{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:62YO2KCBTVOFCRHJUY2AEMZBCN","short_pith_number":"pith:62YO2KCB","canonical_record":{"source":{"id":"1301.1235","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-01-07T15:50:15Z","cross_cats_sorted":["math.DS","math.MP","nlin.CD"],"title_canon_sha256":"7a796c509875564d835d6e26871451e9ac749266826dd7c24306e6a1c50dc4a7","abstract_canon_sha256":"c71161329a96adc6bf388bfed15261e0249a2ec59331187d83391a4f1842bfbc"},"schema_version":"1.0"},"canonical_sha256":"f6b0ed28419d5c5144e9a6340233211342ccda1b80fe6825a7a98baef1247883","source":{"kind":"arxiv","id":"1301.1235","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.1235","created_at":"2026-05-18T02:20:29Z"},{"alias_kind":"arxiv_version","alias_value":"1301.1235v2","created_at":"2026-05-18T02:20:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1235","created_at":"2026-05-18T02:20:29Z"},{"alias_kind":"pith_short_12","alias_value":"62YO2KCBTVOF","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"62YO2KCBTVOFCRHJ","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"62YO2KCB","created_at":"2026-05-18T12:27:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:62YO2KCBTVOFCRHJUY2AEMZBCN","target":"record","payload":{"canonical_record":{"source":{"id":"1301.1235","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-01-07T15:50:15Z","cross_cats_sorted":["math.DS","math.MP","nlin.CD"],"title_canon_sha256":"7a796c509875564d835d6e26871451e9ac749266826dd7c24306e6a1c50dc4a7","abstract_canon_sha256":"c71161329a96adc6bf388bfed15261e0249a2ec59331187d83391a4f1842bfbc"},"schema_version":"1.0"},"canonical_sha256":"f6b0ed28419d5c5144e9a6340233211342ccda1b80fe6825a7a98baef1247883","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:20:29.142262Z","signature_b64":"jt29cd1khzc+nwZtCgR8ddO55BHE5fUSsHO2outzvYFF2QETQI2BHf+/M2UCoRH7GKabzUlTb37iJ0VPejrxAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6b0ed28419d5c5144e9a6340233211342ccda1b80fe6825a7a98baef1247883","last_reissued_at":"2026-05-18T02:20:29.141814Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:20:29.141814Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.1235","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:20:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BbL7yI2Ntam+SZEfIs/SS3ySMk1p6P7u6c+ZAbSlGBy2WLwK6E2k6vuyLVG/7oho8fdedsnY5Tr0vHfOxVruCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T04:56:55.449104Z"},"content_sha256":"1b094149314f565b975cd8c48a61430f3dc5a71e05faa48033b6b2b4752747e6","schema_version":"1.0","event_id":"sha256:1b094149314f565b975cd8c48a61430f3dc5a71e05faa48033b6b2b4752747e6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:62YO2KCBTVOFCRHJUY2AEMZBCN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Controlling General Polynomial Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.MP","nlin.CD"],"primary_cat":"math-ph","authors_text":"Jean-Pierre Eckmann, No\\'e Cuneo","submitted_at":"2013-01-07T15:50:15Z","abstract_excerpt":"We consider networks of massive particles connected by non-linear springs. Some particles interact with heat baths at different temperatures, which are modeled as stochastic driving forces. The structure of the network is arbitrary, but the motion of each particle is 1D. For polynomial interactions, we give sufficient conditions for H\\\"ormander's \"bracket condition\" to hold, which implies the uniqueness of the steady state (if it exists), as well as the controllability of the associated system in control theory. These conditions are constructive; they are formulated in terms of inequivalence o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1235","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T02:20:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sBEIbGObmO76T0QnwAr8C3gGW4PUzfpJx0mPlzFAlJ6U1LvffCdJEQ12UTkDdJn0hbErtfs7LfxA4IztBbGYAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T04:56:55.449471Z"},"content_sha256":"d9618e60531477a1cb4821384185db56965cb391616e82ff2134c70b5ba420d7","schema_version":"1.0","event_id":"sha256:d9618e60531477a1cb4821384185db56965cb391616e82ff2134c70b5ba420d7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/62YO2KCBTVOFCRHJUY2AEMZBCN/bundle.json","state_url":"https://pith.science/pith/62YO2KCBTVOFCRHJUY2AEMZBCN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/62YO2KCBTVOFCRHJUY2AEMZBCN/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":"2026-05-28T04:56:55Z","links":{"resolver":"https://pith.science/pith/62YO2KCBTVOFCRHJUY2AEMZBCN","bundle":"https://pith.science/pith/62YO2KCBTVOFCRHJUY2AEMZBCN/bundle.json","state":"https://pith.science/pith/62YO2KCBTVOFCRHJUY2AEMZBCN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/62YO2KCBTVOFCRHJUY2AEMZBCN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:62YO2KCBTVOFCRHJUY2AEMZBCN","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":"c71161329a96adc6bf388bfed15261e0249a2ec59331187d83391a4f1842bfbc","cross_cats_sorted":["math.DS","math.MP","nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-01-07T15:50:15Z","title_canon_sha256":"7a796c509875564d835d6e26871451e9ac749266826dd7c24306e6a1c50dc4a7"},"schema_version":"1.0","source":{"id":"1301.1235","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.1235","created_at":"2026-05-18T02:20:29Z"},{"alias_kind":"arxiv_version","alias_value":"1301.1235v2","created_at":"2026-05-18T02:20:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1235","created_at":"2026-05-18T02:20:29Z"},{"alias_kind":"pith_short_12","alias_value":"62YO2KCBTVOF","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"62YO2KCBTVOFCRHJ","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"62YO2KCB","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:d9618e60531477a1cb4821384185db56965cb391616e82ff2134c70b5ba420d7","target":"graph","created_at":"2026-05-18T02:20:29Z","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"},"paper":{"abstract_excerpt":"We consider networks of massive particles connected by non-linear springs. Some particles interact with heat baths at different temperatures, which are modeled as stochastic driving forces. The structure of the network is arbitrary, but the motion of each particle is 1D. For polynomial interactions, we give sufficient conditions for H\\\"ormander's \"bracket condition\" to hold, which implies the uniqueness of the steady state (if it exists), as well as the controllability of the associated system in control theory. These conditions are constructive; they are formulated in terms of inequivalence o","authors_text":"Jean-Pierre Eckmann, No\\'e Cuneo","cross_cats":["math.DS","math.MP","nlin.CD"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-01-07T15:50:15Z","title":"Controlling General Polynomial Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1235","kind":"arxiv","version":2},"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":"sha256:1b094149314f565b975cd8c48a61430f3dc5a71e05faa48033b6b2b4752747e6","target":"record","created_at":"2026-05-18T02:20:29Z","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":"c71161329a96adc6bf388bfed15261e0249a2ec59331187d83391a4f1842bfbc","cross_cats_sorted":["math.DS","math.MP","nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-01-07T15:50:15Z","title_canon_sha256":"7a796c509875564d835d6e26871451e9ac749266826dd7c24306e6a1c50dc4a7"},"schema_version":"1.0","source":{"id":"1301.1235","kind":"arxiv","version":2}},"canonical_sha256":"f6b0ed28419d5c5144e9a6340233211342ccda1b80fe6825a7a98baef1247883","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f6b0ed28419d5c5144e9a6340233211342ccda1b80fe6825a7a98baef1247883","first_computed_at":"2026-05-18T02:20:29.141814Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:29.141814Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jt29cd1khzc+nwZtCgR8ddO55BHE5fUSsHO2outzvYFF2QETQI2BHf+/M2UCoRH7GKabzUlTb37iJ0VPejrxAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:29.142262Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.1235","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1b094149314f565b975cd8c48a61430f3dc5a71e05faa48033b6b2b4752747e6","sha256:d9618e60531477a1cb4821384185db56965cb391616e82ff2134c70b5ba420d7"],"state_sha256":"bc360d96f17a29aba21f7bb5360241d7fcde0c6ffb1f808662e97e8ca0f88913"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l9wNnoJGGUo5CW7aweVQUw0hA8INGIqAAwgODl2ShOGbmvW/4v8/oaM31Qf4l17BVr6LZgKj7JLfArGBuuQ9DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T04:56:55.451551Z","bundle_sha256":"4cc36cc879971528ae49e8063ea2b5434a7970733819dff5fb128ae09c018dd2"}}