{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:GYJGYVKLKVENQQNZJWNCMTIXYA","short_pith_number":"pith:GYJGYVKL","canonical_record":{"source":{"id":"1508.00270","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-08-02T18:49:40Z","cross_cats_sorted":[],"title_canon_sha256":"634b610dd0909a2e8f106c5f3df730923f04700b447da99deca610fe2a1d9e7d","abstract_canon_sha256":"d53c61cdd57fa48d867664306df491bd0124bb404f26f390de554eb96a6ac6e0"},"schema_version":"1.0"},"canonical_sha256":"36126c554b5548d841b94d9a264d17c03fd7fbee421e1066df3cecb5add798aa","source":{"kind":"arxiv","id":"1508.00270","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.00270","created_at":"2026-05-18T01:26:57Z"},{"alias_kind":"arxiv_version","alias_value":"1508.00270v1","created_at":"2026-05-18T01:26:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.00270","created_at":"2026-05-18T01:26:57Z"},{"alias_kind":"pith_short_12","alias_value":"GYJGYVKLKVEN","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GYJGYVKLKVENQQNZ","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GYJGYVKL","created_at":"2026-05-18T12:29:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:GYJGYVKLKVENQQNZJWNCMTIXYA","target":"record","payload":{"canonical_record":{"source":{"id":"1508.00270","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-08-02T18:49:40Z","cross_cats_sorted":[],"title_canon_sha256":"634b610dd0909a2e8f106c5f3df730923f04700b447da99deca610fe2a1d9e7d","abstract_canon_sha256":"d53c61cdd57fa48d867664306df491bd0124bb404f26f390de554eb96a6ac6e0"},"schema_version":"1.0"},"canonical_sha256":"36126c554b5548d841b94d9a264d17c03fd7fbee421e1066df3cecb5add798aa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:26:57.369735Z","signature_b64":"42URHWPdv//QrT1sedENLeK6vu9l4x5Qp3cvfyudx+cF9iBdmtJwUcBmQxciVBeVF0shJyT3HFtzNZota+v5Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"36126c554b5548d841b94d9a264d17c03fd7fbee421e1066df3cecb5add798aa","last_reissued_at":"2026-05-18T01:26:57.369071Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:26:57.369071Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.00270","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":"2026-05-18T01:26:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d7ZwMFN0C223lswuU+yppwoWtlHxA9pfXUIM9Pq2H1WN1gZm8VOgdONs89pVVM68CT+z7HUp6qBllsQxGUM/Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T08:37:52.194905Z"},"content_sha256":"79dd90a9392ad825284eea0797b7ee4cbbfda454f413ac0953adb8b73bc4acf8","schema_version":"1.0","event_id":"sha256:79dd90a9392ad825284eea0797b7ee4cbbfda454f413ac0953adb8b73bc4acf8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:GYJGYVKLKVENQQNZJWNCMTIXYA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Permanence and almost periodic solutions for a single-species system with impulsive effects on time scales","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Bing Li, Pan Wang, Yongkun Li","submitted_at":"2015-08-02T18:49:40Z","abstract_excerpt":"In this paper, we first propose a single-species system with impulsive effects on time scales and by establishing some new comparison theorems of impulsive dynamic equations on time scales, we obtain sufficient conditions to guarantee the permanence of the system. Then we prove a Massera type theorem for impulsive dynamic equations on time scales and based on this theorem, we establish a criterion for the existence and uniformly asymptotic stability of unique positive almost periodic solution of the system. Finally, we give an example to show the feasibility of our main results. Our example al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00270","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":"2026-05-18T01:26:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+ncoFepvdmmzzwfiEABfdroTCqZMH+AyH7mU541WmqcoRVRosrtwF3b2gzRnR0Vij3DhK73ZGYkuvQ+4mmtRCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T08:37:52.195607Z"},"content_sha256":"2e0f281b57b463a41ac3bf8f1e38f3df21e16c1a1f7bc9ae665f259df85e81bd","schema_version":"1.0","event_id":"sha256:2e0f281b57b463a41ac3bf8f1e38f3df21e16c1a1f7bc9ae665f259df85e81bd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GYJGYVKLKVENQQNZJWNCMTIXYA/bundle.json","state_url":"https://pith.science/pith/GYJGYVKLKVENQQNZJWNCMTIXYA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GYJGYVKLKVENQQNZJWNCMTIXYA/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":"2026-06-06T08:37:52Z","links":{"resolver":"https://pith.science/pith/GYJGYVKLKVENQQNZJWNCMTIXYA","bundle":"https://pith.science/pith/GYJGYVKLKVENQQNZJWNCMTIXYA/bundle.json","state":"https://pith.science/pith/GYJGYVKLKVENQQNZJWNCMTIXYA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GYJGYVKLKVENQQNZJWNCMTIXYA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:GYJGYVKLKVENQQNZJWNCMTIXYA","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":"d53c61cdd57fa48d867664306df491bd0124bb404f26f390de554eb96a6ac6e0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-08-02T18:49:40Z","title_canon_sha256":"634b610dd0909a2e8f106c5f3df730923f04700b447da99deca610fe2a1d9e7d"},"schema_version":"1.0","source":{"id":"1508.00270","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.00270","created_at":"2026-05-18T01:26:57Z"},{"alias_kind":"arxiv_version","alias_value":"1508.00270v1","created_at":"2026-05-18T01:26:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.00270","created_at":"2026-05-18T01:26:57Z"},{"alias_kind":"pith_short_12","alias_value":"GYJGYVKLKVEN","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GYJGYVKLKVENQQNZ","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GYJGYVKL","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:2e0f281b57b463a41ac3bf8f1e38f3df21e16c1a1f7bc9ae665f259df85e81bd","target":"graph","created_at":"2026-05-18T01:26:57Z","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":"In this paper, we first propose a single-species system with impulsive effects on time scales and by establishing some new comparison theorems of impulsive dynamic equations on time scales, we obtain sufficient conditions to guarantee the permanence of the system. Then we prove a Massera type theorem for impulsive dynamic equations on time scales and based on this theorem, we establish a criterion for the existence and uniformly asymptotic stability of unique positive almost periodic solution of the system. Finally, we give an example to show the feasibility of our main results. Our example al","authors_text":"Bing Li, Pan Wang, Yongkun Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-08-02T18:49:40Z","title":"Permanence and almost periodic solutions for a single-species system with impulsive effects on time scales"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00270","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":"sha256:79dd90a9392ad825284eea0797b7ee4cbbfda454f413ac0953adb8b73bc4acf8","target":"record","created_at":"2026-05-18T01:26:57Z","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":"d53c61cdd57fa48d867664306df491bd0124bb404f26f390de554eb96a6ac6e0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-08-02T18:49:40Z","title_canon_sha256":"634b610dd0909a2e8f106c5f3df730923f04700b447da99deca610fe2a1d9e7d"},"schema_version":"1.0","source":{"id":"1508.00270","kind":"arxiv","version":1}},"canonical_sha256":"36126c554b5548d841b94d9a264d17c03fd7fbee421e1066df3cecb5add798aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"36126c554b5548d841b94d9a264d17c03fd7fbee421e1066df3cecb5add798aa","first_computed_at":"2026-05-18T01:26:57.369071Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:26:57.369071Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"42URHWPdv//QrT1sedENLeK6vu9l4x5Qp3cvfyudx+cF9iBdmtJwUcBmQxciVBeVF0shJyT3HFtzNZota+v5Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T01:26:57.369735Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.00270","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:79dd90a9392ad825284eea0797b7ee4cbbfda454f413ac0953adb8b73bc4acf8","sha256:2e0f281b57b463a41ac3bf8f1e38f3df21e16c1a1f7bc9ae665f259df85e81bd"],"state_sha256":"6bae14012d85b079a8a3e8f382fae82426b5dcf17111ac0ee78aba32e73b62ba"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BBTICbnrSXbXACoXkUbGJ7eBNoEy9OJ4IBSkGPrPTULq1GgaPo2VR2zlGW/bdV1UaUiTLU664TmV4Xjgk2TTAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T08:37:52.199334Z","bundle_sha256":"109e6dcbbd2635945439e42626631b76b3c69780fc37d31290840d2836c7b7f0"}}