{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:VHD3Y5SHYLSKKPM3KZTNSBANIR","short_pith_number":"pith:VHD3Y5SH","canonical_record":{"source":{"id":"1902.00920","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-02-03T16:32:35Z","cross_cats_sorted":[],"title_canon_sha256":"e53b485a1722527d6713c3f32c0339b14be735ff00f96be3343da9d500964584","abstract_canon_sha256":"2cf377a985821747c96d65156d006e4b2e71879d443f142e37a65bab6373bfba"},"schema_version":"1.0"},"canonical_sha256":"a9c7bc7647c2e4a53d9b5666d9040d4459ab8e0f372e7bf1e9918f41da1adb4f","source":{"kind":"arxiv","id":"1902.00920","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.00920","created_at":"2026-05-17T23:54:06Z"},{"alias_kind":"arxiv_version","alias_value":"1902.00920v2","created_at":"2026-05-17T23:54:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.00920","created_at":"2026-05-17T23:54:06Z"},{"alias_kind":"pith_short_12","alias_value":"VHD3Y5SHYLSK","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"VHD3Y5SHYLSKKPM3","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"VHD3Y5SH","created_at":"2026-05-18T12:33:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:VHD3Y5SHYLSKKPM3KZTNSBANIR","target":"record","payload":{"canonical_record":{"source":{"id":"1902.00920","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-02-03T16:32:35Z","cross_cats_sorted":[],"title_canon_sha256":"e53b485a1722527d6713c3f32c0339b14be735ff00f96be3343da9d500964584","abstract_canon_sha256":"2cf377a985821747c96d65156d006e4b2e71879d443f142e37a65bab6373bfba"},"schema_version":"1.0"},"canonical_sha256":"a9c7bc7647c2e4a53d9b5666d9040d4459ab8e0f372e7bf1e9918f41da1adb4f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:06.738798Z","signature_b64":"nhaZc5xyAbP0gcwHmexDef71XILgLMbI4RaKCQwUb2fbEdM7204B8G8xN82bBzKsHou9ik5oRSS6Y6smdy+aCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a9c7bc7647c2e4a53d9b5666d9040d4459ab8e0f372e7bf1e9918f41da1adb4f","last_reissued_at":"2026-05-17T23:54:06.738232Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:06.738232Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.00920","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":"2026-05-17T23:54:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qoiwyqaoo7yYwhOzNgEQf50vPXJvi7fk8X3XpA6HfTu+uQOoajZy8+7oXghiCZZRkXYQMf/uwlQN0fUEbhjaDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T03:49:55.841420Z"},"content_sha256":"9d7564a9ac4af6fabaeee72613636926333054d61919b4ec50dc337ccb26fbd1","schema_version":"1.0","event_id":"sha256:9d7564a9ac4af6fabaeee72613636926333054d61919b4ec50dc337ccb26fbd1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:VHD3Y5SHYLSKKPM3KZTNSBANIR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-harmonic Gohberg's lemma, Gershgorin theory and heat equation on manifolds with boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Juan Pablo Velasquez-Rodriguez, Michael Ruzhansky","submitted_at":"2019-02-03T16:32:35Z","abstract_excerpt":"In this paper, following the works on non-harmonic analysis of boundary value problems by Tokmagambetov, Ruzhansky and Delgado, we use Operator Ideals Theory and Gershgorin Theory to obtain explicit information concerning the spectrum of pseudo-differential operators, on a smooth manifold $\\Omega$ with boundary $\\partial \\Omega$, in the context of the non-harmonic analysis of boundary value problems, introduced by Tokmagambetov and Ruzhansky in terms of a model operator $\\mathfrak{L} $. Under certain assumptions about the eigenfunctions of the model operator, for symbols in the H\\\"ormander cla"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.00920","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":"2026-05-17T23:54:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tWj3r4JkGR7NLYbNnw7MBHr1ha0TKhr5MrVCzQB3HkdY0ekWOVwr/WCaGh3BN7UJr5qRh7E4T1MUOEDoqWSwAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T03:49:55.842405Z"},"content_sha256":"affca7f653067f496a834e7836c603d51081cb9fa68157c45556dd71b2a4a9cd","schema_version":"1.0","event_id":"sha256:affca7f653067f496a834e7836c603d51081cb9fa68157c45556dd71b2a4a9cd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VHD3Y5SHYLSKKPM3KZTNSBANIR/bundle.json","state_url":"https://pith.science/pith/VHD3Y5SHYLSKKPM3KZTNSBANIR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VHD3Y5SHYLSKKPM3KZTNSBANIR/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":"2026-06-10T03:49:55Z","links":{"resolver":"https://pith.science/pith/VHD3Y5SHYLSKKPM3KZTNSBANIR","bundle":"https://pith.science/pith/VHD3Y5SHYLSKKPM3KZTNSBANIR/bundle.json","state":"https://pith.science/pith/VHD3Y5SHYLSKKPM3KZTNSBANIR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VHD3Y5SHYLSKKPM3KZTNSBANIR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:VHD3Y5SHYLSKKPM3KZTNSBANIR","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":"2cf377a985821747c96d65156d006e4b2e71879d443f142e37a65bab6373bfba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-02-03T16:32:35Z","title_canon_sha256":"e53b485a1722527d6713c3f32c0339b14be735ff00f96be3343da9d500964584"},"schema_version":"1.0","source":{"id":"1902.00920","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.00920","created_at":"2026-05-17T23:54:06Z"},{"alias_kind":"arxiv_version","alias_value":"1902.00920v2","created_at":"2026-05-17T23:54:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.00920","created_at":"2026-05-17T23:54:06Z"},{"alias_kind":"pith_short_12","alias_value":"VHD3Y5SHYLSK","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"VHD3Y5SHYLSKKPM3","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"VHD3Y5SH","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:affca7f653067f496a834e7836c603d51081cb9fa68157c45556dd71b2a4a9cd","target":"graph","created_at":"2026-05-17T23:54:06Z","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":"In this paper, following the works on non-harmonic analysis of boundary value problems by Tokmagambetov, Ruzhansky and Delgado, we use Operator Ideals Theory and Gershgorin Theory to obtain explicit information concerning the spectrum of pseudo-differential operators, on a smooth manifold $\\Omega$ with boundary $\\partial \\Omega$, in the context of the non-harmonic analysis of boundary value problems, introduced by Tokmagambetov and Ruzhansky in terms of a model operator $\\mathfrak{L} $. Under certain assumptions about the eigenfunctions of the model operator, for symbols in the H\\\"ormander cla","authors_text":"Juan Pablo Velasquez-Rodriguez, Michael Ruzhansky","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-02-03T16:32:35Z","title":"Non-harmonic Gohberg's lemma, Gershgorin theory and heat equation on manifolds with boundary"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.00920","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":"sha256:9d7564a9ac4af6fabaeee72613636926333054d61919b4ec50dc337ccb26fbd1","target":"record","created_at":"2026-05-17T23:54:06Z","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":"2cf377a985821747c96d65156d006e4b2e71879d443f142e37a65bab6373bfba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-02-03T16:32:35Z","title_canon_sha256":"e53b485a1722527d6713c3f32c0339b14be735ff00f96be3343da9d500964584"},"schema_version":"1.0","source":{"id":"1902.00920","kind":"arxiv","version":2}},"canonical_sha256":"a9c7bc7647c2e4a53d9b5666d9040d4459ab8e0f372e7bf1e9918f41da1adb4f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a9c7bc7647c2e4a53d9b5666d9040d4459ab8e0f372e7bf1e9918f41da1adb4f","first_computed_at":"2026-05-17T23:54:06.738232Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:06.738232Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nhaZc5xyAbP0gcwHmexDef71XILgLMbI4RaKCQwUb2fbEdM7204B8G8xN82bBzKsHou9ik5oRSS6Y6smdy+aCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:06.738798Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.00920","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d7564a9ac4af6fabaeee72613636926333054d61919b4ec50dc337ccb26fbd1","sha256:affca7f653067f496a834e7836c603d51081cb9fa68157c45556dd71b2a4a9cd"],"state_sha256":"3c86debf6f647752220352baf30724a4d270b7bad18a73712447379eaf63d914"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2nmou0dcHb9Z5k173f2Pgp0z44ePNpApRY4aQoEF4q8nXIxAdgOq8iU3u675J1Rgb0VXNLrU5YDWrH7UoBGgDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T03:49:55.846494Z","bundle_sha256":"fadd8261510e1f2d147efbf8981985eefbd0e9202b730e81ea3e5589a392d34b"}}