{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:OUJG4K7TPJGC5PXY64KVO7OC6I","short_pith_number":"pith:OUJG4K7T","canonical_record":{"source":{"id":"1405.4924","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-05-20T00:42:01Z","cross_cats_sorted":[],"title_canon_sha256":"2a3261286869d9bca22be876b41201c158afb2b4802f945cacebdd31dd440ab9","abstract_canon_sha256":"f16dda0a683b5ed5c280e8d9e16839ce42eac42a11f67bf347cdfd0ceb5b4da9"},"schema_version":"1.0"},"canonical_sha256":"75126e2bf37a4c2ebef8f715577dc2f21e3d1c7c8b575febf52933b9fc6236fb","source":{"kind":"arxiv","id":"1405.4924","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.4924","created_at":"2026-05-17T23:53:14Z"},{"alias_kind":"arxiv_version","alias_value":"1405.4924v1","created_at":"2026-05-17T23:53:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.4924","created_at":"2026-05-17T23:53:14Z"},{"alias_kind":"pith_short_12","alias_value":"OUJG4K7TPJGC","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"OUJG4K7TPJGC5PXY","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"OUJG4K7T","created_at":"2026-05-18T12:28:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:OUJG4K7TPJGC5PXY64KVO7OC6I","target":"record","payload":{"canonical_record":{"source":{"id":"1405.4924","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-05-20T00:42:01Z","cross_cats_sorted":[],"title_canon_sha256":"2a3261286869d9bca22be876b41201c158afb2b4802f945cacebdd31dd440ab9","abstract_canon_sha256":"f16dda0a683b5ed5c280e8d9e16839ce42eac42a11f67bf347cdfd0ceb5b4da9"},"schema_version":"1.0"},"canonical_sha256":"75126e2bf37a4c2ebef8f715577dc2f21e3d1c7c8b575febf52933b9fc6236fb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:14.389555Z","signature_b64":"ZzXs9kH9g8mftWEPJ24/RtliVINgeZjMHAC02TT4C7zQe3UF3VGKX9fG9hVk60OknP1KTmr4l5ztqAv+tNx1AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"75126e2bf37a4c2ebef8f715577dc2f21e3d1c7c8b575febf52933b9fc6236fb","last_reissued_at":"2026-05-17T23:53:14.388880Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:14.388880Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.4924","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":"2026-05-17T23:53:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gaKNmSRa7Io9/9NkpBprTMuBFDba6wR7McKmv0DMecjS38HEfSYZgrzyJCwowQRNoLkM9Dzmqso1lDVSQVvZBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T22:07:02.880891Z"},"content_sha256":"41a59291c9218aee9296ef3904f333cc1ea2c1ededc4bc9ee9542bf9b4632ff9","schema_version":"1.0","event_id":"sha256:41a59291c9218aee9296ef3904f333cc1ea2c1ededc4bc9ee9542bf9b4632ff9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:OUJG4K7TPJGC5PXY64KVO7OC6I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Universal Curves in the Center Problem for Abel Differential Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Alexander Brudnyi","submitted_at":"2014-05-20T00:42:01Z","abstract_excerpt":"We study the center problem for the class $\\mathcal E_\\Gamma$ of Abel differential equations $\\frac{dv}{dt}=a_1 v^2+a_2 v^3$, $a_1,a_2\\in L^\\infty ([0,T])$, such that images of Lipschitz paths $\\tilde A:=\\bigl(\\int_0^\\cdot a_1(s)ds, \\int_0^\\cdot a_2(s)ds\\bigr): [0,T]\\rightarrow\\mathbb R^2$ belong to a fixed compact rectifiable curve $\\Gamma$. Such a curve is called universal if whenever an equation in $\\mathcal E_\\Gamma$ has center on $[0,T]$, this center must be universal, i.e. all iterated integrals in coefficients $a_1, a_2$ of this equation must vanish. We investigate some basic properties"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4924","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":"2026-05-17T23:53:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xx//HGxp2PLItrBNoY/3q4zYueRHgf2J6oN+txF8qOmZppkSJ49PohSGQsFu1MZ8OvsdP2IY5d7vumukKqhJBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T22:07:02.881595Z"},"content_sha256":"e45e2bbea97adb6d18f32ccb82a3bb59e8e129619df6dd9e432ba2fddbecbe61","schema_version":"1.0","event_id":"sha256:e45e2bbea97adb6d18f32ccb82a3bb59e8e129619df6dd9e432ba2fddbecbe61"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OUJG4K7TPJGC5PXY64KVO7OC6I/bundle.json","state_url":"https://pith.science/pith/OUJG4K7TPJGC5PXY64KVO7OC6I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OUJG4K7TPJGC5PXY64KVO7OC6I/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":"2026-06-11T22:07:02Z","links":{"resolver":"https://pith.science/pith/OUJG4K7TPJGC5PXY64KVO7OC6I","bundle":"https://pith.science/pith/OUJG4K7TPJGC5PXY64KVO7OC6I/bundle.json","state":"https://pith.science/pith/OUJG4K7TPJGC5PXY64KVO7OC6I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OUJG4K7TPJGC5PXY64KVO7OC6I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:OUJG4K7TPJGC5PXY64KVO7OC6I","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":"f16dda0a683b5ed5c280e8d9e16839ce42eac42a11f67bf347cdfd0ceb5b4da9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-05-20T00:42:01Z","title_canon_sha256":"2a3261286869d9bca22be876b41201c158afb2b4802f945cacebdd31dd440ab9"},"schema_version":"1.0","source":{"id":"1405.4924","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.4924","created_at":"2026-05-17T23:53:14Z"},{"alias_kind":"arxiv_version","alias_value":"1405.4924v1","created_at":"2026-05-17T23:53:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.4924","created_at":"2026-05-17T23:53:14Z"},{"alias_kind":"pith_short_12","alias_value":"OUJG4K7TPJGC","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"OUJG4K7TPJGC5PXY","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"OUJG4K7T","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:e45e2bbea97adb6d18f32ccb82a3bb59e8e129619df6dd9e432ba2fddbecbe61","target":"graph","created_at":"2026-05-17T23:53:14Z","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 study the center problem for the class $\\mathcal E_\\Gamma$ of Abel differential equations $\\frac{dv}{dt}=a_1 v^2+a_2 v^3$, $a_1,a_2\\in L^\\infty ([0,T])$, such that images of Lipschitz paths $\\tilde A:=\\bigl(\\int_0^\\cdot a_1(s)ds, \\int_0^\\cdot a_2(s)ds\\bigr): [0,T]\\rightarrow\\mathbb R^2$ belong to a fixed compact rectifiable curve $\\Gamma$. Such a curve is called universal if whenever an equation in $\\mathcal E_\\Gamma$ has center on $[0,T]$, this center must be universal, i.e. all iterated integrals in coefficients $a_1, a_2$ of this equation must vanish. We investigate some basic properties","authors_text":"Alexander Brudnyi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-05-20T00:42:01Z","title":"Universal Curves in the Center Problem for Abel Differential Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4924","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":"sha256:41a59291c9218aee9296ef3904f333cc1ea2c1ededc4bc9ee9542bf9b4632ff9","target":"record","created_at":"2026-05-17T23:53:14Z","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":"f16dda0a683b5ed5c280e8d9e16839ce42eac42a11f67bf347cdfd0ceb5b4da9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-05-20T00:42:01Z","title_canon_sha256":"2a3261286869d9bca22be876b41201c158afb2b4802f945cacebdd31dd440ab9"},"schema_version":"1.0","source":{"id":"1405.4924","kind":"arxiv","version":1}},"canonical_sha256":"75126e2bf37a4c2ebef8f715577dc2f21e3d1c7c8b575febf52933b9fc6236fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"75126e2bf37a4c2ebef8f715577dc2f21e3d1c7c8b575febf52933b9fc6236fb","first_computed_at":"2026-05-17T23:53:14.388880Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:14.388880Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZzXs9kH9g8mftWEPJ24/RtliVINgeZjMHAC02TT4C7zQe3UF3VGKX9fG9hVk60OknP1KTmr4l5ztqAv+tNx1AA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:14.389555Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.4924","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:41a59291c9218aee9296ef3904f333cc1ea2c1ededc4bc9ee9542bf9b4632ff9","sha256:e45e2bbea97adb6d18f32ccb82a3bb59e8e129619df6dd9e432ba2fddbecbe61"],"state_sha256":"750c6a525b03173b11f6064cc6e6628693586d34ba2a56b69d6d03e656550387"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Sj/+06E73ynL+OSQxCa/IyGdXxMrRFEV8sNrabsfIlbUIxvUzPur4D9yIRKwtOLf0wseEdNBFEmcIbxHWQYQCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T22:07:02.884622Z","bundle_sha256":"25f86b2abc54918041ac7cd7bac99fc598a9df1f1e2ea3734c2ab95aaab07b2f"}}