{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:VYLKUUEPSQJKN6ALG4XZFIFTWX","short_pith_number":"pith:VYLKUUEP","canonical_record":{"source":{"id":"1808.07459","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-08-22T17:49:31Z","cross_cats_sorted":[],"title_canon_sha256":"8951cb5f47d9416d10b2269f25e2787f04c67cb2e3389a68fb26b6aa4b62d719","abstract_canon_sha256":"773977212037365c3731bbd5ce0b38dc3aecc9240f4887010b78247ca8d4b920"},"schema_version":"1.0"},"canonical_sha256":"ae16aa508f9412a6f80b372f92a0b3b5daff5d10aecb5719c5667698e49e4b79","source":{"kind":"arxiv","id":"1808.07459","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.07459","created_at":"2026-05-17T23:57:07Z"},{"alias_kind":"arxiv_version","alias_value":"1808.07459v3","created_at":"2026-05-17T23:57:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.07459","created_at":"2026-05-17T23:57:07Z"},{"alias_kind":"pith_short_12","alias_value":"VYLKUUEPSQJK","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VYLKUUEPSQJKN6AL","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VYLKUUEP","created_at":"2026-05-18T12:32:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:VYLKUUEPSQJKN6ALG4XZFIFTWX","target":"record","payload":{"canonical_record":{"source":{"id":"1808.07459","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-08-22T17:49:31Z","cross_cats_sorted":[],"title_canon_sha256":"8951cb5f47d9416d10b2269f25e2787f04c67cb2e3389a68fb26b6aa4b62d719","abstract_canon_sha256":"773977212037365c3731bbd5ce0b38dc3aecc9240f4887010b78247ca8d4b920"},"schema_version":"1.0"},"canonical_sha256":"ae16aa508f9412a6f80b372f92a0b3b5daff5d10aecb5719c5667698e49e4b79","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:07.389324Z","signature_b64":"1Wh+qUAr7CGdKkxGtfePMbjE3qLXErjJqPk6/7wux/VA0h4xPta7Yex7djqO3xNbGuyVEfcO+5XuYTjC2pAtAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae16aa508f9412a6f80b372f92a0b3b5daff5d10aecb5719c5667698e49e4b79","last_reissued_at":"2026-05-17T23:57:07.388820Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:07.388820Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.07459","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:57:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cZ1ZjPexu4+QV27BgbPIQQ75bJyrHeZP7AyJHSvnaIpAzHp8cd1d3IxUgK2JQpxsbiqsEatm/h8enMvp4nNHCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T23:13:49.166530Z"},"content_sha256":"17402cce380f02a7c5198aa7fbe794f05844c75654da7198898a644f4490c85c","schema_version":"1.0","event_id":"sha256:17402cce380f02a7c5198aa7fbe794f05844c75654da7198898a644f4490c85c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:VYLKUUEPSQJKN6ALG4XZFIFTWX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bifurcations of the polycycle \"tears of the heart\": multiple numerical invariants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Nataliya Goncharuk, Yury Kudryashov","submitted_at":"2018-08-22T17:49:31Z","abstract_excerpt":"\"Tears of the heart\" is a hyperbolic polycycle formed by three separatrix connections of two saddles. It is met in generic 3-parameter families of planar vector fields.\n  In [arXiv:1506.06797], it was discovered that generically, the bifurcation of a vector field with \"tears of the heart\" is structurally unstable. The authors proved that the classification of such bifurcations has a numerical invariant.\n  In this article, we study the bifurcations of \"tears of the heart\" in more detail, and find out that the classification of such bifurcation may have arbitrarily many numerical invariants."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.07459","kind":"arxiv","version":3},"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":"2026-05-17T23:57:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c7NcJQj/JioVUMKPtI1kvzddyllny+r1pONdInFZNykTTRBlZ6lrz7UoXbjRwXX8g284MbaK+LHianhdXzfuAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T23:13:49.167143Z"},"content_sha256":"2e504325d6694a9271ee89d44431348d8bc1122302d9923f24a14e040cd4ca32","schema_version":"1.0","event_id":"sha256:2e504325d6694a9271ee89d44431348d8bc1122302d9923f24a14e040cd4ca32"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VYLKUUEPSQJKN6ALG4XZFIFTWX/bundle.json","state_url":"https://pith.science/pith/VYLKUUEPSQJKN6ALG4XZFIFTWX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VYLKUUEPSQJKN6ALG4XZFIFTWX/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":"2026-06-11T23:13:49Z","links":{"resolver":"https://pith.science/pith/VYLKUUEPSQJKN6ALG4XZFIFTWX","bundle":"https://pith.science/pith/VYLKUUEPSQJKN6ALG4XZFIFTWX/bundle.json","state":"https://pith.science/pith/VYLKUUEPSQJKN6ALG4XZFIFTWX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VYLKUUEPSQJKN6ALG4XZFIFTWX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:VYLKUUEPSQJKN6ALG4XZFIFTWX","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":"773977212037365c3731bbd5ce0b38dc3aecc9240f4887010b78247ca8d4b920","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-08-22T17:49:31Z","title_canon_sha256":"8951cb5f47d9416d10b2269f25e2787f04c67cb2e3389a68fb26b6aa4b62d719"},"schema_version":"1.0","source":{"id":"1808.07459","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.07459","created_at":"2026-05-17T23:57:07Z"},{"alias_kind":"arxiv_version","alias_value":"1808.07459v3","created_at":"2026-05-17T23:57:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.07459","created_at":"2026-05-17T23:57:07Z"},{"alias_kind":"pith_short_12","alias_value":"VYLKUUEPSQJK","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VYLKUUEPSQJKN6AL","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VYLKUUEP","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:2e504325d6694a9271ee89d44431348d8bc1122302d9923f24a14e040cd4ca32","target":"graph","created_at":"2026-05-17T23:57:07Z","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":"\"Tears of the heart\" is a hyperbolic polycycle formed by three separatrix connections of two saddles. It is met in generic 3-parameter families of planar vector fields.\n  In [arXiv:1506.06797], it was discovered that generically, the bifurcation of a vector field with \"tears of the heart\" is structurally unstable. The authors proved that the classification of such bifurcations has a numerical invariant.\n  In this article, we study the bifurcations of \"tears of the heart\" in more detail, and find out that the classification of such bifurcation may have arbitrarily many numerical invariants.","authors_text":"Nataliya Goncharuk, Yury Kudryashov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-08-22T17:49:31Z","title":"Bifurcations of the polycycle \"tears of the heart\": multiple numerical invariants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.07459","kind":"arxiv","version":3},"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":"sha256:17402cce380f02a7c5198aa7fbe794f05844c75654da7198898a644f4490c85c","target":"record","created_at":"2026-05-17T23:57:07Z","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":"773977212037365c3731bbd5ce0b38dc3aecc9240f4887010b78247ca8d4b920","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-08-22T17:49:31Z","title_canon_sha256":"8951cb5f47d9416d10b2269f25e2787f04c67cb2e3389a68fb26b6aa4b62d719"},"schema_version":"1.0","source":{"id":"1808.07459","kind":"arxiv","version":3}},"canonical_sha256":"ae16aa508f9412a6f80b372f92a0b3b5daff5d10aecb5719c5667698e49e4b79","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae16aa508f9412a6f80b372f92a0b3b5daff5d10aecb5719c5667698e49e4b79","first_computed_at":"2026-05-17T23:57:07.388820Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:07.388820Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1Wh+qUAr7CGdKkxGtfePMbjE3qLXErjJqPk6/7wux/VA0h4xPta7Yex7djqO3xNbGuyVEfcO+5XuYTjC2pAtAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:07.389324Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.07459","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:17402cce380f02a7c5198aa7fbe794f05844c75654da7198898a644f4490c85c","sha256:2e504325d6694a9271ee89d44431348d8bc1122302d9923f24a14e040cd4ca32"],"state_sha256":"6961ce0e9413238a759d6b71c869e440e2ce5e17d6759b719dd3863fb125f387"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E1oSUxWigU3vbewHwe+jsmY+PyCe/h7xVZ6WCOEKd+pje/BLNXH2GoigbCx9Ow9P5pnvkvr0b/1mEumI4fYUAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T23:13:49.171044Z","bundle_sha256":"54a932dd2b914237b76d63da6f5491add9322f9c67a012ad5447fbeb24ab8daa"}}