{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:BNJNKYFEKUZD4ELYEJADVETETD","short_pith_number":"pith:BNJNKYFE","canonical_record":{"source":{"id":"2304.07834","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2023-04-16T17:02:04Z","cross_cats_sorted":[],"title_canon_sha256":"114e52870e3d7e32aced2f427ba08781627b1cbdb9439b542b0a87f1975e43b1","abstract_canon_sha256":"c054a1ad90f32feb5162b76b8c8c1468b26a9265287e8a875d7fb59c0467552f"},"schema_version":"1.0"},"canonical_sha256":"0b52d560a455323e117822403a926498c91f86ae7d95195b70b7d1d671f1c815","source":{"kind":"arxiv","id":"2304.07834","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2304.07834","created_at":"2026-07-05T06:01:25Z"},{"alias_kind":"arxiv_version","alias_value":"2304.07834v1","created_at":"2026-07-05T06:01:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.07834","created_at":"2026-07-05T06:01:25Z"},{"alias_kind":"pith_short_12","alias_value":"BNJNKYFEKUZD","created_at":"2026-07-05T06:01:25Z"},{"alias_kind":"pith_short_16","alias_value":"BNJNKYFEKUZD4ELY","created_at":"2026-07-05T06:01:25Z"},{"alias_kind":"pith_short_8","alias_value":"BNJNKYFE","created_at":"2026-07-05T06:01:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:BNJNKYFEKUZD4ELYEJADVETETD","target":"record","payload":{"canonical_record":{"source":{"id":"2304.07834","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2023-04-16T17:02:04Z","cross_cats_sorted":[],"title_canon_sha256":"114e52870e3d7e32aced2f427ba08781627b1cbdb9439b542b0a87f1975e43b1","abstract_canon_sha256":"c054a1ad90f32feb5162b76b8c8c1468b26a9265287e8a875d7fb59c0467552f"},"schema_version":"1.0"},"canonical_sha256":"0b52d560a455323e117822403a926498c91f86ae7d95195b70b7d1d671f1c815","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:01:25.934790Z","signature_b64":"j1kS7rtJiVU9M2iCXGWL8YwHqUdn0o6UozAVmHDRNNx1GyvXtuGIc0eE75BQh849MMIOkR7pouezs5f2THU4AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0b52d560a455323e117822403a926498c91f86ae7d95195b70b7d1d671f1c815","last_reissued_at":"2026-07-05T06:01:25.934370Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:01:25.934370Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2304.07834","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":"2026-07-05T06:01:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e5PiCHHOFKJ6UY2CAtKQTNn7oo2xHTKnr0x6avDlxkzMht2p3l2W87eibzZElvzsY+Mv+vcAKC3GKqB+fPi8AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T08:43:57.806431Z"},"content_sha256":"fe7f2f49c955ba4a5cc0590ef5352eb8de6d8eb718da2198c6dc7e66b68ac21c","schema_version":"1.0","event_id":"sha256:fe7f2f49c955ba4a5cc0590ef5352eb8de6d8eb718da2198c6dc7e66b68ac21c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:BNJNKYFEKUZD4ELYEJADVETETD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Open Maps Preserve Stability","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"James Schmidt","submitted_at":"2023-04-16T17:02:04Z","abstract_excerpt":"Stability is a fundamental notion in dynamical systems and control theory that, traditionally understood, describes asymptotic behavior of solutions around an equilibrium point. This notion may be characterized abstractly as continuity of a map associating to each point in a state-space the corresponding integral curve with specified initial condition. Interpreting stability as such permits a natural perspective of arbitrary trajectories as stable, irrespective of whether they are stationary or even bounded, so long as trajectories starting nearby stay nearby for all time.\n  While methods exis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.07834","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/2304.07834/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":"2026-07-05T06:01:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cGY7ufINgeEA/I79PKXLBsgL+CoYKMjElF/nyVAKSn5F2zyQ3lToh3nTPOkKM4L+6zgw5SqII49FafwswETFCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T08:43:57.806798Z"},"content_sha256":"064cc1bad93cb9b3c19df631751beb58605e35433b5f35b9263a58ee75b35f19","schema_version":"1.0","event_id":"sha256:064cc1bad93cb9b3c19df631751beb58605e35433b5f35b9263a58ee75b35f19"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BNJNKYFEKUZD4ELYEJADVETETD/bundle.json","state_url":"https://pith.science/pith/BNJNKYFEKUZD4ELYEJADVETETD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BNJNKYFEKUZD4ELYEJADVETETD/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":"2026-07-07T08:43:57Z","links":{"resolver":"https://pith.science/pith/BNJNKYFEKUZD4ELYEJADVETETD","bundle":"https://pith.science/pith/BNJNKYFEKUZD4ELYEJADVETETD/bundle.json","state":"https://pith.science/pith/BNJNKYFEKUZD4ELYEJADVETETD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BNJNKYFEKUZD4ELYEJADVETETD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:BNJNKYFEKUZD4ELYEJADVETETD","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":"c054a1ad90f32feb5162b76b8c8c1468b26a9265287e8a875d7fb59c0467552f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2023-04-16T17:02:04Z","title_canon_sha256":"114e52870e3d7e32aced2f427ba08781627b1cbdb9439b542b0a87f1975e43b1"},"schema_version":"1.0","source":{"id":"2304.07834","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2304.07834","created_at":"2026-07-05T06:01:25Z"},{"alias_kind":"arxiv_version","alias_value":"2304.07834v1","created_at":"2026-07-05T06:01:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.07834","created_at":"2026-07-05T06:01:25Z"},{"alias_kind":"pith_short_12","alias_value":"BNJNKYFEKUZD","created_at":"2026-07-05T06:01:25Z"},{"alias_kind":"pith_short_16","alias_value":"BNJNKYFEKUZD4ELY","created_at":"2026-07-05T06:01:25Z"},{"alias_kind":"pith_short_8","alias_value":"BNJNKYFE","created_at":"2026-07-05T06:01:25Z"}],"graph_snapshots":[{"event_id":"sha256:064cc1bad93cb9b3c19df631751beb58605e35433b5f35b9263a58ee75b35f19","target":"graph","created_at":"2026-07-05T06:01:25Z","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/2304.07834/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Stability is a fundamental notion in dynamical systems and control theory that, traditionally understood, describes asymptotic behavior of solutions around an equilibrium point. This notion may be characterized abstractly as continuity of a map associating to each point in a state-space the corresponding integral curve with specified initial condition. Interpreting stability as such permits a natural perspective of arbitrary trajectories as stable, irrespective of whether they are stationary or even bounded, so long as trajectories starting nearby stay nearby for all time.\n  While methods exis","authors_text":"James Schmidt","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2023-04-16T17:02:04Z","title":"Open Maps Preserve Stability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.07834","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:fe7f2f49c955ba4a5cc0590ef5352eb8de6d8eb718da2198c6dc7e66b68ac21c","target":"record","created_at":"2026-07-05T06:01:25Z","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":"c054a1ad90f32feb5162b76b8c8c1468b26a9265287e8a875d7fb59c0467552f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2023-04-16T17:02:04Z","title_canon_sha256":"114e52870e3d7e32aced2f427ba08781627b1cbdb9439b542b0a87f1975e43b1"},"schema_version":"1.0","source":{"id":"2304.07834","kind":"arxiv","version":1}},"canonical_sha256":"0b52d560a455323e117822403a926498c91f86ae7d95195b70b7d1d671f1c815","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0b52d560a455323e117822403a926498c91f86ae7d95195b70b7d1d671f1c815","first_computed_at":"2026-07-05T06:01:25.934370Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:01:25.934370Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j1kS7rtJiVU9M2iCXGWL8YwHqUdn0o6UozAVmHDRNNx1GyvXtuGIc0eE75BQh849MMIOkR7pouezs5f2THU4AQ==","signature_status":"signed_v1","signed_at":"2026-07-05T06:01:25.934790Z","signed_message":"canonical_sha256_bytes"},"source_id":"2304.07834","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fe7f2f49c955ba4a5cc0590ef5352eb8de6d8eb718da2198c6dc7e66b68ac21c","sha256:064cc1bad93cb9b3c19df631751beb58605e35433b5f35b9263a58ee75b35f19"],"state_sha256":"f7dffa54a023820884170219d736d4c7dbf441288b59cd5f883fe1c7a89781c5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kd3wRiZ2xBKoSEA5ADcChvo8ZVG9TLgOFwV/QnaKKkJWsSXj9R3dmB/MmCSpFTD5U4FpLSvWPwSgne9DiPF9CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T08:43:57.808701Z","bundle_sha256":"2f12af502af7ee7b7092ec8172331a71db096178075de3344564d5c6f11ebbdd"}}