{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:GNBO7FAJVHJ2FETYQM2L64FKHT","short_pith_number":"pith:GNBO7FAJ","schema_version":"1.0","canonical_sha256":"3342ef9409a9d3a292788334bf70aa3cea389d555bb7f27569e441f2451b0f31","source":{"kind":"arxiv","id":"0810.4508","version":2},"attestation_state":"computed","paper":{"title":"Logarithmic dimension bounds for the maximal function along a polynomial curve","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Ioannis Parissis","submitted_at":"2008-10-24T17:15:04Z","abstract_excerpt":"Let M denote the maximal function along the polynomial curve p(t)=(t,t^2,...,t^d) in R^d: M(f)=sup_{r>0} (1/2r) \\int_{|t|<r} |f(x-p(t))| dt. We show that the L^2-norm of this operator grows at most logarithmically with the parameter d: ||M||_2 < c log d ||f||_2, where c>0 is an absolute constant. The proof depends on the explicit construction of a \"parabolic\" semi-group of operators which is a mixture of stable semi-groups."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0810.4508","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2008-10-24T17:15:04Z","cross_cats_sorted":[],"title_canon_sha256":"fd556d57a6fa556f6c1e8c031d4149239524a12970045f6e6df871d2255997ca","abstract_canon_sha256":"36c6e6169fcb2f79296b3bd183f0cd988dbef5473e8f684951a77fab5a12c13b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:10:46.234398Z","signature_b64":"i0jg71AFP3peghCqJWFFU/fmtg/cWNXIBciamL3cwxrKzm7qeuiR8mHzsc/+s75KACHkXi22i4MF2L75IwTgDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3342ef9409a9d3a292788334bf70aa3cea389d555bb7f27569e441f2451b0f31","last_reissued_at":"2026-05-18T03:10:46.233609Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:10:46.233609Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Logarithmic dimension bounds for the maximal function along a polynomial curve","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Ioannis Parissis","submitted_at":"2008-10-24T17:15:04Z","abstract_excerpt":"Let M denote the maximal function along the polynomial curve p(t)=(t,t^2,...,t^d) in R^d: M(f)=sup_{r>0} (1/2r) \\int_{|t|<r} |f(x-p(t))| dt. We show that the L^2-norm of this operator grows at most logarithmically with the parameter d: ||M||_2 < c log d ||f||_2, where c>0 is an absolute constant. The proof depends on the explicit construction of a \"parabolic\" semi-group of operators which is a mixture of stable semi-groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.4508","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0810.4508","created_at":"2026-05-18T03:10:46.233726+00:00"},{"alias_kind":"arxiv_version","alias_value":"0810.4508v2","created_at":"2026-05-18T03:10:46.233726+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0810.4508","created_at":"2026-05-18T03:10:46.233726+00:00"},{"alias_kind":"pith_short_12","alias_value":"GNBO7FAJVHJ2","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_16","alias_value":"GNBO7FAJVHJ2FETY","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_8","alias_value":"GNBO7FAJ","created_at":"2026-05-18T12:25:57.157939+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GNBO7FAJVHJ2FETYQM2L64FKHT","json":"https://pith.science/pith/GNBO7FAJVHJ2FETYQM2L64FKHT.json","graph_json":"https://pith.science/api/pith-number/GNBO7FAJVHJ2FETYQM2L64FKHT/graph.json","events_json":"https://pith.science/api/pith-number/GNBO7FAJVHJ2FETYQM2L64FKHT/events.json","paper":"https://pith.science/paper/GNBO7FAJ"},"agent_actions":{"view_html":"https://pith.science/pith/GNBO7FAJVHJ2FETYQM2L64FKHT","download_json":"https://pith.science/pith/GNBO7FAJVHJ2FETYQM2L64FKHT.json","view_paper":"https://pith.science/paper/GNBO7FAJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0810.4508&json=true","fetch_graph":"https://pith.science/api/pith-number/GNBO7FAJVHJ2FETYQM2L64FKHT/graph.json","fetch_events":"https://pith.science/api/pith-number/GNBO7FAJVHJ2FETYQM2L64FKHT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GNBO7FAJVHJ2FETYQM2L64FKHT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GNBO7FAJVHJ2FETYQM2L64FKHT/action/storage_attestation","attest_author":"https://pith.science/pith/GNBO7FAJVHJ2FETYQM2L64FKHT/action/author_attestation","sign_citation":"https://pith.science/pith/GNBO7FAJVHJ2FETYQM2L64FKHT/action/citation_signature","submit_replication":"https://pith.science/pith/GNBO7FAJVHJ2FETYQM2L64FKHT/action/replication_record"}},"created_at":"2026-05-18T03:10:46.233726+00:00","updated_at":"2026-05-18T03:10:46.233726+00:00"}