id":"1301.5222","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2012-12-19T23:26:03Z","cross_cats_sorted":[],"title_canon_sha256":"dddf722f5728ef8f9296f68f0539ef84c2fd3e3dddadc325a5e3b5cc44846be1","abstract_canon_sha256":"ae52dd6d660c78aadca8a24e2edbea61c86e51d006c43838749ea47ae5ec0919"},"schema_version":"1.0"},"canonical_sha256":"668cac5e2dfcea615e1fc80f8ed82ff2690d36deccbf87418e666b72a6cf9f9f","source":{"kind":"arxiv","id":"1301.5222","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.5222","created_at":"2026-05-18T01:31:04Z"},{"alias_kind":"arxiv_version","alias_value":"1301.5222v1","created_at":"2026-05-18T01:31:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.5222","created_at":"2026-05-18T01:31:04Z"},{"alias_kind":"pith_short_12","alias_value":"M2GKYXRN7TVG","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"M2GKYXRN7TVGCXQ7","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"M2GKYXRN","created_at":"2026-05-18T12:27:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:M2GKYXRN7TVGCXQ7ZAHY5WBP6J","target":"record","payload":{"canonical_record":{"source":{"id":"1301.5222","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2012-12-19T23:26:03Z","cross_cats_sorted":[],"title_canon_sha256":"dddf722f5728ef8f9296f68f0539ef84c2fd3e3dddadc325a5e3b5cc44846be1","abstract_canon_sha256":"ae52dd6d660c78aadca8a24e2edbea61c86e51d006c43838749ea47ae5ec0919"},"schema_version":"1.0"},"canonical_sha256":"668cac5e2dfcea615e1fc80f8ed82ff2690d36deccbf87418e666b72a6cf9f9f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:31:04.069478Z","signature_b64":"iENiixBDIfDeB+Go11wg64mkTeGrk7vxq3jiKlI5B+wnUOqxiXJmhsmExXWYjiAja8+fBXCLJgebctsG3TycDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"668cac5e2dfcea615e1fc80f8ed82ff2690d36deccbf87418e666b72a6cf9f9f","last_reissued_at":"2026-05-18T01:31:04.068906Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:31:04.068906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.5222","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":"2026-05-18T01:31:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J2jQxFqAntoeF1mUzvbTjqd/RoUiliiJqFu+ZI02j25F2OEqR+kG8reGNXJjO3IDFwGD0eYbNndTEbBIyN9+BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T04:32:05.516290Z"},"content_sha256":"3a704085078119706967551ade6788c76a701a1eae943352bc42afe6f9d2fdb9","schema_version":"1.0","event_id":"sha256:3a704085078119706967551ade6788c76a701a1eae943352bc42afe6f9d2fdb9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:M2GKYXRN7TVGCXQ7ZAHY5WBP6J","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bifurcations and Competing Coherent Structures in the Cubic-Quintic Ginzburg-Landau Equation I: Plane Wave (CW) Solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.PS","authors_text":"S. Roy Choudhury, Stefan C. Mancas","submitted_at":"2012-12-19T23:26:03Z","abstract_excerpt":"Singularity Theory is used to comprehensively investigate the bifurcations of the steady-states of the traveling wave ODEs of the cubic-quintic Ginzburg-Landau equation (CGLE). These correspond to plane waves of the PDE. In addition to the most general situation, we also derive the degeneracy conditions on the eight coefficients of the CGLE under which the equation for the steady states assumes each of the possible quartic (the quartic fold and an unnamed form), cubic (the pitchfork and the winged cusp), and quadratic (four possible cases) normal forms for singularities of codimension up to th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5222","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":"2026-05-18T01:31:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/GnkX7iT0AzgQCePBWxCZCjdkC6q6HtkhuP4MhsPAA2O4nlbdsVzgDtvQ7MfvBYkC8ssJ9faUefgkscZKcSIAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T04:32:05.516976Z"},"content_sha256":"51c1e2ee83763dd4e56580cfb0789a97acb453872428308616b09bb153c99c42","schema_version":"1.0","event_id":"sha256:51c1e2ee83763dd4e56580cfb0789a97acb453872428308616b09bb153c99c42"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M2GKYXRN7TVGCXQ7ZAHY5WBP6J/bundle.json","state_url":"https://pith.science/pith/M2GKYXRN7TVGCXQ7ZAHY5WBP6J/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M2GKYXRN7TVGCXQ7ZAHY5WBP6J/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":"2026-05-27T04:32:05Z","links":{"resolver":"https://pith.science/pith/M2GKYXRN7TVGCXQ7ZAHY5WBP6J","bundle":"https://pith.science/pith/M2GKYXRN7TVGCXQ7ZAHY5WBP6J/bundle.json","state":"https://pith.science/pith/M2GKYXRN7TVGCXQ7ZAHY5WBP6J/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M2GKYXRN7TVGCXQ7ZAHY5WBP6J/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:M2GKYXRN7TVGCXQ7ZAHY5WBP6J","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":"ae52dd6d660c78aadca8a24e2edbea61c86e51d006c43838749ea47ae5ec0919","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2012-12-19T23:26:03Z","title_canon_sha256":"dddf722f5728ef8f9296f68f0539ef84c2fd3e3dddadc325a5e3b5cc44846be1"},"schema_version":"1.0","source":{"id":"1301.5222","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.5222","created_at":"2026-05-18T01:31:04Z"},{"alias_kind":"arxiv_version","alias_value":"1301.5222v1","created_at":"2026-05-18T01:31:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.5222","created_at":"2026-05-18T01:31:04Z"},{"alias_kind":"pith_short_12","alias_value":"M2GKYXRN7TVG","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"M2GKYXRN7TVGCXQ7","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"M2GKYXRN","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:51c1e2ee83763dd4e56580cfb0789a97acb453872428308616b09bb153c99c42","target":"graph","created_at":"2026-05-18T01:31:04Z","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":"Singularity Theory is used to comprehensively investigate the bifurcations of the steady-states of the traveling wave ODEs of the cubic-quintic Ginzburg-Landau equation (CGLE). These correspond to plane waves of the PDE. In addition to the most general situation, we also derive the degeneracy conditions on the eight coefficients of the CGLE under which the equation for the steady states assumes each of the possible quartic (the quartic fold and an unnamed form), cubic (the pitchfork and the winged cusp), and quadratic (four possible cases) normal forms for singularities of codimension up to th","authors_text":"S. Roy Choudhury, Stefan C. Mancas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2012-12-19T23:26:03Z","title":"Bifurcations and Competing Coherent Structures in the Cubic-Quintic Ginzburg-Landau Equation I: Plane Wave (CW) Solutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5222","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":"sha256:3a704085078119706967551ade6788c76a701a1eae943352bc42afe6f9d2fdb9","target":"record","created_at":"2026-05-18T01:31:04Z","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":"ae52dd6d660c78aadca8a24e2edbea61c86e51d006c43838749ea47ae5ec0919","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2012-12-19T23:26:03Z","title_canon_sha256":"dddf722f5728ef8f9296f68f0539ef84c2fd3e3dddadc325a5e3b5cc44846be1"},"schema_version":"1.0","source":{"id":"1301.5222","kind":"arxiv","version":1}},"canonical_sha256":"668cac5e2dfcea615e1fc80f8ed82ff2690d36deccbf87418e666b72a6cf9f9f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"668cac5e2dfcea615e1fc80f8ed82ff2690d36deccbf87418e666b72a6cf9f9f","first_computed_at":"2026-05-18T01:31:04.068906Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:31:04.068906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iENiixBDIfDeB+Go11wg64mkTeGrk7vxq3jiKlI5B+wnUOqxiXJmhsmExXWYjiAja8+fBXCLJgebctsG3TycDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:31:04.069478Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.5222","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a704085078119706967551ade6788c76a701a1eae943352bc42afe6f9d2fdb9","sha256:51c1e2ee83763dd4e56580cfb0789a97acb453872428308616b09bb153c99c42"],"state_sha256":"c3c9a67538043f2a206dfb1111de846cc955aa5094c50f31f3123ac08bccc4de"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gx3YDWpIkP4WcQS0jDMKs0+r87B6XzSKKZuU9CPF2RUVU6NtRazkxCZHcb5r07zMHe6+hauF3m/bsAPrSv09Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T04:32:05.520668Z","bundle_sha256":"9d271f11a7f388c8d2cb6e5f89a29256adfc336da20e889b8627a23d0334eb4a"}}