{"as_of":"2026-08-14T13:24:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:78fdea90aa61434aadc0064a515afc503850ccacf732f78af4464d009f25402d","coverage":[{"denominator":27,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":27,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-11T04:20:46.924494Z","state":"measured"},{"denominator":27,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":27,"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/2608.07790/citation-record","integrity":"/paper/2608.07790/integrity","json":"/paper/2608.07790/citation-record.json","paper":"/paper/2608.07790"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T04:20:47.445550Z","title":"Metabolic stability and epigenesis in randomly constructed genetic nets","venue":null,"work_id":"d3954534-600b-4aae-a19e-a2135d8507e6","year":1969},"citing_paper":{"arxiv_id":"2608.07790","last_updated":"2026-08-07T22:19:38Z","snapshot_observed_at":"2026-08-13T23:21:15.213743Z","submitted_at":"2026-08-07T22:19:38Z","title":"Permutation theory governs long-term dynamics of critical Boolean networks","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-11T04:20:46.779114Z"},"links":{"citing_paper":"/paper/2608.07790"},"observation_digest":"sha256:2046090653b86d4cb8fa0e0ca8b6a02dcce9268ca992cdf935ea515f3fffaa89","observation_id":"3628f88e-22d9-46c5-86ff-1c094ac3451a","resolution":{"observed_at":"2026-08-11T04:20:47.451027Z","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":"2026-08-11T04:20:47.428723Z","title":"Boolean modeling in systems biology: an overview of methodology and applications.Physical biology, 9(5):055001, 2012","venue":null,"work_id":"9222f3a1-7b9c-4f03-903c-8abeda0dca18","year":2012},"citing_paper":{"arxiv_id":"2608.07790","last_updated":"2026-08-07T22:19:38Z","snapshot_observed_at":"2026-08-13T23:21:15.213743Z","submitted_at":"2026-08-07T22:19:38Z","title":"Permutation theory governs long-term dynamics of critical Boolean networks","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-11T04:20:46.784899Z"},"links":{"citing_paper":"/paper/2608.07790"},"observation_digest":"sha256:8eb87377eaec2bbbb22ba6665fae52736b66f7a4676ea6c6345cb2758f16bce6","observation_id":"df2129a7-71ef-4870-81a7-3bec8b6a4381","resolution":{"observed_at":"2026-08-11T04:20:47.434536Z","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":"2026-08-11T04:20:47.409861Z","title":"The random map model: a disordered model with deter- ministic dynamics.Journal de Physique, 48(6):971–978, 1987","venue":null,"work_id":"5c11d424-e76e-4955-bde8-dc19bc230bf0","year":1987},"citing_paper":{"arxiv_id":"2608.07790","last_updated":"2026-08-07T22:19:38Z","snapshot_observed_at":"2026-08-13T23:21:15.213743Z","submitted_at":"2026-08-07T22:19:38Z","title":"Permutation theory governs long-term dynamics of critical Boolean networks","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-11T04:20:46.789872Z"},"links":{"citing_paper":"/paper/2608.07790"},"observation_digest":"sha256:4041473ba51b312c706ff944d82a837d9e77d5f57875be5cba40c0e4d84a2385","observation_id":"134bb710-ae45-4388-b58c-2aa02dc0d86c","resolution":{"observed_at":"2026-08-11T04:20:47.416382Z","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":"2026-08-11T04:20:47.392116Z","title":"Exact solution of kauffman’s model with connectivity one","venue":null,"work_id":"2c490c54-cb02-4f3b-b25d-16258f0fed77","year":1988},"citing_paper":{"arxiv_id":"2608.07790","last_updated":"2026-08-07T22:19:38Z","snapshot_observed_at":"2026-08-13T23:21:15.213743Z","submitted_at":"2026-08-07T22:19:38Z","title":"Permutation theory governs long-term dynamics of critical Boolean networks","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-11T04:20:46.796249Z"},"links":{"citing_paper":"/paper/2608.07790"},"observation_digest":"sha256:d12e507b4df3b0578e52efafc95d8131ffc229c51afc7e22a38a3cedd9bbf38c","observation_id":"f64966b3-d897-42f4-97e4-770fb0bd4905","resolution":{"observed_at":"2026-08-11T04:20:47.397402Z","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":"2026-08-11T04:20:47.375005Z","title":"Number and length of attractors in a critical kauffman model with connectivity one.Physical review letters, 94(8):088701, 2005","venue":null,"work_id":"986b2601-a627-4291-965f-4b4502c4373c","year":2005},"citing_paper":{"arxiv_id":"2608.07790","last_updated":"2026-08-07T22:19:38Z","snapshot_observed_at":"2026-08-13T23:21:15.213743Z","submitted_at":"2026-08-07T22:19:38Z","title":"Permutation theory governs long-term dynamics of critical Boolean networks","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-11T04:20:46.802571Z"},"links":{"citing_paper":"/paper/2608.07790"},"observation_digest":"sha256:fb32887d17efc50f972426692c2f2f27e9e9f46b633bc0680c8b05293b99979d","observation_id":"88594843-e8fd-46a8-add3-015ef4e98e68","resolution":{"observed_at":"2026-08-11T04:20:47.380513Z","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":"2026-08-11T04:20:47.357785Z","title":"Number of attractors in random boolean networks.Physical Review E—Statistical, Nonlinear, and Soft Matter Physics, 72(1):016110, 2005","venue":null,"work_id":"da9e1214-66d8-4d65-a84a-72bf54b1c7d6","year":2005},"citing_paper":{"arxiv_id":"2608.07790","last_updated":"2026-08-07T22:19:38Z","snapshot_observed_at":"2026-08-13T23:21:15.213743Z","submitted_at":"2026-08-07T22:19:38Z","title":"Permutation theory governs long-term dynamics of critical Boolean networks","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-11T04:20:46.808818Z"},"links":{"citing_paper":"/paper/2608.07790"},"observation_digest":"sha256:c0218f023a2c7327bf254188b7ba03c6d458dd197a20563abc0fa163ff19897e","observation_id":"52fb18f4-40f5-419f-8f33-04546ac3674b","resolution":{"observed_at":"2026-08-11T04:20:47.363721Z","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":"2026-08-11T04:20:47.340308Z","title":"Number of attractors in the critical kauffman model is exponential","venue":null,"work_id":"4780c266-1df0-469d-b1b4-3be771f4b917","year":2023},"citing_paper":{"arxiv_id":"2608.07790","last_updated":"2026-08-07T22:19:38Z","snapshot_observed_at":"2026-08-13T23:21:15.213743Z","submitted_at":"2026-08-07T22:19:38Z","title":"Permutation theory governs long-term dynamics of critical Boolean networks","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-11T04:20:46.814742Z"},"links":{"citing_paper":"/paper/2608.07790"},"observation_digest":"sha256:8921ef499d040f3d4a72fe3596d6bc77a7cf22800123ea116feab6dfc7db5541","observation_id":"a44eaed0-e781-43df-9c68-d2cd63d0a059","resolution":{"observed_at":"2026-08-11T04:20:47.345861Z","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":"2026-08-11T04:20:47.324047Z","title":"Insights from number theory into the critical kauffman model with connectivity one.Journal of Physics A: Mathematical and Theoretical, 57(27):275003, 2024","venue":null,"work_id":"8751c5e3-a130-4e0f-9c70-9debd42a810b","year":2024},"citing_paper":{"arxiv_id":"2608.07790","last_updated":"2026-08-07T22:19:38Z","snapshot_observed_at":"2026-08-13T23:21:15.213743Z","submitted_at":"2026-08-07T22:19:38Z","title":"Permutation theory governs long-term dynamics of critical Boolean networks","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-11T04:20:46.820254Z"},"links":{"citing_paper":"/paper/2608.07790"},"observation_digest":"sha256:9af8f074147e97e05f36085944d56115626b182103be70dc853341552cade2ee","observation_id":"e2e2afcb-b5da-4578-80cf-b4941c7f42ed","resolution":{"observed_at":"2026-08-11T04:20:47.329398Z","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":"2026-08-11T04:20:46.825378Z","title":"Superpolynomial growth in the number of attractors in kauffman networks.Physical Review Letters, 90(9):098701, 2003","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2608.07790","last_updated":"2026-08-07T22:19:38Z","snapshot_observed_at":"2026-08-13T23:21:15.213743Z","submitted_at":"2026-08-07T22:19:38Z","title":"Permutation theory governs long-term dynamics of critical Boolean networks","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-11T04:20:46.825378Z"},"links":{"citing_paper":"/paper/2608.07790"},"observation_digest":"sha256:26db9e550125348fa350b0e0d00036f1c55d5819b3fa2760088a84a2b2fb7284","observation_id":"fac1324b-82aa-4f3f-809e-a88c22118f22","resolution":{"observed_at":"2026-08-11T04:20:46.825378Z","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":"2026-08-11T04:20:46.831041Z","title":"The origins of order: Self-organization and selection in evolution","venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2608.07790","last_updated":"2026-08-07T22:19:38Z","snapshot_observed_at":"2026-08-13T23:21:15.213743Z","submitted_at":"2026-08-07T22:19:38Z","title":"Permutation theory governs long-term dynamics of critical Boolean networks","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-11T04:20:46.831041Z"},"links":{"citing_paper":"/paper/2608.07790"},"observation_digest":"sha256:3d6004dff7cfb40f5212dab5b2097d24055223580235f987a806562d4a76659d","observation_id":"4e314f78-2bdf-46e9-8a5d-a3cb863362f8","resolution":{"observed_at":"2026-08-11T04:20:46.831041Z","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":"2026-08-11T04:20:47.284606Z","title":"Robustness and evolvability in genetic regulatory networks.Journal of theoretical biology, 245(3):433–448, 2007","venue":null,"work_id":"92b8e1b5-9823-4aa1-adf0-3c6f5858af7e","year":2007},"citing_paper":{"arxiv_id":"2608.07790","last_updated":"2026-08-07T22:19:38Z","snapshot_observed_at":"2026-08-13T23:21:15.213743Z","submitted_at":"2026-08-07T22:19:38Z","title":"Permutation theory governs long-term dynamics of critical Boolean networks","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-11T04:20:46.836783Z"},"links":{"citing_paper":"/paper/2608.07790"},"observation_digest":"sha256:0fede12ad5076bb32b1e4ef97fc77e370f87d3c5369064587f5d2cbf718cb60f","observation_id":"151a08c7-42c1-4973-8c22-9a426756b6ac","resolution":{"observed_at":"2026-08-11T04:20:47.291354Z","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":"2026-08-11T04:20:47.262147Z","title":"Critical dynamics in genetic regulatory networks: examples from four kingdoms.PLoS One, 3(6):e2456, 2008","venue":null,"work_id":"ee5835a4-ae7f-4827-93ab-242ca8e25a4e","year":2008},"citing_paper":{"arxiv_id":"2608.07790","last_updated":"2026-08-07T22:19:38Z","snapshot_observed_at":"2026-08-13T23:21:15.213743Z","submitted_at":"2026-08-07T22:19:38Z","title":"Permutation theory governs long-term dynamics of critical Boolean networks","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-11T04:20:46.844323Z"},"links":{"citing_paper":"/paper/2608.07790"},"observation_digest":"sha256:e0abe8c44d05c9e073fe10f9c6b746a115b0dd6f31dbbb4ddf4591cdb5db9e2e","observation_id":"a05df573-8827-4592-9504-b24a092f1bc1","resolution":{"observed_at":"2026-08-11T04:20:47.269997Z","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":"2026-08-11T04:20:47.244641Z","title":"Criticality distinguishes the ensemble of biological regulatory networks.Physical review letters, 121(13):138102, 2018","venue":null,"work_id":"8e4a6c15-c99c-4edc-9052-047d86c053d3","year":2018},"citing_paper":{"arxiv_id":"2608.07790","last_updated":"2026-08-07T22:19:38Z","snapshot_observed_at":"2026-08-13T23:21:15.213743Z","submitted_at":"2026-08-07T22:19:38Z","title":"Permutation theory governs long-term dynamics of critical Boolean networks","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-11T04:20:46.850146Z"},"links":{"citing_paper":"/paper/2608.07790"},"observation_digest":"sha256:f9096492c988bb587ebdf0bf6df6f4cdaa3d35cf30e996239a3b23c8a4dcb960","observation_id":"08a7cded-a1ae-411c-aa6b-822063e27c2d","resolution":{"observed_at":"2026-08-11T04:20:47.250811Z","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":"2026-08-11T04:20:47.223761Z","title":"A meta-analysis of Boolean network models reveals design principles of gene regu- latory networks.Science advances, 10(2):eadj0822, 2024","venue":null,"work_id":"f21e52e3-040f-473c-b488-4787a85af275","year":2024},"citing_paper":{"arxiv_id":"2608.07790","last_updated":"2026-08-07T22:19:38Z","snapshot_observed_at":"2026-08-13T23:21:15.213743Z","submitted_at":"2026-08-07T22:19:38Z","title":"Permutation theory governs long-term dynamics of critical Boolean networks","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-11T04:20:46.856070Z"},"links":{"citing_paper":"/paper/2608.07790"},"observation_digest":"sha256:a0d1e533eb8ed8cefd94d01e4f5f6649e2c6b770ed321e7bcd9c553492fda028","observation_id":"5752270c-b780-4b2a-8c22-46e24a9f44ef","resolution":{"observed_at":"2026-08-11T04:20:47.230667Z","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":"2026-08-11T04:20:47.190822Z","title":"Random boolean networks.Reviews of nonlinear dynamics and complexity, pages 69–110, 2008","venue":null,"work_id":"7526c6b0-ece4-444c-834c-6ca0dea7ef26","year":2008},"citing_paper":{"arxiv_id":"2608.07790","last_updated":"2026-08-07T22:19:38Z","snapshot_observed_at":"2026-08-13T23:21:15.213743Z","submitted_at":"2026-08-07T22:19:38Z","title":"Permutation theory governs long-term dynamics of critical Boolean networks","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-11T04:20:46.861732Z"},"links":{"citing_paper":"/paper/2608.07790"},"observation_digest":"sha256:5518c80cf7c68f9294dbf56519384ddb2fa313f2c5da495fe4b9f9598ca5509f","observation_id":"721c67bf-a2c7-4d4a-89c0-f564b209d013","resolution":{"observed_at":"2026-08-11T04:20:47.208300Z","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":"2026-08-11T04:20:47.170445Z","title":"Investigation of the dynamics of critical k= 2 kauffman networks using second-order loops.Journal of the Physical Society of Japan, 77(9):094002, 2008","venue":null,"work_id":"786b852c-f965-40c1-9063-c213ec973d7e","year":2008},"citing_paper":{"arxiv_id":"2608.07790","last_updated":"2026-08-07T22:19:38Z","snapshot_observed_at":"2026-08-13T23:21:15.213743Z","submitted_at":"2026-08-07T22:19:38Z","title":"Permutation theory governs long-term dynamics of critical Boolean networks","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-11T04:20:46.866535Z"},"links":{"citing_paper":"/paper/2608.07790"},"observation_digest":"sha256:e51319f1954d5399df4af7895946f15b64179b775b5ae0ed668e87dd05e43320","observation_id":"102c1c7d-6b5e-409f-913f-672f6bc481cf","resolution":{"observed_at":"2026-08-11T04:20:47.177058Z","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":"2026-08-11T04:20:47.152794Z","title":"On the number of attractors of posi- tive and negative boolean automata circuits","venue":null,"work_id":"8e58be8c-e06e-456c-8ca5-505e53630656","year":2010},"citing_paper":{"arxiv_id":"2608.07790","last_updated":"2026-08-07T22:19:38Z","snapshot_observed_at":"2026-08-13T23:21:15.213743Z","submitted_at":"2026-08-07T22:19:38Z","title":"Permutation theory governs long-term dynamics of critical Boolean networks","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-11T04:20:46.870898Z"},"links":{"citing_paper":"/paper/2608.07790"},"observation_digest":"sha256:fe84b21cd3e8f8e93fe81d79bb1dd66145d9a5f19f9e617fbebfc5a4cbfc0312","observation_id":"a191ad23-b8be-4757-8c92-77f737b57987","resolution":{"observed_at":"2026-08-11T04:20:47.158678Z","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":"2026-08-11T04:20:47.133410Z","title":"World Scientific, 2017","venue":null,"work_id":"7ef0610d-a6de-4ce8-aa14-e6327a602b0d","year":2017},"citing_paper":{"arxiv_id":"2608.07790","last_updated":"2026-08-07T22:19:38Z","snapshot_observed_at":"2026-08-13T23:21:15.213743Z","submitted_at":"2026-08-07T22:19:38Z","title":"Permutation theory governs long-term dynamics of critical Boolean networks","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-11T04:20:46.875294Z"},"links":{"citing_paper":"/paper/2608.07790"},"observation_digest":"sha256:717bce716253a7702199459afac67463c395eda2db8f06ad3bd2fd7d09b0297d","observation_id":"bf45918d-40a6-4cbb-b8e7-3e9c08a9e57d","resolution":{"observed_at":"2026-08-11T04:20:47.140019Z","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":"2026-08-11T04:20:47.115166Z","title":"On some problems of a statistical group-theory","venue":null,"work_id":"ddfd7164-e45a-4d7b-887c-5b0b367395c7","year":1965},"citing_paper":{"arxiv_id":"2608.07790","last_updated":"2026-08-07T22:19:38Z","snapshot_observed_at":"2026-08-13T23:21:15.213743Z","submitted_at":"2026-08-07T22:19:38Z","title":"Permutation theory governs long-term dynamics of critical Boolean networks","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-11T04:20:46.879606Z"},"links":{"citing_paper":"/paper/2608.07790"},"observation_digest":"sha256:cfd25e25593fc10a01cfac8541c811fd5b14327b28d4fb96b2a61870d4cccf8b","observation_id":"037fa953-6c2a-4b0a-8582-015e899ea592","resolution":{"observed_at":"2026-08-11T04:20:47.122169Z","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":"2026-08-11T04:20:47.091608Z","title":"On some problems of a statistical group-theory","venue":null,"work_id":"9c48612c-da6d-4b57-be62-4bc447e72d6b","year":1967},"citing_paper":{"arxiv_id":"2608.07790","last_updated":"2026-08-07T22:19:38Z","snapshot_observed_at":"2026-08-13T23:21:15.213743Z","submitted_at":"2026-08-07T22:19:38Z","title":"Permutation theory governs long-term dynamics of critical Boolean networks","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-11T04:20:46.884845Z"},"links":{"citing_paper":"/paper/2608.07790"},"observation_digest":"sha256:308e3cb9664342614ec435d207d0586a4ee585f4886942fe191ce78a783cdf3b","observation_id":"f09cd308-49a7-4b38-bc3b-ec30561e8fb9","resolution":{"observed_at":"2026-08-11T04:20:47.102022Z","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":"2026-08-11T04:20:47.071748Z","title":"On some problems of a statistical group-theory","venue":null,"work_id":"3ff79e5d-b0fe-4f68-ae55-308be2feb971","year":1967},"citing_paper":{"arxiv_id":"2608.07790","last_updated":"2026-08-07T22:19:38Z","snapshot_observed_at":"2026-08-13T23:21:15.213743Z","submitted_at":"2026-08-07T22:19:38Z","title":"Permutation theory governs long-term dynamics of critical Boolean networks","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-11T04:20:46.890786Z"},"links":{"citing_paper":"/paper/2608.07790"},"observation_digest":"sha256:1fc73ccb5fa0ebc6e97af5669865829a89cb14d7254dfe2c8dbd518f886c0779","observation_id":"d0354ab4-603e-4c1d-8f0e-3345931171f6","resolution":{"observed_at":"2026-08-11T04:20:47.077710Z","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":"2026-08-11T04:20:47.052919Z","title":"On some problems of a statistical group-theory","venue":null,"work_id":"d733d0b3-4853-400e-aada-a75b00314f29","year":1968},"citing_paper":{"arxiv_id":"2608.07790","last_updated":"2026-08-07T22:19:38Z","snapshot_observed_at":"2026-08-13T23:21:15.213743Z","submitted_at":"2026-08-07T22:19:38Z","title":"Permutation theory governs long-term dynamics of critical Boolean networks","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-11T04:20:46.896146Z"},"links":{"citing_paper":"/paper/2608.07790"},"observation_digest":"sha256:d30ef2c451e17b6457f9d4d7f6671e3bc171163fec47b98e0ba1e4db0341c4ba","observation_id":"2da03d64-6dc3-4aaf-ae3d-3a693b34c4a7","resolution":{"observed_at":"2026-08-11T04:20:47.058339Z","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":"2026-08-11T04:20:47.034215Z","title":"Über die maximalordnung der permutationen gegebenen grades.Archiv der Math","venue":null,"work_id":"cccfcafc-3709-4d33-a522-61a1996b55b9","year":1903},"citing_paper":{"arxiv_id":"2608.07790","last_updated":"2026-08-07T22:19:38Z","snapshot_observed_at":"2026-08-13T23:21:15.213743Z","submitted_at":"2026-08-07T22:19:38Z","title":"Permutation theory governs long-term dynamics of critical Boolean networks","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-11T04:20:46.902138Z"},"links":{"citing_paper":"/paper/2608.07790"},"observation_digest":"sha256:8c0a574ba899d13f7d4ae6b97b176b9c1d0ef015f6e98000ef87a1966dbcdc2a","observation_id":"81cb0838-ec54-4cee-9274-bcfa548a4450","resolution":{"observed_at":"2026-08-11T04:20:47.039844Z","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":"2026-08-11T04:20:47.016432Z","title":"The expected order of a random permutation.Bulletin of the London Mathematical Society, 23(1):34–42, 1991","venue":null,"work_id":"2f44f424-34df-459d-80c1-a928b48cdda7","year":1991},"citing_paper":{"arxiv_id":"2608.07790","last_updated":"2026-08-07T22:19:38Z","snapshot_observed_at":"2026-08-13T23:21:15.213743Z","submitted_at":"2026-08-07T22:19:38Z","title":"Permutation theory governs long-term dynamics of critical Boolean networks","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-11T04:20:46.907938Z"},"links":{"citing_paper":"/paper/2608.07790"},"observation_digest":"sha256:4765ee9bcbaa56c791d6fd50c9bd843aeffa9eb7ebb90a6da4b4cf093ad384f3","observation_id":"c2f7af42-978c-4b94-a2e8-f5769467c5f0","resolution":{"observed_at":"2026-08-11T04:20:47.022267Z","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":{"arxiv_id":"2104.12019","last_updated":"2022-09-07T01:15:40Z","snapshot_observed_at":"2026-08-13T19:34:15.553720Z","submitted_at":"2021-04-24T20:34:42Z","title":"Cycle type of random permutations: A toolkit","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2104.12019","snapshot_observed_at":"2026-08-11T04:20:46.913094Z","title":"Cycle type of random permutations: a toolkit.arXiv preprint arXiv:2104.12019, 2021","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2608.07790","last_updated":"2026-08-07T22:19:38Z","snapshot_observed_at":"2026-08-13T23:21:15.213743Z","submitted_at":"2026-08-07T22:19:38Z","title":"Permutation theory governs long-term dynamics of critical Boolean networks","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-11T04:20:46.913094Z"},"links":{"cited_paper":"/paper/2104.12019","citing_paper":"/paper/2608.07790"},"observation_digest":"sha256:2365506802a57ce60ea8f9482dac2f90ba087b354839f2e558c2c07d2823e2b4","observation_id":"997dee1b-2dba-4117-a179-7fdbd432ea17","resolution":{"observed_at":"2026-08-11T04:20:46.913094Z","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":"2026-08-11T04:20:46.996898Z","title":"Aristotle: Imo-level automated theorem proving, 2025","venue":null,"work_id":"5956afe9-471f-4b7e-b128-ca7c050544e4","year":2025},"citing_paper":{"arxiv_id":"2608.07790","last_updated":"2026-08-07T22:19:38Z","snapshot_observed_at":"2026-08-13T23:21:15.213743Z","submitted_at":"2026-08-07T22:19:38Z","title":"Permutation theory governs long-term dynamics of critical Boolean networks","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-11T04:20:46.919373Z"},"links":{"citing_paper":"/paper/2608.07790"},"observation_digest":"sha256:ee18cfc6d4bedcceeda606b23d9ad8f83d7e667d29a9427139411d99c7afd654","observation_id":"141cc65a-4ded-4370-840b-83ce48686212","resolution":{"observed_at":"2026-08-11T04:20:47.003938Z","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":"2026-08-11T04:20:46.978512Z","title":"Courier Corporation, 1981","venue":null,"work_id":"3fd98933-adfd-4828-87f6-b1aef18db0fb","year":1981},"citing_paper":{"arxiv_id":"2608.07790","last_updated":"2026-08-07T22:19:38Z","snapshot_observed_at":"2026-08-13T23:21:15.213743Z","submitted_at":"2026-08-07T22:19:38Z","title":"Permutation theory governs long-term dynamics of critical Boolean networks","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-11T04:20:46.924494Z"},"links":{"citing_paper":"/paper/2608.07790"},"observation_digest":"sha256:74ac6ce2924ac6495ea766b9e00cd0bc594a4f61044a43028e5370a22fb51c7c","observation_id":"0a101f45-2189-4c48-8407-c8deccba2ce5","resolution":{"observed_at":"2026-08-11T04:20:46.984819Z","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"}}],"paper":{"arxiv_id":"2608.07790","last_updated":"2026-08-07T22:19:38Z","latest_version":1,"primary_category":"q-bio.MN","snapshot_observed_at":"2026-08-13T23:21:15.213743Z","submitted_at":"2026-08-07T22:19:38Z","title":"Permutation theory governs long-term dynamics of critical Boolean networks"},"reference_resolution":{"displayed":27,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":3,"verified_exact":0,"verified_fuzzy":24},"total_outbound_references":27},"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 27 of 27 outbound references and 0 inbound Pith citation observations for arXiv:2608.07790."}