{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:FXP2E4O7YLH26RW73KRJUTMHIF","short_pith_number":"pith:FXP2E4O7","canonical_record":{"source":{"id":"2606.18938","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-06-17T11:21:34Z","cross_cats_sorted":[],"title_canon_sha256":"15685e614feb8c502421335bedd8b681d6c2491a0709ce9e77d25d3cc9eef713","abstract_canon_sha256":"91593ec77da86b68a6e9f66825b3a045a9de2fd1f9f081b5978fbb22a9cca695"},"schema_version":"1.0"},"canonical_sha256":"2ddfa271dfc2cfaf46dfdaa29a4d87414ab49099221675a9b9b825e4cd6eaddd","source":{"kind":"arxiv","id":"2606.18938","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.18938","created_at":"2026-06-19T16:11:52Z"},{"alias_kind":"arxiv_version","alias_value":"2606.18938v1","created_at":"2026-06-19T16:11:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.18938","created_at":"2026-06-19T16:11:52Z"},{"alias_kind":"pith_short_12","alias_value":"FXP2E4O7YLH2","created_at":"2026-06-19T16:11:52Z"},{"alias_kind":"pith_short_16","alias_value":"FXP2E4O7YLH26RW7","created_at":"2026-06-19T16:11:52Z"},{"alias_kind":"pith_short_8","alias_value":"FXP2E4O7","created_at":"2026-06-19T16:11:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:FXP2E4O7YLH26RW73KRJUTMHIF","target":"record","payload":{"canonical_record":{"source":{"id":"2606.18938","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-06-17T11:21:34Z","cross_cats_sorted":[],"title_canon_sha256":"15685e614feb8c502421335bedd8b681d6c2491a0709ce9e77d25d3cc9eef713","abstract_canon_sha256":"91593ec77da86b68a6e9f66825b3a045a9de2fd1f9f081b5978fbb22a9cca695"},"schema_version":"1.0"},"canonical_sha256":"2ddfa271dfc2cfaf46dfdaa29a4d87414ab49099221675a9b9b825e4cd6eaddd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:11:52.374853Z","signature_b64":"PnlrLB3/xQOHcxuEE9vdtCLlUQUtgJUDQ/Oh4OcmUt+HtXm5HxqW+nXP6EKVw0xH4u+Dk/nwm8AX6eMGAb9wBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2ddfa271dfc2cfaf46dfdaa29a4d87414ab49099221675a9b9b825e4cd6eaddd","last_reissued_at":"2026-06-19T16:11:52.374488Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:11:52.374488Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.18938","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":"2026-06-19T16:11:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BQND2LmNEq6rhgmUfbiQhND5VWtucMt9sEsutwGAR8Y+50yPgXjlbNcuhqXm1WkCqrlGG9N7znEPYkIPWWUUBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T01:10:30.384551Z"},"content_sha256":"af3f9b1437168399e5ca0f641d05c43771d09d35265452958fb68870004d86ea","schema_version":"1.0","event_id":"sha256:af3f9b1437168399e5ca0f641d05c43771d09d35265452958fb68870004d86ea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:FXP2E4O7YLH26RW73KRJUTMHIF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"About the Shadowing Theorem for piecewise smooth vector fields with sliding motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Tiago Carvalho","submitted_at":"2026-06-17T11:21:34Z","abstract_excerpt":"Since every modeling process in real-world situations is subject to errors, the study of the so-called shadowing property becomes highly relevant. This property allows for the identification of true orbits that closely follow a chain of trajectories in which some degree of approximation is introduced at each step. The objective of this paper is to establish a version of the Shadowing Theorem for vector fields governed by ordinary differential equations in the piecewise-smooth setting, where the dynamics alternate between distinct regimes, or on-off stages. First, we present an example showing "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.18938","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.18938/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-19T16:11:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Kszgr7jSYEGoPrHsYA4dnQcmB72QRnac10VsgRxdNqkzSuG8xLyRJWLC9TTopcdkCjx77X1bLRhMvIJ80Ng1Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T01:10:30.384916Z"},"content_sha256":"b66b3adde2e6611eef21be3f7711ed817d7dcd2be3a23aac79c136a24224669c","schema_version":"1.0","event_id":"sha256:b66b3adde2e6611eef21be3f7711ed817d7dcd2be3a23aac79c136a24224669c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FXP2E4O7YLH26RW73KRJUTMHIF/bundle.json","state_url":"https://pith.science/pith/FXP2E4O7YLH26RW73KRJUTMHIF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FXP2E4O7YLH26RW73KRJUTMHIF/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":"2026-07-03T01:10:30Z","links":{"resolver":"https://pith.science/pith/FXP2E4O7YLH26RW73KRJUTMHIF","bundle":"https://pith.science/pith/FXP2E4O7YLH26RW73KRJUTMHIF/bundle.json","state":"https://pith.science/pith/FXP2E4O7YLH26RW73KRJUTMHIF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FXP2E4O7YLH26RW73KRJUTMHIF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:FXP2E4O7YLH26RW73KRJUTMHIF","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":"91593ec77da86b68a6e9f66825b3a045a9de2fd1f9f081b5978fbb22a9cca695","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-06-17T11:21:34Z","title_canon_sha256":"15685e614feb8c502421335bedd8b681d6c2491a0709ce9e77d25d3cc9eef713"},"schema_version":"1.0","source":{"id":"2606.18938","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.18938","created_at":"2026-06-19T16:11:52Z"},{"alias_kind":"arxiv_version","alias_value":"2606.18938v1","created_at":"2026-06-19T16:11:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.18938","created_at":"2026-06-19T16:11:52Z"},{"alias_kind":"pith_short_12","alias_value":"FXP2E4O7YLH2","created_at":"2026-06-19T16:11:52Z"},{"alias_kind":"pith_short_16","alias_value":"FXP2E4O7YLH26RW7","created_at":"2026-06-19T16:11:52Z"},{"alias_kind":"pith_short_8","alias_value":"FXP2E4O7","created_at":"2026-06-19T16:11:52Z"}],"graph_snapshots":[{"event_id":"sha256:b66b3adde2e6611eef21be3f7711ed817d7dcd2be3a23aac79c136a24224669c","target":"graph","created_at":"2026-06-19T16:11:52Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.18938/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Since every modeling process in real-world situations is subject to errors, the study of the so-called shadowing property becomes highly relevant. This property allows for the identification of true orbits that closely follow a chain of trajectories in which some degree of approximation is introduced at each step. The objective of this paper is to establish a version of the Shadowing Theorem for vector fields governed by ordinary differential equations in the piecewise-smooth setting, where the dynamics alternate between distinct regimes, or on-off stages. First, we present an example showing ","authors_text":"Tiago Carvalho","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-06-17T11:21:34Z","title":"About the Shadowing Theorem for piecewise smooth vector fields with sliding motion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.18938","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:af3f9b1437168399e5ca0f641d05c43771d09d35265452958fb68870004d86ea","target":"record","created_at":"2026-06-19T16:11:52Z","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":"91593ec77da86b68a6e9f66825b3a045a9de2fd1f9f081b5978fbb22a9cca695","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-06-17T11:21:34Z","title_canon_sha256":"15685e614feb8c502421335bedd8b681d6c2491a0709ce9e77d25d3cc9eef713"},"schema_version":"1.0","source":{"id":"2606.18938","kind":"arxiv","version":1}},"canonical_sha256":"2ddfa271dfc2cfaf46dfdaa29a4d87414ab49099221675a9b9b825e4cd6eaddd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ddfa271dfc2cfaf46dfdaa29a4d87414ab49099221675a9b9b825e4cd6eaddd","first_computed_at":"2026-06-19T16:11:52.374488Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:11:52.374488Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PnlrLB3/xQOHcxuEE9vdtCLlUQUtgJUDQ/Oh4OcmUt+HtXm5HxqW+nXP6EKVw0xH4u+Dk/nwm8AX6eMGAb9wBA==","signature_status":"signed_v1","signed_at":"2026-06-19T16:11:52.374853Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.18938","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:af3f9b1437168399e5ca0f641d05c43771d09d35265452958fb68870004d86ea","sha256:b66b3adde2e6611eef21be3f7711ed817d7dcd2be3a23aac79c136a24224669c"],"state_sha256":"f89e66457ba9579d346af7a8e6725ac617ec8d9a80e483c6e463959ca2cc9a20"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HgUs3gDoVf5+P911Q8nVmKUOun2D5q1QVZSWadRmFY/Z1siyB7+L6f7ritHTDEqWlTO4YHo+d9qPk9FFhb2LDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T01:10:30.386873Z","bundle_sha256":"634738d557b8ef0ebe9328d22953f564801858b5ce12ea4264a97a03b97bea13"}}