{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:RHHNYNLF22I2WVJSQAJJREY3OM","short_pith_number":"pith:RHHNYNLF","canonical_record":{"source":{"id":"1703.05510","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-03-16T08:59:41Z","cross_cats_sorted":[],"title_canon_sha256":"7727a5dc8573ef6a91e0e80fe50142f591b49c58afc61a55852f8e91894b26c6","abstract_canon_sha256":"abf0c20b2e6cfd657b1434780e64ee3fc84853ee19e3af7d9f1378eb50bb60ae"},"schema_version":"1.0"},"canonical_sha256":"89cedc3565d691ab5532801298931b733b7a6055537698466d9453ebe0a95d99","source":{"kind":"arxiv","id":"1703.05510","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.05510","created_at":"2026-05-17T23:40:27Z"},{"alias_kind":"arxiv_version","alias_value":"1703.05510v5","created_at":"2026-05-17T23:40:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.05510","created_at":"2026-05-17T23:40:27Z"},{"alias_kind":"pith_short_12","alias_value":"RHHNYNLF22I2","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"RHHNYNLF22I2WVJS","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"RHHNYNLF","created_at":"2026-05-18T12:31:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:RHHNYNLF22I2WVJSQAJJREY3OM","target":"record","payload":{"canonical_record":{"source":{"id":"1703.05510","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-03-16T08:59:41Z","cross_cats_sorted":[],"title_canon_sha256":"7727a5dc8573ef6a91e0e80fe50142f591b49c58afc61a55852f8e91894b26c6","abstract_canon_sha256":"abf0c20b2e6cfd657b1434780e64ee3fc84853ee19e3af7d9f1378eb50bb60ae"},"schema_version":"1.0"},"canonical_sha256":"89cedc3565d691ab5532801298931b733b7a6055537698466d9453ebe0a95d99","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:27.711190Z","signature_b64":"R7SGru3KNDBmdsdyRUlRl2u2urUiSmW+8buR7Ap3heSXVprAOIagYcQmRmCNfEV2o1aTf2bNEedhriZ9Xug+Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"89cedc3565d691ab5532801298931b733b7a6055537698466d9453ebe0a95d99","last_reissued_at":"2026-05-17T23:40:27.710585Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:27.710585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.05510","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:40:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JXpB7QGz+5W4u3vUTMYuzzf00o3iuO6+Pm51WFXpsH2WbJdQgtA9GHFHZ2HoLFOW7k57DXohTzhiU1gfWN1yDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T14:52:00.794861Z"},"content_sha256":"a17a11c103d5e23015cdf47c31daef837ecd765a67d64f377d5246b49874b6a9","schema_version":"1.0","event_id":"sha256:a17a11c103d5e23015cdf47c31daef837ecd765a67d64f377d5246b49874b6a9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:RHHNYNLF22I2WVJSQAJJREY3OM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Morsifications of real plane curve singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Eugenii Shustin, Peter Leviant","submitted_at":"2017-03-16T08:59:41Z","abstract_excerpt":"A real morsification of a real plane curve singularity is a real deformation given by a family of real analytic functions having only real Morse critical points with all saddles on the zero level. We prove the existence of real morsifications for real plane curve singularities having arbitrary real local branches and pairs of complex conjugate branches satisfying some conditions. This was known before only in the case of all local branches being real (A'Campo, Gusein-Zade). We also discuss a relation between real morsifications and the topology of singularities, extending to arbitrary real mor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.05510","kind":"arxiv","version":5},"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":"2026-05-17T23:40:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mYhJtbQTPaLmKvCj4Ya7eTqJsw5MMFoe+ISjd5wQ8mtBAOBnGsn94qn2hP4bK16mz+1ubbcFfKAtxsapiq+vDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T14:52:00.795466Z"},"content_sha256":"1b6cc5c742aba6908c333973721319e4c421802ea3c3f6d197d42f42305401fc","schema_version":"1.0","event_id":"sha256:1b6cc5c742aba6908c333973721319e4c421802ea3c3f6d197d42f42305401fc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RHHNYNLF22I2WVJSQAJJREY3OM/bundle.json","state_url":"https://pith.science/pith/RHHNYNLF22I2WVJSQAJJREY3OM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RHHNYNLF22I2WVJSQAJJREY3OM/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":"2026-08-17T14:52:00Z","links":{"resolver":"https://pith.science/pith/RHHNYNLF22I2WVJSQAJJREY3OM","bundle":"https://pith.science/pith/RHHNYNLF22I2WVJSQAJJREY3OM/bundle.json","state":"https://pith.science/pith/RHHNYNLF22I2WVJSQAJJREY3OM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RHHNYNLF22I2WVJSQAJJREY3OM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:RHHNYNLF22I2WVJSQAJJREY3OM","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":"abf0c20b2e6cfd657b1434780e64ee3fc84853ee19e3af7d9f1378eb50bb60ae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-03-16T08:59:41Z","title_canon_sha256":"7727a5dc8573ef6a91e0e80fe50142f591b49c58afc61a55852f8e91894b26c6"},"schema_version":"1.0","source":{"id":"1703.05510","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.05510","created_at":"2026-05-17T23:40:27Z"},{"alias_kind":"arxiv_version","alias_value":"1703.05510v5","created_at":"2026-05-17T23:40:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.05510","created_at":"2026-05-17T23:40:27Z"},{"alias_kind":"pith_short_12","alias_value":"RHHNYNLF22I2","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"RHHNYNLF22I2WVJS","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"RHHNYNLF","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:1b6cc5c742aba6908c333973721319e4c421802ea3c3f6d197d42f42305401fc","target":"graph","created_at":"2026-05-17T23:40:27Z","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":"A real morsification of a real plane curve singularity is a real deformation given by a family of real analytic functions having only real Morse critical points with all saddles on the zero level. We prove the existence of real morsifications for real plane curve singularities having arbitrary real local branches and pairs of complex conjugate branches satisfying some conditions. This was known before only in the case of all local branches being real (A'Campo, Gusein-Zade). We also discuss a relation between real morsifications and the topology of singularities, extending to arbitrary real mor","authors_text":"Eugenii Shustin, Peter Leviant","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-03-16T08:59:41Z","title":"Morsifications of real plane curve singularities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.05510","kind":"arxiv","version":5},"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:a17a11c103d5e23015cdf47c31daef837ecd765a67d64f377d5246b49874b6a9","target":"record","created_at":"2026-05-17T23:40:27Z","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":"abf0c20b2e6cfd657b1434780e64ee3fc84853ee19e3af7d9f1378eb50bb60ae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-03-16T08:59:41Z","title_canon_sha256":"7727a5dc8573ef6a91e0e80fe50142f591b49c58afc61a55852f8e91894b26c6"},"schema_version":"1.0","source":{"id":"1703.05510","kind":"arxiv","version":5}},"canonical_sha256":"89cedc3565d691ab5532801298931b733b7a6055537698466d9453ebe0a95d99","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"89cedc3565d691ab5532801298931b733b7a6055537698466d9453ebe0a95d99","first_computed_at":"2026-05-17T23:40:27.710585Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:27.710585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R7SGru3KNDBmdsdyRUlRl2u2urUiSmW+8buR7Ap3heSXVprAOIagYcQmRmCNfEV2o1aTf2bNEedhriZ9Xug+Bw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:27.711190Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.05510","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a17a11c103d5e23015cdf47c31daef837ecd765a67d64f377d5246b49874b6a9","sha256:1b6cc5c742aba6908c333973721319e4c421802ea3c3f6d197d42f42305401fc"],"state_sha256":"42cfa75e7547853c0303ef91c4339eb7d6a3fd2afc98679ae6da6a363e7475d6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WmP3g6CA478R0eyzt8Oa6WiDXKtr8hdJSFsJDbCTwsc3WesevPOm6WJSP3YKaky3Rmpw/lfva9juKdOJTuhtCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T14:52:00.868691Z","bundle_sha256":"2c267f21035d52cdfff1792338cc56c13ce52ee8296763f9f29b11c01efffe1d"}}