{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:DF4N23I4UBVNHFZ4SJ4UDYFUWE","short_pith_number":"pith:DF4N23I4","canonical_record":{"source":{"id":"1502.03862","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-02-13T00:05:39Z","cross_cats_sorted":["nlin.CD"],"title_canon_sha256":"621f2c49135f8f06f1d9c65465ea6abc06a11076a7c468b50bb81006e5b05bcd","abstract_canon_sha256":"a84aac4004e5bd708564b2178e9ec7c4cf6e37c4c6c5e02bb0112f4d5c511e5b"},"schema_version":"1.0"},"canonical_sha256":"1978dd6d1ca06ad3973c927941e0b4b103b1195bc66781db7871aa3177d96f9e","source":{"kind":"arxiv","id":"1502.03862","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.03862","created_at":"2026-05-18T00:22:40Z"},{"alias_kind":"arxiv_version","alias_value":"1502.03862v4","created_at":"2026-05-18T00:22:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.03862","created_at":"2026-05-18T00:22:40Z"},{"alias_kind":"pith_short_12","alias_value":"DF4N23I4UBVN","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DF4N23I4UBVNHFZ4","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DF4N23I4","created_at":"2026-05-18T12:29:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:DF4N23I4UBVNHFZ4SJ4UDYFUWE","target":"record","payload":{"canonical_record":{"source":{"id":"1502.03862","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-02-13T00:05:39Z","cross_cats_sorted":["nlin.CD"],"title_canon_sha256":"621f2c49135f8f06f1d9c65465ea6abc06a11076a7c468b50bb81006e5b05bcd","abstract_canon_sha256":"a84aac4004e5bd708564b2178e9ec7c4cf6e37c4c6c5e02bb0112f4d5c511e5b"},"schema_version":"1.0"},"canonical_sha256":"1978dd6d1ca06ad3973c927941e0b4b103b1195bc66781db7871aa3177d96f9e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:40.604549Z","signature_b64":"/0vRlPVerSXrPYJLWRaq4gS1hmhOaNd5tOBM/OXOTPLC73CBCYp97UusDzAMER5X6x4K/6C5hp7NrKvPTVbYBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1978dd6d1ca06ad3973c927941e0b4b103b1195bc66781db7871aa3177d96f9e","last_reissued_at":"2026-05-18T00:22:40.604088Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:40.604088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.03862","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:22:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cDe+Eas65IvNYY63usp/3wWlCefCnSnY9Oacw13EF5VkDuNoh2Q0Ex9QdI67oj/zaH/+rW8Azp8UkTFifzd+CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T13:42:38.547925Z"},"content_sha256":"65e6f9ea319e34f15964ca09ef405ee9d76d835aa045f9fd233392f002421707","schema_version":"1.0","event_id":"sha256:65e6f9ea319e34f15964ca09ef405ee9d76d835aa045f9fd233392f002421707"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:DF4N23I4UBVNHFZ4SJ4UDYFUWE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Numerical Continuation of Invariant Solutions of the Complex Ginzburg-Landau Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.CD"],"primary_cat":"math.DS","authors_text":"Vanessa L\\'opez","submitted_at":"2015-02-13T00:05:39Z","abstract_excerpt":"We consider the problem of computation and deformation of group orbits of solutions of the complex Ginzburg-Landau equation (CGLE) with cubic nonlinearity in $1\\!+\\!1$ space-time dimension invariant under the action of the three-dimensional Lie group of symmetries $A(x,t) \\rightarrow \\mathrm{e}^{\\mathrm{i}\\theta}A(x+\\sigma,t+\\tau)$. From an initial set of group orbits of invariant solutions, for a particular point in the parameter space of the CGLE, we obtain new sets of group orbits of invariant solutions via numerical continuation along paths in the moduli space. The computed solutions along"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.03862","kind":"arxiv","version":4},"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":"2026-05-18T00:22:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cRJtsQlVQWd1RQSxwwNrtiQbEfT14ge6QlLZxH9fvid7sJsj1ySUnmEaQEIp/I3mpzNncZtzQX8V5I6HxbXLAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T13:42:38.548273Z"},"content_sha256":"cad70eb42510a38ff705b382bd2b047780efad565da0dcb1cad61c250d60e592","schema_version":"1.0","event_id":"sha256:cad70eb42510a38ff705b382bd2b047780efad565da0dcb1cad61c250d60e592"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DF4N23I4UBVNHFZ4SJ4UDYFUWE/bundle.json","state_url":"https://pith.science/pith/DF4N23I4UBVNHFZ4SJ4UDYFUWE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DF4N23I4UBVNHFZ4SJ4UDYFUWE/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":"2026-06-23T13:42:38Z","links":{"resolver":"https://pith.science/pith/DF4N23I4UBVNHFZ4SJ4UDYFUWE","bundle":"https://pith.science/pith/DF4N23I4UBVNHFZ4SJ4UDYFUWE/bundle.json","state":"https://pith.science/pith/DF4N23I4UBVNHFZ4SJ4UDYFUWE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DF4N23I4UBVNHFZ4SJ4UDYFUWE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:DF4N23I4UBVNHFZ4SJ4UDYFUWE","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":"a84aac4004e5bd708564b2178e9ec7c4cf6e37c4c6c5e02bb0112f4d5c511e5b","cross_cats_sorted":["nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-02-13T00:05:39Z","title_canon_sha256":"621f2c49135f8f06f1d9c65465ea6abc06a11076a7c468b50bb81006e5b05bcd"},"schema_version":"1.0","source":{"id":"1502.03862","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.03862","created_at":"2026-05-18T00:22:40Z"},{"alias_kind":"arxiv_version","alias_value":"1502.03862v4","created_at":"2026-05-18T00:22:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.03862","created_at":"2026-05-18T00:22:40Z"},{"alias_kind":"pith_short_12","alias_value":"DF4N23I4UBVN","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DF4N23I4UBVNHFZ4","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DF4N23I4","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:cad70eb42510a38ff705b382bd2b047780efad565da0dcb1cad61c250d60e592","target":"graph","created_at":"2026-05-18T00:22:40Z","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 consider the problem of computation and deformation of group orbits of solutions of the complex Ginzburg-Landau equation (CGLE) with cubic nonlinearity in $1\\!+\\!1$ space-time dimension invariant under the action of the three-dimensional Lie group of symmetries $A(x,t) \\rightarrow \\mathrm{e}^{\\mathrm{i}\\theta}A(x+\\sigma,t+\\tau)$. From an initial set of group orbits of invariant solutions, for a particular point in the parameter space of the CGLE, we obtain new sets of group orbits of invariant solutions via numerical continuation along paths in the moduli space. The computed solutions along","authors_text":"Vanessa L\\'opez","cross_cats":["nlin.CD"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-02-13T00:05:39Z","title":"Numerical Continuation of Invariant Solutions of the Complex Ginzburg-Landau Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.03862","kind":"arxiv","version":4},"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":"sha256:65e6f9ea319e34f15964ca09ef405ee9d76d835aa045f9fd233392f002421707","target":"record","created_at":"2026-05-18T00:22:40Z","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":"a84aac4004e5bd708564b2178e9ec7c4cf6e37c4c6c5e02bb0112f4d5c511e5b","cross_cats_sorted":["nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-02-13T00:05:39Z","title_canon_sha256":"621f2c49135f8f06f1d9c65465ea6abc06a11076a7c468b50bb81006e5b05bcd"},"schema_version":"1.0","source":{"id":"1502.03862","kind":"arxiv","version":4}},"canonical_sha256":"1978dd6d1ca06ad3973c927941e0b4b103b1195bc66781db7871aa3177d96f9e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1978dd6d1ca06ad3973c927941e0b4b103b1195bc66781db7871aa3177d96f9e","first_computed_at":"2026-05-18T00:22:40.604088Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:40.604088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/0vRlPVerSXrPYJLWRaq4gS1hmhOaNd5tOBM/OXOTPLC73CBCYp97UusDzAMER5X6x4K/6C5hp7NrKvPTVbYBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:40.604549Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.03862","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:65e6f9ea319e34f15964ca09ef405ee9d76d835aa045f9fd233392f002421707","sha256:cad70eb42510a38ff705b382bd2b047780efad565da0dcb1cad61c250d60e592"],"state_sha256":"ad3b1bde9c2b5c680dd32b151335e750292c00dbdb53725579c9f2ea5a9c011c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S2tPMIGM9EQWxIzW5wkMGFOTJKY7eO0a04GFtfzEEDtsZjfxBBB4Sn2aFPOQluH4oLcWBHBI2HasVEKV3VgSDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T13:42:38.550402Z","bundle_sha256":"d67536802f000b28e1c8b70aac780fd52d81cbb32de17b91e69f351bf38db7f5"}}