{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:QYIGX3BPQQLOT5N4DGEEYY63SZ","short_pith_number":"pith:QYIGX3BP","canonical_record":{"source":{"id":"1804.03968","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-04-11T13:08:27Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"13681bbca48974bdd7dd1cf5fb64915d11852e50d1c0db8420664269a707c04a","abstract_canon_sha256":"31cbaac27a3ac89b4532ca2bfe82d4653cd9df559ac0455adc2b77385045fa82"},"schema_version":"1.0"},"canonical_sha256":"86106bec2f8416e9f5bc19884c63db964fefaaf290a34d0fa93ff8f43aceafb5","source":{"kind":"arxiv","id":"1804.03968","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.03968","created_at":"2026-05-18T00:15:14Z"},{"alias_kind":"arxiv_version","alias_value":"1804.03968v1","created_at":"2026-05-18T00:15:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.03968","created_at":"2026-05-18T00:15:14Z"},{"alias_kind":"pith_short_12","alias_value":"QYIGX3BPQQLO","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"QYIGX3BPQQLOT5N4","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"QYIGX3BP","created_at":"2026-05-18T12:32:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:QYIGX3BPQQLOT5N4DGEEYY63SZ","target":"record","payload":{"canonical_record":{"source":{"id":"1804.03968","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-04-11T13:08:27Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"13681bbca48974bdd7dd1cf5fb64915d11852e50d1c0db8420664269a707c04a","abstract_canon_sha256":"31cbaac27a3ac89b4532ca2bfe82d4653cd9df559ac0455adc2b77385045fa82"},"schema_version":"1.0"},"canonical_sha256":"86106bec2f8416e9f5bc19884c63db964fefaaf290a34d0fa93ff8f43aceafb5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:14.597792Z","signature_b64":"EyIottMV3ETe11wVoBFKS2c/HKqgj5aYwFHnWbe+XZVyQ1khcSd+q5dvQyMp0GUwxvThNz11LMoeZIEK9Ki0BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"86106bec2f8416e9f5bc19884c63db964fefaaf290a34d0fa93ff8f43aceafb5","last_reissued_at":"2026-05-18T00:15:14.596962Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:14.596962Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.03968","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":"2026-05-18T00:15:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XoRd+nFybHfuoOWm8cyeM93tAtp+UvKyqyghOvtdjSRWslbf/CcJjaWtzUNat/mP1Q5EOndqO/WVhbAJcvEGCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T18:57:16.534193Z"},"content_sha256":"9f907b17067db96a2f0d72f292eabc829f07eaf0511792800b70c44809267921","schema_version":"1.0","event_id":"sha256:9f907b17067db96a2f0d72f292eabc829f07eaf0511792800b70c44809267921"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:QYIGX3BPQQLOT5N4DGEEYY63SZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum mechanical settings inspired by RLC circuits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"F. Bagarello, F. Gargano, G. Alicata, S. Spagnolo","submitted_at":"2018-04-11T13:08:27Z","abstract_excerpt":"In some recent papers several authors used electronic circuits to construct loss and gain systems. This is particularly interesting in the context of PT-quantum mechanics, where this kind of effects appears quite naturally. The electronic circuits used so far are simple, but not so much. Surprisingly enough, a rather trivial RLC circuit can be analyzed with the same perspective and it produces a variety of unexpected results, both from a mathematical and on a physical side. In this paper we show that this circuit produces two biorthogonal bases associated to the Liouville matrix $\\Lc$ used in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03968","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":"2026-05-18T00:15:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Htu0H5ZQTEnljYTvrSa/szV+pnpM1yq5Fyzpe3Ue5xmyDRMqIEmDuFVxKHez8ScMS8k8UR8WfsGTUj3krmfuBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T18:57:16.534546Z"},"content_sha256":"fab371eb7c55132cee160b0cfe9380e73a89fc13c06115b1041eab981dd09c80","schema_version":"1.0","event_id":"sha256:fab371eb7c55132cee160b0cfe9380e73a89fc13c06115b1041eab981dd09c80"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QYIGX3BPQQLOT5N4DGEEYY63SZ/bundle.json","state_url":"https://pith.science/pith/QYIGX3BPQQLOT5N4DGEEYY63SZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QYIGX3BPQQLOT5N4DGEEYY63SZ/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":"2026-06-27T18:57:16Z","links":{"resolver":"https://pith.science/pith/QYIGX3BPQQLOT5N4DGEEYY63SZ","bundle":"https://pith.science/pith/QYIGX3BPQQLOT5N4DGEEYY63SZ/bundle.json","state":"https://pith.science/pith/QYIGX3BPQQLOT5N4DGEEYY63SZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QYIGX3BPQQLOT5N4DGEEYY63SZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:QYIGX3BPQQLOT5N4DGEEYY63SZ","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":"31cbaac27a3ac89b4532ca2bfe82d4653cd9df559ac0455adc2b77385045fa82","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-04-11T13:08:27Z","title_canon_sha256":"13681bbca48974bdd7dd1cf5fb64915d11852e50d1c0db8420664269a707c04a"},"schema_version":"1.0","source":{"id":"1804.03968","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.03968","created_at":"2026-05-18T00:15:14Z"},{"alias_kind":"arxiv_version","alias_value":"1804.03968v1","created_at":"2026-05-18T00:15:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.03968","created_at":"2026-05-18T00:15:14Z"},{"alias_kind":"pith_short_12","alias_value":"QYIGX3BPQQLO","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"QYIGX3BPQQLOT5N4","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"QYIGX3BP","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:fab371eb7c55132cee160b0cfe9380e73a89fc13c06115b1041eab981dd09c80","target":"graph","created_at":"2026-05-18T00:15:14Z","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 some recent papers several authors used electronic circuits to construct loss and gain systems. This is particularly interesting in the context of PT-quantum mechanics, where this kind of effects appears quite naturally. The electronic circuits used so far are simple, but not so much. Surprisingly enough, a rather trivial RLC circuit can be analyzed with the same perspective and it produces a variety of unexpected results, both from a mathematical and on a physical side. In this paper we show that this circuit produces two biorthogonal bases associated to the Liouville matrix $\\Lc$ used in ","authors_text":"F. Bagarello, F. Gargano, G. Alicata, S. Spagnolo","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-04-11T13:08:27Z","title":"Quantum mechanical settings inspired by RLC circuits"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03968","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":"sha256:9f907b17067db96a2f0d72f292eabc829f07eaf0511792800b70c44809267921","target":"record","created_at":"2026-05-18T00:15:14Z","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":"31cbaac27a3ac89b4532ca2bfe82d4653cd9df559ac0455adc2b77385045fa82","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-04-11T13:08:27Z","title_canon_sha256":"13681bbca48974bdd7dd1cf5fb64915d11852e50d1c0db8420664269a707c04a"},"schema_version":"1.0","source":{"id":"1804.03968","kind":"arxiv","version":1}},"canonical_sha256":"86106bec2f8416e9f5bc19884c63db964fefaaf290a34d0fa93ff8f43aceafb5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"86106bec2f8416e9f5bc19884c63db964fefaaf290a34d0fa93ff8f43aceafb5","first_computed_at":"2026-05-18T00:15:14.596962Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:14.596962Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EyIottMV3ETe11wVoBFKS2c/HKqgj5aYwFHnWbe+XZVyQ1khcSd+q5dvQyMp0GUwxvThNz11LMoeZIEK9Ki0BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:14.597792Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.03968","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9f907b17067db96a2f0d72f292eabc829f07eaf0511792800b70c44809267921","sha256:fab371eb7c55132cee160b0cfe9380e73a89fc13c06115b1041eab981dd09c80"],"state_sha256":"89f00cccba68211e4bef30a6959c7f7275938249479b17188aa73301f2f70e4f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Eujn4JV3RwtXdQgL3zgJ3cpWdWvINL7KtrtC2340DHYzy/KPo046Vb9rYlMdWjMoOqNJqSdLSnRKNxpu8muCBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T18:57:16.536729Z","bundle_sha256":"9dfa6157434749b8ca849cda5212ef383f759258dc84717cdb76aaa688e5f07f"}}