{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:LMTE6B5DRLR27ZQTPLXQ7XWJQ3","short_pith_number":"pith:LMTE6B5D","canonical_record":{"source":{"id":"1204.2160","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-04-10T14:14:44Z","cross_cats_sorted":["math.MP","math.OC"],"title_canon_sha256":"d5e68d1d57e9cd6afdaebd60969f4f9bdca058ecae8d0d71997e3f497dfa3e03","abstract_canon_sha256":"30101ed3d380abd00523931b8b1a6a20ae37417719a5ea7147ca7ab8b005c80e"},"schema_version":"1.0"},"canonical_sha256":"5b264f07a38ae3afe6137aef0fdec986e5d2349253a9348973669d4901fe83e8","source":{"kind":"arxiv","id":"1204.2160","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.2160","created_at":"2026-05-18T03:58:13Z"},{"alias_kind":"arxiv_version","alias_value":"1204.2160v1","created_at":"2026-05-18T03:58:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.2160","created_at":"2026-05-18T03:58:13Z"},{"alias_kind":"pith_short_12","alias_value":"LMTE6B5DRLR2","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LMTE6B5DRLR27ZQT","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LMTE6B5D","created_at":"2026-05-18T12:27:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:LMTE6B5DRLR27ZQTPLXQ7XWJQ3","target":"record","payload":{"canonical_record":{"source":{"id":"1204.2160","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-04-10T14:14:44Z","cross_cats_sorted":["math.MP","math.OC"],"title_canon_sha256":"d5e68d1d57e9cd6afdaebd60969f4f9bdca058ecae8d0d71997e3f497dfa3e03","abstract_canon_sha256":"30101ed3d380abd00523931b8b1a6a20ae37417719a5ea7147ca7ab8b005c80e"},"schema_version":"1.0"},"canonical_sha256":"5b264f07a38ae3afe6137aef0fdec986e5d2349253a9348973669d4901fe83e8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:58:13.123136Z","signature_b64":"/WTt0ivc/hHMUl9czildwX5t+bK6yumvosZhuOy4fh8lQyc/NczIYi0+BkjhAsmYIhQ05aKk09EAOkEGWDVHCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5b264f07a38ae3afe6137aef0fdec986e5d2349253a9348973669d4901fe83e8","last_reissued_at":"2026-05-18T03:58:13.122435Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:58:13.122435Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.2160","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":"2026-05-18T03:58:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Dw83Z23JyanW4LA1lNlWHeqn3wvzT39pVzIQOxQPNwa//jpzZW7+e1A6jxwBrfCbxrQfW/kJ/6OKiIF7qJfeBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T01:43:54.497401Z"},"content_sha256":"63811ca4c1397592608b6267f8cae3609f84eef14da05d12aa2512a4ea7bda32","schema_version":"1.0","event_id":"sha256:63811ca4c1397592608b6267f8cae3609f84eef14da05d12aa2512a4ea7bda32"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:LMTE6B5DRLR27ZQTPLXQ7XWJQ3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Controllability of Schroedinger equation with a nonlocal term","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.OC"],"primary_cat":"math-ph","authors_text":"Constanza S\\'anchez Fern\\'andez de la Vega, Diego Rial, Mariano De Leo","submitted_at":"2012-04-10T14:14:44Z","abstract_excerpt":"This paper is concerned with the internal distributed control problem for the 1D Schroedinger equation, $i\\,u_t(x,t)=-u_{xx}+\\alpha(x)\\,u+m(u)\\,u,$ that arises in quantum semiconductor models. Here $m(u)$ is a non local Hartree--type nonlinearity stemming from the coupling with the 1D Poisson equation, and $\\alpha(x)$ is a regular function with linear growth at infinity, including constant electric fields. By means of both the Hilbert Uniqueness Method and the Schauder's fixed point theorem it is shown that for initial and target states belonging to a suitable small neighborhood of the origin,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2160","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":"2026-05-18T03:58:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CW9UPll5vEw2DZyIx9j5iGP6k2u9yR0XrCf3qBxEETfKFnrtayDCP+KvPx1XFnt9ZDbL+044K3ZZdqgqSAK+DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T01:43:54.498212Z"},"content_sha256":"c48a4a6497fa00bdcbb589b1a257d50a450459ed3be6f9fc0a1b5815c6414965","schema_version":"1.0","event_id":"sha256:c48a4a6497fa00bdcbb589b1a257d50a450459ed3be6f9fc0a1b5815c6414965"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LMTE6B5DRLR27ZQTPLXQ7XWJQ3/bundle.json","state_url":"https://pith.science/pith/LMTE6B5DRLR27ZQTPLXQ7XWJQ3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LMTE6B5DRLR27ZQTPLXQ7XWJQ3/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":"2026-06-10T01:43:54Z","links":{"resolver":"https://pith.science/pith/LMTE6B5DRLR27ZQTPLXQ7XWJQ3","bundle":"https://pith.science/pith/LMTE6B5DRLR27ZQTPLXQ7XWJQ3/bundle.json","state":"https://pith.science/pith/LMTE6B5DRLR27ZQTPLXQ7XWJQ3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LMTE6B5DRLR27ZQTPLXQ7XWJQ3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:LMTE6B5DRLR27ZQTPLXQ7XWJQ3","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":"30101ed3d380abd00523931b8b1a6a20ae37417719a5ea7147ca7ab8b005c80e","cross_cats_sorted":["math.MP","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-04-10T14:14:44Z","title_canon_sha256":"d5e68d1d57e9cd6afdaebd60969f4f9bdca058ecae8d0d71997e3f497dfa3e03"},"schema_version":"1.0","source":{"id":"1204.2160","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.2160","created_at":"2026-05-18T03:58:13Z"},{"alias_kind":"arxiv_version","alias_value":"1204.2160v1","created_at":"2026-05-18T03:58:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.2160","created_at":"2026-05-18T03:58:13Z"},{"alias_kind":"pith_short_12","alias_value":"LMTE6B5DRLR2","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LMTE6B5DRLR27ZQT","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LMTE6B5D","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:c48a4a6497fa00bdcbb589b1a257d50a450459ed3be6f9fc0a1b5815c6414965","target":"graph","created_at":"2026-05-18T03:58:13Z","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":"This paper is concerned with the internal distributed control problem for the 1D Schroedinger equation, $i\\,u_t(x,t)=-u_{xx}+\\alpha(x)\\,u+m(u)\\,u,$ that arises in quantum semiconductor models. Here $m(u)$ is a non local Hartree--type nonlinearity stemming from the coupling with the 1D Poisson equation, and $\\alpha(x)$ is a regular function with linear growth at infinity, including constant electric fields. By means of both the Hilbert Uniqueness Method and the Schauder's fixed point theorem it is shown that for initial and target states belonging to a suitable small neighborhood of the origin,","authors_text":"Constanza S\\'anchez Fern\\'andez de la Vega, Diego Rial, Mariano De Leo","cross_cats":["math.MP","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-04-10T14:14:44Z","title":"Controllability of Schroedinger equation with a nonlocal term"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2160","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":"sha256:63811ca4c1397592608b6267f8cae3609f84eef14da05d12aa2512a4ea7bda32","target":"record","created_at":"2026-05-18T03:58:13Z","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":"30101ed3d380abd00523931b8b1a6a20ae37417719a5ea7147ca7ab8b005c80e","cross_cats_sorted":["math.MP","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-04-10T14:14:44Z","title_canon_sha256":"d5e68d1d57e9cd6afdaebd60969f4f9bdca058ecae8d0d71997e3f497dfa3e03"},"schema_version":"1.0","source":{"id":"1204.2160","kind":"arxiv","version":1}},"canonical_sha256":"5b264f07a38ae3afe6137aef0fdec986e5d2349253a9348973669d4901fe83e8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5b264f07a38ae3afe6137aef0fdec986e5d2349253a9348973669d4901fe83e8","first_computed_at":"2026-05-18T03:58:13.122435Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:58:13.122435Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/WTt0ivc/hHMUl9czildwX5t+bK6yumvosZhuOy4fh8lQyc/NczIYi0+BkjhAsmYIhQ05aKk09EAOkEGWDVHCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:58:13.123136Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.2160","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:63811ca4c1397592608b6267f8cae3609f84eef14da05d12aa2512a4ea7bda32","sha256:c48a4a6497fa00bdcbb589b1a257d50a450459ed3be6f9fc0a1b5815c6414965"],"state_sha256":"c35c994390c8e4fb4fbf4f0fc1939eb3c5168760cf4fac8122487026d0b35409"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OpFnVmqqtZgAQN6jx41TEb0SDkVx6bxnLxEFzO4x3uGXXHFLAFeDZP9Q7mCfagTXIq4HAGDtOG/rjeIx18hzCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T01:43:54.502388Z","bundle_sha256":"1d0142b3bee6bbf1cbb2d36b03c6d62107d4eb1326160d63ae40f4d89161ff1a"}}