{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:EHJNL47PFT66XSGKGU36ID6DNW","short_pith_number":"pith:EHJNL47P","canonical_record":{"source":{"id":"1712.05194","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-12-14T12:21:03Z","cross_cats_sorted":[],"title_canon_sha256":"c365d2dd5f1bef80d9d05867d7cbc99cc00b8e0d18c074c24c160ad723483daa","abstract_canon_sha256":"5df9465a5f036b359e1c595dc52afc1d21061439e7be91379125bea2eaf51a1a"},"schema_version":"1.0"},"canonical_sha256":"21d2d5f3ef2cfdebc8ca3537e40fc36d8fd8a2ffe6de124ff94ac8a73969cb67","source":{"kind":"arxiv","id":"1712.05194","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.05194","created_at":"2026-05-18T00:27:58Z"},{"alias_kind":"arxiv_version","alias_value":"1712.05194v1","created_at":"2026-05-18T00:27:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.05194","created_at":"2026-05-18T00:27:58Z"},{"alias_kind":"pith_short_12","alias_value":"EHJNL47PFT66","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EHJNL47PFT66XSGK","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EHJNL47P","created_at":"2026-05-18T12:31:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:EHJNL47PFT66XSGKGU36ID6DNW","target":"record","payload":{"canonical_record":{"source":{"id":"1712.05194","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-12-14T12:21:03Z","cross_cats_sorted":[],"title_canon_sha256":"c365d2dd5f1bef80d9d05867d7cbc99cc00b8e0d18c074c24c160ad723483daa","abstract_canon_sha256":"5df9465a5f036b359e1c595dc52afc1d21061439e7be91379125bea2eaf51a1a"},"schema_version":"1.0"},"canonical_sha256":"21d2d5f3ef2cfdebc8ca3537e40fc36d8fd8a2ffe6de124ff94ac8a73969cb67","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:58.624140Z","signature_b64":"CsE9CHaGYiK27+8gLZyCHmZy/YI9diawqOoV9b8nu1fvKcKmRC6HhTUXhVcUxjF+3WlyMMoanJaF8rJO1g46Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"21d2d5f3ef2cfdebc8ca3537e40fc36d8fd8a2ffe6de124ff94ac8a73969cb67","last_reissued_at":"2026-05-18T00:27:58.623650Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:58.623650Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.05194","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":"2026-05-18T00:27:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rfbilrtdRjSaoDuBsDaxiagKZQyJTq+2JgDL3czOkzcYX9qYIXFYtaTaa7VhUKx6fq+AQDZqG8kZbAKer9WlAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T21:23:28.279438Z"},"content_sha256":"a89dfcbcca62c71fad389b960801b7012af84a7c936ec2296048c1ff1a242e05","schema_version":"1.0","event_id":"sha256:a89dfcbcca62c71fad389b960801b7012af84a7c936ec2296048c1ff1a242e05"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:EHJNL47PFT66XSGKGU36ID6DNW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global an cocycle atractor for non-utonomous reaction-difussion equations . The case of null upper Lyapunov exponente","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Ana M. Sanz, Jose antonio Lnaga, Rafael Obaya, Tomas Caraballo","submitted_at":"2017-12-14T12:21:03Z","abstract_excerpt":"In this paper we obtain a detailed description of the global and cocycle attractors for the skew-product semiflows induced by the mild solutions of a family of scalar linear-dissipative parabolic problems over a minimal and uniquely ergodic flow. We consider the case of null upper Lyapunov exponent for the linear part of the problem. Then, two different types of attractors can appear, depending on whether the linear equations have a bounded or an unbounded associated real cocycle. In the first case (e.g.~in periodic equations), the structure of the attractor is simple, whereas in the second ca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.05194","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":"2026-05-18T00:27:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wCkV/zz85q1hIN1LSgfiwVLebXK6wV6YAh0xpY1EP6+QailPZMT/c5+x7RZaXRvvmn5vogkM7JbJhhQvoSVUBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T21:23:28.280048Z"},"content_sha256":"c7dc342a6fdaf8946d9e157ce499f1f0381496cc88c273a20a3f75db91fb8993","schema_version":"1.0","event_id":"sha256:c7dc342a6fdaf8946d9e157ce499f1f0381496cc88c273a20a3f75db91fb8993"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EHJNL47PFT66XSGKGU36ID6DNW/bundle.json","state_url":"https://pith.science/pith/EHJNL47PFT66XSGKGU36ID6DNW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EHJNL47PFT66XSGKGU36ID6DNW/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":"2026-06-07T21:23:28Z","links":{"resolver":"https://pith.science/pith/EHJNL47PFT66XSGKGU36ID6DNW","bundle":"https://pith.science/pith/EHJNL47PFT66XSGKGU36ID6DNW/bundle.json","state":"https://pith.science/pith/EHJNL47PFT66XSGKGU36ID6DNW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EHJNL47PFT66XSGKGU36ID6DNW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:EHJNL47PFT66XSGKGU36ID6DNW","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":"5df9465a5f036b359e1c595dc52afc1d21061439e7be91379125bea2eaf51a1a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-12-14T12:21:03Z","title_canon_sha256":"c365d2dd5f1bef80d9d05867d7cbc99cc00b8e0d18c074c24c160ad723483daa"},"schema_version":"1.0","source":{"id":"1712.05194","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.05194","created_at":"2026-05-18T00:27:58Z"},{"alias_kind":"arxiv_version","alias_value":"1712.05194v1","created_at":"2026-05-18T00:27:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.05194","created_at":"2026-05-18T00:27:58Z"},{"alias_kind":"pith_short_12","alias_value":"EHJNL47PFT66","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"EHJNL47PFT66XSGK","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"EHJNL47P","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:c7dc342a6fdaf8946d9e157ce499f1f0381496cc88c273a20a3f75db91fb8993","target":"graph","created_at":"2026-05-18T00:27:58Z","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 obtain a detailed description of the global and cocycle attractors for the skew-product semiflows induced by the mild solutions of a family of scalar linear-dissipative parabolic problems over a minimal and uniquely ergodic flow. We consider the case of null upper Lyapunov exponent for the linear part of the problem. Then, two different types of attractors can appear, depending on whether the linear equations have a bounded or an unbounded associated real cocycle. In the first case (e.g.~in periodic equations), the structure of the attractor is simple, whereas in the second ca","authors_text":"Ana M. Sanz, Jose antonio Lnaga, Rafael Obaya, Tomas Caraballo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-12-14T12:21:03Z","title":"Global an cocycle atractor for non-utonomous reaction-difussion equations . The case of null upper Lyapunov exponente"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.05194","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:a89dfcbcca62c71fad389b960801b7012af84a7c936ec2296048c1ff1a242e05","target":"record","created_at":"2026-05-18T00:27:58Z","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":"5df9465a5f036b359e1c595dc52afc1d21061439e7be91379125bea2eaf51a1a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-12-14T12:21:03Z","title_canon_sha256":"c365d2dd5f1bef80d9d05867d7cbc99cc00b8e0d18c074c24c160ad723483daa"},"schema_version":"1.0","source":{"id":"1712.05194","kind":"arxiv","version":1}},"canonical_sha256":"21d2d5f3ef2cfdebc8ca3537e40fc36d8fd8a2ffe6de124ff94ac8a73969cb67","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"21d2d5f3ef2cfdebc8ca3537e40fc36d8fd8a2ffe6de124ff94ac8a73969cb67","first_computed_at":"2026-05-18T00:27:58.623650Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:58.623650Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CsE9CHaGYiK27+8gLZyCHmZy/YI9diawqOoV9b8nu1fvKcKmRC6HhTUXhVcUxjF+3WlyMMoanJaF8rJO1g46Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:58.624140Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.05194","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a89dfcbcca62c71fad389b960801b7012af84a7c936ec2296048c1ff1a242e05","sha256:c7dc342a6fdaf8946d9e157ce499f1f0381496cc88c273a20a3f75db91fb8993"],"state_sha256":"a53de671f821296248158e92bc8ccb8c8595212353a4bd8ab96fe1381b3a6cd4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7YZUUTlhcgGsAVk9WtiXjZpG0bSRX2htEByYQCzXz6ULXeuh6tCkHnqV35tWIQj8rwW9kMvOe7m+h7LmBxHCDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T21:23:28.283442Z","bundle_sha256":"9c62dd74ba3ef88db1e4a31bdb897a2e91cea98bab1bd42d52f38e3dace430c1"}}