{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:7HE5ITS24CDQLWSN2B46YODGOT","short_pith_number":"pith:7HE5ITS2","canonical_record":{"source":{"id":"1706.05041","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-06-15T18:54:44Z","cross_cats_sorted":[],"title_canon_sha256":"3e51dee330b6a59554f1149ef1268b0dbc05b21ad2a66821d5b3724447586041","abstract_canon_sha256":"6d5a3552ab8ea81bacb66455f353a079c66d1b38aca55dfc1b86239d5e849a19"},"schema_version":"1.0"},"canonical_sha256":"f9c9d44e5ae08705da4dd079ec386674c6fefe2400534cf0a5971558f10f8bfd","source":{"kind":"arxiv","id":"1706.05041","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.05041","created_at":"2026-05-18T00:42:16Z"},{"alias_kind":"arxiv_version","alias_value":"1706.05041v1","created_at":"2026-05-18T00:42:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.05041","created_at":"2026-05-18T00:42:16Z"},{"alias_kind":"pith_short_12","alias_value":"7HE5ITS24CDQ","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7HE5ITS24CDQLWSN","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7HE5ITS2","created_at":"2026-05-18T12:31:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:7HE5ITS24CDQLWSN2B46YODGOT","target":"record","payload":{"canonical_record":{"source":{"id":"1706.05041","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-06-15T18:54:44Z","cross_cats_sorted":[],"title_canon_sha256":"3e51dee330b6a59554f1149ef1268b0dbc05b21ad2a66821d5b3724447586041","abstract_canon_sha256":"6d5a3552ab8ea81bacb66455f353a079c66d1b38aca55dfc1b86239d5e849a19"},"schema_version":"1.0"},"canonical_sha256":"f9c9d44e5ae08705da4dd079ec386674c6fefe2400534cf0a5971558f10f8bfd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:16.886723Z","signature_b64":"dKUft/Zq7MhieHMZp49ZuAZVvnc0VEwtVs5wekZfUDDEyYeZMoy18SgGu4A37aG8lZhVXysezl4yI9h4GKjTDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f9c9d44e5ae08705da4dd079ec386674c6fefe2400534cf0a5971558f10f8bfd","last_reissued_at":"2026-05-18T00:42:16.886131Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:16.886131Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.05041","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":"2026-05-18T00:42:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BFaIqhj3J/9VmsHF4dxyhOIpLPmUdtIDH3wqFLeTUwytPYa92MerwJF7J5AixGO0h8x9dVZgSkBCR5pcgg/TBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T08:35:53.709571Z"},"content_sha256":"f6716aafb907d964a333d4f81d9706b1f27a95c45862958660dd8c06c848a345","schema_version":"1.0","event_id":"sha256:f6716aafb907d964a333d4f81d9706b1f27a95c45862958660dd8c06c848a345"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:7HE5ITS24CDQLWSN2B46YODGOT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Internal Stabilization of a Class of Parabolic Integro-Differential Equations: Application to Viscoelastic Fluids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Debopriya Mukherjee, Sheetal Dharmatti, Utpal Manna","submitted_at":"2017-06-15T18:54:44Z","abstract_excerpt":"In this paper, we prove the stabilizability of abstract Parabolic Integro-Differential Equations (PIDE) in a Hilbert space with decay rate $e^{-\\gamma t} $ for certain $\\gamma > 0,$ by means of a finite dimensional controller in the feedback form. We determine a linear feedback law which is obtained by solving an algebraic Riccati equation. To prove the existence of the Riccati operator, we consider a linear quadratic optimal control problem with unbounded observation operator.\n  The abstract theory of stabilization developed here is applied to specific problems related to viscoelastic fluids,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.05041","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":"2026-05-18T00:42:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4MI8qu/vsLgU6k54MZ8mtKe75b2+TeZNKATQu3R2xokI5+DMlRt7MznMTo9JKH87cJwzJQzz6LUpCqEmXCjlBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T08:35:53.709923Z"},"content_sha256":"f9f5226af2aca927e6712adf64760b204f8fb67d79197d0778579f1e0a189598","schema_version":"1.0","event_id":"sha256:f9f5226af2aca927e6712adf64760b204f8fb67d79197d0778579f1e0a189598"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7HE5ITS24CDQLWSN2B46YODGOT/bundle.json","state_url":"https://pith.science/pith/7HE5ITS24CDQLWSN2B46YODGOT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7HE5ITS24CDQLWSN2B46YODGOT/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":"2026-06-03T08:35:53Z","links":{"resolver":"https://pith.science/pith/7HE5ITS24CDQLWSN2B46YODGOT","bundle":"https://pith.science/pith/7HE5ITS24CDQLWSN2B46YODGOT/bundle.json","state":"https://pith.science/pith/7HE5ITS24CDQLWSN2B46YODGOT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7HE5ITS24CDQLWSN2B46YODGOT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:7HE5ITS24CDQLWSN2B46YODGOT","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":"6d5a3552ab8ea81bacb66455f353a079c66d1b38aca55dfc1b86239d5e849a19","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-06-15T18:54:44Z","title_canon_sha256":"3e51dee330b6a59554f1149ef1268b0dbc05b21ad2a66821d5b3724447586041"},"schema_version":"1.0","source":{"id":"1706.05041","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.05041","created_at":"2026-05-18T00:42:16Z"},{"alias_kind":"arxiv_version","alias_value":"1706.05041v1","created_at":"2026-05-18T00:42:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.05041","created_at":"2026-05-18T00:42:16Z"},{"alias_kind":"pith_short_12","alias_value":"7HE5ITS24CDQ","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7HE5ITS24CDQLWSN","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7HE5ITS2","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:f9f5226af2aca927e6712adf64760b204f8fb67d79197d0778579f1e0a189598","target":"graph","created_at":"2026-05-18T00:42:16Z","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 prove the stabilizability of abstract Parabolic Integro-Differential Equations (PIDE) in a Hilbert space with decay rate $e^{-\\gamma t} $ for certain $\\gamma > 0,$ by means of a finite dimensional controller in the feedback form. We determine a linear feedback law which is obtained by solving an algebraic Riccati equation. To prove the existence of the Riccati operator, we consider a linear quadratic optimal control problem with unbounded observation operator.\n  The abstract theory of stabilization developed here is applied to specific problems related to viscoelastic fluids,","authors_text":"Debopriya Mukherjee, Sheetal Dharmatti, Utpal Manna","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-06-15T18:54:44Z","title":"Internal Stabilization of a Class of Parabolic Integro-Differential Equations: Application to Viscoelastic Fluids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.05041","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:f6716aafb907d964a333d4f81d9706b1f27a95c45862958660dd8c06c848a345","target":"record","created_at":"2026-05-18T00:42:16Z","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":"6d5a3552ab8ea81bacb66455f353a079c66d1b38aca55dfc1b86239d5e849a19","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-06-15T18:54:44Z","title_canon_sha256":"3e51dee330b6a59554f1149ef1268b0dbc05b21ad2a66821d5b3724447586041"},"schema_version":"1.0","source":{"id":"1706.05041","kind":"arxiv","version":1}},"canonical_sha256":"f9c9d44e5ae08705da4dd079ec386674c6fefe2400534cf0a5971558f10f8bfd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f9c9d44e5ae08705da4dd079ec386674c6fefe2400534cf0a5971558f10f8bfd","first_computed_at":"2026-05-18T00:42:16.886131Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:16.886131Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dKUft/Zq7MhieHMZp49ZuAZVvnc0VEwtVs5wekZfUDDEyYeZMoy18SgGu4A37aG8lZhVXysezl4yI9h4GKjTDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:16.886723Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.05041","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f6716aafb907d964a333d4f81d9706b1f27a95c45862958660dd8c06c848a345","sha256:f9f5226af2aca927e6712adf64760b204f8fb67d79197d0778579f1e0a189598"],"state_sha256":"55d6852b407197ee182e277a23db36604f03935165434cee61b37d5f82d605f6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i6wVcf7CNi4Wzye0ss00izpgMKotlsp8PRoWHNsgobtJ4EGbU+RlneZ8YCwV5liSRpoCJe53GW/tOENtoo+zCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T08:35:53.711844Z","bundle_sha256":"27d5df7d386528422ea75edd0495b583c6a767ac7ecf1b089f6ec43eca35472a"}}