{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:CX7K7SWOGKPNK4RNXTRJIF43N7","short_pith_number":"pith:CX7K7SWO","canonical_record":{"source":{"id":"1403.3564","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-03-14T13:05:11Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"c745f4819c203b4d4c75010e6a06fdb3a8e1156b5f0a11b11d7882fd073c35d7","abstract_canon_sha256":"73be38833b2ccbc6bcbe8af7f3b09768f731d90166b5b4009efc06a67f70baf7"},"schema_version":"1.0"},"canonical_sha256":"15feafcace329ed5722dbce294179b6fd596e43d449f21273406a385919c9041","source":{"kind":"arxiv","id":"1403.3564","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.3564","created_at":"2026-05-18T01:27:38Z"},{"alias_kind":"arxiv_version","alias_value":"1403.3564v2","created_at":"2026-05-18T01:27:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.3564","created_at":"2026-05-18T01:27:38Z"},{"alias_kind":"pith_short_12","alias_value":"CX7K7SWOGKPN","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"CX7K7SWOGKPNK4RN","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"CX7K7SWO","created_at":"2026-05-18T12:28:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:CX7K7SWOGKPNK4RNXTRJIF43N7","target":"record","payload":{"canonical_record":{"source":{"id":"1403.3564","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-03-14T13:05:11Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"c745f4819c203b4d4c75010e6a06fdb3a8e1156b5f0a11b11d7882fd073c35d7","abstract_canon_sha256":"73be38833b2ccbc6bcbe8af7f3b09768f731d90166b5b4009efc06a67f70baf7"},"schema_version":"1.0"},"canonical_sha256":"15feafcace329ed5722dbce294179b6fd596e43d449f21273406a385919c9041","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:38.702960Z","signature_b64":"I+Qfd9YELORWIONC4bm2Ea6KKB2ABL6TAT6WK62jMTN5o8SGisqu6igx1r9B1rfrReqhOevMz7Y93sIJFC5sCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"15feafcace329ed5722dbce294179b6fd596e43d449f21273406a385919c9041","last_reissued_at":"2026-05-18T01:27:38.702431Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:38.702431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.3564","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":"2026-05-18T01:27:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qHmD7yteY6CQB0yqDCNAvFL1hAe2+yzbVkejI+oY8UdZM88x9VZqhRclhL83yMs3TIYsTeRkxa+VHSmfi8+EDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:43:18.644074Z"},"content_sha256":"ad64363434d02824a8db62badd2e4927077a4677cf537c6dada21ebeb93474ea","schema_version":"1.0","event_id":"sha256:ad64363434d02824a8db62badd2e4927077a4677cf537c6dada21ebeb93474ea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:CX7K7SWOGKPNK4RNXTRJIF43N7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Feedback theory extended for proving generation of contraction semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OC","authors_text":"Hans Zwart, Mikael Kurula","submitted_at":"2014-03-14T13:05:11Z","abstract_excerpt":"Recently, the following novel method for proving the existence of solutions for certain linear time-invariant PDEs was introduced: The operator associated to a given PDE is represented by a (larger) operator with an internal loop. If the larger operator (without the internal loop) generates a contraction semigroup, the internal loop is accretive, and some non-restrictive technical assumptions are fulfilled, then the original operator generates a contraction semigroup as well. Beginning with the undamped wave equation, this general idea can be applied to show that the heat equation and wave equ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3564","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":"2026-05-18T01:27:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R2+x+YenV3++WXgEzugVpyACNGFY4Aphw9yTy+Ld8mn5H25D0/0VVHDLRUDTflSiiij3wlqGMNuyx1lYNVwHDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:43:18.644526Z"},"content_sha256":"65702a9d1a6a007d397c12151efe03b5f692ae0f7f6bce8f1ffd29a0c7c06ca8","schema_version":"1.0","event_id":"sha256:65702a9d1a6a007d397c12151efe03b5f692ae0f7f6bce8f1ffd29a0c7c06ca8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CX7K7SWOGKPNK4RNXTRJIF43N7/bundle.json","state_url":"https://pith.science/pith/CX7K7SWOGKPNK4RNXTRJIF43N7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CX7K7SWOGKPNK4RNXTRJIF43N7/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":"2026-05-28T20:43:18Z","links":{"resolver":"https://pith.science/pith/CX7K7SWOGKPNK4RNXTRJIF43N7","bundle":"https://pith.science/pith/CX7K7SWOGKPNK4RNXTRJIF43N7/bundle.json","state":"https://pith.science/pith/CX7K7SWOGKPNK4RNXTRJIF43N7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CX7K7SWOGKPNK4RNXTRJIF43N7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:CX7K7SWOGKPNK4RNXTRJIF43N7","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":"73be38833b2ccbc6bcbe8af7f3b09768f731d90166b5b4009efc06a67f70baf7","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-03-14T13:05:11Z","title_canon_sha256":"c745f4819c203b4d4c75010e6a06fdb3a8e1156b5f0a11b11d7882fd073c35d7"},"schema_version":"1.0","source":{"id":"1403.3564","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.3564","created_at":"2026-05-18T01:27:38Z"},{"alias_kind":"arxiv_version","alias_value":"1403.3564v2","created_at":"2026-05-18T01:27:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.3564","created_at":"2026-05-18T01:27:38Z"},{"alias_kind":"pith_short_12","alias_value":"CX7K7SWOGKPN","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"CX7K7SWOGKPNK4RN","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"CX7K7SWO","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:65702a9d1a6a007d397c12151efe03b5f692ae0f7f6bce8f1ffd29a0c7c06ca8","target":"graph","created_at":"2026-05-18T01:27:38Z","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":"Recently, the following novel method for proving the existence of solutions for certain linear time-invariant PDEs was introduced: The operator associated to a given PDE is represented by a (larger) operator with an internal loop. If the larger operator (without the internal loop) generates a contraction semigroup, the internal loop is accretive, and some non-restrictive technical assumptions are fulfilled, then the original operator generates a contraction semigroup as well. Beginning with the undamped wave equation, this general idea can be applied to show that the heat equation and wave equ","authors_text":"Hans Zwart, Mikael Kurula","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-03-14T13:05:11Z","title":"Feedback theory extended for proving generation of contraction semigroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3564","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:ad64363434d02824a8db62badd2e4927077a4677cf537c6dada21ebeb93474ea","target":"record","created_at":"2026-05-18T01:27:38Z","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":"73be38833b2ccbc6bcbe8af7f3b09768f731d90166b5b4009efc06a67f70baf7","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-03-14T13:05:11Z","title_canon_sha256":"c745f4819c203b4d4c75010e6a06fdb3a8e1156b5f0a11b11d7882fd073c35d7"},"schema_version":"1.0","source":{"id":"1403.3564","kind":"arxiv","version":2}},"canonical_sha256":"15feafcace329ed5722dbce294179b6fd596e43d449f21273406a385919c9041","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"15feafcace329ed5722dbce294179b6fd596e43d449f21273406a385919c9041","first_computed_at":"2026-05-18T01:27:38.702431Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:27:38.702431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"I+Qfd9YELORWIONC4bm2Ea6KKB2ABL6TAT6WK62jMTN5o8SGisqu6igx1r9B1rfrReqhOevMz7Y93sIJFC5sCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:27:38.702960Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.3564","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ad64363434d02824a8db62badd2e4927077a4677cf537c6dada21ebeb93474ea","sha256:65702a9d1a6a007d397c12151efe03b5f692ae0f7f6bce8f1ffd29a0c7c06ca8"],"state_sha256":"1c08822e62e354271b87abb0fe96941a3903be006d7390051188318863f87768"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QpSBYaWs6u5eCbE4kaoxkmFCaN3AjGwL/BLASl2dKFW5Kr915CNh97VJOKWMz6g0KbMOGv6OGJmFqmOyWAYxDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T20:43:18.647109Z","bundle_sha256":"0e3f5a9c09c2798b38171ce23082c7a6672114fae92c30f0376a7aed34508784"}}