{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:L7AODX56ZLTZVYCXR5ICPCCG52","short_pith_number":"pith:L7AODX56","canonical_record":{"source":{"id":"math/0604616","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.FA","submitted_at":"2006-04-28T04:56:36Z","cross_cats_sorted":[],"title_canon_sha256":"f58ff93ba36850c753ada6542c8d6258640c6f112bf0d235292377607ea7f1e1","abstract_canon_sha256":"d445f19bb91c16c525e472fc0fc9bde5437b43b7aa30f374a171db8dd3f3d1ba"},"schema_version":"1.0"},"canonical_sha256":"5fc0e1dfbecae79ae0578f50278846eea98730c3768c926d9bd08c5d20c9717a","source":{"kind":"arxiv","id":"math/0604616","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0604616","created_at":"2026-05-18T01:09:15Z"},{"alias_kind":"arxiv_version","alias_value":"math/0604616v1","created_at":"2026-05-18T01:09:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0604616","created_at":"2026-05-18T01:09:15Z"},{"alias_kind":"pith_short_12","alias_value":"L7AODX56ZLTZ","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"L7AODX56ZLTZVYCX","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"L7AODX56","created_at":"2026-05-18T12:25:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:L7AODX56ZLTZVYCXR5ICPCCG52","target":"record","payload":{"canonical_record":{"source":{"id":"math/0604616","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.FA","submitted_at":"2006-04-28T04:56:36Z","cross_cats_sorted":[],"title_canon_sha256":"f58ff93ba36850c753ada6542c8d6258640c6f112bf0d235292377607ea7f1e1","abstract_canon_sha256":"d445f19bb91c16c525e472fc0fc9bde5437b43b7aa30f374a171db8dd3f3d1ba"},"schema_version":"1.0"},"canonical_sha256":"5fc0e1dfbecae79ae0578f50278846eea98730c3768c926d9bd08c5d20c9717a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:15.598448Z","signature_b64":"EU/cgSvSHPADNbPGfO1dEa2iDY+xB7u+CeinKy73LP5YxlcKJUYDwxma+tOD8HdtAAdcxM/UzB7iwM2nx5cbDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5fc0e1dfbecae79ae0578f50278846eea98730c3768c926d9bd08c5d20c9717a","last_reissued_at":"2026-05-18T01:09:15.597843Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:15.597843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0604616","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":"2026-05-18T01:09:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YSNhUUuZXUWTnFJJ3eWpX8TLh2atlKxgH2BJ9e7ca2cx2RCvftGdHDzD46m63SL2LJ8NMjaMsXn6mIp3Mjh7Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T11:02:18.730880Z"},"content_sha256":"aa870c741230292b2fd0a300cb42232c534e6f77f32804f21e3fbdd3759ecf91","schema_version":"1.0","event_id":"sha256:aa870c741230292b2fd0a300cb42232c534e6f77f32804f21e3fbdd3759ecf91"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:L7AODX56ZLTZVYCXR5ICPCCG52","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A remark on the spectrum of the analytic generator","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"P. M. So{\\l}tan","submitted_at":"2006-04-28T04:56:36Z","abstract_excerpt":"It is shown that although the spectrum of the analytic generator of a one--parameter group of isometries of a Banach space may be equal to the whole complex plane, a simple operation of ampliating the analytic generator onto its graph locates its spectrum in the positive halfline."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0604616","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":"2026-05-18T01:09:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nz1+MIgExpCUtEXOSYhfj3NV99CpZKdOqSS7q94ZHm6xgGFuEtjPfuhh+ZKt63xE+V4XNicNYh+F8Gr1TKSUAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T11:02:18.731449Z"},"content_sha256":"8a4f971419a9316798249369598cd8610c7c571983ed633ae854895975e7b709","schema_version":"1.0","event_id":"sha256:8a4f971419a9316798249369598cd8610c7c571983ed633ae854895975e7b709"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L7AODX56ZLTZVYCXR5ICPCCG52/bundle.json","state_url":"https://pith.science/pith/L7AODX56ZLTZVYCXR5ICPCCG52/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L7AODX56ZLTZVYCXR5ICPCCG52/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":"2026-06-26T11:02:18Z","links":{"resolver":"https://pith.science/pith/L7AODX56ZLTZVYCXR5ICPCCG52","bundle":"https://pith.science/pith/L7AODX56ZLTZVYCXR5ICPCCG52/bundle.json","state":"https://pith.science/pith/L7AODX56ZLTZVYCXR5ICPCCG52/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L7AODX56ZLTZVYCXR5ICPCCG52/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:L7AODX56ZLTZVYCXR5ICPCCG52","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":"d445f19bb91c16c525e472fc0fc9bde5437b43b7aa30f374a171db8dd3f3d1ba","cross_cats_sorted":[],"license":"","primary_cat":"math.FA","submitted_at":"2006-04-28T04:56:36Z","title_canon_sha256":"f58ff93ba36850c753ada6542c8d6258640c6f112bf0d235292377607ea7f1e1"},"schema_version":"1.0","source":{"id":"math/0604616","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0604616","created_at":"2026-05-18T01:09:15Z"},{"alias_kind":"arxiv_version","alias_value":"math/0604616v1","created_at":"2026-05-18T01:09:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0604616","created_at":"2026-05-18T01:09:15Z"},{"alias_kind":"pith_short_12","alias_value":"L7AODX56ZLTZ","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"L7AODX56ZLTZVYCX","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"L7AODX56","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:8a4f971419a9316798249369598cd8610c7c571983ed633ae854895975e7b709","target":"graph","created_at":"2026-05-18T01:09:15Z","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":"It is shown that although the spectrum of the analytic generator of a one--parameter group of isometries of a Banach space may be equal to the whole complex plane, a simple operation of ampliating the analytic generator onto its graph locates its spectrum in the positive halfline.","authors_text":"P. M. So{\\l}tan","cross_cats":[],"headline":"","license":"","primary_cat":"math.FA","submitted_at":"2006-04-28T04:56:36Z","title":"A remark on the spectrum of the analytic generator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0604616","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:aa870c741230292b2fd0a300cb42232c534e6f77f32804f21e3fbdd3759ecf91","target":"record","created_at":"2026-05-18T01:09:15Z","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":"d445f19bb91c16c525e472fc0fc9bde5437b43b7aa30f374a171db8dd3f3d1ba","cross_cats_sorted":[],"license":"","primary_cat":"math.FA","submitted_at":"2006-04-28T04:56:36Z","title_canon_sha256":"f58ff93ba36850c753ada6542c8d6258640c6f112bf0d235292377607ea7f1e1"},"schema_version":"1.0","source":{"id":"math/0604616","kind":"arxiv","version":1}},"canonical_sha256":"5fc0e1dfbecae79ae0578f50278846eea98730c3768c926d9bd08c5d20c9717a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5fc0e1dfbecae79ae0578f50278846eea98730c3768c926d9bd08c5d20c9717a","first_computed_at":"2026-05-18T01:09:15.597843Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:15.597843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EU/cgSvSHPADNbPGfO1dEa2iDY+xB7u+CeinKy73LP5YxlcKJUYDwxma+tOD8HdtAAdcxM/UzB7iwM2nx5cbDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:15.598448Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0604616","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa870c741230292b2fd0a300cb42232c534e6f77f32804f21e3fbdd3759ecf91","sha256:8a4f971419a9316798249369598cd8610c7c571983ed633ae854895975e7b709"],"state_sha256":"fa2010db015281d36a38fba404c1e41a8aeae3fa2961c8257a10543674ad6df1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ied6fTCM6jXjzfKyU1JBRzzW7CsPxN/wUvyvIZdU30RKAcc/BW+Z4HOeowV5YGLf+7wngEAWVjA5pQESbFKbAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T11:02:18.734033Z","bundle_sha256":"b0d8c15736456f6659ae68513ac9f039013f891ace194e91d3817b504c50720d"}}