{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:DRM5RNVF4BPDG74L5VGLUIVW5M","short_pith_number":"pith:DRM5RNVF","canonical_record":{"source":{"id":"1309.3082","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2013-09-12T09:54:45Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"ff5d19388d96a9d44ba1c742522af718993c7e7b21822627e77def8dadc8b027","abstract_canon_sha256":"03195ad9f51bbb11043c772511cdae4a1a2161ad5ea409043c7b0f6adaee7ec7"},"schema_version":"1.0"},"canonical_sha256":"1c59d8b6a5e05e337f8bed4cba22b6eb0c9730e1cdbcf12cf01ad12f78222bec","source":{"kind":"arxiv","id":"1309.3082","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.3082","created_at":"2026-05-18T03:13:32Z"},{"alias_kind":"arxiv_version","alias_value":"1309.3082v1","created_at":"2026-05-18T03:13:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.3082","created_at":"2026-05-18T03:13:32Z"},{"alias_kind":"pith_short_12","alias_value":"DRM5RNVF4BPD","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DRM5RNVF4BPDG74L","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DRM5RNVF","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:DRM5RNVF4BPDG74L5VGLUIVW5M","target":"record","payload":{"canonical_record":{"source":{"id":"1309.3082","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2013-09-12T09:54:45Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"ff5d19388d96a9d44ba1c742522af718993c7e7b21822627e77def8dadc8b027","abstract_canon_sha256":"03195ad9f51bbb11043c772511cdae4a1a2161ad5ea409043c7b0f6adaee7ec7"},"schema_version":"1.0"},"canonical_sha256":"1c59d8b6a5e05e337f8bed4cba22b6eb0c9730e1cdbcf12cf01ad12f78222bec","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:13:32.919399Z","signature_b64":"R/5m/Bwb9dURFVgu+nhDpzLPpYEygd6vcUUn4H8Z2d2gAcPpjGsvN2PIAOsm850AE53oy10bMceWvdsBK4S+Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1c59d8b6a5e05e337f8bed4cba22b6eb0c9730e1cdbcf12cf01ad12f78222bec","last_reissued_at":"2026-05-18T03:13:32.918773Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:13:32.918773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.3082","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":"kX4KFuCoZ4MluVcy6odmUXcxJ4rX6sL9E9OKu5jo3n2z803x+vdCwm0VNdAKxhmzhHc9H0to7ZlvJXHJL77zDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T01:25:40.133433Z"},"content_sha256":"6f77902cfad8ee0cd66152da93d20fbe40b6d59d52b8fa87a2bd4bb5357316f3","schema_version":"1.0","event_id":"sha256:6f77902cfad8ee0cd66152da93d20fbe40b6d59d52b8fa87a2bd4bb5357316f3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:DRM5RNVF4BPDG74L5VGLUIVW5M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the linearization of isochronous centre of a modified Emden equation with linear external forcing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"nlin.SI","authors_text":"M I Sabiya Shakila, M Senthilvelan, R Mohanasubha","submitted_at":"2013-09-12T09:54:45Z","abstract_excerpt":"In this work, we carry out a detailed study on the linearization of isochronous centre of a modified Emden equation with linear external forcing. We construct inverse integrating factor and time independent first integral for this system through Darboux method. To linearize the isochronous centre we explore a transverse commuting dynamical system and its first integral. With the help of first integrals of the original dynamical system and its transverse commuting system we derive the linearizing transformation and reduce the nonlinear system into linear isochronous one. We also point out certa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.3082","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":"p1eheQ4k//7og6KB/GQjcXxyuZd7CMHsEVw4ZzbtF/ocBAnQk+47Cb7yFw7u3QaMJhfE3EA3bNnlQ8ok9GiUDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T01:25:40.133777Z"},"content_sha256":"b97d6c7caccd80c12c5d2cf4bb67bec5ac354587a8a55ee5301f9250f9368c23","schema_version":"1.0","event_id":"sha256:b97d6c7caccd80c12c5d2cf4bb67bec5ac354587a8a55ee5301f9250f9368c23"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DRM5RNVF4BPDG74L5VGLUIVW5M/bundle.json","state_url":"https://pith.science/pith/DRM5RNVF4BPDG74L5VGLUIVW5M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DRM5RNVF4BPDG74L5VGLUIVW5M/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":"2026-06-24T01:25:40Z","links":{"resolver":"https://pith.science/pith/DRM5RNVF4BPDG74L5VGLUIVW5M","bundle":"https://pith.science/pith/DRM5RNVF4BPDG74L5VGLUIVW5M/bundle.json","state":"https://pith.science/pith/DRM5RNVF4BPDG74L5VGLUIVW5M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DRM5RNVF4BPDG74L5VGLUIVW5M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:DRM5RNVF4BPDG74L5VGLUIVW5M","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":"03195ad9f51bbb11043c772511cdae4a1a2161ad5ea409043c7b0f6adaee7ec7","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2013-09-12T09:54:45Z","title_canon_sha256":"ff5d19388d96a9d44ba1c742522af718993c7e7b21822627e77def8dadc8b027"},"schema_version":"1.0","source":{"id":"1309.3082","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.3082","created_at":"2026-05-18T03:13:32Z"},{"alias_kind":"arxiv_version","alias_value":"1309.3082v1","created_at":"2026-05-18T03:13:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.3082","created_at":"2026-05-18T03:13:32Z"},{"alias_kind":"pith_short_12","alias_value":"DRM5RNVF4BPD","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DRM5RNVF4BPDG74L","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DRM5RNVF","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:b97d6c7caccd80c12c5d2cf4bb67bec5ac354587a8a55ee5301f9250f9368c23","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":"In this work, we carry out a detailed study on the linearization of isochronous centre of a modified Emden equation with linear external forcing. We construct inverse integrating factor and time independent first integral for this system through Darboux method. To linearize the isochronous centre we explore a transverse commuting dynamical system and its first integral. With the help of first integrals of the original dynamical system and its transverse commuting system we derive the linearizing transformation and reduce the nonlinear system into linear isochronous one. We also point out certa","authors_text":"M I Sabiya Shakila, M Senthilvelan, R Mohanasubha","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2013-09-12T09:54:45Z","title":"On the linearization of isochronous centre of a modified Emden equation with linear external forcing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.3082","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":"sha256:6f77902cfad8ee0cd66152da93d20fbe40b6d59d52b8fa87a2bd4bb5357316f3","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":"03195ad9f51bbb11043c772511cdae4a1a2161ad5ea409043c7b0f6adaee7ec7","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.SI","submitted_at":"2013-09-12T09:54:45Z","title_canon_sha256":"ff5d19388d96a9d44ba1c742522af718993c7e7b21822627e77def8dadc8b027"},"schema_version":"1.0","source":{"id":"1309.3082","kind":"arxiv","version":1}},"canonical_sha256":"1c59d8b6a5e05e337f8bed4cba22b6eb0c9730e1cdbcf12cf01ad12f78222bec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c59d8b6a5e05e337f8bed4cba22b6eb0c9730e1cdbcf12cf01ad12f78222bec","first_computed_at":"2026-05-18T03:13:32.918773Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:13:32.918773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R/5m/Bwb9dURFVgu+nhDpzLPpYEygd6vcUUn4H8Z2d2gAcPpjGsvN2PIAOsm850AE53oy10bMceWvdsBK4S+Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:13:32.919399Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.3082","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6f77902cfad8ee0cd66152da93d20fbe40b6d59d52b8fa87a2bd4bb5357316f3","sha256:b97d6c7caccd80c12c5d2cf4bb67bec5ac354587a8a55ee5301f9250f9368c23"],"state_sha256":"5f52a80bf2f9d0ef08b882cc3caa1d0035841864489ba240417d60f3c2c1928f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4tNZJUGMzTiZo66Qj2LCWmNrJf296u+sG8hhOvEJQygSWVxAxTZommQabVOEOSkYHID7BkiJTroZQvWHUfVWCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T01:25:40.135792Z","bundle_sha256":"25a957f2129c4c2e3fd1dc23971ad7e279af4d93c48196fa200ae9ebf693e79a"}}