{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:EMTF6V45SACFHOI7Y5L4CGNPJD","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":"cbc6b2b4df7c045a8391437ea83c288fa7b5539e591e19b2df05ddf9b264ada7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-05-27T00:54:54Z","title_canon_sha256":"fa35d996dc9d7701326e02cc74c4ecf32a7ea5d6e1e944a8288f4a22b9d25a0b"},"schema_version":"1.0","source":{"id":"2605.27806","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.27806","created_at":"2026-05-28T01:04:49Z"},{"alias_kind":"arxiv_version","alias_value":"2605.27806v1","created_at":"2026-05-28T01:04:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.27806","created_at":"2026-05-28T01:04:49Z"},{"alias_kind":"pith_short_12","alias_value":"EMTF6V45SACF","created_at":"2026-05-28T01:04:49Z"},{"alias_kind":"pith_short_16","alias_value":"EMTF6V45SACFHOI7","created_at":"2026-05-28T01:04:49Z"},{"alias_kind":"pith_short_8","alias_value":"EMTF6V45","created_at":"2026-05-28T01:04:49Z"}],"graph_snapshots":[{"event_id":"sha256:bdfd0c93b0f215e81fbbc9aab554a719dd5cda839c80a28bb2874cc9c9096e37","target":"graph","created_at":"2026-05-28T01:04:49Z","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/2605.27806/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work, we formulate a two-species Lotka--Volterra competition model on time scales. To derive the global dynamics of solutions of this planar model, we introduce a dynamic augmented phase plane analysis that extends the traditional phase plane analysis known to be a powerful tool in the analysis of planar differential equations. In the case of a constant graininess, the method is consistent with the augmented phase portrait introduced for the discrete space. However, for non-constant graininess, this augmented phase plane is time-dependent and therefore dynamic. Despite the dynamic char","authors_text":"Gail S. K. Wolkowicz, Sabrina Streipert","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-05-27T00:54:54Z","title":"Phase Plane Analysis on Time Scales for a Lotka-Volterra Competition Model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.27806","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":"sha256:175855637161b7aa5592f21976c269b6f071abaa9d39231c583e05644c3efe3c","target":"record","created_at":"2026-05-28T01:04:49Z","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":"cbc6b2b4df7c045a8391437ea83c288fa7b5539e591e19b2df05ddf9b264ada7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-05-27T00:54:54Z","title_canon_sha256":"fa35d996dc9d7701326e02cc74c4ecf32a7ea5d6e1e944a8288f4a22b9d25a0b"},"schema_version":"1.0","source":{"id":"2605.27806","kind":"arxiv","version":1}},"canonical_sha256":"23265f579d900453b91fc757c119af48da6fcad9490ffc4009c5ef7f4756798d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"23265f579d900453b91fc757c119af48da6fcad9490ffc4009c5ef7f4756798d","first_computed_at":"2026-05-28T01:04:49.166788Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-28T01:04:49.166788Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VPRGo1xFpWkYEBIVFRGKOl05ipSOj24CC8o/I8Ary4OmUpjO4wNSkMH68Gk6Kkqykm4i37HWtbOYLtqOJE8KCw==","signature_status":"signed_v1","signed_at":"2026-05-28T01:04:49.167180Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.27806","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:175855637161b7aa5592f21976c269b6f071abaa9d39231c583e05644c3efe3c","sha256:bdfd0c93b0f215e81fbbc9aab554a719dd5cda839c80a28bb2874cc9c9096e37"],"state_sha256":"67fc78aa3eefb65836e9b08fb6b54dff4669d0aa4f28ba1e14bac41b85759065"}