{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:5PHHZH77TD7NPK4LLNIIWLAHLO","short_pith_number":"pith:5PHHZH77","canonical_record":{"source":{"id":"1703.06344","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-03-18T20:17:41Z","cross_cats_sorted":[],"title_canon_sha256":"c4249bc1ccd8bf9059dbf43fa64c2446ea8853393a0e62d8fabefceb0f1b4075","abstract_canon_sha256":"6c8ea97c62557aa1f0ae9ae6c4621db0341742082ce9cfc695524f5ccbb5dfd4"},"schema_version":"1.0"},"canonical_sha256":"ebce7c9fff98fed7ab8b5b508b2c075bb54642a2455ce3adfc6bff2a128f2eae","source":{"kind":"arxiv","id":"1703.06344","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.06344","created_at":"2026-05-18T00:25:20Z"},{"alias_kind":"arxiv_version","alias_value":"1703.06344v1","created_at":"2026-05-18T00:25:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.06344","created_at":"2026-05-18T00:25:20Z"},{"alias_kind":"pith_short_12","alias_value":"5PHHZH77TD7N","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5PHHZH77TD7NPK4L","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5PHHZH77","created_at":"2026-05-18T12:31:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:5PHHZH77TD7NPK4LLNIIWLAHLO","target":"record","payload":{"canonical_record":{"source":{"id":"1703.06344","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-03-18T20:17:41Z","cross_cats_sorted":[],"title_canon_sha256":"c4249bc1ccd8bf9059dbf43fa64c2446ea8853393a0e62d8fabefceb0f1b4075","abstract_canon_sha256":"6c8ea97c62557aa1f0ae9ae6c4621db0341742082ce9cfc695524f5ccbb5dfd4"},"schema_version":"1.0"},"canonical_sha256":"ebce7c9fff98fed7ab8b5b508b2c075bb54642a2455ce3adfc6bff2a128f2eae","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:20.916573Z","signature_b64":"J5akzOG+G2NIzohYvYuJkBNt63eXGKTd8DNoWHkn5yuGhdaqfqjcfvI098MduwAxbhEILfgIuX7KNrHY6IK5CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ebce7c9fff98fed7ab8b5b508b2c075bb54642a2455ce3adfc6bff2a128f2eae","last_reissued_at":"2026-05-18T00:25:20.915951Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:20.915951Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.06344","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":"2026-05-18T00:25:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vR27rNSofKVKbLQfuBt58hxK8vCr5LMSyUvjhFV4pM51UHHzvUQtbTi5U5Cmirc5D6bBoOmvhVe2X02vqhhABA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T12:19:24.709171Z"},"content_sha256":"c7e29825f64b3df1dcf558b18a1004e9f3a9975f9a8cd080d6fb10d9d76a2a7f","schema_version":"1.0","event_id":"sha256:c7e29825f64b3df1dcf558b18a1004e9f3a9975f9a8cd080d6fb10d9d76a2a7f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:5PHHZH77TD7NPK4LLNIIWLAHLO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Essential spectrum of elliptic systems of pseudo-differential operators on $L^2(\\mathbb{R}^N)\\oplus L^2(\\mathbb{R}^N)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Christiane Tretter, Orif O. Ibrogimov","submitted_at":"2017-03-18T20:17:41Z","abstract_excerpt":"Inspired by a result of Wong (Commun. Partial Differ. Equ. 13(10):1209-1221, 1988), we establish an analytic description of the essential spectrum of non-self-adjoint mixed-order systems of pseudo-differential operators on $L^2(\\mathbb{R}^N) \\oplus L^2(\\mathbb{R}^N)$ that are uniformly Douglis-Nirenberg elliptic with positive-order diagonal entries. We apply our result to a problem arising in the dynamics of falling liquid films."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.06344","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":"2026-05-18T00:25:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JpntmAmQ7JVzZkzS7+EjCBED1Ba87K6JOZRszVyb4xQyGXwb2fDlyRuaecmUbI4LTIOh6qjn6i3mRHwnH8RmBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T12:19:24.709534Z"},"content_sha256":"2c4e0647fe7e8886339f06ae13ebc7f6c703ea901786e3b93d66e4a1408ae672","schema_version":"1.0","event_id":"sha256:2c4e0647fe7e8886339f06ae13ebc7f6c703ea901786e3b93d66e4a1408ae672"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5PHHZH77TD7NPK4LLNIIWLAHLO/bundle.json","state_url":"https://pith.science/pith/5PHHZH77TD7NPK4LLNIIWLAHLO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5PHHZH77TD7NPK4LLNIIWLAHLO/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":"2026-06-22T12:19:24Z","links":{"resolver":"https://pith.science/pith/5PHHZH77TD7NPK4LLNIIWLAHLO","bundle":"https://pith.science/pith/5PHHZH77TD7NPK4LLNIIWLAHLO/bundle.json","state":"https://pith.science/pith/5PHHZH77TD7NPK4LLNIIWLAHLO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5PHHZH77TD7NPK4LLNIIWLAHLO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:5PHHZH77TD7NPK4LLNIIWLAHLO","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":"6c8ea97c62557aa1f0ae9ae6c4621db0341742082ce9cfc695524f5ccbb5dfd4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-03-18T20:17:41Z","title_canon_sha256":"c4249bc1ccd8bf9059dbf43fa64c2446ea8853393a0e62d8fabefceb0f1b4075"},"schema_version":"1.0","source":{"id":"1703.06344","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.06344","created_at":"2026-05-18T00:25:20Z"},{"alias_kind":"arxiv_version","alias_value":"1703.06344v1","created_at":"2026-05-18T00:25:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.06344","created_at":"2026-05-18T00:25:20Z"},{"alias_kind":"pith_short_12","alias_value":"5PHHZH77TD7N","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5PHHZH77TD7NPK4L","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5PHHZH77","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:2c4e0647fe7e8886339f06ae13ebc7f6c703ea901786e3b93d66e4a1408ae672","target":"graph","created_at":"2026-05-18T00:25:20Z","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":"Inspired by a result of Wong (Commun. Partial Differ. Equ. 13(10):1209-1221, 1988), we establish an analytic description of the essential spectrum of non-self-adjoint mixed-order systems of pseudo-differential operators on $L^2(\\mathbb{R}^N) \\oplus L^2(\\mathbb{R}^N)$ that are uniformly Douglis-Nirenberg elliptic with positive-order diagonal entries. We apply our result to a problem arising in the dynamics of falling liquid films.","authors_text":"Christiane Tretter, Orif O. Ibrogimov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-03-18T20:17:41Z","title":"Essential spectrum of elliptic systems of pseudo-differential operators on $L^2(\\mathbb{R}^N)\\oplus L^2(\\mathbb{R}^N)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.06344","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:c7e29825f64b3df1dcf558b18a1004e9f3a9975f9a8cd080d6fb10d9d76a2a7f","target":"record","created_at":"2026-05-18T00:25:20Z","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":"6c8ea97c62557aa1f0ae9ae6c4621db0341742082ce9cfc695524f5ccbb5dfd4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-03-18T20:17:41Z","title_canon_sha256":"c4249bc1ccd8bf9059dbf43fa64c2446ea8853393a0e62d8fabefceb0f1b4075"},"schema_version":"1.0","source":{"id":"1703.06344","kind":"arxiv","version":1}},"canonical_sha256":"ebce7c9fff98fed7ab8b5b508b2c075bb54642a2455ce3adfc6bff2a128f2eae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ebce7c9fff98fed7ab8b5b508b2c075bb54642a2455ce3adfc6bff2a128f2eae","first_computed_at":"2026-05-18T00:25:20.915951Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:20.915951Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J5akzOG+G2NIzohYvYuJkBNt63eXGKTd8DNoWHkn5yuGhdaqfqjcfvI098MduwAxbhEILfgIuX7KNrHY6IK5CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:20.916573Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.06344","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c7e29825f64b3df1dcf558b18a1004e9f3a9975f9a8cd080d6fb10d9d76a2a7f","sha256:2c4e0647fe7e8886339f06ae13ebc7f6c703ea901786e3b93d66e4a1408ae672"],"state_sha256":"0cdd1dd73bd75f55d72d3ffa189f02f3da5db480ab521bf2ba027060c8b915d0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lzN0oWonYY/DzuFz504tfKBy2Uo7sHWqnJPCBMhoIhYBhs7Z+cvdJMh9T33adaNQ6tPzrnLMeJel3dBLaIR9AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T12:19:24.711498Z","bundle_sha256":"11e43fac5e27f359c99dff3da0e5091e83bd49159ba245fde4b42baa04825dd5"}}