{"as_of":"2026-08-14T18:05:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:767299ba631d72fc5923bb6ab1726b7f5805df6ae4e028753a0c67e7a05a18d7","coverage":[{"denominator":59,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":59,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T05:51:31.678108Z","state":"measured"},{"denominator":59,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":59,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-14T06:32:32.682623+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/2506.12080/citation-record","integrity":"/paper/2506.12080/integrity","json":"/paper/2506.12080/citation-record.json","paper":"/paper/2506.12080"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:51:33.704452Z","title":"Huang, Statistical mechanics, New York: Wiley, 2008","venue":null,"work_id":"1c0f558d-4ce6-41fa-913f-c842adbc68bc","year":2008},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:30.929980Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:7e655b31958e6f690b620f1246f7a269ce51cbe44291d9cb17f35a5df37b1b9b","observation_id":"2f7b6444-1ad9-478e-af5b-a786caad829c","resolution":{"observed_at":"2026-08-07T05:51:33.714373Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:51:30.945927Z","title":null,"venue":null,"work_id":null,"year":1984},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:30.945927Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:e6625b99de1665b8beabe07d322e67255650033901564a1c6b0434a8dda8521c","observation_id":"cb5397f2-f983-4d44-9cd2-0686dffe5b15","resolution":{"observed_at":"2026-08-07T05:51:30.945927Z","resolver_source":null,"status":"malformed_identifier"},"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":"2026-08-07T05:51:30.952713Z","title":"Barahona, On the computational complexity of Ising spin glass models, J","venue":null,"work_id":null,"year":1982},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:30.952713Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:99b18ebb123832817a04f372284375f6c0e794afe6c12e178d2f0652099d9984","observation_id":"3f9abfa8-897f-4788-ba99-6628bcc63151","resolution":{"observed_at":"2026-08-07T05:51:30.952713Z","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":"2026-08-07T05:51:30.960590Z","title":null,"venue":null,"work_id":null,"year":1975},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:30.960590Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:66d27ee8b583a2ef24a09fc0c2f4b59b207517ad366c12e36495d1a5d3270e10","observation_id":"85f4531a-2a9f-4374-8d63-8747faa66e55","resolution":{"observed_at":"2026-08-07T05:51:30.960590Z","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":"5305.33531","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:51:33.423228Z","title":"Istrail , Statistical mechanics, three -dimensionality and NP -completeness: I","venue":null,"work_id":"de87e792-3921-43bd-9e46-fab7b937c536","year":2000},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:30.968444Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:8dd9a8f100e967415777e3ef86d0ecf2e25422a3856ffd6d89d23fa8af4ab333","observation_id":"713bbd9d-4f70-45ce-9583-b7e178bb0876","resolution":{"observed_at":"2026-08-07T05:51:33.437267Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:51:33.678147Z","title":null,"venue":null,"work_id":"71b4557f-eac4-4e88-a9cd-6405e8d8f6c4","year":2013},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:30.982259Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:71382c5de9bf5154c42b8e6cd829701fbae66c7edd0c38ef4161625c3d74ea1e","observation_id":"8ebc215e-61bc-4bb8-92a8-68fc290da7d7","resolution":{"observed_at":"2026-08-07T05:51:33.683083Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:51:30.991423Z","title":"Ising, Beitrag zur theorie des ferromagnetismus, Z","venue":null,"work_id":null,"year":1925},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:30.991423Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:67452a8860e8e4707c8ff7f53f2e78b107bcfdefd45a2524c93e52972367e423","observation_id":"1b318685-3644-4ddd-b9fc-ab918cc01e8f","resolution":{"observed_at":"2026-08-07T05:51:30.991423Z","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":"2026-08-07T05:51:31.003478Z","title":"Onsager, Crystal statistics I: a two -dimensional model with an order -disorder transition, Phys","venue":null,"work_id":null,"year":1944},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.003478Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:63778466829322744328a955dc14d88e9b304c526c5b337577d2e2e678046777","observation_id":"55132d88-0675-42db-98b5-719aa6229ffb","resolution":{"observed_at":"2026-08-07T05:51:31.003478Z","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":"2026-08-07T05:51:31.013382Z","title":null,"venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.013382Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:165841ad49540cc429866105cd3a3b511a5fe1b5db19726d7d9c2b190665dc32","observation_id":"0ded23e1-9d31-42c1-90de-39230822202b","resolution":{"observed_at":"2026-08-07T05:51:31.013382Z","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":"2026-08-07T05:51:33.651272Z","title":"Garey, D","venue":null,"work_id":"ab703092-545c-45c4-9c3a-15eab1f4791d","year":1979},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.019615Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:a8a614696bd2aad7f38935d439f2cc47b99b139616764abc67fa9d49396947fc","observation_id":"7145c306-a900-44a7-a925-823fedd94a64","resolution":{"observed_at":"2026-08-07T05:51:33.658799Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:51:33.620276Z","title":null,"venue":null,"work_id":"6199a0db-46b9-4251-9139-d573dab08efb","year":1994},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.026220Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:999dab549033803e14d7d444e3f51d3ad8185a14bca2e684ae352aabfbec9a9d","observation_id":"4dddc203-6455-4ea3-9438-96a3a583f274","resolution":{"observed_at":"2026-08-07T05:51:33.633573Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:51:31.032091Z","title":"Cook, The complexity of theorem-proving procedures, Proceedings of the third annual ACM symposium on Theory of computing , 1971, 151 –158","venue":null,"work_id":null,"year":1971},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.032091Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:04e1a6da3a8aba88e16b59a2e9a2b368d89935c4a1e74ceea2544ba903a0dc98","observation_id":"a0c91697-4430-4e2d-803e-0401a07c2463","resolution":{"observed_at":"2026-08-07T05:51:31.032091Z","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":"2026-08-07T05:51:33.594538Z","title":null,"venue":null,"work_id":"dcd4fc08-1bd4-4fa9-a82f-9829f6dc2a63","year":1973},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.038518Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:071506eeec7e7476f5e85b1a2fa5ce56140cec2853aa2333574496148a9127ee","observation_id":"253d7a27-adf7-463f-ad0b-732f1e7a2de1","resolution":{"observed_at":"2026-08-07T05:51:33.604261Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.jmst.2019.12.009","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":null,"venue":"Journal of Material Science and Technology","work_id":"7b01f77d-af1d-4f51-870c-d1fb209b6175","year":2020},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.044676Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:1eafcc5fb57d340a66f015b9cee316ceb262a5b448739f99660dbf367344bf1f","observation_id":"f3de960e-dd5b-4f35-8aae-0b8bdae1dd6f","resolution":{"observed_at":"2026-08-07T05:51:32.548266Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.3390/math11010237","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":null,"venue":"Mathematics","work_id":"ded62803-05d7-4802-9949-d2c5c20f8889","year":2023},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.050535Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:a9ccef0d9fe046614ec8e1ba32db9e4836456c65eec26d03214aaf983949e42e","observation_id":"4c1e1f24-4d5b-4787-9f1a-dce99f255dce","resolution":{"observed_at":"2026-08-07T05:51:32.524379Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:51:33.567559Z","title":"Dantzig, Numbers: the language of science, London: George Allen & Unwin, Ltd., 1930","venue":null,"work_id":"7bfa8d1f-7f24-4793-aa99-c03e96b53dbe","year":1930},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.058942Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:5e9079a444d3e1fc0bc2d9b4d4cb4bafa6635b0d0b68e5dde2592c4f5fa624b7","observation_id":"3d367796-e3cd-4fae-8a5a-c9277567d0a7","resolution":{"observed_at":"2026-08-07T05:51:33.575063Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1112/plms/s1-28.1.486","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":null,"venue":"Proceedings of the London Mathematical Society","work_id":"33101a05-f18a-424f-86b5-70f55e743e95","year":null},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.067757Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:f608e30917c3614da7df6eb81c1fe48f5f60c846acb19489fd8e23162683db80","observation_id":"f22aeb39-8355-4f5e-9562-541d6316d0be","resolution":{"observed_at":"2026-08-07T05:51:32.503073Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/s0377-2217(99)00260-x","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Mar tello, D","venue":"European Journal of Operational Research","work_id":"a4f1b728-295e-4e12-b13c-1d7c6cdf6141","year":2000},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.073608Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:9bafd5a892a6ae6d1c431fe4afac95a388651be5a700dd42be1878de0d246fa6","observation_id":"e1e9041d-bcf4-4234-844a-ca1216e9a850","resolution":{"observed_at":"2026-08-07T05:51:32.465948Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:51:31.080773Z","title":"Pisinger, Where are the hard knapsack problems? Comput","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.080773Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:acbef9d490e350ab6a16928930ee229a78bb80f53c9c2aabf1e5dfdc2b840091","observation_id":"9bba41b9-bd0f-4ab9-a42f-230a26afcae4","resolution":{"observed_at":"2026-08-07T05:51:31.080773Z","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":"10.1007/bf01580448","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-09T00:03:45.533247Z","title":"Fayard, G","venue":"Mathematical Programming","work_id":"dd780250-70ef-4e53-ae0f-ce0f1ae9f737","year":1975},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.089134Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:66d5f09578ace3aa46a4469b1ad142397e529469b302801824b729891d804f40","observation_id":"800f1586-b8f9-4803-ae5b-0365ba7052bd","resolution":{"observed_at":"2026-08-07T05:51:32.426160Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:51:31.105588Z","title":"Al -Shihabi, A novel core -based optimization framework for binary integer programs- the multidemand multidimesional knapsack problem as a test problem, Oper","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.105588Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:8474ea874eca9034b8f4540dd8bc86484cbe1fa9cb06fdcf1cfa8f17115af8e0","observation_id":"afca7d5f-1cd7-4428-a10c-3d387c2c0ee6","resolution":{"observed_at":"2026-08-07T05:51:31.105588Z","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":"10.1016/j.dam.2004.09.007","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":null,"venue":"Discrete Applied Mathematics","work_id":"3f9b7235-7ee6-4a58-9fda-0cc3b604b6ef","year":2005},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.112392Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:9485bc0355d05bed2d9093cab5cdf7ca39eca7755275353f42ceb40ab3efcc33","observation_id":"4a70dae9-b111-4d4c-92c6-24bf15ac41b8","resolution":{"observed_at":"2026-08-07T05:51:32.401167Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:51:31.118656Z","title":null,"venue":null,"work_id":null,"year":1974},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.118656Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:3939ae29af795410ff60d38ab62e8b16a4c200e38d95c4f685c853db246f55e6","observation_id":"42f5af2b-c5db-4f0a-9aaa-02af878ecd01","resolution":{"observed_at":"2026-08-07T05:51:31.118656Z","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":"10.1016/s0377-2217(99)00453-1","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Toth, Optimization enginee ring techniques for the exact solution of NP -hard combinatorial optimization problems, Eur","venue":"European Journal of Operational Research","work_id":"9ca43d20-eb91-4b17-a00e-6c0876c5b4c9","year":2000},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.125063Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:f9019e7318dd2e361c5ee88cd653d7f427bc823e6f61cd5c9df72e6c11665b1e","observation_id":"60291dfd-a8d6-4991-958b-b6622c2c0bc5","resolution":{"observed_at":"2026-08-07T05:51:32.358102Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/bf02846491","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-09T00:03:45.533247Z","title":"Venkataraman, G","venue":"Pramana","work_id":"b902798c-9c4c-410f-a4ac-8c107d1c70d4","year":1991},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.131534Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:25b7fc65086fb478b4be9944a27b9e53b413195173bf49157a95cd17c2513eb1","observation_id":"3c22afc1-99f6-4842-8930-3b0c425ea35f","resolution":{"observed_at":"2026-08-07T05:51:32.339505Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00006-018-","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:51:32.314647Z","title":null,"venue":null,"work_id":"acf00a5a-5a78-4eed-89d4-2c4c46d189f4","year":2019},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.137909Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:99f885618dc66d3f25e82c40a411cdf473c0527a3b7b6be64f0157966183a241","observation_id":"42436a86-a564-4283-9bbd-928b22f75e79","resolution":{"observed_at":"2026-08-07T05:51:32.319835Z","resolver_source":"doi_truncated","status":"malformed_identifier"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.3390/math9070776","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Suzuki, Z","venue":"Mathematics","work_id":"7554daed-da2f-4988-85f7-5caf787cb8d8","year":2021},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.148600Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:a89367e1ae51a8e656208af84f2fcef8a1b08eaa68ebe3b5f2c58837da245513","observation_id":"7254e908-550a-4859-a374-7ba4e5dded67","resolution":{"observed_at":"2026-08-07T05:51:32.301311Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.cjph.2024.05.021","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":null,"venue":"Chinese Journal of Physics","work_id":"f4965a6e-9740-4823-a0b3-c869b8e08848","year":2024},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.158615Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:ff1fa43e253f2ba62e36e550d649b480dbad0f2419aeee03a6ee64d014bf97cd","observation_id":"050d3acb-67f2-4778-97c8-375209b0b20e","resolution":{"observed_at":"2026-08-07T05:51:32.281634Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1103/physrevlett.81.4740","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Ghosh, C","venue":"Physical Review Letters","work_id":"a53c6d70-708c-471c-8432-381c0b1767b3","year":1998},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.167013Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:798e6d1066c7b645eebff3cc559ad2d05ea6a524a3ee6652410258fbf7aaaf16","observation_id":"6c3e3f26-fde8-40d7-99c1-b263fdbc22ef","resolution":{"observed_at":"2026-08-07T05:51:32.257442Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1103/physrevlett.22.603","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":null,"venue":"Physical Review Letters","work_id":"811fe07a-6dd9-4d11-a9b6-9addaac508b0","year":1969},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.176427Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:9a6f28f4f20e1052e9eecbf9dbb6736a7e4a4f6441b405edf5b7aafa3b8bf2db","observation_id":"ace4666f-671c-41aa-be98-8459bf04d697","resolution":{"observed_at":"2026-08-07T05:51:32.227172Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1103/physrevb.96.144429","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":null,"venue":"Physical review. B./Physical review. B","work_id":"27720a09-6bb3-4946-8488-90bc07f3825d","year":2017},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.195335Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:151068998bbcdffe2b52a69be99c4ac075c4c90370f1359018193997910cccfe","observation_id":"4a3c2b3f-37b5-44ee-82bc-f3641a8b49af","resolution":{"observed_at":"2026-08-07T05:51:32.195140Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1103/physreva.108.012415","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":null,"venue":"Physical review. A/Physical review, A","work_id":"41dde362-7892-4a20-87ca-a53355387a33","year":2023},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.202675Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:4686bca6f0b897e37c72be745bb9f65ef41ebdafc999f3ffb3b1b35e3f19e438","observation_id":"d5fac23d-d3b0-40ae-9d6a-223c2f59f1ed","resolution":{"observed_at":"2026-08-07T05:51:32.167585Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1103/physreve.109.055301","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":null,"venue":"Physical review. E","work_id":"ab68a799-7dbf-4d38-bc2e-4f391179cee9","year":2024},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.213849Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:5bd99abf9a27ff403e8b1341a35e4f2c949e7e8a54da3ddadbbf84ba368f3abc","observation_id":"e2ced49d-6858-44a8-915b-2a94505898a0","resolution":{"observed_at":"2026-08-07T05:51:32.140098Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.3390/e25030541","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":null,"venue":"Entropy","work_id":"d220ebfd-61a1-4df4-a899-3ba00b8ccb37","year":2023},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.221474Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:4d2e55485d1b150c8084d9433b40061dcaf4dd87d7b4339bd6f8b2ff0b3f2425","observation_id":"a6263670-0c89-47de-8015-fd32bb28f032","resolution":{"observed_at":"2026-08-07T05:51:32.115286Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"1864.32187","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:51:33.193707Z","title":"Ladner, On the structure of polynomial time r educibility, J","venue":null,"work_id":"6749496d-7120-4e47-95a8-d13e7001e880","year":1975},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.233872Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:b660478f8f4ef3bf65eed3a746aa89993987ddb0110d989cd2f8788ecefa41fe","observation_id":"8fbd07bb-bc0a-4535-b9a4-66efb2b431b6","resolution":{"observed_at":"2026-08-07T05:51:33.203941Z","resolver_source":"raw_fallback","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.tcs.2015.03.009","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Jonsson, V","venue":"Theoretical Computer Science","work_id":"b49f1b66-a764-45dc-84fc-fa7ee6997eb8","year":2015},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.246353Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:b4d36dd87192320ca0beac56c26bfb84918c92f128637047877d8cfe7f011146","observation_id":"4afa2839-ff7e-4d06-9b2a-571d1404587d","resolution":{"observed_at":"2026-08-07T05:51:32.085129Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:51:31.258265Z","title":"Bellman, A Markovian decision process, J","venue":null,"work_id":null,"year":1957},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.258265Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:e0d2be85075ea7b7755b05ad005bbafd389bbf5794581b6ff72887cae5a0aa7f","observation_id":"7150838b-fdfe-4773-9595-29cc6c1a7b68","resolution":{"observed_at":"2026-08-07T05:51:31.258265Z","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":"10.1103/physrevb.99.195301","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Kyriienko, H","venue":"Physical review. B./Physical review. B","work_id":"3a235d4b-461f-4f54-a729-01b7185bdc83","year":2019},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.271511Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:eac688ad793d6bbdfaecb8043d1fa04cb845371b0679ee7a16feece766c3dc73","observation_id":"9b8ebbf6-cc0f-489b-9009-07d1a3a94618","resolution":{"observed_at":"2026-08-07T05:51:32.048964Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:51:33.542049Z","title":null,"venue":null,"work_id":"430b8689-2686-4861-9cea-44822f373166","year":1957},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.287445Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:5a169bb1a4bad62aecc360419e384dcbca3b60c414d3eb56bbda2a45ca3c87d9","observation_id":"12d00436-440b-4f1f-81c7-ae8b5446db8c","resolution":{"observed_at":"2026-08-07T05:51:33.550467Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1287/opre.5.5.723","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Bellman, Letter to the Editor–Comment on Dantzig’s paper on discrete-variable extremum problems, Oper","venue":"Operations Research","work_id":"5224e11d-115d-4512-b3a1-a4ad5e70d4db","year":1957},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.313927Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:6a962196c3889e00622a4d4b24170b039ec7e5d2e8774d0ae51d9c1609847728","observation_id":"fc5cb31b-cede-4cb9-9d02-942aea44d5f6","resolution":{"observed_at":"2026-08-07T05:51:31.999597Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:51:31.351647Z","title":"Cacchiani, M","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.351647Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:caa22725e1e7b80ea2e513a4e85c085ac061c91635103ccac5f9063fe5452680","observation_id":"9741ba24-b4c1-402b-914f-2674cc1c2dc2","resolution":{"observed_at":"2026-08-07T05:51:31.351647Z","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":"2026-08-07T05:51:31.368647Z","title":"Kellerer, U","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.368647Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:2b8cc2625bacb1670aa47c3004b0ef2b59a09d24e763256d4724745da2dc6c6e","observation_id":"c919d3bb-756f-4748-a120-39aa83e82e5b","resolution":{"observed_at":"2026-08-07T05:51:31.368647Z","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":"2026-08-07T05:51:33.511254Z","title":"Nishimori, Statistical physics of spin glasses and information processing: an introduction, Oxford University Press, 2001","venue":null,"work_id":"1e25be0c-8092-4a96-b058-90eedd87cde2","year":2001},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.452067Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:e8725956add2f4ce7f213d0f38c7ce5ed1a392911d7c0472c8d1bdaf75e3dd65","observation_id":"3fad99de-fbf5-4e9b-8030-ff371e157cda","resolution":{"observed_at":"2026-08-07T05:51:33.518976Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:51:31.565117Z","title":"Kirkpatrick, D","venue":null,"work_id":null,"year":1978},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.565117Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:061bf4937db32943083aa6ac6dd794ce697747724e90f70113064e33c81653b6","observation_id":"851a3394-3147-414a-889e-0933405599ff","resolution":{"observed_at":"2026-08-07T05:51:31.565117Z","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":"2026-08-07T05:51:31.602810Z","title":"Sherrington, S","venue":null,"work_id":null,"year":1975},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.602810Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:0e72447b0e1286973c82caa4a78f6005d821c7fa63cdbbeb30081367be215ee8","observation_id":"6badbebc-56a1-4712-88e7-e6fbde2f83f9","resolution":{"observed_at":"2026-08-07T05:51:31.602810Z","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":"2026-08-07T05:51:31.607906Z","title":"Boccaletti, V","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.607906Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:30ecf7ab8b992ab4f5525929b599552f402e663bb77c667bc0bc20b9180f21a8","observation_id":"777ca0b4-9cd0-4e8d-b340-5adb8cb5278d","resolution":{"observed_at":"2026-08-07T05:51:31.607906Z","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":"2026-08-07T05:51:31.612688Z","title":null,"venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.612688Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:6345571d8b7e157e5964dfd168bc2e7e4cec1ecb0bc1ed843d92de4eb9be2a0c","observation_id":"14d40a88-239d-4c5d-9de6-f476657ec99e","resolution":{"observed_at":"2026-08-07T05:51:31.612688Z","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":"2026-08-07T05:51:33.483959Z","title":null,"venue":null,"work_id":"947b05bc-1300-45c4-ae70-7f8f100c2a37","year":1962},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.618702Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:31e3f287c74f6544f6380057b95c2625f5bf2823f724b83261b7e4b282648cef","observation_id":"7ef9f044-8d89-4d0e-b2af-d983529578fa","resolution":{"observed_at":"2026-08-07T05:51:33.490427Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:51:33.458008Z","title":null,"venue":null,"work_id":"011ca0e0-c42c-4374-a752-cdf5986bddd3","year":2009},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.625057Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:2334d5e325f252b6bfc0b5685b2afdc17bc36c08d8ac209a2411c0fc40141262","observation_id":"2cccff25-110f-4fc2-9f7c-ca78d8130b2b","resolution":{"observed_at":"2026-08-07T05:51:33.466560Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:51:31.638071Z","title":"Bertsimas , R","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.638071Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:b859ec49b545ca9a11f5de99c89cfe26bce7ae0866eee0513f1a2b24afe7a1af","observation_id":"726b8f03-8d1c-4127-8084-2d4638bbf017","resolution":{"observed_at":"2026-08-07T05:51:31.638071Z","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":"10.1287/ijoc.12.1.57.11901","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":null,"venue":"INFORMS journal on computing","work_id":"2cc72413-3618-46f2-af2f-e38c9660dfac","year":2000},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.643752Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:a2e714e23c620d9ae83d96dc95e0ecc21e2b3ff938af7797c35cd915d179a95b","observation_id":"23725bb5-0059-449e-a20c-8d4d9c6479b0","resolution":{"observed_at":"2026-08-07T05:51:31.856376Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1287/ijoc.13.1.56.9748","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":"Balas, N","venue":"INFORMS journal on computing","work_id":"be22fc9b-5a37-411a-88a8-9d985ad2d264","year":2001},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.648911Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:4dc3088a162a07118200aaae0bf053b893c0872791f2b0abb1436957770f9f51","observation_id":"16c75b9d-b8b7-4c1a-9d98-07826a7aa786","resolution":{"observed_at":"2026-08-07T05:51:31.830244Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2013.0060","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:51:32.767491Z","title":null,"venue":null,"work_id":"192c5585-d9e3-4c4d-b93f-be15cff62963","year":2013},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.653609Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:2e8686c143cd1789e0f0f90f32ecd4c1177e0bcc4ef186ea9117ef8c9cb9feb9","observation_id":"8d41ffe9-49f9-46b5-81cb-84918a4bf763","resolution":{"observed_at":"2026-08-07T05:51:32.779247Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1023/a:1009642405419","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":null,"venue":"Journal of Heuristics","work_id":"1016d970-5dd7-4399-8dfe-58d097e164db","year":1998},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.659116Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:904d02b5788292acee5cdbd4aa6bf49b058022212a24a79863794d801d313fb0","observation_id":"119657dc-47b5-4d38-a0e2-f5ecee25ef83","resolution":{"observed_at":"2026-08-07T05:51:31.808611Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1103/physrevb.59.3617","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":null,"venue":"Physical review. B, Condensed matter","work_id":"d4b7d8cd-21fc-4fa1-b1b2-436a4c004e0f","year":1999},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.665549Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:6fa7ec4f6ce0984f8e157158a06fb938a6e57ea1891c64dcea379ac9674a2423","observation_id":"8cfaf676-9302-4d2a-96a1-2756d2f97f77","resolution":{"observed_at":"2026-08-07T05:51:31.787815Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.ejor.2004.09.057","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":null,"venue":"European Journal of Operational Research","work_id":"f971aefd-b1b1-4ed4-bd38-fceb87805f02","year":2006},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.671610Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:1cba400d635664f8ca97ea11ae54255d66d22b8f71328e7a8d7eabf9c59fb2cd","observation_id":"0797d8f7-09f2-4d55-8a98-5a55bf63af75","resolution":{"observed_at":"2026-08-07T05:51:31.764605Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+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":"2026-08-07T05:51:31.678108Z","title":"Larranaga, C","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.678108Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:d166bf1c6f13f06089915b4352e190b843fa8d86d546c64bd42d3e666b0a6a02","observation_id":"f3a5067e-e4b7-4870-8e08-7b376c819a38","resolution":{"observed_at":"2026-08-07T05:51:31.678108Z","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":"10.1287/opre.5.2.266","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":null,"venue":"Operations Research","work_id":"b5358210-e466-411d-a8c4-f01ae391a111","year":null},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":306,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.301926Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:32cea6c92a7fc794831dc71c8bb4005225250633df3553cfde665ac0e4dc82a1","observation_id":"95235410-0577-40d8-85c5-d6892a2263df","resolution":{"observed_at":"2026-08-07T05:51:32.024489Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2008.0163","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T05:51:32.887207Z","title":null,"venue":null,"work_id":"c49177b3-f7d0-497b-b157-3c6a49faba04","year":2008},"citing_paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems","version":1},"reference_index":743,"source":"pdf_text","source_observed_at":"2026-08-07T05:51:31.632215Z"},"links":{"citing_paper":"/paper/2506.12080"},"observation_digest":"sha256:433f23bbf21d3bc7a183eca12fd3b9498d7be436b71e196903753f3cb8a081bc","observation_id":"56c022e9-a663-47fd-9855-1a6099099783","resolution":{"observed_at":"2026-08-07T05:51:32.900435Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2506.12080","last_updated":"2025-06-08T00:40:50Z","latest_version":1,"primary_category":"physics.gen-ph","snapshot_observed_at":"2026-08-13T15:17:58.560767Z","submitted_at":"2025-06-08T00:40:50Z","title":"Lower bound of computational complexity of knapsack problems"},"reference_resolution":{"displayed":59,"state_counts":{"malformed_identifier":2,"metadata_mismatch":2,"parse_uncertain":0,"unresolved":24,"verified_exact":27,"verified_fuzzy":4},"total_outbound_references":59},"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":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"thesis":"As of 14 August 2026, this Paper Citation Record lists 59 of 59 outbound references and 0 inbound Pith citation observations for arXiv:2506.12080."}