{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:Z2FJMWY6K4BBJBEPWTJAEQKXQR","short_pith_number":"pith:Z2FJMWY6","canonical_record":{"source":{"id":"1810.07494","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-10-17T11:57:35Z","cross_cats_sorted":[],"title_canon_sha256":"f750ed37f0a1ac17de10642e6ccf3ad6b4e50d359ff0155a30efa7a251e6b15d","abstract_canon_sha256":"5e3f1460dbd80dd9887f231cb33c3bf2f0e51022ecd7e70bde6ef5671dd4f79d"},"schema_version":"1.0"},"canonical_sha256":"ce8a965b1e570214848fb4d2024157847e1561b47be8abaacd6c9f5bd3bea546","source":{"kind":"arxiv","id":"1810.07494","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.07494","created_at":"2026-05-18T00:02:56Z"},{"alias_kind":"arxiv_version","alias_value":"1810.07494v1","created_at":"2026-05-18T00:02:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.07494","created_at":"2026-05-18T00:02:56Z"},{"alias_kind":"pith_short_12","alias_value":"Z2FJMWY6K4BB","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"Z2FJMWY6K4BBJBEP","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"Z2FJMWY6","created_at":"2026-05-18T12:33:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:Z2FJMWY6K4BBJBEPWTJAEQKXQR","target":"record","payload":{"canonical_record":{"source":{"id":"1810.07494","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-10-17T11:57:35Z","cross_cats_sorted":[],"title_canon_sha256":"f750ed37f0a1ac17de10642e6ccf3ad6b4e50d359ff0155a30efa7a251e6b15d","abstract_canon_sha256":"5e3f1460dbd80dd9887f231cb33c3bf2f0e51022ecd7e70bde6ef5671dd4f79d"},"schema_version":"1.0"},"canonical_sha256":"ce8a965b1e570214848fb4d2024157847e1561b47be8abaacd6c9f5bd3bea546","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:56.197933Z","signature_b64":"DbBcLt29Pbuf5/5Uz92N4RVT3Ca90HbkuInfDvJit7LwPGlIuQDI/0uLw1kvSSzvFbpluHpJQd0qC1llzOMgCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ce8a965b1e570214848fb4d2024157847e1561b47be8abaacd6c9f5bd3bea546","last_reissued_at":"2026-05-18T00:02:56.197206Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:56.197206Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.07494","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":"2026-05-18T00:02:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HlsbYqjHoxGzqyTgmA+0MFVIobMjiDwuWLt7rP4NPr51hIdVCtft9rItiVw7kjc7hZe/GfXEruQpDHTCGmFSAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T02:34:02.051539Z"},"content_sha256":"da5f5bee51c519be1921d2453e79e533a49cb3710bfe1498533d528eac88228c","schema_version":"1.0","event_id":"sha256:da5f5bee51c519be1921d2453e79e533a49cb3710bfe1498533d528eac88228c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:Z2FJMWY6K4BBJBEPWTJAEQKXQR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$C_0$-semigroups of $m$-isometries on Hilbert spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"A. bonilla, H. Zaway, T. Bermudez","submitted_at":"2018-10-17T11:57:35Z","abstract_excerpt":"Let $\\{T(t)\\}_{t\\ge 0}$ be a $C_0$-semigroup on a separable Hilbert space $H$. We characterize that $T(t)$ is an $m$-isometry for every $t$ in terms that the mapping $t\\in \\Bbb R^+ \\rightarrow \\|T(t)x\\|^2$ is a polynomial of degree less than $m$ for each $x\\in H$. This fact is used to study $m$-isometric right translation semigroup on weighted $L^p$-spaces. We characterize the above property in terms of conditions on the infinitesimal generator operator or in terms of the cogenerator operator of $\\{ T(t)\\}_{t\\geq 0}$. Moreover, we prove that a non-unitary $2$-isometry on a Hilbert space satisf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.07494","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":"2026-05-18T00:02:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rgRN+n/FNb/wcxKVnX5/Eq0hAktIRqHB7sa59zvsjJq0GZIkIwo9m2/GfVaUvi73IJG6lmR1mNWArV1idPadCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T02:34:02.051890Z"},"content_sha256":"88296e71703dde98bd3a1becc277967e334aaec53f32f221d3e7e44bb702bef7","schema_version":"1.0","event_id":"sha256:88296e71703dde98bd3a1becc277967e334aaec53f32f221d3e7e44bb702bef7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z2FJMWY6K4BBJBEPWTJAEQKXQR/bundle.json","state_url":"https://pith.science/pith/Z2FJMWY6K4BBJBEPWTJAEQKXQR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z2FJMWY6K4BBJBEPWTJAEQKXQR/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":"2026-06-04T02:34:02Z","links":{"resolver":"https://pith.science/pith/Z2FJMWY6K4BBJBEPWTJAEQKXQR","bundle":"https://pith.science/pith/Z2FJMWY6K4BBJBEPWTJAEQKXQR/bundle.json","state":"https://pith.science/pith/Z2FJMWY6K4BBJBEPWTJAEQKXQR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z2FJMWY6K4BBJBEPWTJAEQKXQR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:Z2FJMWY6K4BBJBEPWTJAEQKXQR","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":"5e3f1460dbd80dd9887f231cb33c3bf2f0e51022ecd7e70bde6ef5671dd4f79d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-10-17T11:57:35Z","title_canon_sha256":"f750ed37f0a1ac17de10642e6ccf3ad6b4e50d359ff0155a30efa7a251e6b15d"},"schema_version":"1.0","source":{"id":"1810.07494","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.07494","created_at":"2026-05-18T00:02:56Z"},{"alias_kind":"arxiv_version","alias_value":"1810.07494v1","created_at":"2026-05-18T00:02:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.07494","created_at":"2026-05-18T00:02:56Z"},{"alias_kind":"pith_short_12","alias_value":"Z2FJMWY6K4BB","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"Z2FJMWY6K4BBJBEP","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"Z2FJMWY6","created_at":"2026-05-18T12:33:04Z"}],"graph_snapshots":[{"event_id":"sha256:88296e71703dde98bd3a1becc277967e334aaec53f32f221d3e7e44bb702bef7","target":"graph","created_at":"2026-05-18T00:02:56Z","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 $\\{T(t)\\}_{t\\ge 0}$ be a $C_0$-semigroup on a separable Hilbert space $H$. We characterize that $T(t)$ is an $m$-isometry for every $t$ in terms that the mapping $t\\in \\Bbb R^+ \\rightarrow \\|T(t)x\\|^2$ is a polynomial of degree less than $m$ for each $x\\in H$. This fact is used to study $m$-isometric right translation semigroup on weighted $L^p$-spaces. We characterize the above property in terms of conditions on the infinitesimal generator operator or in terms of the cogenerator operator of $\\{ T(t)\\}_{t\\geq 0}$. Moreover, we prove that a non-unitary $2$-isometry on a Hilbert space satisf","authors_text":"A. bonilla, H. Zaway, T. Bermudez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-10-17T11:57:35Z","title":"$C_0$-semigroups of $m$-isometries on Hilbert spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.07494","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:da5f5bee51c519be1921d2453e79e533a49cb3710bfe1498533d528eac88228c","target":"record","created_at":"2026-05-18T00:02:56Z","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":"5e3f1460dbd80dd9887f231cb33c3bf2f0e51022ecd7e70bde6ef5671dd4f79d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-10-17T11:57:35Z","title_canon_sha256":"f750ed37f0a1ac17de10642e6ccf3ad6b4e50d359ff0155a30efa7a251e6b15d"},"schema_version":"1.0","source":{"id":"1810.07494","kind":"arxiv","version":1}},"canonical_sha256":"ce8a965b1e570214848fb4d2024157847e1561b47be8abaacd6c9f5bd3bea546","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ce8a965b1e570214848fb4d2024157847e1561b47be8abaacd6c9f5bd3bea546","first_computed_at":"2026-05-18T00:02:56.197206Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:56.197206Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DbBcLt29Pbuf5/5Uz92N4RVT3Ca90HbkuInfDvJit7LwPGlIuQDI/0uLw1kvSSzvFbpluHpJQd0qC1llzOMgCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:56.197933Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.07494","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:da5f5bee51c519be1921d2453e79e533a49cb3710bfe1498533d528eac88228c","sha256:88296e71703dde98bd3a1becc277967e334aaec53f32f221d3e7e44bb702bef7"],"state_sha256":"054137cf5d667cd3dd86585bbf9b7d7360bb64caa9626a7cac5d294788020152"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"egDk+uy3uRCJfa5Lyh3Ma67eajdTlkP2h6eUFHYs40ciAZawbFt2doVhyl5aa6YFdUi0vGCSeM03PWPa5wN4DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T02:34:02.054542Z","bundle_sha256":"a83b08b3085bafdc356d5a23e98a697ae4ad431b9f3c074e4ceb54251175b860"}}