{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:V7ZHCEMY5AWUAQM6OCXNQYTEFE","short_pith_number":"pith:V7ZHCEMY","canonical_record":{"source":{"id":"1705.02112","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-05T07:54:07Z","cross_cats_sorted":[],"title_canon_sha256":"69e159041e6d60657f811012f40bb6498876982c9de24f9f0d3de15032d79862","abstract_canon_sha256":"69b8600fd26253dd3ef3bc164c08d5c5fb1584b868452ab7adc47b0367a3c9d3"},"schema_version":"1.0"},"canonical_sha256":"aff2711198e82d40419e70aed86264292276b7ab437fa290b408595d6c59b8c3","source":{"kind":"arxiv","id":"1705.02112","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.02112","created_at":"2026-05-18T00:45:00Z"},{"alias_kind":"arxiv_version","alias_value":"1705.02112v1","created_at":"2026-05-18T00:45:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.02112","created_at":"2026-05-18T00:45:00Z"},{"alias_kind":"pith_short_12","alias_value":"V7ZHCEMY5AWU","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"V7ZHCEMY5AWUAQM6","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"V7ZHCEMY","created_at":"2026-05-18T12:31:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:V7ZHCEMY5AWUAQM6OCXNQYTEFE","target":"record","payload":{"canonical_record":{"source":{"id":"1705.02112","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-05T07:54:07Z","cross_cats_sorted":[],"title_canon_sha256":"69e159041e6d60657f811012f40bb6498876982c9de24f9f0d3de15032d79862","abstract_canon_sha256":"69b8600fd26253dd3ef3bc164c08d5c5fb1584b868452ab7adc47b0367a3c9d3"},"schema_version":"1.0"},"canonical_sha256":"aff2711198e82d40419e70aed86264292276b7ab437fa290b408595d6c59b8c3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:00.604762Z","signature_b64":"2aO2lFJTlRrV5RP8fR6IS1ECwzvOtL68cONMZ38nr99Eii8hMIW9IVfLpcJZcLDE6n7i4e/pSaSL/UZL4yykCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aff2711198e82d40419e70aed86264292276b7ab437fa290b408595d6c59b8c3","last_reissued_at":"2026-05-18T00:45:00.604131Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:00.604131Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.02112","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":"2026-05-18T00:45:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h/X0j2MdI/ioenLll9m1gDUFrc2ckE6fTSNCVJYMvvpBVK+xRvfPv6IFj56/jtzyopigOBVTblEfy5S0DqprDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T12:39:59.256028Z"},"content_sha256":"14cbac69dc13d2142b825bc89143008675315e97386614badbeacbacdaa6e1f0","schema_version":"1.0","event_id":"sha256:14cbac69dc13d2142b825bc89143008675315e97386614badbeacbacdaa6e1f0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:V7ZHCEMY5AWUAQM6OCXNQYTEFE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global attractors for the Benjamin-Bona-Mahony equation with memory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Filippo Dell'Oro, Olivier Goubet, Vittorino Pata, Youcef Mammeri","submitted_at":"2017-05-05T07:54:07Z","abstract_excerpt":"We consider the nonlinear integrodifferential Benjamin-Bona-Mahony equation $$ u_t - u_{txx} + u_x - \\int_0^\\infty g(s) u_{xx}(t-s) {\\rm d} s + u u_x = f $$ where the dissipation is entirely contributed by the memory term. Under a suitable smallness assumption on the external force $f$, we show that the related solution semigroup possesses the global attractor in the natural weak energy space. The result is obtained by means of a nonstandard approach based on the construction of a suitable family of attractors on certain invariant sets of the phase space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.02112","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":"2026-05-18T00:45:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FpbMnAJ5mNnyNrMmEvnCU9I+UGXX654AsWXpG5fhojx92v5lcJmp8sszdZa6+sB6hbsrkzeK/uaxUT5T8hlOCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T12:39:59.256392Z"},"content_sha256":"f2b63e7570ce14dc26fe993c77c2db767da0b36d9d5458a084cbebe847656b7e","schema_version":"1.0","event_id":"sha256:f2b63e7570ce14dc26fe993c77c2db767da0b36d9d5458a084cbebe847656b7e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V7ZHCEMY5AWUAQM6OCXNQYTEFE/bundle.json","state_url":"https://pith.science/pith/V7ZHCEMY5AWUAQM6OCXNQYTEFE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V7ZHCEMY5AWUAQM6OCXNQYTEFE/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":"2026-05-28T12:39:59Z","links":{"resolver":"https://pith.science/pith/V7ZHCEMY5AWUAQM6OCXNQYTEFE","bundle":"https://pith.science/pith/V7ZHCEMY5AWUAQM6OCXNQYTEFE/bundle.json","state":"https://pith.science/pith/V7ZHCEMY5AWUAQM6OCXNQYTEFE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V7ZHCEMY5AWUAQM6OCXNQYTEFE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:V7ZHCEMY5AWUAQM6OCXNQYTEFE","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":"69b8600fd26253dd3ef3bc164c08d5c5fb1584b868452ab7adc47b0367a3c9d3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-05T07:54:07Z","title_canon_sha256":"69e159041e6d60657f811012f40bb6498876982c9de24f9f0d3de15032d79862"},"schema_version":"1.0","source":{"id":"1705.02112","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.02112","created_at":"2026-05-18T00:45:00Z"},{"alias_kind":"arxiv_version","alias_value":"1705.02112v1","created_at":"2026-05-18T00:45:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.02112","created_at":"2026-05-18T00:45:00Z"},{"alias_kind":"pith_short_12","alias_value":"V7ZHCEMY5AWU","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"V7ZHCEMY5AWUAQM6","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"V7ZHCEMY","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:f2b63e7570ce14dc26fe993c77c2db767da0b36d9d5458a084cbebe847656b7e","target":"graph","created_at":"2026-05-18T00:45:00Z","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 the nonlinear integrodifferential Benjamin-Bona-Mahony equation $$ u_t - u_{txx} + u_x - \\int_0^\\infty g(s) u_{xx}(t-s) {\\rm d} s + u u_x = f $$ where the dissipation is entirely contributed by the memory term. Under a suitable smallness assumption on the external force $f$, we show that the related solution semigroup possesses the global attractor in the natural weak energy space. The result is obtained by means of a nonstandard approach based on the construction of a suitable family of attractors on certain invariant sets of the phase space.","authors_text":"Filippo Dell'Oro, Olivier Goubet, Vittorino Pata, Youcef Mammeri","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-05T07:54:07Z","title":"Global attractors for the Benjamin-Bona-Mahony equation with memory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.02112","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":"sha256:14cbac69dc13d2142b825bc89143008675315e97386614badbeacbacdaa6e1f0","target":"record","created_at":"2026-05-18T00:45:00Z","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":"69b8600fd26253dd3ef3bc164c08d5c5fb1584b868452ab7adc47b0367a3c9d3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-05T07:54:07Z","title_canon_sha256":"69e159041e6d60657f811012f40bb6498876982c9de24f9f0d3de15032d79862"},"schema_version":"1.0","source":{"id":"1705.02112","kind":"arxiv","version":1}},"canonical_sha256":"aff2711198e82d40419e70aed86264292276b7ab437fa290b408595d6c59b8c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aff2711198e82d40419e70aed86264292276b7ab437fa290b408595d6c59b8c3","first_computed_at":"2026-05-18T00:45:00.604131Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:00.604131Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2aO2lFJTlRrV5RP8fR6IS1ECwzvOtL68cONMZ38nr99Eii8hMIW9IVfLpcJZcLDE6n7i4e/pSaSL/UZL4yykCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:00.604762Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.02112","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:14cbac69dc13d2142b825bc89143008675315e97386614badbeacbacdaa6e1f0","sha256:f2b63e7570ce14dc26fe993c77c2db767da0b36d9d5458a084cbebe847656b7e"],"state_sha256":"c50afdcdc74f17182509ccb08c8a3650f8ae45f0a40bff5c83802956c2d66669"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jtQYtaH8VDXbgVgihfeneTOKSTlM6wOCvUM90Blkr000YYoMqs5xbFeUN4/3RcTLT97E8Ip8G0EoyeFn7fG+AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T12:39:59.258360Z","bundle_sha256":"2edf68091b6ce3e10e8ac74c33fe945581d63088a5484b42964178d4b9a8d517"}}