{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:WXJCS2JA5LM5AACRGQFK2MKP22","short_pith_number":"pith:WXJCS2JA","canonical_record":{"source":{"id":"1708.02926","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-08-09T17:53:55Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"6609f9a7e1163890e0d3436b16ee47d1f4ba1d81b535f841b01186f85ead65c8","abstract_canon_sha256":"5927cb29821ed03ff97f0c1ad5f743970fbe3a1f143bf704fd5802f923943443"},"schema_version":"1.0"},"canonical_sha256":"b5d2296920ead9d00051340aad314fd68e40d9c6cd682ce62618674d3300f7fe","source":{"kind":"arxiv","id":"1708.02926","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.02926","created_at":"2026-05-18T00:16:31Z"},{"alias_kind":"arxiv_version","alias_value":"1708.02926v1","created_at":"2026-05-18T00:16:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.02926","created_at":"2026-05-18T00:16:31Z"},{"alias_kind":"pith_short_12","alias_value":"WXJCS2JA5LM5","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WXJCS2JA5LM5AACR","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WXJCS2JA","created_at":"2026-05-18T12:31:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:WXJCS2JA5LM5AACRGQFK2MKP22","target":"record","payload":{"canonical_record":{"source":{"id":"1708.02926","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-08-09T17:53:55Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"6609f9a7e1163890e0d3436b16ee47d1f4ba1d81b535f841b01186f85ead65c8","abstract_canon_sha256":"5927cb29821ed03ff97f0c1ad5f743970fbe3a1f143bf704fd5802f923943443"},"schema_version":"1.0"},"canonical_sha256":"b5d2296920ead9d00051340aad314fd68e40d9c6cd682ce62618674d3300f7fe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:31.670269Z","signature_b64":"mzsjFEeThEf7HUTLrhTBfqmBPVhIwFPSVLwW8q5LA0Bg167BmINRIn6rG+yBiivdPmGnX5QCcKeVpMws8FavBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b5d2296920ead9d00051340aad314fd68e40d9c6cd682ce62618674d3300f7fe","last_reissued_at":"2026-05-18T00:16:31.669793Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:31.669793Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.02926","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":"2026-05-18T00:16:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uPI1Dh/rASDwiUyrprcnejqlgsUSIpcPSaSbgY0/gDgxws7YPIoRs6kMM+rrXma81kqley2CbI7CZafteB9tBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T20:24:44.391157Z"},"content_sha256":"08cd603ada3cbca9f3c66fa2b72a2d45841fcbc97daa3e0cdae515f70c7f8a1d","schema_version":"1.0","event_id":"sha256:08cd603ada3cbca9f3c66fa2b72a2d45841fcbc97daa3e0cdae515f70c7f8a1d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:WXJCS2JA5LM5AACRGQFK2MKP22","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectral semi-classical analysis of a complex Schr\\\"odinger operator in exterior domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Bernard Helffer, Denis Grebenkov, Yaniv Almog","submitted_at":"2017-08-09T17:53:55Z","abstract_excerpt":"Generalizing previous results obtained for the spectrum of the Dirichlet and Neumann realizations in a bounded domain of a Schr\\\"odinger operator with a purely imaginary potential $h^2\\Delta+iV$ in the semiclassical limit $h\\to 0$ we address the same problem in exterior domains. In particular we obtain the left margin of the spectrum, and the emptiness of the essential part of the spectrum under some additional assumptions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.02926","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":"2026-05-18T00:16:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"720gHG3pXPHmsh1XgKe0mozbBtM+zV0iTwgL80szG9Cl3V96QEGbGPp6ASBk7rJ7oYWDraeRjXAJbn0wxP5OBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T20:24:44.391548Z"},"content_sha256":"9e0b43433e6e6137575154a4a96eed5d2833754ee1cca6ff84bc663b558936a1","schema_version":"1.0","event_id":"sha256:9e0b43433e6e6137575154a4a96eed5d2833754ee1cca6ff84bc663b558936a1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WXJCS2JA5LM5AACRGQFK2MKP22/bundle.json","state_url":"https://pith.science/pith/WXJCS2JA5LM5AACRGQFK2MKP22/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WXJCS2JA5LM5AACRGQFK2MKP22/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":"2026-06-02T20:24:44Z","links":{"resolver":"https://pith.science/pith/WXJCS2JA5LM5AACRGQFK2MKP22","bundle":"https://pith.science/pith/WXJCS2JA5LM5AACRGQFK2MKP22/bundle.json","state":"https://pith.science/pith/WXJCS2JA5LM5AACRGQFK2MKP22/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WXJCS2JA5LM5AACRGQFK2MKP22/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:WXJCS2JA5LM5AACRGQFK2MKP22","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":"5927cb29821ed03ff97f0c1ad5f743970fbe3a1f143bf704fd5802f923943443","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-08-09T17:53:55Z","title_canon_sha256":"6609f9a7e1163890e0d3436b16ee47d1f4ba1d81b535f841b01186f85ead65c8"},"schema_version":"1.0","source":{"id":"1708.02926","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.02926","created_at":"2026-05-18T00:16:31Z"},{"alias_kind":"arxiv_version","alias_value":"1708.02926v1","created_at":"2026-05-18T00:16:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.02926","created_at":"2026-05-18T00:16:31Z"},{"alias_kind":"pith_short_12","alias_value":"WXJCS2JA5LM5","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WXJCS2JA5LM5AACR","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WXJCS2JA","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:9e0b43433e6e6137575154a4a96eed5d2833754ee1cca6ff84bc663b558936a1","target":"graph","created_at":"2026-05-18T00:16:31Z","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":"Generalizing previous results obtained for the spectrum of the Dirichlet and Neumann realizations in a bounded domain of a Schr\\\"odinger operator with a purely imaginary potential $h^2\\Delta+iV$ in the semiclassical limit $h\\to 0$ we address the same problem in exterior domains. In particular we obtain the left margin of the spectrum, and the emptiness of the essential part of the spectrum under some additional assumptions.","authors_text":"Bernard Helffer, Denis Grebenkov, Yaniv Almog","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-08-09T17:53:55Z","title":"Spectral semi-classical analysis of a complex Schr\\\"odinger operator in exterior domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.02926","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":"sha256:08cd603ada3cbca9f3c66fa2b72a2d45841fcbc97daa3e0cdae515f70c7f8a1d","target":"record","created_at":"2026-05-18T00:16:31Z","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":"5927cb29821ed03ff97f0c1ad5f743970fbe3a1f143bf704fd5802f923943443","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-08-09T17:53:55Z","title_canon_sha256":"6609f9a7e1163890e0d3436b16ee47d1f4ba1d81b535f841b01186f85ead65c8"},"schema_version":"1.0","source":{"id":"1708.02926","kind":"arxiv","version":1}},"canonical_sha256":"b5d2296920ead9d00051340aad314fd68e40d9c6cd682ce62618674d3300f7fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b5d2296920ead9d00051340aad314fd68e40d9c6cd682ce62618674d3300f7fe","first_computed_at":"2026-05-18T00:16:31.669793Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:31.669793Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mzsjFEeThEf7HUTLrhTBfqmBPVhIwFPSVLwW8q5LA0Bg167BmINRIn6rG+yBiivdPmGnX5QCcKeVpMws8FavBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:31.670269Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.02926","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08cd603ada3cbca9f3c66fa2b72a2d45841fcbc97daa3e0cdae515f70c7f8a1d","sha256:9e0b43433e6e6137575154a4a96eed5d2833754ee1cca6ff84bc663b558936a1"],"state_sha256":"a46fa44760a4fcee9d61196622b0b981014c3d7967bd0192943f843cace19c66"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dUWX4e+iJVSleUR9l3o+74Tjhy6XSAh1WWI42y/LWoHZ1sFH8UJLfJee7G/E5VhZonL71K/UN4MbV3RsKB6iCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T20:24:44.393536Z","bundle_sha256":"8da2fcb0d571cf4101958a3cf381118e112c73c99fd931bd1ede6fcb7211041c"}}