{"as_of":"2026-08-07T23:31:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:9f5103f40ef385a6cb9570bb58453813901f905eeb623ffc16d1301d29f5183f","coverage":[{"denominator":39,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":39,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T05:40:25.707694Z","state":"measured"},{"denominator":39,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":39,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-07T06:34:17.273281+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2506.07635/citation-record","integrity":"/paper/2506.07635/integrity","json":"/paper/2506.07635/citation-record.json","paper":"/paper/2506.07635"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:40:26.152672Z","title":"Quantum error correction below the surface code threshold,","venue":null,"work_id":"87c9df92-a795-489b-b520-deaf12712481","year":2025},"citing_paper":{"arxiv_id":"2506.07635","last_updated":"2025-06-19T20:52:27Z","snapshot_observed_at":"2026-08-07T05:26:46.492361Z","submitted_at":"2025-06-09T11:01:17Z","title":"Verification of Quantum Circuits through Barrier Certificates using a Scenario Approach","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T05:40:25.567299Z"},"links":{"citing_paper":"/paper/2506.07635"},"observation_digest":"sha256:f91529d8233d4226aff720daab06689a02d62c4737357b6df5a413bf242a0d41","observation_id":"a3800093-6f88-40c4-8e6b-15ecf295be08","resolution":{"observed_at":"2026-08-07T05:40:26.156673Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:40:26.139956Z","title":"Hardware-efficient quantum error correction via concatenated bosonic qubits,","venue":null,"work_id":"62dbd6c6-e32e-4281-bf3e-77861c572e94","year":2025},"citing_paper":{"arxiv_id":"2506.07635","last_updated":"2025-06-19T20:52:27Z","snapshot_observed_at":"2026-08-07T05:26:46.492361Z","submitted_at":"2025-06-09T11:01:17Z","title":"Verification of Quantum Circuits through Barrier Certificates using a Scenario Approach","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T05:40:25.571504Z"},"links":{"citing_paper":"/paper/2506.07635"},"observation_digest":"sha256:b4f83d569a6ee518d18bc46eefd04626189989eecdd45d130c13b35a3ded8364","observation_id":"4c3d3b57-ac09-480e-8120-57d281ee92c3","resolution":{"observed_at":"2026-08-07T05:40:26.144181Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:40:26.126467Z","title":"Fault-tolerant quantum computation by anyons,","venue":null,"work_id":"93b153c3-8b26-45f0-8ef5-755161cd3a89","year":2003},"citing_paper":{"arxiv_id":"2506.07635","last_updated":"2025-06-19T20:52:27Z","snapshot_observed_at":"2026-08-07T05:26:46.492361Z","submitted_at":"2025-06-09T11:01:17Z","title":"Verification of Quantum Circuits through Barrier Certificates using a Scenario Approach","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T05:40:25.575107Z"},"links":{"citing_paper":"/paper/2506.07635"},"observation_digest":"sha256:c9f413cdd2146943667430fbb1b8a457ac815afa8b26905862e33a5afb35cd7f","observation_id":"bda3db3c-6669-4858-81d9-b4ba5f2a2c5e","resolution":{"observed_at":"2026-08-07T05:40:26.131415Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:40:26.115615Z","title":"Interferometric single-shot parity measure- ment in InAs–Al hybrid devices,","venue":null,"work_id":"531a8d6d-d126-4755-90c7-e9ef8e761b89","year":2025},"citing_paper":{"arxiv_id":"2506.07635","last_updated":"2025-06-19T20:52:27Z","snapshot_observed_at":"2026-08-07T05:26:46.492361Z","submitted_at":"2025-06-09T11:01:17Z","title":"Verification of Quantum Circuits through Barrier Certificates using a Scenario Approach","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-07T05:40:25.578558Z"},"links":{"citing_paper":"/paper/2506.07635"},"observation_digest":"sha256:45dd5cf7f2bae37b8a71da828b8428855da98ceadb0bb8b2c590fd35ac61ae0d","observation_id":"b338f37a-1017-4a09-8c09-2a1ae4f8733e","resolution":{"observed_at":"2026-08-07T05:40:26.119198Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:40:25.582232Z","title":"Quantum Computing in the NISQ era and beyond,","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2506.07635","last_updated":"2025-06-19T20:52:27Z","snapshot_observed_at":"2026-08-07T05:26:46.492361Z","submitted_at":"2025-06-09T11:01:17Z","title":"Verification of Quantum Circuits through Barrier Certificates using a Scenario Approach","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T05:40:25.582232Z"},"links":{"citing_paper":"/paper/2506.07635"},"observation_digest":"sha256:72d93715733cd7622f1edfd833135582a34a14b6eb250be6ea06cfc89874ce73","observation_id":"197a8ca7-2baf-48c9-910b-d326177f187f","resolution":{"observed_at":"2026-08-07T05:40:25.582232Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2502.17368","last_updated":"2025-03-12T16:42:00Z","snapshot_observed_at":"2026-08-07T17:52:33.335535Z","submitted_at":"2025-02-24T17:48:41Z","title":"Beyond NISQ: The Megaquop Machine","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2502.17368","snapshot_observed_at":"2026-08-07T05:40:25.585941Z","title":"Beyond NISQ: The Megaquop Machine,","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2506.07635","last_updated":"2025-06-19T20:52:27Z","snapshot_observed_at":"2026-08-07T05:26:46.492361Z","submitted_at":"2025-06-09T11:01:17Z","title":"Verification of Quantum Circuits through Barrier Certificates using a Scenario Approach","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T05:40:25.585941Z"},"links":{"cited_paper":"/paper/2502.17368","citing_paper":"/paper/2506.07635"},"observation_digest":"sha256:b28722995011c6b72596afcfc797569565118795abafd05d58b1a6877d3364c7","observation_id":"fc8732d4-b2c7-4d0a-a13c-492281a9228d","resolution":{"observed_at":"2026-08-07T05:40:25.585941Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:40:25.590203Z","title":"Simulating physics with computers,","venue":null,"work_id":null,"year":1982},"citing_paper":{"arxiv_id":"2506.07635","last_updated":"2025-06-19T20:52:27Z","snapshot_observed_at":"2026-08-07T05:26:46.492361Z","submitted_at":"2025-06-09T11:01:17Z","title":"Verification of Quantum Circuits through Barrier Certificates using a Scenario Approach","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T05:40:25.590203Z"},"links":{"citing_paper":"/paper/2506.07635"},"observation_digest":"sha256:39acdde48ff4db1a2a0d8f4684534cdf30f3c4f7154d0bbcc5fc71fe5a61ca31","observation_id":"ac2dd6a9-2e16-4217-acc1-b9a6e6cb680d","resolution":{"observed_at":"2026-08-07T05:40:25.590203Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:40:26.091212Z","title":"Improved simulation of stabilizer circuits,","venue":null,"work_id":"9762601b-08bd-47b6-a055-a1e4e3881c9b","year":2004},"citing_paper":{"arxiv_id":"2506.07635","last_updated":"2025-06-19T20:52:27Z","snapshot_observed_at":"2026-08-07T05:26:46.492361Z","submitted_at":"2025-06-09T11:01:17Z","title":"Verification of Quantum Circuits through Barrier Certificates using a Scenario Approach","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-07T05:40:25.593660Z"},"links":{"citing_paper":"/paper/2506.07635"},"observation_digest":"sha256:eca59fedae32c9a2a9cf60a051ed4e536dd0e0c3284bb9f53d4850097f2aaa64","observation_id":"731d466f-6475-49d3-a946-8133f9dac127","resolution":{"observed_at":"2026-08-07T05:40:26.094823Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:40:26.080381Z","title":"Safety verification of hybrid systems using barrier certificates,","venue":null,"work_id":"18c0193e-a33c-4572-997d-89e4fc60ca07","year":2004},"citing_paper":{"arxiv_id":"2506.07635","last_updated":"2025-06-19T20:52:27Z","snapshot_observed_at":"2026-08-07T05:26:46.492361Z","submitted_at":"2025-06-09T11:01:17Z","title":"Verification of Quantum Circuits through Barrier Certificates using a Scenario Approach","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T05:40:25.597065Z"},"links":{"citing_paper":"/paper/2506.07635"},"observation_digest":"sha256:ccc5172e6c36f35d9578f6e82d10065803a1764dde7327e5712789ade7d1fd01","observation_id":"546c040a-51df-4a75-9909-d56ab5007da3","resolution":{"observed_at":"2026-08-07T05:40:26.084306Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:40:26.069428Z","title":"Hybrid automata: An algorithmic approach to the specification and verification of hybrid systems,","venue":null,"work_id":"93ea9f5e-4553-4670-80ac-f2850d2fba80","year":1993},"citing_paper":{"arxiv_id":"2506.07635","last_updated":"2025-06-19T20:52:27Z","snapshot_observed_at":"2026-08-07T05:26:46.492361Z","submitted_at":"2025-06-09T11:01:17Z","title":"Verification of Quantum Circuits through Barrier Certificates using a Scenario Approach","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T05:40:25.600486Z"},"links":{"citing_paper":"/paper/2506.07635"},"observation_digest":"sha256:133a38ec4461a2512edb1dcc94c39f648af282e25160c1b26cb23dc8e4f8a5cb","observation_id":"f52bd32c-40bd-4e9f-b57e-607b38734e4d","resolution":{"observed_at":"2026-08-07T05:40:26.073389Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:40:26.058369Z","title":"A scenario approach for syn- thesizing k-inductive barrier certificates,","venue":null,"work_id":"f9ca9ba3-f60a-4473-a5ce-01356fedc40c","year":2022},"citing_paper":{"arxiv_id":"2506.07635","last_updated":"2025-06-19T20:52:27Z","snapshot_observed_at":"2026-08-07T05:26:46.492361Z","submitted_at":"2025-06-09T11:01:17Z","title":"Verification of Quantum Circuits through Barrier Certificates using a Scenario Approach","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-07T05:40:25.604198Z"},"links":{"citing_paper":"/paper/2506.07635"},"observation_digest":"sha256:ffc06dd70341f60aab94eb6b8530dbc257ff3f43674a76a6578a310110054042","observation_id":"77636720-b246-4509-9235-84234463de05","resolution":{"observed_at":"2026-08-07T05:40:26.062804Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:40:26.047424Z","title":"A fast quantum mechanical algorithm for database search,","venue":null,"work_id":"98e36cc3-361a-4309-a147-9300b00b2b08","year":1996},"citing_paper":{"arxiv_id":"2506.07635","last_updated":"2025-06-19T20:52:27Z","snapshot_observed_at":"2026-08-07T05:26:46.492361Z","submitted_at":"2025-06-09T11:01:17Z","title":"Verification of Quantum Circuits through Barrier Certificates using a Scenario Approach","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-07T05:40:25.607761Z"},"links":{"citing_paper":"/paper/2506.07635"},"observation_digest":"sha256:01eeeeefcfcf369026617c054a2005dbc1e715d4c433496395a8610e9fd22609","observation_id":"bfa52003-4bf5-4cb0-b522-bde0003b3c36","resolution":{"observed_at":"2026-08-07T05:40:26.051484Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:40:26.036139Z","title":"Towards Quantum Programs Verification: From Quipper Circuits to QPMC,","venue":null,"work_id":"b9f8266c-644e-4859-b279-1b9bbe24cf16","year":2016},"citing_paper":{"arxiv_id":"2506.07635","last_updated":"2025-06-19T20:52:27Z","snapshot_observed_at":"2026-08-07T05:26:46.492361Z","submitted_at":"2025-06-09T11:01:17Z","title":"Verification of Quantum Circuits through Barrier Certificates using a Scenario Approach","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-07T05:40:25.611417Z"},"links":{"citing_paper":"/paper/2506.07635"},"observation_digest":"sha256:68cdbac125129387f291e75acacf78da0efe57027fdbe92f3338b41d36bd2245","observation_id":"0aefe544-eab9-4829-b13c-a7996fcb153d","resolution":{"observed_at":"2026-08-07T05:40:26.040484Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:40:26.024193Z","title":"An automated deductive verification framework for circuit-building quantum programs,","venue":null,"work_id":"51953e77-9102-4b41-864c-fab361aa0b18","year":2021},"citing_paper":{"arxiv_id":"2506.07635","last_updated":"2025-06-19T20:52:27Z","snapshot_observed_at":"2026-08-07T05:26:46.492361Z","submitted_at":"2025-06-09T11:01:17Z","title":"Verification of Quantum Circuits through Barrier Certificates using a Scenario Approach","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-07T05:40:25.614902Z"},"links":{"citing_paper":"/paper/2506.07635"},"observation_digest":"sha256:be6791e75d4c4e0aee7517481c804b55703ee8eb2b86f744e65452f8fbd26236","observation_id":"95fc5f95-a826-4be6-b6de-4b8f74c59de6","resolution":{"observed_at":"2026-08-07T05:40:26.028817Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:40:26.012873Z","title":"Giallar: Push-button verification for the Qiskit quantum compiler,","venue":null,"work_id":"01fefa43-cf12-40c1-a51f-7ca272b9d236","year":2022},"citing_paper":{"arxiv_id":"2506.07635","last_updated":"2025-06-19T20:52:27Z","snapshot_observed_at":"2026-08-07T05:26:46.492361Z","submitted_at":"2025-06-09T11:01:17Z","title":"Verification of Quantum Circuits through Barrier Certificates using a Scenario Approach","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T05:40:25.618332Z"},"links":{"citing_paper":"/paper/2506.07635"},"observation_digest":"sha256:29528b5ae180b621b228b77ec6e4f87f91caf5033e3b03f2acfc809af4459dc1","observation_id":"a2d64223-e4c2-43ac-97ec-b7e218eb7e76","resolution":{"observed_at":"2026-08-07T05:40:26.017363Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:40:26.001966Z","title":"Quantum abstract interpretation,","venue":null,"work_id":"17063d1f-fae9-4f41-8211-af4132eaabc5","year":2021},"citing_paper":{"arxiv_id":"2506.07635","last_updated":"2025-06-19T20:52:27Z","snapshot_observed_at":"2026-08-07T05:26:46.492361Z","submitted_at":"2025-06-09T11:01:17Z","title":"Verification of Quantum Circuits through Barrier Certificates using a Scenario Approach","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-07T05:40:25.622188Z"},"links":{"citing_paper":"/paper/2506.07635"},"observation_digest":"sha256:38adf35f4fc08a1b338e9e305e1b43d605c709dcfae58649a5abe1b29fe8bc45","observation_id":"a665b1cb-c0db-4f11-b62d-eba815f170b2","resolution":{"observed_at":"2026-08-07T05:40:26.005859Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:40:25.990299Z","title":"Analyzing quantum programs with LintQ: A static analysis framework for Qiskit,","venue":null,"work_id":"46081808-859f-4db5-8287-430a60c2bc0e","year":2024},"citing_paper":{"arxiv_id":"2506.07635","last_updated":"2025-06-19T20:52:27Z","snapshot_observed_at":"2026-08-07T05:26:46.492361Z","submitted_at":"2025-06-09T11:01:17Z","title":"Verification of Quantum Circuits through Barrier Certificates using a Scenario Approach","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-07T05:40:25.625876Z"},"links":{"citing_paper":"/paper/2506.07635"},"observation_digest":"sha256:d9a336c4a105cb46c35523b29a97f39a1326daf7a9516ba72c11a7e0366acde1","observation_id":"ce6bcbb0-5aee-415d-9957-b37be3a11a3a","resolution":{"observed_at":"2026-08-07T05:40:25.994728Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:40:25.979758Z","title":"Au- toQ: An automata-based quantum circuit verifier,","venue":null,"work_id":"c69bd1dd-4257-4a87-93af-973698987ec0","year":2023},"citing_paper":{"arxiv_id":"2506.07635","last_updated":"2025-06-19T20:52:27Z","snapshot_observed_at":"2026-08-07T05:26:46.492361Z","submitted_at":"2025-06-09T11:01:17Z","title":"Verification of Quantum Circuits through Barrier Certificates using a Scenario Approach","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-07T05:40:25.630082Z"},"links":{"citing_paper":"/paper/2506.07635"},"observation_digest":"sha256:285f7de3a07b1939651d852ed3fa1551b8f786194d7fd65cccdb7bea8cdae661","observation_id":"b238a371-9b12-44c3-ac35-5d28ab53f693","resolution":{"observed_at":"2026-08-07T05:40:25.983581Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:40:25.968361Z","title":"An automata-based framework for verification and bug hunting in quantum circuits,","venue":null,"work_id":"e02ef3a5-b2a3-436f-b286-2a286600d70c","year":2023},"citing_paper":{"arxiv_id":"2506.07635","last_updated":"2025-06-19T20:52:27Z","snapshot_observed_at":"2026-08-07T05:26:46.492361Z","submitted_at":"2025-06-09T11:01:17Z","title":"Verification of Quantum Circuits through Barrier Certificates using a Scenario Approach","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-07T05:40:25.634006Z"},"links":{"citing_paper":"/paper/2506.07635"},"observation_digest":"sha256:d55f2a752b7a7348af443595b619d435b198b91bcf9c4c0926a7e09904ec00d2","observation_id":"a3574be8-2d10-4d48-8a87-cad6a1571ae9","resolution":{"observed_at":"2026-08-07T05:40:25.972724Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2408.07591","last_updated":"2024-08-14T14:42:55Z","snapshot_observed_at":"2026-08-05T13:35:26.511207Z","submitted_at":"2024-08-14T14:42:55Z","title":"Verification of Quantum Circuits through Discrete-Time Barrier Certificates","version":1},"cited_work":{"arxiv_id":"2408.07591","doi":null,"metadata_source":"pith","pith_arxiv_id":"2408.07591","snapshot_observed_at":"2026-08-07T05:40:25.738885Z","title":"Verification of Quantum Circuits through Discrete-Time Barrier Certificates","venue":"quant-ph","work_id":"8ec8a55b-8cc2-45ec-b511-9783a7f31edd","year":2024},"citing_paper":{"arxiv_id":"2506.07635","last_updated":"2025-06-19T20:52:27Z","snapshot_observed_at":"2026-08-07T05:26:46.492361Z","submitted_at":"2025-06-09T11:01:17Z","title":"Verification of Quantum Circuits through Barrier Certificates using a Scenario Approach","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-07T05:40:25.637860Z"},"links":{"cited_paper":"/paper/2408.07591","citing_paper":"/paper/2506.07635"},"observation_digest":"sha256:9528bf9a95d1f5a02871e47ff1e23bf0e09ac5fca6e885521bec2eff134dd8f7","observation_id":"dd093dcf-002e-44e2-a670-448ef09afdce","resolution":{"observed_at":"2026-08-07T05:40:25.745214Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:40:25.956450Z","title":"Formal verification of quantum programs: Theory, tools, and challenges,","venue":null,"work_id":"ca2dc19b-939f-421a-9ac8-beae9f7a8be6","year":2023},"citing_paper":{"arxiv_id":"2506.07635","last_updated":"2025-06-19T20:52:27Z","snapshot_observed_at":"2026-08-07T05:26:46.492361Z","submitted_at":"2025-06-09T11:01:17Z","title":"Verification of Quantum Circuits through Barrier Certificates using a Scenario Approach","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-07T05:40:25.641950Z"},"links":{"citing_paper":"/paper/2506.07635"},"observation_digest":"sha256:09c616b81ca171b0b143c4ed0669024e803f36d7473d2074baef969ba869121c","observation_id":"b4cf86ac-1c15-478d-ae64-82dade1403d6","resolution":{"observed_at":"2026-08-07T05:40:25.960488Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:40:25.944921Z","title":"Formal methods for quantum algorithms,","venue":null,"work_id":"f66e626d-79f6-4eb9-9a62-dd34e4bf98bf","year":2023},"citing_paper":{"arxiv_id":"2506.07635","last_updated":"2025-06-19T20:52:27Z","snapshot_observed_at":"2026-08-07T05:26:46.492361Z","submitted_at":"2025-06-09T11:01:17Z","title":"Verification of Quantum Circuits through Barrier Certificates using a Scenario Approach","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-07T05:40:25.645655Z"},"links":{"citing_paper":"/paper/2506.07635"},"observation_digest":"sha256:518bf29b9b2d392fa578e2c73623cd7f2dacac34cda83f736af8b4e82984c53f","observation_id":"4a85423d-5e81-46fb-bacc-43d5dc818376","resolution":{"observed_at":"2026-08-07T05:40:25.948909Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:40:25.934336Z","title":"Automated verification of silq quantum programs using smt solvers,","venue":null,"work_id":"bdce332b-a803-42b9-9980-8670ac6f2d71","year":2024},"citing_paper":{"arxiv_id":"2506.07635","last_updated":"2025-06-19T20:52:27Z","snapshot_observed_at":"2026-08-07T05:26:46.492361Z","submitted_at":"2025-06-09T11:01:17Z","title":"Verification of Quantum Circuits through Barrier Certificates using a Scenario Approach","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-07T05:40:25.649277Z"},"links":{"citing_paper":"/paper/2506.07635"},"observation_digest":"sha256:ac4ffc27ab2bc66f7c059ff64ae0ad0600ca6db025c989c1c5b03752c20e1381","observation_id":"7f390e97-454a-4268-bd5c-78acc9c26ef2","resolution":{"observed_at":"2026-08-07T05:40:25.938019Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:40:25.922806Z","title":"Safety verification of dynamical systems via k-inductive barrier certificates,","venue":null,"work_id":"c7531156-1b4d-40e2-ac94-b83d2252c680","year":2021},"citing_paper":{"arxiv_id":"2506.07635","last_updated":"2025-06-19T20:52:27Z","snapshot_observed_at":"2026-08-07T05:26:46.492361Z","submitted_at":"2025-06-09T11:01:17Z","title":"Verification of Quantum Circuits through Barrier Certificates using a Scenario Approach","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-07T05:40:25.652665Z"},"links":{"citing_paper":"/paper/2506.07635"},"observation_digest":"sha256:20bb32f6f23776ff4ef19f06d1ed99de77b9208ac883cfc82d7576382df9f3e8","observation_id":"5b77613d-dbf8-4b67-a6ac-7d55baeebf63","resolution":{"observed_at":"2026-08-07T05:40:25.927272Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:40:25.911891Z","title":"Formal verification of unknown discrete- and continuous-time systems: A data- driven approach,","venue":null,"work_id":"c4279fde-0091-4bf3-813f-778189eeaf0e","year":2023},"citing_paper":{"arxiv_id":"2506.07635","last_updated":"2025-06-19T20:52:27Z","snapshot_observed_at":"2026-08-07T05:26:46.492361Z","submitted_at":"2025-06-09T11:01:17Z","title":"Verification of Quantum Circuits through Barrier Certificates using a Scenario Approach","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-07T05:40:25.656306Z"},"links":{"citing_paper":"/paper/2506.07635"},"observation_digest":"sha256:6f164e665901d5d7d3361358203ef13f5e79b1b526cdf5d0e30168d16f3685da","observation_id":"c7dbaa2e-e02b-4aba-9709-12f67ec70dd7","resolution":{"observed_at":"2026-08-07T05:40:25.916081Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:40:25.900656Z","title":"Fossil 2.0: Formal certificate synthesis for the verification and control of dynamical models,","venue":null,"work_id":"c07acbd5-28d3-4e40-9e96-fbe34dbf4e50","year":2024},"citing_paper":{"arxiv_id":"2506.07635","last_updated":"2025-06-19T20:52:27Z","snapshot_observed_at":"2026-08-07T05:26:46.492361Z","submitted_at":"2025-06-09T11:01:17Z","title":"Verification of Quantum Circuits through Barrier Certificates using a Scenario Approach","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-07T05:40:25.660132Z"},"links":{"citing_paper":"/paper/2506.07635"},"observation_digest":"sha256:9b5048373a6a01d0dc0cc301088d2feb921ca24bf7b6b13479ec4dba0c3cdaeb","observation_id":"a3aeee34-36b8-4e0e-a87f-e12376b94b20","resolution":{"observed_at":"2026-08-07T05:40:25.905174Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:40:25.663763Z","title":"On the necessity of barrier certificates,","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2506.07635","last_updated":"2025-06-19T20:52:27Z","snapshot_observed_at":"2026-08-07T05:26:46.492361Z","submitted_at":"2025-06-09T11:01:17Z","title":"Verification of Quantum Circuits through Barrier Certificates using a Scenario Approach","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-07T05:40:25.663763Z"},"links":{"citing_paper":"/paper/2506.07635"},"observation_digest":"sha256:b46036f13e111e06b0460b8e4c2c5dbcc6b300223975c6ce838ea7aa1a1c729a","observation_id":"eb56ef90-d9e4-46ca-a502-6b86e81eb880","resolution":{"observed_at":"2026-08-07T05:40:25.663763Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:40:25.884837Z","title":"Non-convex scenario optimization,","venue":null,"work_id":"5a534d72-7412-45b6-bac4-efa9bbac4746","year":2024},"citing_paper":{"arxiv_id":"2506.07635","last_updated":"2025-06-19T20:52:27Z","snapshot_observed_at":"2026-08-07T05:26:46.492361Z","submitted_at":"2025-06-09T11:01:17Z","title":"Verification of Quantum Circuits through Barrier Certificates using a Scenario Approach","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-07T05:40:25.667165Z"},"links":{"citing_paper":"/paper/2506.07635"},"observation_digest":"sha256:5527cc69eb1814ba80158902c0d30472d3e0a3704e2a8109061368056efa1759","observation_id":"b2f37aca-f41e-46ea-a3c8-43f87e655bb2","resolution":{"observed_at":"2026-08-07T05:40:25.888141Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:40:25.874173Z","title":"Delta-decidability over the reals,","venue":null,"work_id":"be39535a-b93b-4e8b-8e80-4e176dc8b1a9","year":2012},"citing_paper":{"arxiv_id":"2506.07635","last_updated":"2025-06-19T20:52:27Z","snapshot_observed_at":"2026-08-07T05:26:46.492361Z","submitted_at":"2025-06-09T11:01:17Z","title":"Verification of Quantum Circuits through Barrier Certificates using a Scenario Approach","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-07T05:40:25.670881Z"},"links":{"citing_paper":"/paper/2506.07635"},"observation_digest":"sha256:42c8c23548448fc6c285b1bec796202fcecd674a8b949fb22a82873cd7c5a8cf","observation_id":"2cc4b8ba-f7ff-4f95-ac9e-aa6c84143087","resolution":{"observed_at":"2026-08-07T05:40:25.877625Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:40:25.863154Z","title":"Distribution of points in a cube and approximate evalu- ation of integrals,","venue":null,"work_id":"68fdce98-8631-4fc9-8b5f-a8773425fde2","year":1967},"citing_paper":{"arxiv_id":"2506.07635","last_updated":"2025-06-19T20:52:27Z","snapshot_observed_at":"2026-08-07T05:26:46.492361Z","submitted_at":"2025-06-09T11:01:17Z","title":"Verification of Quantum Circuits through Barrier Certificates using a Scenario Approach","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-07T05:40:25.674594Z"},"links":{"citing_paper":"/paper/2506.07635"},"observation_digest":"sha256:898ccf6c89e1e1a3d10027048ae46825afed7125ad2bfc16c8618f0e682ae474","observation_id":"93e321cf-a8d8-4338-965b-ce2baf799e8b","resolution":{"observed_at":"2026-08-07T05:40:25.867208Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:40:25.852964Z","title":"Parallelizing the dual revised simplex method,","venue":null,"work_id":"6affd83e-579b-4237-9d49-bac243cda7cd","year":2018},"citing_paper":{"arxiv_id":"2506.07635","last_updated":"2025-06-19T20:52:27Z","snapshot_observed_at":"2026-08-07T05:26:46.492361Z","submitted_at":"2025-06-09T11:01:17Z","title":"Verification of Quantum Circuits through Barrier Certificates using a Scenario Approach","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-07T05:40:25.678143Z"},"links":{"citing_paper":"/paper/2506.07635"},"observation_digest":"sha256:7b44151b2a9410b03134837de34ea2f1189c08fd97f8816a3904ed44967e144e","observation_id":"8a5f3fa2-2685-4c21-ab30-916625e58df6","resolution":{"observed_at":"2026-08-07T05:40:25.856695Z","resolver_source":"raw_fallback","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:40:25.843202Z","title":"Z3: An Efficient SMT Solver,","venue":null,"work_id":"b719a08c-3067-487a-8835-2f1f4edda833","year":2008},"citing_paper":{"arxiv_id":"2506.07635","last_updated":"2025-06-19T20:52:27Z","snapshot_observed_at":"2026-08-07T05:26:46.492361Z","submitted_at":"2025-06-09T11:01:17Z","title":"Verification of Quantum Circuits through Barrier Certificates using a Scenario Approach","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-07T05:40:25.681704Z"},"links":{"citing_paper":"/paper/2506.07635"},"observation_digest":"sha256:dd624b4f5414d64e1e995601a0fb34c4bdfcd147ac8cf333732709c70782f527","observation_id":"e47eff6b-2236-4ffa-9be2-a94b3699d552","resolution":{"observed_at":"2026-08-07T05:40:25.846580Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:40:25.834203Z","title":"Quantum computation,","venue":null,"work_id":"29c0cb09-33b9-42fe-86be-a9b4b6ea6d35","year":1999},"citing_paper":{"arxiv_id":"2506.07635","last_updated":"2025-06-19T20:52:27Z","snapshot_observed_at":"2026-08-07T05:26:46.492361Z","submitted_at":"2025-06-09T11:01:17Z","title":"Verification of Quantum Circuits through Barrier Certificates using a Scenario Approach","version":2},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-07T05:40:25.685061Z"},"links":{"citing_paper":"/paper/2506.07635"},"observation_digest":"sha256:2e269db89ffcaf9f71f395208a269ea2aaa887a2241bccfbc884a20fe6b9bb51","observation_id":"088d1e29-cf78-4733-988c-9034e6022ea8","resolution":{"observed_at":"2026-08-07T05:40:25.837256Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:40:25.823777Z","title":"Safe reach set computation via neural barrier certificates,","venue":null,"work_id":"7d11e47b-18b0-4aee-bb0f-a5fd02985b75","year":2024},"citing_paper":{"arxiv_id":"2506.07635","last_updated":"2025-06-19T20:52:27Z","snapshot_observed_at":"2026-08-07T05:26:46.492361Z","submitted_at":"2025-06-09T11:01:17Z","title":"Verification of Quantum Circuits through Barrier Certificates using a Scenario Approach","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-07T05:40:25.688710Z"},"links":{"citing_paper":"/paper/2506.07635"},"observation_digest":"sha256:828214783d558c5427ae5bc5de2caae4cabe2b8bba85e540dca7702721592f78","observation_id":"f44e592a-e9b9-454a-9d19-97fef3a40154","resolution":{"observed_at":"2026-08-07T05:40:25.827696Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:40:25.811670Z","title":"Uniform sample generation in semialgebraic sets,","venue":null,"work_id":"56c4796a-20ae-4d3d-86b0-203ef813833e","year":2014},"citing_paper":{"arxiv_id":"2506.07635","last_updated":"2025-06-19T20:52:27Z","snapshot_observed_at":"2026-08-07T05:26:46.492361Z","submitted_at":"2025-06-09T11:01:17Z","title":"Verification of Quantum Circuits through Barrier Certificates using a Scenario Approach","version":2},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-07T05:40:25.692494Z"},"links":{"citing_paper":"/paper/2506.07635"},"observation_digest":"sha256:9d4532c537ba9659c561c5ac7f22a6710954e44fe7f657477b667901eb09deac","observation_id":"5037ed4b-f16f-44d3-877a-2a32c4884e0e","resolution":{"observed_at":"2026-08-07T05:40:25.815357Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:40:25.799761Z","title":"Compositional construction of control barrier functions for continuous-time stochastic hybrid systems,","venue":null,"work_id":"ea6a154f-27b2-4693-b3dc-f909fc40fa36","year":2022},"citing_paper":{"arxiv_id":"2506.07635","last_updated":"2025-06-19T20:52:27Z","snapshot_observed_at":"2026-08-07T05:26:46.492361Z","submitted_at":"2025-06-09T11:01:17Z","title":"Verification of Quantum Circuits through Barrier Certificates using a Scenario Approach","version":2},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-07T05:40:25.696155Z"},"links":{"citing_paper":"/paper/2506.07635"},"observation_digest":"sha256:5128055b9a6bcf7b4174188af6414551ae0be8084405096605b78da0c7ed5722","observation_id":"ca8f953d-63d2-419b-8183-65197815cc4f","resolution":{"observed_at":"2026-08-07T05:40:25.803688Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:40:25.787361Z","title":"Necessary and sufficient certificates for almost sure reachability,","venue":null,"work_id":"2274ce94-2a19-4789-b36b-746614932dc2","year":2024},"citing_paper":{"arxiv_id":"2506.07635","last_updated":"2025-06-19T20:52:27Z","snapshot_observed_at":"2026-08-07T05:26:46.492361Z","submitted_at":"2025-06-09T11:01:17Z","title":"Verification of Quantum Circuits through Barrier Certificates using a Scenario Approach","version":2},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-07T05:40:25.700089Z"},"links":{"citing_paper":"/paper/2506.07635"},"observation_digest":"sha256:a765c2e8746229b5cc875babd7338b0ebaf0979291b6a1271f49618935afeaef","observation_id":"aa25b73e-d16c-4e73-869e-f699e39eb2fd","resolution":{"observed_at":"2026-08-07T05:40:25.791311Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:40:25.775305Z","title":"Data-driven distributionally robust safety verification using barrier certificates and conditional mean embeddings,","venue":null,"work_id":"ae7b483c-4bf3-42cb-afaf-4e91dfd180ef","year":2024},"citing_paper":{"arxiv_id":"2506.07635","last_updated":"2025-06-19T20:52:27Z","snapshot_observed_at":"2026-08-07T05:26:46.492361Z","submitted_at":"2025-06-09T11:01:17Z","title":"Verification of Quantum Circuits through Barrier Certificates using a Scenario Approach","version":2},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-07T05:40:25.703907Z"},"links":{"citing_paper":"/paper/2506.07635"},"observation_digest":"sha256:bce4985c8b7972471d0aff32dbc7712780718dc1e4a2545a8f3855d1cfd54456","observation_id":"b8c20691-8858-430b-9a47-895242817267","resolution":{"observed_at":"2026-08-07T05:40:25.779156Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:40:25.763760Z","title":"Control barrier functions for stochastic systems under signal temporal logic tasks,","venue":null,"work_id":"a249d192-6be2-461b-ac58-596831c37b7b","year":2024},"citing_paper":{"arxiv_id":"2506.07635","last_updated":"2025-06-19T20:52:27Z","snapshot_observed_at":"2026-08-07T05:26:46.492361Z","submitted_at":"2025-06-09T11:01:17Z","title":"Verification of Quantum Circuits through Barrier Certificates using a Scenario Approach","version":2},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-07T05:40:25.707694Z"},"links":{"citing_paper":"/paper/2506.07635"},"observation_digest":"sha256:247968279c461ee835eb9cd09b3418ec8594ef7b90276d41d6009310123c4287","observation_id":"d1abe27e-1a01-480a-bd75-82091f623248","resolution":{"observed_at":"2026-08-07T05:40:25.768231Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2506.07635","last_updated":"2025-06-19T20:52:27Z","latest_version":2,"primary_category":"cs.LO","snapshot_observed_at":"2026-08-07T05:26:46.492361Z","submitted_at":"2025-06-09T11:01:17Z","title":"Verification of Quantum Circuits through Barrier Certificates using a Scenario Approach"},"reference_resolution":{"displayed":39,"state_counts":{"malformed_identifier":1,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":4,"verified_exact":1,"verified_fuzzy":33},"total_outbound_references":39},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"thesis":"As of 7 August 2026, this Paper Citation Record lists 39 of 39 outbound references and 0 inbound Pith citation observations for arXiv:2506.07635."}