{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:M5OIPWHEIFSF7XHYG6SJ4YQV72","short_pith_number":"pith:M5OIPWHE","canonical_record":{"source":{"id":"1106.1412","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-06-07T18:41:21Z","cross_cats_sorted":["cs.SY","math-ph","math.MP","math.OC"],"title_canon_sha256":"1e1bd2586bd6e328a3d6168846c55fd262bfcd25bb44b7a6dc4b6b7418dc6b04","abstract_canon_sha256":"44258cea4db036637f66852830295883c2c561609adfc7f74a911d764d80f21a"},"schema_version":"1.0"},"canonical_sha256":"675c87d8e441645fdcf837a49e6215fe87193e769e34477d34c260bfd4d37fbb","source":{"kind":"arxiv","id":"1106.1412","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.1412","created_at":"2026-05-18T04:20:23Z"},{"alias_kind":"arxiv_version","alias_value":"1106.1412v1","created_at":"2026-05-18T04:20:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.1412","created_at":"2026-05-18T04:20:23Z"},{"alias_kind":"pith_short_12","alias_value":"M5OIPWHEIFSF","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"M5OIPWHEIFSF7XHY","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"M5OIPWHE","created_at":"2026-05-18T12:26:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:M5OIPWHEIFSF7XHYG6SJ4YQV72","target":"record","payload":{"canonical_record":{"source":{"id":"1106.1412","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-06-07T18:41:21Z","cross_cats_sorted":["cs.SY","math-ph","math.MP","math.OC"],"title_canon_sha256":"1e1bd2586bd6e328a3d6168846c55fd262bfcd25bb44b7a6dc4b6b7418dc6b04","abstract_canon_sha256":"44258cea4db036637f66852830295883c2c561609adfc7f74a911d764d80f21a"},"schema_version":"1.0"},"canonical_sha256":"675c87d8e441645fdcf837a49e6215fe87193e769e34477d34c260bfd4d37fbb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:20:23.724187Z","signature_b64":"aqLgWyPL7QLqFI2NYBUpvq58YLKHxxPi1XxwpUUGCFOMNL6YpQzYFV3hg/JreLWKcmBK7boIBGz0t2RapmbPCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"675c87d8e441645fdcf837a49e6215fe87193e769e34477d34c260bfd4d37fbb","last_reissued_at":"2026-05-18T04:20:23.723559Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:20:23.723559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1106.1412","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":"2026-05-18T04:20:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gl7GmRAY3wQTbh3fGxwrTCxUQHCP4n609X3618Cpw2O1itnEhGxkaK+/55tMC6f8xbvXXrH3SoBpE3ng6Y+JBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T22:52:04.607737Z"},"content_sha256":"b228d67d7a452f0d900b8d80e212e3667bb9ba74ff0bace54c786946ecfd70ad","schema_version":"1.0","event_id":"sha256:b228d67d7a452f0d900b8d80e212e3667bb9ba74ff0bace54c786946ecfd70ad"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:M5OIPWHEIFSF7XHYG6SJ4YQV72","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Control for Schroedinger operators on tori","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY","math-ph","math.MP","math.OC"],"primary_cat":"math.AP","authors_text":"Maciej Zworski, Nicolas Burq","submitted_at":"2011-06-07T18:41:21Z","abstract_excerpt":"A well known result of Jaffard states that an arbitrary region on a torus controls, in the L2 sense, solutions of the free stationary and dynamical Schroedinger equations. In this note we show that the same result is valid in the presence of a smooth time-independent potential. The methods apply to continuous potentials as well and we conjecture that the L2 control is valid for any bounded time dependent potential."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.1412","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":""},"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":"2026-05-18T04:20:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x8fWrYb7gd3AhzYAUab3TT2OYnNyFmpMvftRSHAuHHfSVvvOCBEkQXwpJ0z8biYAcW4NcsSHXi/S3qWrnwoEBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T22:52:04.608465Z"},"content_sha256":"a4d1ae066b498de2aaf084a76922fcdc27f47c883f31ab491386303066c6773b","schema_version":"1.0","event_id":"sha256:a4d1ae066b498de2aaf084a76922fcdc27f47c883f31ab491386303066c6773b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M5OIPWHEIFSF7XHYG6SJ4YQV72/bundle.json","state_url":"https://pith.science/pith/M5OIPWHEIFSF7XHYG6SJ4YQV72/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M5OIPWHEIFSF7XHYG6SJ4YQV72/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":"2026-06-07T22:52:04Z","links":{"resolver":"https://pith.science/pith/M5OIPWHEIFSF7XHYG6SJ4YQV72","bundle":"https://pith.science/pith/M5OIPWHEIFSF7XHYG6SJ4YQV72/bundle.json","state":"https://pith.science/pith/M5OIPWHEIFSF7XHYG6SJ4YQV72/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M5OIPWHEIFSF7XHYG6SJ4YQV72/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:M5OIPWHEIFSF7XHYG6SJ4YQV72","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":"44258cea4db036637f66852830295883c2c561609adfc7f74a911d764d80f21a","cross_cats_sorted":["cs.SY","math-ph","math.MP","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-06-07T18:41:21Z","title_canon_sha256":"1e1bd2586bd6e328a3d6168846c55fd262bfcd25bb44b7a6dc4b6b7418dc6b04"},"schema_version":"1.0","source":{"id":"1106.1412","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.1412","created_at":"2026-05-18T04:20:23Z"},{"alias_kind":"arxiv_version","alias_value":"1106.1412v1","created_at":"2026-05-18T04:20:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.1412","created_at":"2026-05-18T04:20:23Z"},{"alias_kind":"pith_short_12","alias_value":"M5OIPWHEIFSF","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"M5OIPWHEIFSF7XHY","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"M5OIPWHE","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:a4d1ae066b498de2aaf084a76922fcdc27f47c883f31ab491386303066c6773b","target":"graph","created_at":"2026-05-18T04:20:23Z","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":"A well known result of Jaffard states that an arbitrary region on a torus controls, in the L2 sense, solutions of the free stationary and dynamical Schroedinger equations. In this note we show that the same result is valid in the presence of a smooth time-independent potential. The methods apply to continuous potentials as well and we conjecture that the L2 control is valid for any bounded time dependent potential.","authors_text":"Maciej Zworski, Nicolas Burq","cross_cats":["cs.SY","math-ph","math.MP","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-06-07T18:41:21Z","title":"Control for Schroedinger operators on tori"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.1412","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:b228d67d7a452f0d900b8d80e212e3667bb9ba74ff0bace54c786946ecfd70ad","target":"record","created_at":"2026-05-18T04:20:23Z","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":"44258cea4db036637f66852830295883c2c561609adfc7f74a911d764d80f21a","cross_cats_sorted":["cs.SY","math-ph","math.MP","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-06-07T18:41:21Z","title_canon_sha256":"1e1bd2586bd6e328a3d6168846c55fd262bfcd25bb44b7a6dc4b6b7418dc6b04"},"schema_version":"1.0","source":{"id":"1106.1412","kind":"arxiv","version":1}},"canonical_sha256":"675c87d8e441645fdcf837a49e6215fe87193e769e34477d34c260bfd4d37fbb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"675c87d8e441645fdcf837a49e6215fe87193e769e34477d34c260bfd4d37fbb","first_computed_at":"2026-05-18T04:20:23.723559Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:20:23.723559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aqLgWyPL7QLqFI2NYBUpvq58YLKHxxPi1XxwpUUGCFOMNL6YpQzYFV3hg/JreLWKcmBK7boIBGz0t2RapmbPCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:20:23.724187Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.1412","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b228d67d7a452f0d900b8d80e212e3667bb9ba74ff0bace54c786946ecfd70ad","sha256:a4d1ae066b498de2aaf084a76922fcdc27f47c883f31ab491386303066c6773b"],"state_sha256":"5cc1d5ca811651dd17b35503cc7ec263929d466a016f69a74f2a1d9b1c3291fd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jIDHne8AUV+t29jI7kbPDQTtK5XDSF2nQyYF+ayhiiZjTpJ7IbcpY/HU9Yw5PvrkcJcChqr/cXHmrZopMfs9Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T22:52:04.612376Z","bundle_sha256":"281fee51525a43a25707166f7c43724f945c5ec733b40cded8ed316928afc0ef"}}