{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:KCRCEKKSS6HTB6QHVPPFU5ZAQO","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":"d17fe6067a6325b1ea514ff283cf5b8f78c5b590a9b8c7551e7c7180e8f6d515","cross_cats_sorted":["math.DS"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.SG","submitted_at":"2025-07-18T13:59:00Z","title_canon_sha256":"34a9d813434118ca36d2d3d2ca60a993a2537f7171fae29f40bc5ecc61aca222"},"schema_version":"1.0","source":{"id":"2507.13924","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.13924","created_at":"2026-07-05T11:53:05Z"},{"alias_kind":"arxiv_version","alias_value":"2507.13924v2","created_at":"2026-07-05T11:53:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.13924","created_at":"2026-07-05T11:53:05Z"},{"alias_kind":"pith_short_12","alias_value":"KCRCEKKSS6HT","created_at":"2026-07-05T11:53:05Z"},{"alias_kind":"pith_short_16","alias_value":"KCRCEKKSS6HTB6QH","created_at":"2026-07-05T11:53:05Z"},{"alias_kind":"pith_short_8","alias_value":"KCRCEKKS","created_at":"2026-07-05T11:53:05Z"}],"graph_snapshots":[{"event_id":"sha256:1b65e692594d4f13cb5acd675c54620ce9fe755ff45a1615c52fe1f9c1d6ceed","target":"graph","created_at":"2026-07-05T11:53:05Z","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/2507.13924/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In earlier work, we constructed counterexamples to Lagrangian Poincar\\'e recurrence for many toric symplectic four manifolds. Here we provide a few more examples extending the family of counterexamples to include all non-monotone toric symplectic four manifolds.\n  This work has been incorporated into arXiv:2506.23754v2 Section 3.3","authors_text":"Joel Schmitz","cross_cats":["math.DS"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.SG","submitted_at":"2025-07-18T13:59:00Z","title":"More counterexamples to Lagrangian Poincar\\'e recurrence in dimension four"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.13924","kind":"arxiv","version":2},"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:abb0c24e2c2547a24e23dfb18e5e4534fc9f71bfe6cdb16d00a9a3712bd93110","target":"record","created_at":"2026-07-05T11:53:05Z","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":"d17fe6067a6325b1ea514ff283cf5b8f78c5b590a9b8c7551e7c7180e8f6d515","cross_cats_sorted":["math.DS"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.SG","submitted_at":"2025-07-18T13:59:00Z","title_canon_sha256":"34a9d813434118ca36d2d3d2ca60a993a2537f7171fae29f40bc5ecc61aca222"},"schema_version":"1.0","source":{"id":"2507.13924","kind":"arxiv","version":2}},"canonical_sha256":"50a2222952978f30fa07abde5a772083afcdfb004142e173ec801926a5a9997c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"50a2222952978f30fa07abde5a772083afcdfb004142e173ec801926a5a9997c","first_computed_at":"2026-07-05T11:53:05.420878Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:53:05.420878Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/YKLHFsWYN5uW+w+lbqSd6ncnNs+kr+D06QhrOW7QndJjLItiD5EkMkNBWhZGptQv7IrVOaktahhtFhzUlZFCA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:53:05.421306Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.13924","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:abb0c24e2c2547a24e23dfb18e5e4534fc9f71bfe6cdb16d00a9a3712bd93110","sha256:1b65e692594d4f13cb5acd675c54620ce9fe755ff45a1615c52fe1f9c1d6ceed"],"state_sha256":"86d886e6181720194f6e332307426f68fd5cdf33da6bc7ba1cbcaec991f6d82a"}