{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:XKCLHECBMZZYKKYEX35VOEHNOA","short_pith_number":"pith:XKCLHECB","canonical_record":{"source":{"id":"1208.6496","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-08-31T13:44:42Z","cross_cats_sorted":["math.AG","math.AP"],"title_canon_sha256":"8dfa906ccce4a18e68e5a2e5fc2aade3aec9607035cc58232fd052e1fe447c34","abstract_canon_sha256":"54576762791a8a27d9bc1e568675ba0990aeaa79c51f0d3b2f4256fe453f20ef"},"schema_version":"1.0"},"canonical_sha256":"ba84b390416673852b04befb5710ed7011d0b8920851b13892cfd8422ed9d94d","source":{"kind":"arxiv","id":"1208.6496","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.6496","created_at":"2026-05-18T03:38:32Z"},{"alias_kind":"arxiv_version","alias_value":"1208.6496v2","created_at":"2026-05-18T03:38:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.6496","created_at":"2026-05-18T03:38:32Z"},{"alias_kind":"pith_short_12","alias_value":"XKCLHECBMZZY","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XKCLHECBMZZYKKYE","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XKCLHECB","created_at":"2026-05-18T12:27:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:XKCLHECBMZZYKKYEX35VOEHNOA","target":"record","payload":{"canonical_record":{"source":{"id":"1208.6496","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-08-31T13:44:42Z","cross_cats_sorted":["math.AG","math.AP"],"title_canon_sha256":"8dfa906ccce4a18e68e5a2e5fc2aade3aec9607035cc58232fd052e1fe447c34","abstract_canon_sha256":"54576762791a8a27d9bc1e568675ba0990aeaa79c51f0d3b2f4256fe453f20ef"},"schema_version":"1.0"},"canonical_sha256":"ba84b390416673852b04befb5710ed7011d0b8920851b13892cfd8422ed9d94d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:32.738710Z","signature_b64":"2s9VdvS7qdqdG/tNm+CKV5OZtw/u+au6X3uUO2jgFRqFYRZCWnY8ewVPvU7wfC3Ism5vODWLWyAwk9dts0gyBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ba84b390416673852b04befb5710ed7011d0b8920851b13892cfd8422ed9d94d","last_reissued_at":"2026-05-18T03:38:32.738110Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:32.738110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.6496","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":"2026-05-18T03:38:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PfHt6LX75Obh0qfNNqNzdhqpb8ThWqVeSkELNfZswBvO9TK4OEJDjeqU8YZdktRCUhO0GEn+e3lsw6LLPybuBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T17:22:41.367666Z"},"content_sha256":"a25b9c693a6e969e058ec8740a5c9f163605e5f988aa9b24a2738d83fa91269e","schema_version":"1.0","event_id":"sha256:a25b9c693a6e969e058ec8740a5c9f163605e5f988aa9b24a2738d83fa91269e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:XKCLHECBMZZYKKYEX35VOEHNOA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Algebraic characterization of autonomy and controllability of behaviours of spatially invariant systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.AP"],"primary_cat":"math.OC","authors_text":"Amol Sasane","submitted_at":"2012-08-31T13:44:42Z","abstract_excerpt":"We give algebraic characterizations of the properties of autonomy and of controllability of behaviours of spatially invariant dynamical systems, consisting of distributional solutions, that are periodic in the spatial variables, to a system pf partial differential equations corresponding to a polynomial matrix M in (C[\\xi_1,...,\\xi_d, \\tau])^{m \\times n}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.6496","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":"2026-05-18T03:38:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j8cN3ESsNQ5Fb9ztrf1/Q2oSxJSXGwoZkG9vjjEswMRObGujY+IOzF8bb2/bRfFWwNSBDo3njFLLlfOsX3a5Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T17:22:41.368464Z"},"content_sha256":"e7e9eaaf8a9dca617beda49de696da0719f33193e4c2fdc7ace9ee45636cf3af","schema_version":"1.0","event_id":"sha256:e7e9eaaf8a9dca617beda49de696da0719f33193e4c2fdc7ace9ee45636cf3af"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XKCLHECBMZZYKKYEX35VOEHNOA/bundle.json","state_url":"https://pith.science/pith/XKCLHECBMZZYKKYEX35VOEHNOA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XKCLHECBMZZYKKYEX35VOEHNOA/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":"2026-06-08T17:22:41Z","links":{"resolver":"https://pith.science/pith/XKCLHECBMZZYKKYEX35VOEHNOA","bundle":"https://pith.science/pith/XKCLHECBMZZYKKYEX35VOEHNOA/bundle.json","state":"https://pith.science/pith/XKCLHECBMZZYKKYEX35VOEHNOA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XKCLHECBMZZYKKYEX35VOEHNOA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:XKCLHECBMZZYKKYEX35VOEHNOA","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":"54576762791a8a27d9bc1e568675ba0990aeaa79c51f0d3b2f4256fe453f20ef","cross_cats_sorted":["math.AG","math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-08-31T13:44:42Z","title_canon_sha256":"8dfa906ccce4a18e68e5a2e5fc2aade3aec9607035cc58232fd052e1fe447c34"},"schema_version":"1.0","source":{"id":"1208.6496","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.6496","created_at":"2026-05-18T03:38:32Z"},{"alias_kind":"arxiv_version","alias_value":"1208.6496v2","created_at":"2026-05-18T03:38:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.6496","created_at":"2026-05-18T03:38:32Z"},{"alias_kind":"pith_short_12","alias_value":"XKCLHECBMZZY","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XKCLHECBMZZYKKYE","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XKCLHECB","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:e7e9eaaf8a9dca617beda49de696da0719f33193e4c2fdc7ace9ee45636cf3af","target":"graph","created_at":"2026-05-18T03:38:32Z","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 give algebraic characterizations of the properties of autonomy and of controllability of behaviours of spatially invariant dynamical systems, consisting of distributional solutions, that are periodic in the spatial variables, to a system pf partial differential equations corresponding to a polynomial matrix M in (C[\\xi_1,...,\\xi_d, \\tau])^{m \\times n}.","authors_text":"Amol Sasane","cross_cats":["math.AG","math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-08-31T13:44:42Z","title":"Algebraic characterization of autonomy and controllability of behaviours of spatially invariant systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.6496","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:a25b9c693a6e969e058ec8740a5c9f163605e5f988aa9b24a2738d83fa91269e","target":"record","created_at":"2026-05-18T03:38:32Z","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":"54576762791a8a27d9bc1e568675ba0990aeaa79c51f0d3b2f4256fe453f20ef","cross_cats_sorted":["math.AG","math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-08-31T13:44:42Z","title_canon_sha256":"8dfa906ccce4a18e68e5a2e5fc2aade3aec9607035cc58232fd052e1fe447c34"},"schema_version":"1.0","source":{"id":"1208.6496","kind":"arxiv","version":2}},"canonical_sha256":"ba84b390416673852b04befb5710ed7011d0b8920851b13892cfd8422ed9d94d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ba84b390416673852b04befb5710ed7011d0b8920851b13892cfd8422ed9d94d","first_computed_at":"2026-05-18T03:38:32.738110Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:32.738110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2s9VdvS7qdqdG/tNm+CKV5OZtw/u+au6X3uUO2jgFRqFYRZCWnY8ewVPvU7wfC3Ism5vODWLWyAwk9dts0gyBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:32.738710Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.6496","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a25b9c693a6e969e058ec8740a5c9f163605e5f988aa9b24a2738d83fa91269e","sha256:e7e9eaaf8a9dca617beda49de696da0719f33193e4c2fdc7ace9ee45636cf3af"],"state_sha256":"5150adc8dc36f916e6325ba8b3e7ab250449879ac4632a454e088a04f0c9e307"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qWy0ujByrRDS0joC6kJ8VEZt+Ub+nE75e1Rn733uiSGJKgqv0t4LUbzOLKT2KXp0myQJtCF76JJPGynMoY74CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T17:22:41.372607Z","bundle_sha256":"cf8a4345fcbc4c8a3b5fcf40cd23a6f54d0659bb577229eb4ee01db49f37241b"}}