{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:SFWVFFPLFQBJY2KYZ5IJNTTERH","short_pith_number":"pith:SFWVFFPL","canonical_record":{"source":{"id":"2303.00967","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2023-03-02T05:04:02Z","cross_cats_sorted":[],"title_canon_sha256":"67800d85fe9fa28c140b3ad3a9b56fb94fd315b00de29afe94797de448f212a6","abstract_canon_sha256":"f2766a5e30c81939b3034e609532ed08f8c0d8304c1eb449a90dd8815259e8fd"},"schema_version":"1.0"},"canonical_sha256":"916d5295eb2c029c6958cf5096ce6489f60ce864c4d4bb3f19500c059e6a79b1","source":{"kind":"arxiv","id":"2303.00967","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.00967","created_at":"2026-07-05T05:47:24Z"},{"alias_kind":"arxiv_version","alias_value":"2303.00967v1","created_at":"2026-07-05T05:47:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.00967","created_at":"2026-07-05T05:47:24Z"},{"alias_kind":"pith_short_12","alias_value":"SFWVFFPLFQBJ","created_at":"2026-07-05T05:47:24Z"},{"alias_kind":"pith_short_16","alias_value":"SFWVFFPLFQBJY2KY","created_at":"2026-07-05T05:47:24Z"},{"alias_kind":"pith_short_8","alias_value":"SFWVFFPL","created_at":"2026-07-05T05:47:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:SFWVFFPLFQBJY2KYZ5IJNTTERH","target":"record","payload":{"canonical_record":{"source":{"id":"2303.00967","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2023-03-02T05:04:02Z","cross_cats_sorted":[],"title_canon_sha256":"67800d85fe9fa28c140b3ad3a9b56fb94fd315b00de29afe94797de448f212a6","abstract_canon_sha256":"f2766a5e30c81939b3034e609532ed08f8c0d8304c1eb449a90dd8815259e8fd"},"schema_version":"1.0"},"canonical_sha256":"916d5295eb2c029c6958cf5096ce6489f60ce864c4d4bb3f19500c059e6a79b1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:47:24.951705Z","signature_b64":"PpER29NocleNuKFRBazxks3CHvDyY62Lt3kUmSPSFqdc4bMbmxzytAckSnfqIFP4s4TRDm6JqWN7RCQhbqt4CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"916d5295eb2c029c6958cf5096ce6489f60ce864c4d4bb3f19500c059e6a79b1","last_reissued_at":"2026-07-05T05:47:24.951257Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:47:24.951257Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2303.00967","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":"2026-07-05T05:47:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+BI/ftU+grorFot77NOGSWbTQloat2mIC3TMuJIUPCCvPK4xd0LV7MNnW3u2ca0ofaUDxUBcqSIGIk22Cv8bDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-13T22:17:49.130537Z"},"content_sha256":"28fbf4ed40e4073f3cf486e31e5b525e4c00c1aeddb5b9db65780610e867ad25","schema_version":"1.0","event_id":"sha256:28fbf4ed40e4073f3cf486e31e5b525e4c00c1aeddb5b9db65780610e867ad25"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:SFWVFFPLFQBJY2KYZ5IJNTTERH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stability switching in Lotka-Volterra and Ricker-type predator-prey systems with arbitrary step size","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Kate J. Helmstedt, Kevin Burrage, Pamela M. Burrage, Shamika P. Kekulthotuwage Don","submitted_at":"2023-03-02T05:04:02Z","abstract_excerpt":"Dynamical properties of numerically approximated discrete systems may become inconsistent with those of the corresponding continuous-time system. We present a qualitative analysis of the dynamical properties of two species Lotka-Volterra and Ricker-type predator-prey systems under discrete and continuous settings. By creating an arbitrary time discretisation, we obtain stability conditions that preserve the characteristics of continuous-time models and their numerically approximated systems. Here, we show that even small changes to some of the model parameters may alter the system dynamics unl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.00967","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/2303.00967/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":"2026-07-05T05:47:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lvkiI5xzQ2P4VgKPu1xObDxSAFTQAWeJ/9gND1O5lGsMaUqcv+HN6BX1XxG61bOaoyYVqdyyhvx5qNd98P/CCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-13T22:17:49.130929Z"},"content_sha256":"fd1aa2f39bd69ecaaa384641e5515d516aaae3756dd2135bd589413e8f2a0211","schema_version":"1.0","event_id":"sha256:fd1aa2f39bd69ecaaa384641e5515d516aaae3756dd2135bd589413e8f2a0211"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SFWVFFPLFQBJY2KYZ5IJNTTERH/bundle.json","state_url":"https://pith.science/pith/SFWVFFPLFQBJY2KYZ5IJNTTERH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SFWVFFPLFQBJY2KYZ5IJNTTERH/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":"2026-07-13T22:17:49Z","links":{"resolver":"https://pith.science/pith/SFWVFFPLFQBJY2KYZ5IJNTTERH","bundle":"https://pith.science/pith/SFWVFFPLFQBJY2KYZ5IJNTTERH/bundle.json","state":"https://pith.science/pith/SFWVFFPLFQBJY2KYZ5IJNTTERH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SFWVFFPLFQBJY2KYZ5IJNTTERH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:SFWVFFPLFQBJY2KYZ5IJNTTERH","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":"f2766a5e30c81939b3034e609532ed08f8c0d8304c1eb449a90dd8815259e8fd","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2023-03-02T05:04:02Z","title_canon_sha256":"67800d85fe9fa28c140b3ad3a9b56fb94fd315b00de29afe94797de448f212a6"},"schema_version":"1.0","source":{"id":"2303.00967","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.00967","created_at":"2026-07-05T05:47:24Z"},{"alias_kind":"arxiv_version","alias_value":"2303.00967v1","created_at":"2026-07-05T05:47:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.00967","created_at":"2026-07-05T05:47:24Z"},{"alias_kind":"pith_short_12","alias_value":"SFWVFFPLFQBJ","created_at":"2026-07-05T05:47:24Z"},{"alias_kind":"pith_short_16","alias_value":"SFWVFFPLFQBJY2KY","created_at":"2026-07-05T05:47:24Z"},{"alias_kind":"pith_short_8","alias_value":"SFWVFFPL","created_at":"2026-07-05T05:47:24Z"}],"graph_snapshots":[{"event_id":"sha256:fd1aa2f39bd69ecaaa384641e5515d516aaae3756dd2135bd589413e8f2a0211","target":"graph","created_at":"2026-07-05T05:47:24Z","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/2303.00967/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Dynamical properties of numerically approximated discrete systems may become inconsistent with those of the corresponding continuous-time system. We present a qualitative analysis of the dynamical properties of two species Lotka-Volterra and Ricker-type predator-prey systems under discrete and continuous settings. By creating an arbitrary time discretisation, we obtain stability conditions that preserve the characteristics of continuous-time models and their numerically approximated systems. Here, we show that even small changes to some of the model parameters may alter the system dynamics unl","authors_text":"Kate J. Helmstedt, Kevin Burrage, Pamela M. Burrage, Shamika P. Kekulthotuwage Don","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2023-03-02T05:04:02Z","title":"Stability switching in Lotka-Volterra and Ricker-type predator-prey systems with arbitrary step size"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.00967","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":"sha256:28fbf4ed40e4073f3cf486e31e5b525e4c00c1aeddb5b9db65780610e867ad25","target":"record","created_at":"2026-07-05T05:47:24Z","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":"f2766a5e30c81939b3034e609532ed08f8c0d8304c1eb449a90dd8815259e8fd","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2023-03-02T05:04:02Z","title_canon_sha256":"67800d85fe9fa28c140b3ad3a9b56fb94fd315b00de29afe94797de448f212a6"},"schema_version":"1.0","source":{"id":"2303.00967","kind":"arxiv","version":1}},"canonical_sha256":"916d5295eb2c029c6958cf5096ce6489f60ce864c4d4bb3f19500c059e6a79b1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"916d5295eb2c029c6958cf5096ce6489f60ce864c4d4bb3f19500c059e6a79b1","first_computed_at":"2026-07-05T05:47:24.951257Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:47:24.951257Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PpER29NocleNuKFRBazxks3CHvDyY62Lt3kUmSPSFqdc4bMbmxzytAckSnfqIFP4s4TRDm6JqWN7RCQhbqt4CQ==","signature_status":"signed_v1","signed_at":"2026-07-05T05:47:24.951705Z","signed_message":"canonical_sha256_bytes"},"source_id":"2303.00967","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:28fbf4ed40e4073f3cf486e31e5b525e4c00c1aeddb5b9db65780610e867ad25","sha256:fd1aa2f39bd69ecaaa384641e5515d516aaae3756dd2135bd589413e8f2a0211"],"state_sha256":"1b862b8716a45e3bf2f76a79284c2d0fa9bcada36be05563dc23a6aa9adfc51e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5sG925S+MSdTEV7gyK5nDAuLLLH60BHGykFU+m+3C8MSNM/e/daCjJuvAD2Dm9plwFrt3vsIHosXfTG1wNGqBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-13T22:17:49.133150Z","bundle_sha256":"eec0824d58c115dcf6b653e21320cd7d1b268449287d11640a2d3cb766f43219"}}