{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:XTLFNBMZG4T3PKWIDBNJCC6QXP","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":"c740b6b049adccea92bdd9b397effb2725fba5b379c8c1bf88fae197d777ba97","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-07-27T11:18:14Z","title_canon_sha256":"aff6157b1cb8059fd558d24b192b58465244343f5243dd5b32034c5af8180a2c"},"schema_version":"1.0","source":{"id":"1807.10536","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.10536","created_at":"2026-05-18T00:09:40Z"},{"alias_kind":"arxiv_version","alias_value":"1807.10536v1","created_at":"2026-05-18T00:09:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.10536","created_at":"2026-05-18T00:09:40Z"},{"alias_kind":"pith_short_12","alias_value":"XTLFNBMZG4T3","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XTLFNBMZG4T3PKWI","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XTLFNBMZ","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:840723947ad120fe1ea360ec9901de4cd96f0907ebb4f1d438955d0a0c377fca","target":"graph","created_at":"2026-05-18T00:09:40Z","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":"We investigate the internal observability of the wave equation with Dirichlet boundary conditions in a triangular domain. More precisely, the domain taken into exam is the half of the equilateral triangle. Our approach is based on Fourier analysis and on tessellation theory: by means of a suitable tiling of the rectangle, we extend earlier observability results in the rectangle to the case of a triangular domain. The paper includes a general result relating problems in general domains to their tiles, and a discussion of the triangular case. As an application, we provide an estimation of the ob","authors_text":"Anna Chiara Lai, Paola Loreti, Vilmos Komornik","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-07-27T11:18:14Z","title":"Internal observability of the wave equation in a triangular domain"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.10536","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:d5e8a8b7fb924be9a6d5547e683169668df92af208a2f3d76c3a431b3b194467","target":"record","created_at":"2026-05-18T00:09:40Z","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":"c740b6b049adccea92bdd9b397effb2725fba5b379c8c1bf88fae197d777ba97","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-07-27T11:18:14Z","title_canon_sha256":"aff6157b1cb8059fd558d24b192b58465244343f5243dd5b32034c5af8180a2c"},"schema_version":"1.0","source":{"id":"1807.10536","kind":"arxiv","version":1}},"canonical_sha256":"bcd65685993727b7aac8185a910bd0bbfc2e2702a6643d1ceacd5ae13009f0ba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bcd65685993727b7aac8185a910bd0bbfc2e2702a6643d1ceacd5ae13009f0ba","first_computed_at":"2026-05-18T00:09:40.300516Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:40.300516Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lTe7CwAIv0VysTIQQCcjA++Cf9V3Pgi0jKMXY5+K6c+mRXSmxWJLlKFnac713uQHKZ9jqh6fPissOhf6QkLMBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:40.301109Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.10536","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d5e8a8b7fb924be9a6d5547e683169668df92af208a2f3d76c3a431b3b194467","sha256:840723947ad120fe1ea360ec9901de4cd96f0907ebb4f1d438955d0a0c377fca"],"state_sha256":"43b4458a45731f1c78dc315389600cad2222188fa3072a7856ee7998fa41e3d0"}