{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:C5O2LTS7UQHCZDLCH7VDZ3RCA7","short_pith_number":"pith:C5O2LTS7","canonical_record":{"source":{"id":"1612.08304","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-12-25T23:07:47Z","cross_cats_sorted":[],"title_canon_sha256":"26db73aa73289c25552954894d73c61bbba606e3e5fbea83e4bc9ae39b619592","abstract_canon_sha256":"6548c1f3e0376dd1edd0ca2badcb5089b7ad4645d327eb2880bfdca42781ff00"},"schema_version":"1.0"},"canonical_sha256":"175da5ce5fa40e2c8d623fea3cee2207fbb1130fa99ae10a1458d3e5284afd8f","source":{"kind":"arxiv","id":"1612.08304","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.08304","created_at":"2026-05-18T00:15:24Z"},{"alias_kind":"arxiv_version","alias_value":"1612.08304v2","created_at":"2026-05-18T00:15:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.08304","created_at":"2026-05-18T00:15:24Z"},{"alias_kind":"pith_short_12","alias_value":"C5O2LTS7UQHC","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"C5O2LTS7UQHCZDLC","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"C5O2LTS7","created_at":"2026-05-18T12:30:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:C5O2LTS7UQHCZDLCH7VDZ3RCA7","target":"record","payload":{"canonical_record":{"source":{"id":"1612.08304","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-12-25T23:07:47Z","cross_cats_sorted":[],"title_canon_sha256":"26db73aa73289c25552954894d73c61bbba606e3e5fbea83e4bc9ae39b619592","abstract_canon_sha256":"6548c1f3e0376dd1edd0ca2badcb5089b7ad4645d327eb2880bfdca42781ff00"},"schema_version":"1.0"},"canonical_sha256":"175da5ce5fa40e2c8d623fea3cee2207fbb1130fa99ae10a1458d3e5284afd8f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:24.678665Z","signature_b64":"38F0s/8s75qZznuvl4pAneCdDaxwYeo6LTfklyTKZWau17C0LnIAlSJLmnxRr9p5jQrRkIxqJvXJaH7Ak1/8Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"175da5ce5fa40e2c8d623fea3cee2207fbb1130fa99ae10a1458d3e5284afd8f","last_reissued_at":"2026-05-18T00:15:24.678157Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:24.678157Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.08304","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:15:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"isWEkHlU9epDyyQcTvrwYzcF+6z788d11phX989QWe1VEjLZLQ1cbctMwWaX8loybdKPs65Ex527zuwBUaxVDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T06:04:48.081536Z"},"content_sha256":"f50e43f543b75aec5cef874e976d45332ddcd4013b0fa2495ba3afdac4a1d303","schema_version":"1.0","event_id":"sha256:f50e43f543b75aec5cef874e976d45332ddcd4013b0fa2495ba3afdac4a1d303"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:C5O2LTS7UQHCZDLCH7VDZ3RCA7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A generalized Hilbert operator acting on conformally invariant spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Daniel Girela, Noel Merch\\'an","submitted_at":"2016-12-25T23:07:47Z","abstract_excerpt":"If $\\mu $ is a positive Borel measure on the interval $[0, 1)$ we let $\\mathcal H_\\mu $ be the Hankel matrix $\\mathcal H_\\mu =(\\mu_{n, k})_{n,k\\ge 0}$ with entries $\\mu_{n, k}=\\mu_{n+k}$, where, for $n\\,=\\,0, 1, 2, \\dots $, $\\mu_n$ denotes the moment of orden $n$ of $\\mu $. This matrix induces formally the operator $$\\mathcal{H}_\\mu (f)(z)= \\sum_{n=0}^{\\infty}\\left(\\sum_{k=0}^{\\infty} \\mu_{n,k}{a_k}\\right)z^n$$ on the space of all analytic functions $f(z)=\\sum_{k=0}^\\infty a_kz^k$, in the unit disc $\\D $. This is a natural generalization of the classical Hilbert operator. The action of the ope"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.08304","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:15:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uO5NEJVJ37mMGiCi1PpHA/4irZLEqm+QEfBpa2LO1VUNTEOhxx6CUhE3S5H7OGEdTmkc+k95elvOVvDksNx8Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T06:04:48.081886Z"},"content_sha256":"069abb349af871700d84d8cd2b0342d1d4de88e0ef20c5a52ae7811acb2497be","schema_version":"1.0","event_id":"sha256:069abb349af871700d84d8cd2b0342d1d4de88e0ef20c5a52ae7811acb2497be"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C5O2LTS7UQHCZDLCH7VDZ3RCA7/bundle.json","state_url":"https://pith.science/pith/C5O2LTS7UQHCZDLCH7VDZ3RCA7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C5O2LTS7UQHCZDLCH7VDZ3RCA7/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":"2026-06-23T06:04:48Z","links":{"resolver":"https://pith.science/pith/C5O2LTS7UQHCZDLCH7VDZ3RCA7","bundle":"https://pith.science/pith/C5O2LTS7UQHCZDLCH7VDZ3RCA7/bundle.json","state":"https://pith.science/pith/C5O2LTS7UQHCZDLCH7VDZ3RCA7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C5O2LTS7UQHCZDLCH7VDZ3RCA7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:C5O2LTS7UQHCZDLCH7VDZ3RCA7","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":"6548c1f3e0376dd1edd0ca2badcb5089b7ad4645d327eb2880bfdca42781ff00","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-12-25T23:07:47Z","title_canon_sha256":"26db73aa73289c25552954894d73c61bbba606e3e5fbea83e4bc9ae39b619592"},"schema_version":"1.0","source":{"id":"1612.08304","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.08304","created_at":"2026-05-18T00:15:24Z"},{"alias_kind":"arxiv_version","alias_value":"1612.08304v2","created_at":"2026-05-18T00:15:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.08304","created_at":"2026-05-18T00:15:24Z"},{"alias_kind":"pith_short_12","alias_value":"C5O2LTS7UQHC","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"C5O2LTS7UQHCZDLC","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"C5O2LTS7","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:069abb349af871700d84d8cd2b0342d1d4de88e0ef20c5a52ae7811acb2497be","target":"graph","created_at":"2026-05-18T00:15:24Z","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":"If $\\mu $ is a positive Borel measure on the interval $[0, 1)$ we let $\\mathcal H_\\mu $ be the Hankel matrix $\\mathcal H_\\mu =(\\mu_{n, k})_{n,k\\ge 0}$ with entries $\\mu_{n, k}=\\mu_{n+k}$, where, for $n\\,=\\,0, 1, 2, \\dots $, $\\mu_n$ denotes the moment of orden $n$ of $\\mu $. This matrix induces formally the operator $$\\mathcal{H}_\\mu (f)(z)= \\sum_{n=0}^{\\infty}\\left(\\sum_{k=0}^{\\infty} \\mu_{n,k}{a_k}\\right)z^n$$ on the space of all analytic functions $f(z)=\\sum_{k=0}^\\infty a_kz^k$, in the unit disc $\\D $. This is a natural generalization of the classical Hilbert operator. The action of the ope","authors_text":"Daniel Girela, Noel Merch\\'an","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-12-25T23:07:47Z","title":"A generalized Hilbert operator acting on conformally invariant spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.08304","kind":"arxiv","version":2},"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:f50e43f543b75aec5cef874e976d45332ddcd4013b0fa2495ba3afdac4a1d303","target":"record","created_at":"2026-05-18T00:15:24Z","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":"6548c1f3e0376dd1edd0ca2badcb5089b7ad4645d327eb2880bfdca42781ff00","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-12-25T23:07:47Z","title_canon_sha256":"26db73aa73289c25552954894d73c61bbba606e3e5fbea83e4bc9ae39b619592"},"schema_version":"1.0","source":{"id":"1612.08304","kind":"arxiv","version":2}},"canonical_sha256":"175da5ce5fa40e2c8d623fea3cee2207fbb1130fa99ae10a1458d3e5284afd8f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"175da5ce5fa40e2c8d623fea3cee2207fbb1130fa99ae10a1458d3e5284afd8f","first_computed_at":"2026-05-18T00:15:24.678157Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:24.678157Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"38F0s/8s75qZznuvl4pAneCdDaxwYeo6LTfklyTKZWau17C0LnIAlSJLmnxRr9p5jQrRkIxqJvXJaH7Ak1/8Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:24.678665Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.08304","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f50e43f543b75aec5cef874e976d45332ddcd4013b0fa2495ba3afdac4a1d303","sha256:069abb349af871700d84d8cd2b0342d1d4de88e0ef20c5a52ae7811acb2497be"],"state_sha256":"43418bcc70cd739649deb942029fae2e12d503cb8fc5748e1faaf7d4264c0a8b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RY1V4ksrC36pTroM/ucKOAaddpCLru4n2qB/Ryg3gMzTsH3W6z859bsOs1j0XOjHmvxdqZ15NR956dLqRPLiCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T06:04:48.084007Z","bundle_sha256":"302f15e2de840272bb309e387ef06cc67d8fb705aa76e168452ac893b013cc35"}}