{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:GU3HAZ35ZQG2PUCLC4ZE4DO3VU","short_pith_number":"pith:GU3HAZ35","canonical_record":{"source":{"id":"1611.07576","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-11-22T23:04:47Z","cross_cats_sorted":[],"title_canon_sha256":"7c72e81d65c97f08505afe16017e491e970b3a7a7ed100fda4ac09ddddbfe83a","abstract_canon_sha256":"45de8581b3570a8dd9cd80ab9e8ff4cac8fda1a27fdd8cff4e95296bb3758636"},"schema_version":"1.0"},"canonical_sha256":"353670677dcc0da7d04b17324e0ddbad09d27a8c188671f72d477934f595005b","source":{"kind":"arxiv","id":"1611.07576","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.07576","created_at":"2026-05-18T00:57:00Z"},{"alias_kind":"arxiv_version","alias_value":"1611.07576v1","created_at":"2026-05-18T00:57:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.07576","created_at":"2026-05-18T00:57:00Z"},{"alias_kind":"pith_short_12","alias_value":"GU3HAZ35ZQG2","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GU3HAZ35ZQG2PUCL","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GU3HAZ35","created_at":"2026-05-18T12:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:GU3HAZ35ZQG2PUCLC4ZE4DO3VU","target":"record","payload":{"canonical_record":{"source":{"id":"1611.07576","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-11-22T23:04:47Z","cross_cats_sorted":[],"title_canon_sha256":"7c72e81d65c97f08505afe16017e491e970b3a7a7ed100fda4ac09ddddbfe83a","abstract_canon_sha256":"45de8581b3570a8dd9cd80ab9e8ff4cac8fda1a27fdd8cff4e95296bb3758636"},"schema_version":"1.0"},"canonical_sha256":"353670677dcc0da7d04b17324e0ddbad09d27a8c188671f72d477934f595005b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:57:00.439572Z","signature_b64":"2pXilggWCS8OOWa9Z9cLyBA+77P8+u5hBrcul3AiMzzcD6oPqOMUlQm+r8+7uD2eRIi/QOzfDLqsAJ8HCpo3AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"353670677dcc0da7d04b17324e0ddbad09d27a8c188671f72d477934f595005b","last_reissued_at":"2026-05-18T00:57:00.439106Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:57:00.439106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.07576","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":"2026-05-18T00:57:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c0xX3ADcve6BdpH8zTzUuxd/mx+iXYBrtA0n7ySzh46DyF0x292varmfZ3Gx7/7g7bKhjfN/PsfMj7RPi/yKAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T01:01:40.196175Z"},"content_sha256":"28b3f3cd5c0256c288bacb1fea02ba8a830910a00ba681cb173b363c8e6033fe","schema_version":"1.0","event_id":"sha256:28b3f3cd5c0256c288bacb1fea02ba8a830910a00ba681cb173b363c8e6033fe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:GU3HAZ35ZQG2PUCLC4ZE4DO3VU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Normal forms of para-CR hypersurfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Alessandro Ottazzi, Gerd Schmalz","submitted_at":"2016-11-22T23:04:47Z","abstract_excerpt":"We consider hypersurfaces of finite type in a direct product space ${\\mathbb R}^2 \\times {\\mathbb R}^2$, which are analogues to real hypersurfaces of finite type in ${\\mathbb C}^2$. We shall consider separately the cases where such hypersurfaces are regular and singular, in a sense that corresponds to Levi degeneracy in hypersurfaces in ${\\mathbb C}^2$. For the regular case, we study formal normal forms and prove convergence by following Chern and Moser. The normal form of such an hypersurface, considered as the solution manifold of a 2nd order ODE, gives rise to a normal form of the correspon"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.07576","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":"2026-05-18T00:57:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xxV3PFNAqmMLJMKr7VV17P72RvdWEmEiCjC4HR5GNPY5x1lbdI6U36UZQvXPgYZOiqgXdOjbjFJVMyMpI6fNBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T01:01:40.196538Z"},"content_sha256":"fa73e3093a038a94fa1c90cdadd7de9b6f999ff0712c031d5bd8ed3d7bcf27f7","schema_version":"1.0","event_id":"sha256:fa73e3093a038a94fa1c90cdadd7de9b6f999ff0712c031d5bd8ed3d7bcf27f7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GU3HAZ35ZQG2PUCLC4ZE4DO3VU/bundle.json","state_url":"https://pith.science/pith/GU3HAZ35ZQG2PUCLC4ZE4DO3VU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GU3HAZ35ZQG2PUCLC4ZE4DO3VU/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":"2026-06-03T01:01:40Z","links":{"resolver":"https://pith.science/pith/GU3HAZ35ZQG2PUCLC4ZE4DO3VU","bundle":"https://pith.science/pith/GU3HAZ35ZQG2PUCLC4ZE4DO3VU/bundle.json","state":"https://pith.science/pith/GU3HAZ35ZQG2PUCLC4ZE4DO3VU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GU3HAZ35ZQG2PUCLC4ZE4DO3VU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GU3HAZ35ZQG2PUCLC4ZE4DO3VU","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":"45de8581b3570a8dd9cd80ab9e8ff4cac8fda1a27fdd8cff4e95296bb3758636","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-11-22T23:04:47Z","title_canon_sha256":"7c72e81d65c97f08505afe16017e491e970b3a7a7ed100fda4ac09ddddbfe83a"},"schema_version":"1.0","source":{"id":"1611.07576","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.07576","created_at":"2026-05-18T00:57:00Z"},{"alias_kind":"arxiv_version","alias_value":"1611.07576v1","created_at":"2026-05-18T00:57:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.07576","created_at":"2026-05-18T00:57:00Z"},{"alias_kind":"pith_short_12","alias_value":"GU3HAZ35ZQG2","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GU3HAZ35ZQG2PUCL","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GU3HAZ35","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:fa73e3093a038a94fa1c90cdadd7de9b6f999ff0712c031d5bd8ed3d7bcf27f7","target":"graph","created_at":"2026-05-18T00:57:00Z","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 consider hypersurfaces of finite type in a direct product space ${\\mathbb R}^2 \\times {\\mathbb R}^2$, which are analogues to real hypersurfaces of finite type in ${\\mathbb C}^2$. We shall consider separately the cases where such hypersurfaces are regular and singular, in a sense that corresponds to Levi degeneracy in hypersurfaces in ${\\mathbb C}^2$. For the regular case, we study formal normal forms and prove convergence by following Chern and Moser. The normal form of such an hypersurface, considered as the solution manifold of a 2nd order ODE, gives rise to a normal form of the correspon","authors_text":"Alessandro Ottazzi, Gerd Schmalz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-11-22T23:04:47Z","title":"Normal forms of para-CR hypersurfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.07576","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":"sha256:28b3f3cd5c0256c288bacb1fea02ba8a830910a00ba681cb173b363c8e6033fe","target":"record","created_at":"2026-05-18T00:57:00Z","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":"45de8581b3570a8dd9cd80ab9e8ff4cac8fda1a27fdd8cff4e95296bb3758636","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-11-22T23:04:47Z","title_canon_sha256":"7c72e81d65c97f08505afe16017e491e970b3a7a7ed100fda4ac09ddddbfe83a"},"schema_version":"1.0","source":{"id":"1611.07576","kind":"arxiv","version":1}},"canonical_sha256":"353670677dcc0da7d04b17324e0ddbad09d27a8c188671f72d477934f595005b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"353670677dcc0da7d04b17324e0ddbad09d27a8c188671f72d477934f595005b","first_computed_at":"2026-05-18T00:57:00.439106Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:57:00.439106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2pXilggWCS8OOWa9Z9cLyBA+77P8+u5hBrcul3AiMzzcD6oPqOMUlQm+r8+7uD2eRIi/QOzfDLqsAJ8HCpo3AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:57:00.439572Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.07576","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:28b3f3cd5c0256c288bacb1fea02ba8a830910a00ba681cb173b363c8e6033fe","sha256:fa73e3093a038a94fa1c90cdadd7de9b6f999ff0712c031d5bd8ed3d7bcf27f7"],"state_sha256":"a9f65fa9844ede704a027a31033a431b259c8bdee377c8de2e4df5cd55081937"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9MJimasGe6JEs0KBuybb2kvoNNGfXZMcDDNlPRfBYkj5WGOEs5C5Wy77w5tQugadhSQgFnOxOMBb2DhoZS8RBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T01:01:40.198377Z","bundle_sha256":"036d0adc497190b6264dc3d3acbd2baa3ad0f8ac8d79c0ae31b93db0d006b419"}}