{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:6EHFOTP4DUXFZD5BE76L6SPQRA","short_pith_number":"pith:6EHFOTP4","canonical_record":{"source":{"id":"1812.07278","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-12-18T10:35:28Z","cross_cats_sorted":[],"title_canon_sha256":"a3362a329449ef441d8849e16de3f8edc320c3a51a7c55222387858cca395676","abstract_canon_sha256":"f298c0f86434eb122477c00a24e4077eae9842681d940b9e077a7a264a592788"},"schema_version":"1.0"},"canonical_sha256":"f10e574dfc1d2e5c8fa127fcbf49f08833047500a60c51df25d3cd3e6e8efd2b","source":{"kind":"arxiv","id":"1812.07278","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.07278","created_at":"2026-05-17T23:58:00Z"},{"alias_kind":"arxiv_version","alias_value":"1812.07278v1","created_at":"2026-05-17T23:58:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.07278","created_at":"2026-05-17T23:58:00Z"},{"alias_kind":"pith_short_12","alias_value":"6EHFOTP4DUXF","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"6EHFOTP4DUXFZD5B","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"6EHFOTP4","created_at":"2026-05-18T12:32:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:6EHFOTP4DUXFZD5BE76L6SPQRA","target":"record","payload":{"canonical_record":{"source":{"id":"1812.07278","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-12-18T10:35:28Z","cross_cats_sorted":[],"title_canon_sha256":"a3362a329449ef441d8849e16de3f8edc320c3a51a7c55222387858cca395676","abstract_canon_sha256":"f298c0f86434eb122477c00a24e4077eae9842681d940b9e077a7a264a592788"},"schema_version":"1.0"},"canonical_sha256":"f10e574dfc1d2e5c8fa127fcbf49f08833047500a60c51df25d3cd3e6e8efd2b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:00.972299Z","signature_b64":"xqi6vbY/tSKNfr3XRvpuDngxTMU1uB9db5E9knHWgdWkkQiU15vLcc1vTyDbMBq2K4t/hOh4XAJ2fijeGT7gAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f10e574dfc1d2e5c8fa127fcbf49f08833047500a60c51df25d3cd3e6e8efd2b","last_reissued_at":"2026-05-17T23:58:00.971626Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:00.971626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.07278","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":"2026-05-17T23:58:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kNdWz4qMBHFXLBWwjMmRwnwmphRe5tX7sjprOCHVf1mCg2QMNxZ3SMHqlWuejPT0HDQude5++iNpZFAe42o6Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T09:13:41.220436Z"},"content_sha256":"78ce67fbec3bb90a82205e603edc0f00c616eed52b439e0f59dacceb0021cc75","schema_version":"1.0","event_id":"sha256:78ce67fbec3bb90a82205e603edc0f00c616eed52b439e0f59dacceb0021cc75"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:6EHFOTP4DUXFZD5BE76L6SPQRA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Semi-Fredholm and Semi-Browder Spectra For $C_0$-Quasi-Semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Abdelaziz Tajmouati, Youness Zahouan","submitted_at":"2018-12-18T10:35:28Z","abstract_excerpt":"In this paper, we describe the different spectra of the $C_0$-quasi-semigroups by the spectra of their generators. Specially, essential ascent and descent,Drazin invertible, upper and lower semi-Fredholm and semi-Browder spectra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.07278","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":"2026-05-17T23:58:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u6QJfOPLAn0DI5WTb89ruInhnXP0UhFgklvVBtcal4ej5149b0zzlpdt1B00U6zLYEnHTkt59E71JlYYaNEOBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T09:13:41.220784Z"},"content_sha256":"80d2188630d3ca51275bf568da5104b11a9351d8fc34a3460a24af2abf90264b","schema_version":"1.0","event_id":"sha256:80d2188630d3ca51275bf568da5104b11a9351d8fc34a3460a24af2abf90264b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6EHFOTP4DUXFZD5BE76L6SPQRA/bundle.json","state_url":"https://pith.science/pith/6EHFOTP4DUXFZD5BE76L6SPQRA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6EHFOTP4DUXFZD5BE76L6SPQRA/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":"2026-06-22T09:13:41Z","links":{"resolver":"https://pith.science/pith/6EHFOTP4DUXFZD5BE76L6SPQRA","bundle":"https://pith.science/pith/6EHFOTP4DUXFZD5BE76L6SPQRA/bundle.json","state":"https://pith.science/pith/6EHFOTP4DUXFZD5BE76L6SPQRA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6EHFOTP4DUXFZD5BE76L6SPQRA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:6EHFOTP4DUXFZD5BE76L6SPQRA","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":"f298c0f86434eb122477c00a24e4077eae9842681d940b9e077a7a264a592788","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-12-18T10:35:28Z","title_canon_sha256":"a3362a329449ef441d8849e16de3f8edc320c3a51a7c55222387858cca395676"},"schema_version":"1.0","source":{"id":"1812.07278","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.07278","created_at":"2026-05-17T23:58:00Z"},{"alias_kind":"arxiv_version","alias_value":"1812.07278v1","created_at":"2026-05-17T23:58:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.07278","created_at":"2026-05-17T23:58:00Z"},{"alias_kind":"pith_short_12","alias_value":"6EHFOTP4DUXF","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"6EHFOTP4DUXFZD5B","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"6EHFOTP4","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:80d2188630d3ca51275bf568da5104b11a9351d8fc34a3460a24af2abf90264b","target":"graph","created_at":"2026-05-17T23:58:00Z","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, we describe the different spectra of the $C_0$-quasi-semigroups by the spectra of their generators. Specially, essential ascent and descent,Drazin invertible, upper and lower semi-Fredholm and semi-Browder spectra.","authors_text":"Abdelaziz Tajmouati, Youness Zahouan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-12-18T10:35:28Z","title":"Semi-Fredholm and Semi-Browder Spectra For $C_0$-Quasi-Semigroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.07278","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":"sha256:78ce67fbec3bb90a82205e603edc0f00c616eed52b439e0f59dacceb0021cc75","target":"record","created_at":"2026-05-17T23:58:00Z","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":"f298c0f86434eb122477c00a24e4077eae9842681d940b9e077a7a264a592788","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2018-12-18T10:35:28Z","title_canon_sha256":"a3362a329449ef441d8849e16de3f8edc320c3a51a7c55222387858cca395676"},"schema_version":"1.0","source":{"id":"1812.07278","kind":"arxiv","version":1}},"canonical_sha256":"f10e574dfc1d2e5c8fa127fcbf49f08833047500a60c51df25d3cd3e6e8efd2b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f10e574dfc1d2e5c8fa127fcbf49f08833047500a60c51df25d3cd3e6e8efd2b","first_computed_at":"2026-05-17T23:58:00.971626Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:00.971626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xqi6vbY/tSKNfr3XRvpuDngxTMU1uB9db5E9knHWgdWkkQiU15vLcc1vTyDbMBq2K4t/hOh4XAJ2fijeGT7gAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:00.972299Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.07278","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:78ce67fbec3bb90a82205e603edc0f00c616eed52b439e0f59dacceb0021cc75","sha256:80d2188630d3ca51275bf568da5104b11a9351d8fc34a3460a24af2abf90264b"],"state_sha256":"29e1cbf84448308c904dee7e8cff0ab8aa25eec7c7152da713b0c7495a556c74"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p41dZDPvv4F/TPiYuAzuUUzPKNwIFaYYCH0naxpza7Kutm3ftIg5BZby3242S1fI1urv9vtrc2Q0mLaak7CuAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T09:13:41.222809Z","bundle_sha256":"58a0acb09fc9a4720e50adaa96a2017fd713dbace673f68fdab51f014be438f1"}}