{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:T4KTN74RORBXZY52VJH4VUXSSZ","short_pith_number":"pith:T4KTN74R","canonical_record":{"source":{"id":"1706.01904","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-06-06T18:06:47Z","cross_cats_sorted":[],"title_canon_sha256":"f378af5c3c59f022d1f2b49a80bfcf485fdc54115393ce9b1cb5b3bac7096452","abstract_canon_sha256":"b2135e4218b0c25aca943a0bb54424636cf356db748da834f6318a26b294f7d8"},"schema_version":"1.0"},"canonical_sha256":"9f1536ff9174437ce3baaa4fcad2f2964f014abd1d0f527eab8ad2a59fa51e12","source":{"kind":"arxiv","id":"1706.01904","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.01904","created_at":"2026-05-18T00:25:18Z"},{"alias_kind":"arxiv_version","alias_value":"1706.01904v2","created_at":"2026-05-18T00:25:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.01904","created_at":"2026-05-18T00:25:18Z"},{"alias_kind":"pith_short_12","alias_value":"T4KTN74RORBX","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"T4KTN74RORBXZY52","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"T4KTN74R","created_at":"2026-05-18T12:31:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:T4KTN74RORBXZY52VJH4VUXSSZ","target":"record","payload":{"canonical_record":{"source":{"id":"1706.01904","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-06-06T18:06:47Z","cross_cats_sorted":[],"title_canon_sha256":"f378af5c3c59f022d1f2b49a80bfcf485fdc54115393ce9b1cb5b3bac7096452","abstract_canon_sha256":"b2135e4218b0c25aca943a0bb54424636cf356db748da834f6318a26b294f7d8"},"schema_version":"1.0"},"canonical_sha256":"9f1536ff9174437ce3baaa4fcad2f2964f014abd1d0f527eab8ad2a59fa51e12","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:18.372095Z","signature_b64":"pSxPueDtAppySqtAM8RPfZ8dxYbf3Id0DH53voBrCQQup6fD/G6Jty7PxoISalul/gnzCS1pF/RMCwWyarTzAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f1536ff9174437ce3baaa4fcad2f2964f014abd1d0f527eab8ad2a59fa51e12","last_reissued_at":"2026-05-18T00:25:18.371374Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:18.371374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.01904","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":"2026-05-18T00:25:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rlgjf7XX3h1I1QL5pMCQZth+PAum2iPqVCDQLLgWuiKtqRzm7tWVEr5LLMVNc3z+Y0q33UP2X0IlzlydPRVtBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T04:33:10.427574Z"},"content_sha256":"4dee93ba877be4c1f7733f00b3d7d30390ce035f0d10fe6f52a1a7de579f97ea","schema_version":"1.0","event_id":"sha256:4dee93ba877be4c1f7733f00b3d7d30390ce035f0d10fe6f52a1a7de579f97ea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:T4KTN74RORBXZY52VJH4VUXSSZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Non-Proper Dissipative Extensions of a Dual Pair","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Christoph Fischbacher","submitted_at":"2017-06-06T18:06:47Z","abstract_excerpt":"We consider dissipative operators $A$ of the form $A=S+iV$, where both $S$ and $V\\geq 0$ are assumed to be symmetric but neither of them needs to be (essentially) selfadjoint. After a brief discussion of the relation of the operators $S\\pm iV $to dual pairs with the so called common core property, we present a necessary and suffcient condition for any extension of $A$ with domain contained in $\\mathcal{D}((S-iV)^*)$ to be dissipative. We will discuss several special situations in which this condition can be expressed in a particularly nice form -- accessible to direct computations. Examples in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.01904","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":"2026-05-18T00:25:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E+I4aB/uljgakGys7L55pGOZxTjgizAHyxMCu+zgKP7wzMNZ0fZkYKsRSkQoEIhwfoVBlcksxP5KWt0GRZIcBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T04:33:10.427924Z"},"content_sha256":"5fd79a4c5d636d3f793f1bbd13c3f56c5bf867b47447586e729b9cd562bbe7f1","schema_version":"1.0","event_id":"sha256:5fd79a4c5d636d3f793f1bbd13c3f56c5bf867b47447586e729b9cd562bbe7f1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T4KTN74RORBXZY52VJH4VUXSSZ/bundle.json","state_url":"https://pith.science/pith/T4KTN74RORBXZY52VJH4VUXSSZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T4KTN74RORBXZY52VJH4VUXSSZ/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":"2026-06-29T04:33:10Z","links":{"resolver":"https://pith.science/pith/T4KTN74RORBXZY52VJH4VUXSSZ","bundle":"https://pith.science/pith/T4KTN74RORBXZY52VJH4VUXSSZ/bundle.json","state":"https://pith.science/pith/T4KTN74RORBXZY52VJH4VUXSSZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T4KTN74RORBXZY52VJH4VUXSSZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:T4KTN74RORBXZY52VJH4VUXSSZ","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":"b2135e4218b0c25aca943a0bb54424636cf356db748da834f6318a26b294f7d8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-06-06T18:06:47Z","title_canon_sha256":"f378af5c3c59f022d1f2b49a80bfcf485fdc54115393ce9b1cb5b3bac7096452"},"schema_version":"1.0","source":{"id":"1706.01904","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.01904","created_at":"2026-05-18T00:25:18Z"},{"alias_kind":"arxiv_version","alias_value":"1706.01904v2","created_at":"2026-05-18T00:25:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.01904","created_at":"2026-05-18T00:25:18Z"},{"alias_kind":"pith_short_12","alias_value":"T4KTN74RORBX","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"T4KTN74RORBXZY52","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"T4KTN74R","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:5fd79a4c5d636d3f793f1bbd13c3f56c5bf867b47447586e729b9cd562bbe7f1","target":"graph","created_at":"2026-05-18T00:25:18Z","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":"We consider dissipative operators $A$ of the form $A=S+iV$, where both $S$ and $V\\geq 0$ are assumed to be symmetric but neither of them needs to be (essentially) selfadjoint. After a brief discussion of the relation of the operators $S\\pm iV $to dual pairs with the so called common core property, we present a necessary and suffcient condition for any extension of $A$ with domain contained in $\\mathcal{D}((S-iV)^*)$ to be dissipative. We will discuss several special situations in which this condition can be expressed in a particularly nice form -- accessible to direct computations. Examples in","authors_text":"Christoph Fischbacher","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-06-06T18:06:47Z","title":"The Non-Proper Dissipative Extensions of a Dual Pair"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.01904","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":"sha256:4dee93ba877be4c1f7733f00b3d7d30390ce035f0d10fe6f52a1a7de579f97ea","target":"record","created_at":"2026-05-18T00:25:18Z","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":"b2135e4218b0c25aca943a0bb54424636cf356db748da834f6318a26b294f7d8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-06-06T18:06:47Z","title_canon_sha256":"f378af5c3c59f022d1f2b49a80bfcf485fdc54115393ce9b1cb5b3bac7096452"},"schema_version":"1.0","source":{"id":"1706.01904","kind":"arxiv","version":2}},"canonical_sha256":"9f1536ff9174437ce3baaa4fcad2f2964f014abd1d0f527eab8ad2a59fa51e12","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f1536ff9174437ce3baaa4fcad2f2964f014abd1d0f527eab8ad2a59fa51e12","first_computed_at":"2026-05-18T00:25:18.371374Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:18.371374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pSxPueDtAppySqtAM8RPfZ8dxYbf3Id0DH53voBrCQQup6fD/G6Jty7PxoISalul/gnzCS1pF/RMCwWyarTzAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:18.372095Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.01904","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4dee93ba877be4c1f7733f00b3d7d30390ce035f0d10fe6f52a1a7de579f97ea","sha256:5fd79a4c5d636d3f793f1bbd13c3f56c5bf867b47447586e729b9cd562bbe7f1"],"state_sha256":"7f6df0dcc3cbe75fafe4f06cc87747ce30a8bb868cdb42e691044feca03d3f7a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uPGJG6dSgj9wulEiBfbNQRBIXo+X91/+bokGSzZsHeJ3NrbwS7y3RlhSEvDj9stkQTeX9K7/eob41sWHsMK1BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T04:33:10.429828Z","bundle_sha256":"c6f84ff26cb65b7b80c9fbabbf1bb1264e73470063947cd7b9f1e9f6964cbe0c"}}