{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:YNKCJAGVSR663USMAFYKONTZY6","short_pith_number":"pith:YNKCJAGV","schema_version":"1.0","canonical_sha256":"c3542480d5947dedd24c0170a73679c79f1a930ec470725eb985c5ab58bcff46","source":{"kind":"arxiv","id":"2605.14522","version":1},"attestation_state":"computed","paper":{"title":"Matrix-Product Belief Propagation for continuous-state-space variables","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Matrix-Product Belief Propagation extends to continuous variables through a Hilbert basis expansion.","cross_cats":["cond-mat.dis-nn"],"primary_cat":"cond-mat.stat-mech","authors_text":"Alfredo Braunstein, Federico Florio","submitted_at":"2026-05-14T08:06:32Z","abstract_excerpt":"Computation of observables in discrete stochastic, possibly conditioned, dynamics over large sparse networks is at the basis of a myriad of applications. The Matrix-Product Belief Propagation method allows a semi-analytical estimation of such observables with a controlled error that depends on the size of the employed matrices, called bond size. Its computational cost is linear in the time horizon and the network size for a large family of models with discrete degrees of freedom. Here, a generalization of this method to models with continuous or mixed continuous/discrete degrees of freedom is "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":true,"formal_links_present":true},"canonical_record":{"source":{"id":"2605.14522","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-05-14T08:06:32Z","cross_cats_sorted":["cond-mat.dis-nn"],"title_canon_sha256":"e4b2500c08acad6145ae6f827b9981e3b5587b86ad9d998d38de4c16746668e9","abstract_canon_sha256":"02a3253f390cab4e5e31e259b684042cf41c24491609953472353ace75097e69"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:06.055911Z","signature_b64":"IivSiWYNIdgDgchG+Bobk2/BK2cw9KrE0czheGq67SmnLJmbzdn7YygSjeccl6XmAtG4vnS+1ZOi809l6JvuDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c3542480d5947dedd24c0170a73679c79f1a930ec470725eb985c5ab58bcff46","last_reissued_at":"2026-05-17T23:39:06.055224Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:06.055224Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Matrix-Product Belief Propagation for continuous-state-space variables","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Matrix-Product Belief Propagation extends to continuous variables through a Hilbert basis expansion.","cross_cats":["cond-mat.dis-nn"],"primary_cat":"cond-mat.stat-mech","authors_text":"Alfredo Braunstein, Federico Florio","submitted_at":"2026-05-14T08:06:32Z","abstract_excerpt":"Computation of observables in discrete stochastic, possibly conditioned, dynamics over large sparse networks is at the basis of a myriad of applications. The Matrix-Product Belief Propagation method allows a semi-analytical estimation of such observables with a controlled error that depends on the size of the employed matrices, called bond size. Its computational cost is linear in the time horizon and the network size for a large family of models with discrete degrees of freedom. Here, a generalization of this method to models with continuous or mixed continuous/discrete degrees of freedom is "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"A generalization of this method to models with continuous or mixed continuous/discrete degrees of freedom is presented, using a tunable expansion in a Hilbert function basis.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That a finite expansion in the chosen Hilbert basis (e.g., Fourier) can accurately represent the continuous degrees of freedom with controlled error for the target models.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Generalizes matrix-product belief propagation to continuous variables using Hilbert basis expansions, enabling linear-cost computation of dynamics and large deviations in mixed-state kinetic Ising models.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Matrix-Product Belief Propagation extends to continuous variables through a Hilbert basis expansion.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"8c7838b6944073c5fdfa85d25551930d27ef7479f3f2abe700924954c864e329"},"source":{"id":"2605.14522","kind":"arxiv","version":1},"verdict":{"id":"d1fafaa4-cf1b-4557-adc1-071153cb7699","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T01:19:18.083370Z","strongest_claim":"A generalization of this method to models with continuous or mixed continuous/discrete degrees of freedom is presented, using a tunable expansion in a Hilbert function basis.","one_line_summary":"Generalizes matrix-product belief propagation to continuous variables using Hilbert basis expansions, enabling linear-cost computation of dynamics and large deviations in mixed-state kinetic Ising models.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That a finite expansion in the chosen Hilbert basis (e.g., Fourier) can accurately represent the continuous degrees of freedom with controlled error for the target models.","pith_extraction_headline":"Matrix-Product Belief Propagation extends to continuous variables through a Hilbert basis expansion."},"references":{"count":19,"sample":[{"doi":"","year":2014,"title":"N. Antulov-Fantulin, A. Lancic, H. Stefancic, M. Si- kic, and T. Smuc, Statistical Inference Framework for Source Detection of Contagion Processes on Arbitrary Network Structures, in2014 IEEE Eighth I","work_id":"bbe95f48-0721-4e47-90d1-567e6c87a9ff","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2023,"title":"A. Braunstein, G. Catania, L. Dall’Asta, M. Mariani, and A. P. Muntoni, Inference in conditioned dynamics through causality restoration, Scientific Reports13, 7350 (2023)","work_id":"4b602cab-5428-461a-818c-f8d6f239a4c4","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1103/physreve.85.031119","year":2012,"title":"Aurell, Dynamic mean-field and cavity methods for diluted Ising systems, Physical Review E85, 10.1103/PhysRevE.85.031119 (2012)","work_id":"ce036210-6178-4858-9085-f4a5e9249756","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2010,"title":"B. Karrer and M. E. J. Newman, Message passing ap- proach for general epidemic models, Physical Review E 82, 016101 (2010)","work_id":"e559fbe1-d5b6-480d-8f86-0d70e3c915eb","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"A. Braunstein, G. Catania, L. Dall’Asta, M. Mariani, F. Mazza, and M. Tarabolo, Small-coupling dynamic cav- ity: A Bayesian mean-field framework for epidemic infer- ence, Physical Review Research7, 02","work_id":"ede4dc89-8428-402e-99f1-bd94768620de","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":19,"snapshot_sha256":"6eacbc42ca9740b9085107de4a0f7cd2d617a218633ccc45f2e0a74dd4bc6f83","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"17a02ec95d336c14cb01d13f78517d901c7271aa5d5fd77a99572183228a2332"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2605.14522","created_at":"2026-05-17T23:39:06.055321+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.14522v1","created_at":"2026-05-17T23:39:06.055321+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.14522","created_at":"2026-05-17T23:39:06.055321+00:00"},{"alias_kind":"pith_short_12","alias_value":"YNKCJAGVSR66","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_16","alias_value":"YNKCJAGVSR663USM","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_8","alias_value":"YNKCJAGV","created_at":"2026-05-18T12:33:37.589309+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":2,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YNKCJAGVSR663USMAFYKONTZY6","json":"https://pith.science/pith/YNKCJAGVSR663USMAFYKONTZY6.json","graph_json":"https://pith.science/api/pith-number/YNKCJAGVSR663USMAFYKONTZY6/graph.json","events_json":"https://pith.science/api/pith-number/YNKCJAGVSR663USMAFYKONTZY6/events.json","paper":"https://pith.science/paper/YNKCJAGV"},"agent_actions":{"view_html":"https://pith.science/pith/YNKCJAGVSR663USMAFYKONTZY6","download_json":"https://pith.science/pith/YNKCJAGVSR663USMAFYKONTZY6.json","view_paper":"https://pith.science/paper/YNKCJAGV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.14522&json=true","fetch_graph":"https://pith.science/api/pith-number/YNKCJAGVSR663USMAFYKONTZY6/graph.json","fetch_events":"https://pith.science/api/pith-number/YNKCJAGVSR663USMAFYKONTZY6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YNKCJAGVSR663USMAFYKONTZY6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YNKCJAGVSR663USMAFYKONTZY6/action/storage_attestation","attest_author":"https://pith.science/pith/YNKCJAGVSR663USMAFYKONTZY6/action/author_attestation","sign_citation":"https://pith.science/pith/YNKCJAGVSR663USMAFYKONTZY6/action/citation_signature","submit_replication":"https://pith.science/pith/YNKCJAGVSR663USMAFYKONTZY6/action/replication_record"}},"created_at":"2026-05-17T23:39:06.055321+00:00","updated_at":"2026-05-17T23:39:06.055321+00:00"}