{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:VXHID4HH2VZGVU6SGLVZRD3P5Z","short_pith_number":"pith:VXHID4HH","canonical_record":{"source":{"id":"1708.01512","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-08-02T19:34:16Z","cross_cats_sorted":[],"title_canon_sha256":"39e822ed838fcf4fa934f803dc548e3cfbc6e9efdec0cc5ec20a74e7f932682f","abstract_canon_sha256":"04d7338b6e2eddcfa26b87cda884b62e3b95385bba2df233fac7448019a5f1c1"},"schema_version":"1.0"},"canonical_sha256":"adce81f0e7d5726ad3d232eb988f6fee6570d1e0287521cd7c253909b6c3e8d8","source":{"kind":"arxiv","id":"1708.01512","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.01512","created_at":"2026-05-18T00:38:37Z"},{"alias_kind":"arxiv_version","alias_value":"1708.01512v1","created_at":"2026-05-18T00:38:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.01512","created_at":"2026-05-18T00:38:37Z"},{"alias_kind":"pith_short_12","alias_value":"VXHID4HH2VZG","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VXHID4HH2VZGVU6S","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VXHID4HH","created_at":"2026-05-18T12:31:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:VXHID4HH2VZGVU6SGLVZRD3P5Z","target":"record","payload":{"canonical_record":{"source":{"id":"1708.01512","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-08-02T19:34:16Z","cross_cats_sorted":[],"title_canon_sha256":"39e822ed838fcf4fa934f803dc548e3cfbc6e9efdec0cc5ec20a74e7f932682f","abstract_canon_sha256":"04d7338b6e2eddcfa26b87cda884b62e3b95385bba2df233fac7448019a5f1c1"},"schema_version":"1.0"},"canonical_sha256":"adce81f0e7d5726ad3d232eb988f6fee6570d1e0287521cd7c253909b6c3e8d8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:37.194763Z","signature_b64":"FfmGpoMOQbzv9NIDJfoQbp0eyZpDEraw/5mqj83QeT3se5VHjTFHK5sliSN9VgI5O2ZhltEMHPXYidpp90TECg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"adce81f0e7d5726ad3d232eb988f6fee6570d1e0287521cd7c253909b6c3e8d8","last_reissued_at":"2026-05-18T00:38:37.194302Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:37.194302Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.01512","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":"2026-05-18T00:38:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lmL2srMM+QiN3znA/UFOKP8ezaskZNcWh/xjHDMtpFFdy9SeGNfmNLKljSoTTbWRUrSuNnKkCxiLxBjTjaxLAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T15:41:32.131335Z"},"content_sha256":"4b07f023896093dc9800fd8b10795936b6e191d0b19026ee20022e80b0ed4565","schema_version":"1.0","event_id":"sha256:4b07f023896093dc9800fd8b10795936b6e191d0b19026ee20022e80b0ed4565"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:VXHID4HH2VZGVU6SGLVZRD3P5Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Moment Condition and Center Condition for Abel Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Ab\\'ilio Lemos, Alexandre M. Alves, Anderson L. A. de Araujo","submitted_at":"2017-08-02T19:34:16Z","abstract_excerpt":"In this paper we consider Abel equation $x' = g(t)x^2+f(t)x^3$, where $f$ and $g$ are analytical functions. We proved that if the equation has a center at $x=0$, then the Moment Conditions, i. e., $m_k=\\int_{-1}^1f(t)(G(t))^kdt=0,~~k=0,1,2$, is satisfied where $G(t)=\\int_{-1}^tg(s)ds$. Besides, we give partial a positive answer to a conjecture proposed by Y. Lijun and T. Yun in 2001."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.01512","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":"2026-05-18T00:38:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ft92+7b5Leo1hOxB7oosETEtvmJxMlOxn+qF9PnvsJA2kGd24pXlUGvW/wtsiLLkL/4GsiAV8g/btyLPAUHRDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T15:41:32.131723Z"},"content_sha256":"5133f45a4a757836c8337fb301f4de61b6410941ebe7b8df3dc97acb02fc528d","schema_version":"1.0","event_id":"sha256:5133f45a4a757836c8337fb301f4de61b6410941ebe7b8df3dc97acb02fc528d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VXHID4HH2VZGVU6SGLVZRD3P5Z/bundle.json","state_url":"https://pith.science/pith/VXHID4HH2VZGVU6SGLVZRD3P5Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VXHID4HH2VZGVU6SGLVZRD3P5Z/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":"2026-06-23T15:41:32Z","links":{"resolver":"https://pith.science/pith/VXHID4HH2VZGVU6SGLVZRD3P5Z","bundle":"https://pith.science/pith/VXHID4HH2VZGVU6SGLVZRD3P5Z/bundle.json","state":"https://pith.science/pith/VXHID4HH2VZGVU6SGLVZRD3P5Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VXHID4HH2VZGVU6SGLVZRD3P5Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:VXHID4HH2VZGVU6SGLVZRD3P5Z","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":"04d7338b6e2eddcfa26b87cda884b62e3b95385bba2df233fac7448019a5f1c1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-08-02T19:34:16Z","title_canon_sha256":"39e822ed838fcf4fa934f803dc548e3cfbc6e9efdec0cc5ec20a74e7f932682f"},"schema_version":"1.0","source":{"id":"1708.01512","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.01512","created_at":"2026-05-18T00:38:37Z"},{"alias_kind":"arxiv_version","alias_value":"1708.01512v1","created_at":"2026-05-18T00:38:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.01512","created_at":"2026-05-18T00:38:37Z"},{"alias_kind":"pith_short_12","alias_value":"VXHID4HH2VZG","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VXHID4HH2VZGVU6S","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VXHID4HH","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:5133f45a4a757836c8337fb301f4de61b6410941ebe7b8df3dc97acb02fc528d","target":"graph","created_at":"2026-05-18T00:38:37Z","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 paper we consider Abel equation $x' = g(t)x^2+f(t)x^3$, where $f$ and $g$ are analytical functions. We proved that if the equation has a center at $x=0$, then the Moment Conditions, i. e., $m_k=\\int_{-1}^1f(t)(G(t))^kdt=0,~~k=0,1,2$, is satisfied where $G(t)=\\int_{-1}^tg(s)ds$. Besides, we give partial a positive answer to a conjecture proposed by Y. Lijun and T. Yun in 2001.","authors_text":"Ab\\'ilio Lemos, Alexandre M. Alves, Anderson L. A. de Araujo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-08-02T19:34:16Z","title":"On Moment Condition and Center Condition for Abel Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.01512","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":"sha256:4b07f023896093dc9800fd8b10795936b6e191d0b19026ee20022e80b0ed4565","target":"record","created_at":"2026-05-18T00:38:37Z","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":"04d7338b6e2eddcfa26b87cda884b62e3b95385bba2df233fac7448019a5f1c1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-08-02T19:34:16Z","title_canon_sha256":"39e822ed838fcf4fa934f803dc548e3cfbc6e9efdec0cc5ec20a74e7f932682f"},"schema_version":"1.0","source":{"id":"1708.01512","kind":"arxiv","version":1}},"canonical_sha256":"adce81f0e7d5726ad3d232eb988f6fee6570d1e0287521cd7c253909b6c3e8d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"adce81f0e7d5726ad3d232eb988f6fee6570d1e0287521cd7c253909b6c3e8d8","first_computed_at":"2026-05-18T00:38:37.194302Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:37.194302Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FfmGpoMOQbzv9NIDJfoQbp0eyZpDEraw/5mqj83QeT3se5VHjTFHK5sliSN9VgI5O2ZhltEMHPXYidpp90TECg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:37.194763Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.01512","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4b07f023896093dc9800fd8b10795936b6e191d0b19026ee20022e80b0ed4565","sha256:5133f45a4a757836c8337fb301f4de61b6410941ebe7b8df3dc97acb02fc528d"],"state_sha256":"69e5b01d5c291a0f20b6f25ea632344fbc13874891fe1fbcd04534624ad4bb38"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f7b2U+85Qi2Qlbxjj2GSYIuJ76VTckUAN4Z4rFijcPAHj3PH/hD0GLDs9fGhefF61sVqAo+iEQ99dRNUsSfvBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T15:41:32.133734Z","bundle_sha256":"708e05313e53089de581cdc1b91141a79b458cdaae3da18d4172c041cc937abe"}}