{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:RAA34QXIGI6R6ADENMWU2MKD6G","short_pith_number":"pith:RAA34QXI","canonical_record":{"source":{"id":"2507.14040","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2025-07-18T16:10:52Z","cross_cats_sorted":["nlin.CD"],"title_canon_sha256":"2eecaa21eeb5def98af6e1d596ee5e9a971e2cd0d45b865bcfe9f01749bd47f6","abstract_canon_sha256":"4254e766a2c515dcc3dd20f10fa2e301eaa050e769b838415cfee582242572bf"},"schema_version":"1.0"},"canonical_sha256":"8801be42e8323d1f00646b2d4d3143f18665c105271622d75b44f2b14238a14a","source":{"kind":"arxiv","id":"2507.14040","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.14040","created_at":"2026-07-05T11:39:27Z"},{"alias_kind":"arxiv_version","alias_value":"2507.14040v1","created_at":"2026-07-05T11:39:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.14040","created_at":"2026-07-05T11:39:27Z"},{"alias_kind":"pith_short_12","alias_value":"RAA34QXIGI6R","created_at":"2026-07-05T11:39:27Z"},{"alias_kind":"pith_short_16","alias_value":"RAA34QXIGI6R6ADE","created_at":"2026-07-05T11:39:27Z"},{"alias_kind":"pith_short_8","alias_value":"RAA34QXI","created_at":"2026-07-05T11:39:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:RAA34QXIGI6R6ADENMWU2MKD6G","target":"record","payload":{"canonical_record":{"source":{"id":"2507.14040","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2025-07-18T16:10:52Z","cross_cats_sorted":["nlin.CD"],"title_canon_sha256":"2eecaa21eeb5def98af6e1d596ee5e9a971e2cd0d45b865bcfe9f01749bd47f6","abstract_canon_sha256":"4254e766a2c515dcc3dd20f10fa2e301eaa050e769b838415cfee582242572bf"},"schema_version":"1.0"},"canonical_sha256":"8801be42e8323d1f00646b2d4d3143f18665c105271622d75b44f2b14238a14a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:39:27.602475Z","signature_b64":"skm1JbutgTYx2uAcY7QA97CTYk+Ww7AuB0xpl/Jeyfhm0mlGJ/2Hh9PC8/JiDrzMs6W+gExQUrvL+sRA/mENBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8801be42e8323d1f00646b2d4d3143f18665c105271622d75b44f2b14238a14a","last_reissued_at":"2026-07-05T11:39:27.601883Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:39:27.601883Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.14040","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:39:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7CL72u2p1lbQpYnDF5lC8pO1/cglPwcC7T4RmJfvK3Hv2w2V7l+xfpcYAdmGLvNqzXz6ClXhMpxFNPgf/mibAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T15:30:03.623118Z"},"content_sha256":"b1253d11e28c3f8255b05a56d3e09e56e7255ff06f8eeee16bcdf98db9343ff7","schema_version":"1.0","event_id":"sha256:b1253d11e28c3f8255b05a56d3e09e56e7255ff06f8eeee16bcdf98db9343ff7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:RAA34QXIGI6R6ADENMWU2MKD6G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Markov matrix perturbations to optimize dynamical and entropy functionals","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["nlin.CD"],"primary_cat":"math.DS","authors_text":"Giulia Carigi, Manuel Santos Gutierrez, Niccolo Zagli","submitted_at":"2025-07-18T16:10:52Z","abstract_excerpt":"An important problem in applied dynamical systems is to compute the external forcing that provokes the largest response of a desired observable quantity. For this, we investigate the perturbation theory of Markov matrices in connection with linear response theory in statistical physics. We use perturbative expansions to derive linear algorithms to optimize physically relevant quantities such as: entropy, Kullback-Liebler-divergence and entropy production of Markov matrices and their related probability vectors. These optimization algorithms are applied to Markov chain representations of discre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.14040","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.14040/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:39:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eHSvT02yG+76JLDduAmklif8F1eOSn5VMqrYl/+/K0gvTV2QiReql9JKdimvIl1Lm/OYwptBpTa1p7LpMlXJCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T15:30:03.623638Z"},"content_sha256":"2d9b33a61184e4d06a31f06fe2b1d22148f7cabca622c1878e4a78f53c343fd2","schema_version":"1.0","event_id":"sha256:2d9b33a61184e4d06a31f06fe2b1d22148f7cabca622c1878e4a78f53c343fd2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RAA34QXIGI6R6ADENMWU2MKD6G/bundle.json","state_url":"https://pith.science/pith/RAA34QXIGI6R6ADENMWU2MKD6G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RAA34QXIGI6R6ADENMWU2MKD6G/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-09T15:30:03Z","links":{"resolver":"https://pith.science/pith/RAA34QXIGI6R6ADENMWU2MKD6G","bundle":"https://pith.science/pith/RAA34QXIGI6R6ADENMWU2MKD6G/bundle.json","state":"https://pith.science/pith/RAA34QXIGI6R6ADENMWU2MKD6G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RAA34QXIGI6R6ADENMWU2MKD6G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:RAA34QXIGI6R6ADENMWU2MKD6G","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"4254e766a2c515dcc3dd20f10fa2e301eaa050e769b838415cfee582242572bf","cross_cats_sorted":["nlin.CD"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2025-07-18T16:10:52Z","title_canon_sha256":"2eecaa21eeb5def98af6e1d596ee5e9a971e2cd0d45b865bcfe9f01749bd47f6"},"schema_version":"1.0","source":{"id":"2507.14040","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.14040","created_at":"2026-07-05T11:39:27Z"},{"alias_kind":"arxiv_version","alias_value":"2507.14040v1","created_at":"2026-07-05T11:39:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.14040","created_at":"2026-07-05T11:39:27Z"},{"alias_kind":"pith_short_12","alias_value":"RAA34QXIGI6R","created_at":"2026-07-05T11:39:27Z"},{"alias_kind":"pith_short_16","alias_value":"RAA34QXIGI6R6ADE","created_at":"2026-07-05T11:39:27Z"},{"alias_kind":"pith_short_8","alias_value":"RAA34QXI","created_at":"2026-07-05T11:39:27Z"}],"graph_snapshots":[{"event_id":"sha256:2d9b33a61184e4d06a31f06fe2b1d22148f7cabca622c1878e4a78f53c343fd2","target":"graph","created_at":"2026-07-05T11:39:27Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2507.14040/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"An important problem in applied dynamical systems is to compute the external forcing that provokes the largest response of a desired observable quantity. For this, we investigate the perturbation theory of Markov matrices in connection with linear response theory in statistical physics. We use perturbative expansions to derive linear algorithms to optimize physically relevant quantities such as: entropy, Kullback-Liebler-divergence and entropy production of Markov matrices and their related probability vectors. These optimization algorithms are applied to Markov chain representations of discre","authors_text":"Giulia Carigi, Manuel Santos Gutierrez, Niccolo Zagli","cross_cats":["nlin.CD"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2025-07-18T16:10:52Z","title":"Markov matrix perturbations to optimize dynamical and entropy functionals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.14040","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b1253d11e28c3f8255b05a56d3e09e56e7255ff06f8eeee16bcdf98db9343ff7","target":"record","created_at":"2026-07-05T11:39:27Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"4254e766a2c515dcc3dd20f10fa2e301eaa050e769b838415cfee582242572bf","cross_cats_sorted":["nlin.CD"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2025-07-18T16:10:52Z","title_canon_sha256":"2eecaa21eeb5def98af6e1d596ee5e9a971e2cd0d45b865bcfe9f01749bd47f6"},"schema_version":"1.0","source":{"id":"2507.14040","kind":"arxiv","version":1}},"canonical_sha256":"8801be42e8323d1f00646b2d4d3143f18665c105271622d75b44f2b14238a14a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8801be42e8323d1f00646b2d4d3143f18665c105271622d75b44f2b14238a14a","first_computed_at":"2026-07-05T11:39:27.601883Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:39:27.601883Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"skm1JbutgTYx2uAcY7QA97CTYk+Ww7AuB0xpl/Jeyfhm0mlGJ/2Hh9PC8/JiDrzMs6W+gExQUrvL+sRA/mENBg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:39:27.602475Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.14040","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b1253d11e28c3f8255b05a56d3e09e56e7255ff06f8eeee16bcdf98db9343ff7","sha256:2d9b33a61184e4d06a31f06fe2b1d22148f7cabca622c1878e4a78f53c343fd2"],"state_sha256":"7b1d02887b8b46a6ca3bbabbf1355d9cbf4e2f19bb4de830623d8ecd226b3cbb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qo9rO+iqG3+Qr1JX95Woxr9jEOlGcQh6uyg4nK6e5OqWem3MH5CYfnoU7LUHm2Fk+RzXPumIBjpSjzL4kN43Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T15:30:03.627347Z","bundle_sha256":"8c92dcccb839e50a254ba0a513c790a326cc2f2cd006c316027d6be91ddfe275"}}