{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:OPFFQYA2372TMLCEVMLAF6UPPH","short_pith_number":"pith:OPFFQYA2","canonical_record":{"source":{"id":"math/0506036","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DS","submitted_at":"2005-06-02T08:28:11Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"299cbb95d9263c93c36b47296d9a91e6e2a8a6df5e8be1850d7afbfbc586e15f","abstract_canon_sha256":"eca16937d2e5a30587d0dfbd8395b7b091df604eeb70a15d0705790f164c7f28"},"schema_version":"1.0"},"canonical_sha256":"73ca58601adff5362c44ab1602fa8f79d284fec0544b27d6a2f201b37bf25bac","source":{"kind":"arxiv","id":"math/0506036","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0506036","created_at":"2026-05-18T00:44:18Z"},{"alias_kind":"arxiv_version","alias_value":"math/0506036v1","created_at":"2026-05-18T00:44:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0506036","created_at":"2026-05-18T00:44:18Z"},{"alias_kind":"pith_short_12","alias_value":"OPFFQYA2372T","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"OPFFQYA2372TMLCE","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"OPFFQYA2","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:OPFFQYA2372TMLCEVMLAF6UPPH","target":"record","payload":{"canonical_record":{"source":{"id":"math/0506036","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DS","submitted_at":"2005-06-02T08:28:11Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"299cbb95d9263c93c36b47296d9a91e6e2a8a6df5e8be1850d7afbfbc586e15f","abstract_canon_sha256":"eca16937d2e5a30587d0dfbd8395b7b091df604eeb70a15d0705790f164c7f28"},"schema_version":"1.0"},"canonical_sha256":"73ca58601adff5362c44ab1602fa8f79d284fec0544b27d6a2f201b37bf25bac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:18.919793Z","signature_b64":"xC5jeY0iqA00U6x3AdiU3aDA/d/q1PPS8KxbOTgahVgk8RtymirILRYb26/S6u5LuX4NaxgMs9fz1GirlJ/6DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"73ca58601adff5362c44ab1602fa8f79d284fec0544b27d6a2f201b37bf25bac","last_reissued_at":"2026-05-18T00:44:18.919261Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:18.919261Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0506036","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":"2026-05-18T00:44:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1Sk8NphJX4HvZXazbpYEoUWEZxOwzqUojcoXGONzO1va2kAMdpgrFKiIvZDI34yVqyF3ddX9jp/fnzMqBu2fDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:19:17.778257Z"},"content_sha256":"71c1448b6ab94b754b90128a4cf4193f5520d5a860e678668313d64fbc939b3e","schema_version":"1.0","event_id":"sha256:71c1448b6ab94b754b90128a4cf4193f5520d5a860e678668313d64fbc939b3e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:OPFFQYA2372TMLCEVMLAF6UPPH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The role of algebraic solutions in planar polynomial differential systems","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"math.DS","authors_text":"H\\'ector Giacomini, Jaume Gin\\'e, Maite Grau","submitted_at":"2005-06-02T08:28:11Z","abstract_excerpt":"We study a planar polynomial differential system, given by \\dot{x}=P(x,y), \\dot{y}=Q(x,y). We consider a function I(x,y)=\\exp \\{h_2(x) A_1(x,y) \\diagup A_0(x,y) \\} h_1(x) \\prod_{i=1}^{\\ell} (y-g_i(x))^{\\alpha_i}, where g_i(x) are algebraic functions, A_1(x,y)=\\prod_{k=1}^r (y-a_k(x)), A_0(x,y)=\\prod_{j=1}^s (y-\\tilde{g}_j(x)) with a_k(x) and \\tilde{g}_j(x) algebraic functions, A_0 and A_1 do not share any common factor, h_2(x) is a rational function, h(x) and h_1(x) are functions with a rational logarithmic derivative and \\alpha_i are complex numbers. We show that if I(x,y) is a first integral"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0506036","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":"2026-05-18T00:44:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1hXnKLapkSrxnLgQK/h52bFtgF0Bh1kkAaW4Y1l/TC5KoPBMMLvTmKpHh1y7OdwAvyXMIItTrNSiT3pCHT2xAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:19:17.778692Z"},"content_sha256":"f25fde6b96bfc7b32a01269b378de745e68f05bec913d23e15c4a23c533caab8","schema_version":"1.0","event_id":"sha256:f25fde6b96bfc7b32a01269b378de745e68f05bec913d23e15c4a23c533caab8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OPFFQYA2372TMLCEVMLAF6UPPH/bundle.json","state_url":"https://pith.science/pith/OPFFQYA2372TMLCEVMLAF6UPPH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OPFFQYA2372TMLCEVMLAF6UPPH/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":"2026-05-30T08:19:17Z","links":{"resolver":"https://pith.science/pith/OPFFQYA2372TMLCEVMLAF6UPPH","bundle":"https://pith.science/pith/OPFFQYA2372TMLCEVMLAF6UPPH/bundle.json","state":"https://pith.science/pith/OPFFQYA2372TMLCEVMLAF6UPPH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OPFFQYA2372TMLCEVMLAF6UPPH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:OPFFQYA2372TMLCEVMLAF6UPPH","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":"eca16937d2e5a30587d0dfbd8395b7b091df604eeb70a15d0705790f164c7f28","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"math.DS","submitted_at":"2005-06-02T08:28:11Z","title_canon_sha256":"299cbb95d9263c93c36b47296d9a91e6e2a8a6df5e8be1850d7afbfbc586e15f"},"schema_version":"1.0","source":{"id":"math/0506036","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0506036","created_at":"2026-05-18T00:44:18Z"},{"alias_kind":"arxiv_version","alias_value":"math/0506036v1","created_at":"2026-05-18T00:44:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0506036","created_at":"2026-05-18T00:44:18Z"},{"alias_kind":"pith_short_12","alias_value":"OPFFQYA2372T","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"OPFFQYA2372TMLCE","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"OPFFQYA2","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:f25fde6b96bfc7b32a01269b378de745e68f05bec913d23e15c4a23c533caab8","target":"graph","created_at":"2026-05-18T00:44:18Z","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 a planar polynomial differential system, given by \\dot{x}=P(x,y), \\dot{y}=Q(x,y). We consider a function I(x,y)=\\exp \\{h_2(x) A_1(x,y) \\diagup A_0(x,y) \\} h_1(x) \\prod_{i=1}^{\\ell} (y-g_i(x))^{\\alpha_i}, where g_i(x) are algebraic functions, A_1(x,y)=\\prod_{k=1}^r (y-a_k(x)), A_0(x,y)=\\prod_{j=1}^s (y-\\tilde{g}_j(x)) with a_k(x) and \\tilde{g}_j(x) algebraic functions, A_0 and A_1 do not share any common factor, h_2(x) is a rational function, h(x) and h_1(x) are functions with a rational logarithmic derivative and \\alpha_i are complex numbers. We show that if I(x,y) is a first integral","authors_text":"H\\'ector Giacomini, Jaume Gin\\'e, Maite Grau","cross_cats":["math.AG"],"headline":"","license":"","primary_cat":"math.DS","submitted_at":"2005-06-02T08:28:11Z","title":"The role of algebraic solutions in planar polynomial differential systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0506036","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":"sha256:71c1448b6ab94b754b90128a4cf4193f5520d5a860e678668313d64fbc939b3e","target":"record","created_at":"2026-05-18T00:44:18Z","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":"eca16937d2e5a30587d0dfbd8395b7b091df604eeb70a15d0705790f164c7f28","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"math.DS","submitted_at":"2005-06-02T08:28:11Z","title_canon_sha256":"299cbb95d9263c93c36b47296d9a91e6e2a8a6df5e8be1850d7afbfbc586e15f"},"schema_version":"1.0","source":{"id":"math/0506036","kind":"arxiv","version":1}},"canonical_sha256":"73ca58601adff5362c44ab1602fa8f79d284fec0544b27d6a2f201b37bf25bac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"73ca58601adff5362c44ab1602fa8f79d284fec0544b27d6a2f201b37bf25bac","first_computed_at":"2026-05-18T00:44:18.919261Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:18.919261Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xC5jeY0iqA00U6x3AdiU3aDA/d/q1PPS8KxbOTgahVgk8RtymirILRYb26/S6u5LuX4NaxgMs9fz1GirlJ/6DA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:18.919793Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0506036","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:71c1448b6ab94b754b90128a4cf4193f5520d5a860e678668313d64fbc939b3e","sha256:f25fde6b96bfc7b32a01269b378de745e68f05bec913d23e15c4a23c533caab8"],"state_sha256":"59a2bb105ee9884f8aaef0bf67d459690410c6ce7f055a05de35b77b7e1886d6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JtlcKyY4Y1w3/723VDHaEY9ex+FZgOSQ6+esH9M57Z+aFmBVwSZcQ4qJCc/jE/hvV/psdKgA7d8xsK3Fv9iYCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T08:19:17.781612Z","bundle_sha256":"9f8c378f23b29367cb48f034fd068dbbfdd89dc8734388290732cf042bf22c9f"}}