{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:P5IGH73U45LBXAK47M7S2HLNVY","short_pith_number":"pith:P5IGH73U","canonical_record":{"source":{"id":"1805.10048","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-05-25T09:02:47Z","cross_cats_sorted":[],"title_canon_sha256":"ef97bfca6f005ddb7f8ae7aa008b248e1a83a2891fe7cb95ba9140ecc0546ffc","abstract_canon_sha256":"26df679a537273dfeeb3ef61f03ed02470d3ac0d24b4e9cba853dafe30bca4f4"},"schema_version":"1.0"},"canonical_sha256":"7f5063ff74e7561b815cfb3f2d1d6dae36f268dde8356bc731f0f9318c72a5b2","source":{"kind":"arxiv","id":"1805.10048","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.10048","created_at":"2026-05-18T00:14:58Z"},{"alias_kind":"arxiv_version","alias_value":"1805.10048v1","created_at":"2026-05-18T00:14:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.10048","created_at":"2026-05-18T00:14:58Z"},{"alias_kind":"pith_short_12","alias_value":"P5IGH73U45LB","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"P5IGH73U45LBXAK4","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"P5IGH73U","created_at":"2026-05-18T12:32:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:P5IGH73U45LBXAK47M7S2HLNVY","target":"record","payload":{"canonical_record":{"source":{"id":"1805.10048","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-05-25T09:02:47Z","cross_cats_sorted":[],"title_canon_sha256":"ef97bfca6f005ddb7f8ae7aa008b248e1a83a2891fe7cb95ba9140ecc0546ffc","abstract_canon_sha256":"26df679a537273dfeeb3ef61f03ed02470d3ac0d24b4e9cba853dafe30bca4f4"},"schema_version":"1.0"},"canonical_sha256":"7f5063ff74e7561b815cfb3f2d1d6dae36f268dde8356bc731f0f9318c72a5b2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:58.397694Z","signature_b64":"SFWjG3gO8VVcnNqa4ieJnwjbcvKhUxetAos6yROjlKDRHPoTeg8NMzNer+gO4FxzPwQYMsPyf3KafDY4IV10Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f5063ff74e7561b815cfb3f2d1d6dae36f268dde8356bc731f0f9318c72a5b2","last_reissued_at":"2026-05-18T00:14:58.396987Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:58.396987Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.10048","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":"2026-05-18T00:14:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lcErcYqT3Ki4EF06p8eJaAFzU3p7zr5vIPABh6XF2UeuJXQkN0Z0chaLo/cGSOhidDj7LXFL6FwLhT7R9U/0DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T05:54:29.835305Z"},"content_sha256":"2094be5538556cd8888b4e695c22f1240be5612d9ccc195b89c2e2f68d93f255","schema_version":"1.0","event_id":"sha256:2094be5538556cd8888b4e695c22f1240be5612d9ccc195b89c2e2f68d93f255"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:P5IGH73U45LBXAK47M7S2HLNVY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Chaotic behaviour of the Fourier multipliers on Riemannian symmetric spaces of noncompact type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Rudra P. Sarkar, Swagato K. Ray","submitted_at":"2018-05-25T09:02:47Z","abstract_excerpt":"Let $X$ be a Riemannian symmetric space of noncompact type and $T$ be a linear translation-invariant operator which is bounded on $L^p(X)$. We shall show that if $T$ is not a constant multiple of identity then there exist complex constants $z$ such that $zT$ is chaotic on $L^p(X)$ when $p$ is in the sharp range $2<p<\\infty$. This vastly generalizes the result that dynamics of the (perturbed) heat semigroup is chaotic on $X$ proved in [15, 17]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.10048","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":"2026-05-18T00:14:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LPk2Zi2FwbWnjYK24xVuAXvUKwNhOI988U9uVBXHV+7fC0axf6bHDIVW47IrVK30USJDC+uWbKXlQFlV0HXaBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T05:54:29.836089Z"},"content_sha256":"5146444dce8f811458ed0eab4454e1d884e485b172c6939567b379e56ce7af75","schema_version":"1.0","event_id":"sha256:5146444dce8f811458ed0eab4454e1d884e485b172c6939567b379e56ce7af75"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P5IGH73U45LBXAK47M7S2HLNVY/bundle.json","state_url":"https://pith.science/pith/P5IGH73U45LBXAK47M7S2HLNVY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P5IGH73U45LBXAK47M7S2HLNVY/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":"2026-05-30T05:54:29Z","links":{"resolver":"https://pith.science/pith/P5IGH73U45LBXAK47M7S2HLNVY","bundle":"https://pith.science/pith/P5IGH73U45LBXAK47M7S2HLNVY/bundle.json","state":"https://pith.science/pith/P5IGH73U45LBXAK47M7S2HLNVY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P5IGH73U45LBXAK47M7S2HLNVY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:P5IGH73U45LBXAK47M7S2HLNVY","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":"26df679a537273dfeeb3ef61f03ed02470d3ac0d24b4e9cba853dafe30bca4f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-05-25T09:02:47Z","title_canon_sha256":"ef97bfca6f005ddb7f8ae7aa008b248e1a83a2891fe7cb95ba9140ecc0546ffc"},"schema_version":"1.0","source":{"id":"1805.10048","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.10048","created_at":"2026-05-18T00:14:58Z"},{"alias_kind":"arxiv_version","alias_value":"1805.10048v1","created_at":"2026-05-18T00:14:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.10048","created_at":"2026-05-18T00:14:58Z"},{"alias_kind":"pith_short_12","alias_value":"P5IGH73U45LB","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"P5IGH73U45LBXAK4","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"P5IGH73U","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:5146444dce8f811458ed0eab4454e1d884e485b172c6939567b379e56ce7af75","target":"graph","created_at":"2026-05-18T00:14:58Z","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":"Let $X$ be a Riemannian symmetric space of noncompact type and $T$ be a linear translation-invariant operator which is bounded on $L^p(X)$. We shall show that if $T$ is not a constant multiple of identity then there exist complex constants $z$ such that $zT$ is chaotic on $L^p(X)$ when $p$ is in the sharp range $2<p<\\infty$. This vastly generalizes the result that dynamics of the (perturbed) heat semigroup is chaotic on $X$ proved in [15, 17].","authors_text":"Rudra P. Sarkar, Swagato K. Ray","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-05-25T09:02:47Z","title":"Chaotic behaviour of the Fourier multipliers on Riemannian symmetric spaces of noncompact type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.10048","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":"sha256:2094be5538556cd8888b4e695c22f1240be5612d9ccc195b89c2e2f68d93f255","target":"record","created_at":"2026-05-18T00:14:58Z","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":"26df679a537273dfeeb3ef61f03ed02470d3ac0d24b4e9cba853dafe30bca4f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-05-25T09:02:47Z","title_canon_sha256":"ef97bfca6f005ddb7f8ae7aa008b248e1a83a2891fe7cb95ba9140ecc0546ffc"},"schema_version":"1.0","source":{"id":"1805.10048","kind":"arxiv","version":1}},"canonical_sha256":"7f5063ff74e7561b815cfb3f2d1d6dae36f268dde8356bc731f0f9318c72a5b2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f5063ff74e7561b815cfb3f2d1d6dae36f268dde8356bc731f0f9318c72a5b2","first_computed_at":"2026-05-18T00:14:58.396987Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:58.396987Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SFWjG3gO8VVcnNqa4ieJnwjbcvKhUxetAos6yROjlKDRHPoTeg8NMzNer+gO4FxzPwQYMsPyf3KafDY4IV10Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:58.397694Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.10048","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2094be5538556cd8888b4e695c22f1240be5612d9ccc195b89c2e2f68d93f255","sha256:5146444dce8f811458ed0eab4454e1d884e485b172c6939567b379e56ce7af75"],"state_sha256":"11e1c4c62e53619475a9fac9cbb3b5219f37e44d597fa80ae2316e2f514046ce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cwAeoaiXDqBCTrepDMC5DnVTQKXLKJHghG1RrNvwEE1yZUtlOyM5AZSGkeCpxaqM7tmgioVLopBxXkOX+fuECQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T05:54:29.839788Z","bundle_sha256":"9974241a76cef6dc3fe1f4484ddcdaabd5316dc8410bf58e6e0dff4852e3a041"}}