{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:CWETYAIRLZJNAHOILAPSIO3PAT","short_pith_number":"pith:CWETYAIR","canonical_record":{"source":{"id":"1509.01678","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-09-05T08:33:11Z","cross_cats_sorted":[],"title_canon_sha256":"e2753f799525d51a9c4d1306c290cdef19442b8f3e8426e92afaafd02f3cd618","abstract_canon_sha256":"e5a119e71666bc266b1d5265afc6ad5dac34754e03bdb7fda2882b66c9dd175b"},"schema_version":"1.0"},"canonical_sha256":"15893c01115e52d01dc8581f243b6f04e4d79879666ca5efc5cdb3e6eed8389d","source":{"kind":"arxiv","id":"1509.01678","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.01678","created_at":"2026-05-18T01:16:48Z"},{"alias_kind":"arxiv_version","alias_value":"1509.01678v1","created_at":"2026-05-18T01:16:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.01678","created_at":"2026-05-18T01:16:48Z"},{"alias_kind":"pith_short_12","alias_value":"CWETYAIRLZJN","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"CWETYAIRLZJNAHOI","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"CWETYAIR","created_at":"2026-05-18T12:29:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:CWETYAIRLZJNAHOILAPSIO3PAT","target":"record","payload":{"canonical_record":{"source":{"id":"1509.01678","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-09-05T08:33:11Z","cross_cats_sorted":[],"title_canon_sha256":"e2753f799525d51a9c4d1306c290cdef19442b8f3e8426e92afaafd02f3cd618","abstract_canon_sha256":"e5a119e71666bc266b1d5265afc6ad5dac34754e03bdb7fda2882b66c9dd175b"},"schema_version":"1.0"},"canonical_sha256":"15893c01115e52d01dc8581f243b6f04e4d79879666ca5efc5cdb3e6eed8389d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:48.918614Z","signature_b64":"ZhceO8GaJ4D8vqkv8YgsS1JlT6oKDgPkF9QIqVVFJOsgzIrEAdWhsMnNulHETcC9EnCxybDqUszCwPLnWKYxAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"15893c01115e52d01dc8581f243b6f04e4d79879666ca5efc5cdb3e6eed8389d","last_reissued_at":"2026-05-18T01:16:48.917873Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:48.917873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.01678","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":"2026-05-18T01:16:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"umMpst3/Ism+Pa3cSas5xiyGcHa3LI7TDnno4rlhbAHHZGNwBgV/EbaCr8jUPfb6jFIrKOT6EybgIZiGjh7RAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T06:47:51.404621Z"},"content_sha256":"83005a62a002807a70289275f2ae60bcdc7fc340044946bf038e3d2c430ee087","schema_version":"1.0","event_id":"sha256:83005a62a002807a70289275f2ae60bcdc7fc340044946bf038e3d2c430ee087"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:CWETYAIRLZJNAHOILAPSIO3PAT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Discontinuous dynamics with grazing points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Aysegul Kivilcim, Marat Akhmet","submitted_at":"2015-09-05T08:33:11Z","abstract_excerpt":"Discontinuous dynamical systems with grazing solutions are discussed. The group property, continuation of solutions, continuity and smoothness of motions are thoroughly analyzed. A variational system around a grazing solution which depends on near solutions is constructed. Orbital stability of grazing cycles is examined by linearization. Small parameter method is extended for analysis of neighborhoods of grazing orbits, and grazing bifurcation of cycles is observed in an example. Linearization around an equilibrium grazing point is discussed. The mathematical background of the study relies on "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01678","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":"2026-05-18T01:16:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Aa6/wkMYJVfnonR/CJwUhMkptsse0pf3wsQ2i0MXCiaur14yC5fd4Izs8/JCbpxstfpLHXTt4SSrZbBCkrp8DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T06:47:51.404965Z"},"content_sha256":"e279cc771240377b703eb3766ff8c163dcb926e6b317b41a19c2596aa8baf67f","schema_version":"1.0","event_id":"sha256:e279cc771240377b703eb3766ff8c163dcb926e6b317b41a19c2596aa8baf67f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CWETYAIRLZJNAHOILAPSIO3PAT/bundle.json","state_url":"https://pith.science/pith/CWETYAIRLZJNAHOILAPSIO3PAT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CWETYAIRLZJNAHOILAPSIO3PAT/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":"2026-06-24T06:47:51Z","links":{"resolver":"https://pith.science/pith/CWETYAIRLZJNAHOILAPSIO3PAT","bundle":"https://pith.science/pith/CWETYAIRLZJNAHOILAPSIO3PAT/bundle.json","state":"https://pith.science/pith/CWETYAIRLZJNAHOILAPSIO3PAT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CWETYAIRLZJNAHOILAPSIO3PAT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:CWETYAIRLZJNAHOILAPSIO3PAT","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":"e5a119e71666bc266b1d5265afc6ad5dac34754e03bdb7fda2882b66c9dd175b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-09-05T08:33:11Z","title_canon_sha256":"e2753f799525d51a9c4d1306c290cdef19442b8f3e8426e92afaafd02f3cd618"},"schema_version":"1.0","source":{"id":"1509.01678","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.01678","created_at":"2026-05-18T01:16:48Z"},{"alias_kind":"arxiv_version","alias_value":"1509.01678v1","created_at":"2026-05-18T01:16:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.01678","created_at":"2026-05-18T01:16:48Z"},{"alias_kind":"pith_short_12","alias_value":"CWETYAIRLZJN","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"CWETYAIRLZJNAHOI","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"CWETYAIR","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:e279cc771240377b703eb3766ff8c163dcb926e6b317b41a19c2596aa8baf67f","target":"graph","created_at":"2026-05-18T01:16:48Z","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":"Discontinuous dynamical systems with grazing solutions are discussed. The group property, continuation of solutions, continuity and smoothness of motions are thoroughly analyzed. A variational system around a grazing solution which depends on near solutions is constructed. Orbital stability of grazing cycles is examined by linearization. Small parameter method is extended for analysis of neighborhoods of grazing orbits, and grazing bifurcation of cycles is observed in an example. Linearization around an equilibrium grazing point is discussed. The mathematical background of the study relies on ","authors_text":"Aysegul Kivilcim, Marat Akhmet","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-09-05T08:33:11Z","title":"Discontinuous dynamics with grazing points"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01678","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":"sha256:83005a62a002807a70289275f2ae60bcdc7fc340044946bf038e3d2c430ee087","target":"record","created_at":"2026-05-18T01:16:48Z","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":"e5a119e71666bc266b1d5265afc6ad5dac34754e03bdb7fda2882b66c9dd175b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-09-05T08:33:11Z","title_canon_sha256":"e2753f799525d51a9c4d1306c290cdef19442b8f3e8426e92afaafd02f3cd618"},"schema_version":"1.0","source":{"id":"1509.01678","kind":"arxiv","version":1}},"canonical_sha256":"15893c01115e52d01dc8581f243b6f04e4d79879666ca5efc5cdb3e6eed8389d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"15893c01115e52d01dc8581f243b6f04e4d79879666ca5efc5cdb3e6eed8389d","first_computed_at":"2026-05-18T01:16:48.917873Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:48.917873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZhceO8GaJ4D8vqkv8YgsS1JlT6oKDgPkF9QIqVVFJOsgzIrEAdWhsMnNulHETcC9EnCxybDqUszCwPLnWKYxAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:48.918614Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.01678","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:83005a62a002807a70289275f2ae60bcdc7fc340044946bf038e3d2c430ee087","sha256:e279cc771240377b703eb3766ff8c163dcb926e6b317b41a19c2596aa8baf67f"],"state_sha256":"6618929dc6984a5bf39ec3c90bee1edf59cb7009fe4b8ab583fd3e7ed5bd33f4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A0U+HHB8DQ3gpAifpG/3+cbUAoTTyW+D2xGtAzEN0DqPR/MpDqibLf7Ta6pbQM4AOZi+Gu/IUQB0pUI6nvi0CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T06:47:51.406931Z","bundle_sha256":"f877e1941e2c8762302cac19e9c0dbebb3cb4a7d0dfb4dbefe9d5027541fe292"}}