{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:XQVJQBKCTGLKXOPAKKZKCIG7UT","short_pith_number":"pith:XQVJQBKC","canonical_record":{"source":{"id":"1012.5201","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-12-23T13:48:59Z","cross_cats_sorted":[],"title_canon_sha256":"b6fdba7e15251bd6b2f2145d9f5627f0edc171f9b4d4b57d4b76f834df68d0dc","abstract_canon_sha256":"353abace0a390a27f2fb8e27988b2d2d71241aed2ff2eac2d3dbbc56c46ff099"},"schema_version":"1.0"},"canonical_sha256":"bc2a9805429996abb9e052b2a120dfa4cd675eaa06b8145d31b93bb6573c3991","source":{"kind":"arxiv","id":"1012.5201","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.5201","created_at":"2026-05-18T04:32:35Z"},{"alias_kind":"arxiv_version","alias_value":"1012.5201v1","created_at":"2026-05-18T04:32:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.5201","created_at":"2026-05-18T04:32:35Z"},{"alias_kind":"pith_short_12","alias_value":"XQVJQBKCTGLK","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"XQVJQBKCTGLKXOPA","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"XQVJQBKC","created_at":"2026-05-18T12:26:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:XQVJQBKCTGLKXOPAKKZKCIG7UT","target":"record","payload":{"canonical_record":{"source":{"id":"1012.5201","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-12-23T13:48:59Z","cross_cats_sorted":[],"title_canon_sha256":"b6fdba7e15251bd6b2f2145d9f5627f0edc171f9b4d4b57d4b76f834df68d0dc","abstract_canon_sha256":"353abace0a390a27f2fb8e27988b2d2d71241aed2ff2eac2d3dbbc56c46ff099"},"schema_version":"1.0"},"canonical_sha256":"bc2a9805429996abb9e052b2a120dfa4cd675eaa06b8145d31b93bb6573c3991","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:32:35.607763Z","signature_b64":"gZdvvyTqCFU2FicwMpQGNw64AnhzrKeTcCc112x2sQSioLYf5PmlXXX8t5DIFmTn9UVC0JiTDw1f+gvF1XUrCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bc2a9805429996abb9e052b2a120dfa4cd675eaa06b8145d31b93bb6573c3991","last_reissued_at":"2026-05-18T04:32:35.607254Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:32:35.607254Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.5201","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":"2026-05-18T04:32:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pefxKKiRlZtSlflNVtBSyg03XBK4+GMGjZLOm8H2K//yVL8fc2dW+U2Ns96LSZSAkdHowjpz8htltc2/tx/lBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T21:00:20.796562Z"},"content_sha256":"e7c9b7418997827c5e77a81643c0e9c1efc89a942cc3236df5c5e2fc29bdacb8","schema_version":"1.0","event_id":"sha256:e7c9b7418997827c5e77a81643c0e9c1efc89a942cc3236df5c5e2fc29bdacb8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:XQVJQBKCTGLKXOPAKKZKCIG7UT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Upper bounds for the number of zeroes for some Abelian integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Armengol Gasull, Joan Torregrosa, J. Tom\\'as L\\'azaro","submitted_at":"2010-12-23T13:48:59Z","abstract_excerpt":"Consider the vector field $x'= -yG(x, y), y'=xG(x, y),$ where the set of critical points $\\{G(x, y) = 0\\}$ is formed by $K$ straight lines, not passing through the origin and parallel to one or two orthogonal directions. We perturb it with a general polynomial perturbation of degree $n$ and study which is the maximum number of limit cycles that can bifurcate from the period annulus of the origin in terms of $K$ and $n.$ Our approach is based on the explicit computation of the Abelian integral that controls the bifurcation and in a new result for bounding the number of zeroes of a certain famil"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5201","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":"2026-05-18T04:32:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/rioUNADCIMmG4ghZsDdjoyRi4nSEvu2zTi/5mRLaTHO9yrUkiFCp5aQKUqSCLKy38V3hLVe9+a6ji/nNp20Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T21:00:20.796908Z"},"content_sha256":"56d7583aec8236f7f2f63a5ebba105a9aa7656d5d1b497df938ebe3da0f8e2dd","schema_version":"1.0","event_id":"sha256:56d7583aec8236f7f2f63a5ebba105a9aa7656d5d1b497df938ebe3da0f8e2dd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XQVJQBKCTGLKXOPAKKZKCIG7UT/bundle.json","state_url":"https://pith.science/pith/XQVJQBKCTGLKXOPAKKZKCIG7UT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XQVJQBKCTGLKXOPAKKZKCIG7UT/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":"2026-06-20T21:00:20Z","links":{"resolver":"https://pith.science/pith/XQVJQBKCTGLKXOPAKKZKCIG7UT","bundle":"https://pith.science/pith/XQVJQBKCTGLKXOPAKKZKCIG7UT/bundle.json","state":"https://pith.science/pith/XQVJQBKCTGLKXOPAKKZKCIG7UT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XQVJQBKCTGLKXOPAKKZKCIG7UT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:XQVJQBKCTGLKXOPAKKZKCIG7UT","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":"353abace0a390a27f2fb8e27988b2d2d71241aed2ff2eac2d3dbbc56c46ff099","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-12-23T13:48:59Z","title_canon_sha256":"b6fdba7e15251bd6b2f2145d9f5627f0edc171f9b4d4b57d4b76f834df68d0dc"},"schema_version":"1.0","source":{"id":"1012.5201","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.5201","created_at":"2026-05-18T04:32:35Z"},{"alias_kind":"arxiv_version","alias_value":"1012.5201v1","created_at":"2026-05-18T04:32:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.5201","created_at":"2026-05-18T04:32:35Z"},{"alias_kind":"pith_short_12","alias_value":"XQVJQBKCTGLK","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"XQVJQBKCTGLKXOPA","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"XQVJQBKC","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:56d7583aec8236f7f2f63a5ebba105a9aa7656d5d1b497df938ebe3da0f8e2dd","target":"graph","created_at":"2026-05-18T04:32:35Z","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":"Consider the vector field $x'= -yG(x, y), y'=xG(x, y),$ where the set of critical points $\\{G(x, y) = 0\\}$ is formed by $K$ straight lines, not passing through the origin and parallel to one or two orthogonal directions. We perturb it with a general polynomial perturbation of degree $n$ and study which is the maximum number of limit cycles that can bifurcate from the period annulus of the origin in terms of $K$ and $n.$ Our approach is based on the explicit computation of the Abelian integral that controls the bifurcation and in a new result for bounding the number of zeroes of a certain famil","authors_text":"Armengol Gasull, Joan Torregrosa, J. Tom\\'as L\\'azaro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-12-23T13:48:59Z","title":"Upper bounds for the number of zeroes for some Abelian integrals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5201","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:e7c9b7418997827c5e77a81643c0e9c1efc89a942cc3236df5c5e2fc29bdacb8","target":"record","created_at":"2026-05-18T04:32:35Z","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":"353abace0a390a27f2fb8e27988b2d2d71241aed2ff2eac2d3dbbc56c46ff099","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-12-23T13:48:59Z","title_canon_sha256":"b6fdba7e15251bd6b2f2145d9f5627f0edc171f9b4d4b57d4b76f834df68d0dc"},"schema_version":"1.0","source":{"id":"1012.5201","kind":"arxiv","version":1}},"canonical_sha256":"bc2a9805429996abb9e052b2a120dfa4cd675eaa06b8145d31b93bb6573c3991","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bc2a9805429996abb9e052b2a120dfa4cd675eaa06b8145d31b93bb6573c3991","first_computed_at":"2026-05-18T04:32:35.607254Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:32:35.607254Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gZdvvyTqCFU2FicwMpQGNw64AnhzrKeTcCc112x2sQSioLYf5PmlXXX8t5DIFmTn9UVC0JiTDw1f+gvF1XUrCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:32:35.607763Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.5201","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e7c9b7418997827c5e77a81643c0e9c1efc89a942cc3236df5c5e2fc29bdacb8","sha256:56d7583aec8236f7f2f63a5ebba105a9aa7656d5d1b497df938ebe3da0f8e2dd"],"state_sha256":"fa7dc19247c268fe26495eda52759debcd9da00d21c461b6542a326aada4a269"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fcsHR/03kD9592QRHrmp0H6n5h8KrnoIFO18D4SO3jX5KKLwhRV8bXXYtZunRMP3CAzOYV0XD35bwXb+fW9hDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T21:00:20.798816Z","bundle_sha256":"931eb8be06e65a635179a50f3dd73191e1642ec619e14d5e368b3f44e906c5ce"}}