{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:Y5I6IIED54D5OMBY7KYXO5XZC6","short_pith_number":"pith:Y5I6IIED","canonical_record":{"source":{"id":"2306.00701","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-06-01T14:10:43Z","cross_cats_sorted":[],"title_canon_sha256":"8c562faab2aab291aa88b401623b1cae668ba3021f9e8820c4033d7835405099","abstract_canon_sha256":"adc6b90644d7f93cec30f20c1018c371ef6b928ff5a5dabd7be5c215e3feeddf"},"schema_version":"1.0"},"canonical_sha256":"c751e42083ef07d73038fab17776f917a85584b0c2d58df1b030d233b8f5269b","source":{"kind":"arxiv","id":"2306.00701","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2306.00701","created_at":"2026-07-05T06:16:29Z"},{"alias_kind":"arxiv_version","alias_value":"2306.00701v1","created_at":"2026-07-05T06:16:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.00701","created_at":"2026-07-05T06:16:29Z"},{"alias_kind":"pith_short_12","alias_value":"Y5I6IIED54D5","created_at":"2026-07-05T06:16:29Z"},{"alias_kind":"pith_short_16","alias_value":"Y5I6IIED54D5OMBY","created_at":"2026-07-05T06:16:29Z"},{"alias_kind":"pith_short_8","alias_value":"Y5I6IIED","created_at":"2026-07-05T06:16:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:Y5I6IIED54D5OMBY7KYXO5XZC6","target":"record","payload":{"canonical_record":{"source":{"id":"2306.00701","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-06-01T14:10:43Z","cross_cats_sorted":[],"title_canon_sha256":"8c562faab2aab291aa88b401623b1cae668ba3021f9e8820c4033d7835405099","abstract_canon_sha256":"adc6b90644d7f93cec30f20c1018c371ef6b928ff5a5dabd7be5c215e3feeddf"},"schema_version":"1.0"},"canonical_sha256":"c751e42083ef07d73038fab17776f917a85584b0c2d58df1b030d233b8f5269b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:16:29.974600Z","signature_b64":"2/DgewfaOd8ToAaZnm1mdSUcR9rA+hHw6l9zMOC1QPYCn1kCg6Xp47/hzD7Npbg/aqW2FU8XXQhrS2n8TuNfDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c751e42083ef07d73038fab17776f917a85584b0c2d58df1b030d233b8f5269b","last_reissued_at":"2026-07-05T06:16:29.974014Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:16:29.974014Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2306.00701","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":"2026-07-05T06:16:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w3dkc/jBLYps1jKObXjY+EIaA22WSSl7RsW2LSuK7HOTEhbUggh+FIwH48RVhVz8YBsdazUrV/G90qtwWLGNCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T06:39:53.649986Z"},"content_sha256":"b7db9191718a6a1f8fcdfc52b16ff4ceda2f09c290e0bb5fce29f99e1d512f4b","schema_version":"1.0","event_id":"sha256:b7db9191718a6a1f8fcdfc52b16ff4ceda2f09c290e0bb5fce29f99e1d512f4b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:Y5I6IIED54D5OMBY7KYXO5XZC6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Traveling Waves of Modified Leslie-Gower Predator-prey Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hongliang Li, Min Zhao, Rong Yuan","submitted_at":"2023-06-01T14:10:43Z","abstract_excerpt":"The spreading phenomena in modified Leslie-Gower reaction-diffusion predator-prey systems are the topic of this paper. We mainly study the existence of two different types of traveling waves. Be specific, with the aid of the upper and lower solutions method, we establish the existence of traveling wave connecting the prey-present state and the coexistence state or the prey-present state and the prey-free state by constructing different and appropriate Lyapunov functions. Moreover, for traveling wave connecting the prey-present state and the prey-free state, we gain more monotonicity informatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.00701","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/2306.00701/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":"2026-07-05T06:16:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gbOK7hUa3Mos7/ABvuhmjSsrcBQ1k9gnx79j0TpSH5dW+ZPczQEZ/I9hu+mT74cPbmyb7XB3eZGmlpAVqDqMCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-07T06:39:53.650579Z"},"content_sha256":"564dc3fa0236bfb6cff7bffccfa0111ab4ac886932ace9d929252965ddb88a92","schema_version":"1.0","event_id":"sha256:564dc3fa0236bfb6cff7bffccfa0111ab4ac886932ace9d929252965ddb88a92"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y5I6IIED54D5OMBY7KYXO5XZC6/bundle.json","state_url":"https://pith.science/pith/Y5I6IIED54D5OMBY7KYXO5XZC6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y5I6IIED54D5OMBY7KYXO5XZC6/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":"2026-08-07T06:39:53Z","links":{"resolver":"https://pith.science/pith/Y5I6IIED54D5OMBY7KYXO5XZC6","bundle":"https://pith.science/pith/Y5I6IIED54D5OMBY7KYXO5XZC6/bundle.json","state":"https://pith.science/pith/Y5I6IIED54D5OMBY7KYXO5XZC6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y5I6IIED54D5OMBY7KYXO5XZC6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:Y5I6IIED54D5OMBY7KYXO5XZC6","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":"adc6b90644d7f93cec30f20c1018c371ef6b928ff5a5dabd7be5c215e3feeddf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-06-01T14:10:43Z","title_canon_sha256":"8c562faab2aab291aa88b401623b1cae668ba3021f9e8820c4033d7835405099"},"schema_version":"1.0","source":{"id":"2306.00701","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2306.00701","created_at":"2026-07-05T06:16:29Z"},{"alias_kind":"arxiv_version","alias_value":"2306.00701v1","created_at":"2026-07-05T06:16:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.00701","created_at":"2026-07-05T06:16:29Z"},{"alias_kind":"pith_short_12","alias_value":"Y5I6IIED54D5","created_at":"2026-07-05T06:16:29Z"},{"alias_kind":"pith_short_16","alias_value":"Y5I6IIED54D5OMBY","created_at":"2026-07-05T06:16:29Z"},{"alias_kind":"pith_short_8","alias_value":"Y5I6IIED","created_at":"2026-07-05T06:16:29Z"}],"graph_snapshots":[{"event_id":"sha256:564dc3fa0236bfb6cff7bffccfa0111ab4ac886932ace9d929252965ddb88a92","target":"graph","created_at":"2026-07-05T06:16:29Z","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/2306.00701/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The spreading phenomena in modified Leslie-Gower reaction-diffusion predator-prey systems are the topic of this paper. We mainly study the existence of two different types of traveling waves. Be specific, with the aid of the upper and lower solutions method, we establish the existence of traveling wave connecting the prey-present state and the coexistence state or the prey-present state and the prey-free state by constructing different and appropriate Lyapunov functions. Moreover, for traveling wave connecting the prey-present state and the prey-free state, we gain more monotonicity informatio","authors_text":"Hongliang Li, Min Zhao, Rong Yuan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-06-01T14:10:43Z","title":"Traveling Waves of Modified Leslie-Gower Predator-prey Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.00701","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:b7db9191718a6a1f8fcdfc52b16ff4ceda2f09c290e0bb5fce29f99e1d512f4b","target":"record","created_at":"2026-07-05T06:16:29Z","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":"adc6b90644d7f93cec30f20c1018c371ef6b928ff5a5dabd7be5c215e3feeddf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-06-01T14:10:43Z","title_canon_sha256":"8c562faab2aab291aa88b401623b1cae668ba3021f9e8820c4033d7835405099"},"schema_version":"1.0","source":{"id":"2306.00701","kind":"arxiv","version":1}},"canonical_sha256":"c751e42083ef07d73038fab17776f917a85584b0c2d58df1b030d233b8f5269b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c751e42083ef07d73038fab17776f917a85584b0c2d58df1b030d233b8f5269b","first_computed_at":"2026-07-05T06:16:29.974014Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:16:29.974014Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2/DgewfaOd8ToAaZnm1mdSUcR9rA+hHw6l9zMOC1QPYCn1kCg6Xp47/hzD7Npbg/aqW2FU8XXQhrS2n8TuNfDg==","signature_status":"signed_v1","signed_at":"2026-07-05T06:16:29.974600Z","signed_message":"canonical_sha256_bytes"},"source_id":"2306.00701","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b7db9191718a6a1f8fcdfc52b16ff4ceda2f09c290e0bb5fce29f99e1d512f4b","sha256:564dc3fa0236bfb6cff7bffccfa0111ab4ac886932ace9d929252965ddb88a92"],"state_sha256":"df227184a64ce6b93e568a7bed837e525f0cc9c0924159b9e7b59792c5f8cd5b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GNBLb4NqbpKKpZ3LJpnbbAXnxxu5GPgqxGZSromLBLEmv8fER54lxXJFdMU7Jp6svNmDAxU2QsaGz2gIEFPfAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-07T06:39:53.654675Z","bundle_sha256":"0a05fc56a5f363e45ed42288191fd0f5bdc8f76f3410ef572b4983ea3a2ec189"}}