{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:YOVX5T7LPLXNNBN2IH5UEZGMII","short_pith_number":"pith:YOVX5T7L","canonical_record":{"source":{"id":"1603.07685","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-03-23T13:53:42Z","cross_cats_sorted":["math.AP","math.FA"],"title_canon_sha256":"72ae91a364dc0072697693f88b7d187e18a88a8b853447f108021f32698376b0","abstract_canon_sha256":"0fe55c4edd1288116d3cefd2e117577529ee575606543a893010812c6f420b7b"},"schema_version":"1.0"},"canonical_sha256":"c3ab7ecfeb7aeed685ba41fb4264cc4219059bf8287c148baaa6f85771d20611","source":{"kind":"arxiv","id":"1603.07685","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.07685","created_at":"2026-05-18T00:35:10Z"},{"alias_kind":"arxiv_version","alias_value":"1603.07685v2","created_at":"2026-05-18T00:35:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.07685","created_at":"2026-05-18T00:35:10Z"},{"alias_kind":"pith_short_12","alias_value":"YOVX5T7LPLXN","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YOVX5T7LPLXNNBN2","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YOVX5T7L","created_at":"2026-05-18T12:30:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:YOVX5T7LPLXNNBN2IH5UEZGMII","target":"record","payload":{"canonical_record":{"source":{"id":"1603.07685","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-03-23T13:53:42Z","cross_cats_sorted":["math.AP","math.FA"],"title_canon_sha256":"72ae91a364dc0072697693f88b7d187e18a88a8b853447f108021f32698376b0","abstract_canon_sha256":"0fe55c4edd1288116d3cefd2e117577529ee575606543a893010812c6f420b7b"},"schema_version":"1.0"},"canonical_sha256":"c3ab7ecfeb7aeed685ba41fb4264cc4219059bf8287c148baaa6f85771d20611","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:10.785560Z","signature_b64":"VyHYhj1YO/OMw/5n0Uz99JhQ5SblI/Bu1aqMn57uDovUv6j0zvgK3ylzfEBo462v/ikSM/SMd6LkfsAEGRnwAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c3ab7ecfeb7aeed685ba41fb4264cc4219059bf8287c148baaa6f85771d20611","last_reissued_at":"2026-05-18T00:35:10.785048Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:10.785048Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.07685","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":"2026-05-18T00:35:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NFW+ORma4c4+9CD8s0FNBPIXG6FkR5gLmo17LxV4C3Z9CVHKeAbgpw8iSJ2vrAKUk1mUxeLSfSaU+nWkL3n9CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T18:23:13.496760Z"},"content_sha256":"cfcec05f36bd33ca5f41ad4e7fb4dd8f0dd46d297aadc99177d5cd84817c52aa","schema_version":"1.0","event_id":"sha256:cfcec05f36bd33ca5f41ad4e7fb4dd8f0dd46d297aadc99177d5cd84817c52aa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:YOVX5T7LPLXNNBN2IH5UEZGMII","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hardy spaces for Bessel-Schr\\\"odinger operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.FA"],"primary_cat":"math.CA","authors_text":"Edyta Kania, Marcin Preisner","submitted_at":"2016-03-23T13:53:42Z","abstract_excerpt":"Consider the Bessel operator with a potential on L^2((0,infty), x^a dx), namely Lf(x) = -f\"(x) - a/x f'(x) + V(x)f(x). We assume that a>0 and V\\in L^1_{loc}((0,infty), x^a dx) is a non-negative function. By definition, a function f\\in L^1((0,infty), x^a dx) belongs to the Hardy space H^1(L) if sup_{t>0} |e^{-tL} f| \\in L^1((0,infty), x^a dx). Under certain assumptions on V we characterize the space H^1(L) in terms of atomic decompositions of local type. In the second part we prove that this characterization can be applied to L for a \\in (0,1) with no additional assumptions on the potential V."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07685","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":"2026-05-18T00:35:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V2UEN6/v/BbBVC1kwVbnU+QnVO4wnOukeTVabTF4Hj9ajiqmd+Bo/qOlhFDUufL3Jb0bNpQngv/XN0dTaBydDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T18:23:13.497106Z"},"content_sha256":"e8875ef51a5ed192be6da1ad413050b4fea9c4c9ce53c07586f0119d9a9a1f3c","schema_version":"1.0","event_id":"sha256:e8875ef51a5ed192be6da1ad413050b4fea9c4c9ce53c07586f0119d9a9a1f3c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YOVX5T7LPLXNNBN2IH5UEZGMII/bundle.json","state_url":"https://pith.science/pith/YOVX5T7LPLXNNBN2IH5UEZGMII/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YOVX5T7LPLXNNBN2IH5UEZGMII/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":"2026-06-03T18:23:13Z","links":{"resolver":"https://pith.science/pith/YOVX5T7LPLXNNBN2IH5UEZGMII","bundle":"https://pith.science/pith/YOVX5T7LPLXNNBN2IH5UEZGMII/bundle.json","state":"https://pith.science/pith/YOVX5T7LPLXNNBN2IH5UEZGMII/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YOVX5T7LPLXNNBN2IH5UEZGMII/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:YOVX5T7LPLXNNBN2IH5UEZGMII","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":"0fe55c4edd1288116d3cefd2e117577529ee575606543a893010812c6f420b7b","cross_cats_sorted":["math.AP","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-03-23T13:53:42Z","title_canon_sha256":"72ae91a364dc0072697693f88b7d187e18a88a8b853447f108021f32698376b0"},"schema_version":"1.0","source":{"id":"1603.07685","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.07685","created_at":"2026-05-18T00:35:10Z"},{"alias_kind":"arxiv_version","alias_value":"1603.07685v2","created_at":"2026-05-18T00:35:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.07685","created_at":"2026-05-18T00:35:10Z"},{"alias_kind":"pith_short_12","alias_value":"YOVX5T7LPLXN","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YOVX5T7LPLXNNBN2","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YOVX5T7L","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:e8875ef51a5ed192be6da1ad413050b4fea9c4c9ce53c07586f0119d9a9a1f3c","target":"graph","created_at":"2026-05-18T00:35:10Z","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":"Consider the Bessel operator with a potential on L^2((0,infty), x^a dx), namely Lf(x) = -f\"(x) - a/x f'(x) + V(x)f(x). We assume that a>0 and V\\in L^1_{loc}((0,infty), x^a dx) is a non-negative function. By definition, a function f\\in L^1((0,infty), x^a dx) belongs to the Hardy space H^1(L) if sup_{t>0} |e^{-tL} f| \\in L^1((0,infty), x^a dx). Under certain assumptions on V we characterize the space H^1(L) in terms of atomic decompositions of local type. In the second part we prove that this characterization can be applied to L for a \\in (0,1) with no additional assumptions on the potential V.","authors_text":"Edyta Kania, Marcin Preisner","cross_cats":["math.AP","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-03-23T13:53:42Z","title":"Hardy spaces for Bessel-Schr\\\"odinger operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07685","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:cfcec05f36bd33ca5f41ad4e7fb4dd8f0dd46d297aadc99177d5cd84817c52aa","target":"record","created_at":"2026-05-18T00:35:10Z","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":"0fe55c4edd1288116d3cefd2e117577529ee575606543a893010812c6f420b7b","cross_cats_sorted":["math.AP","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-03-23T13:53:42Z","title_canon_sha256":"72ae91a364dc0072697693f88b7d187e18a88a8b853447f108021f32698376b0"},"schema_version":"1.0","source":{"id":"1603.07685","kind":"arxiv","version":2}},"canonical_sha256":"c3ab7ecfeb7aeed685ba41fb4264cc4219059bf8287c148baaa6f85771d20611","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c3ab7ecfeb7aeed685ba41fb4264cc4219059bf8287c148baaa6f85771d20611","first_computed_at":"2026-05-18T00:35:10.785048Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:10.785048Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VyHYhj1YO/OMw/5n0Uz99JhQ5SblI/Bu1aqMn57uDovUv6j0zvgK3ylzfEBo462v/ikSM/SMd6LkfsAEGRnwAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:10.785560Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.07685","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cfcec05f36bd33ca5f41ad4e7fb4dd8f0dd46d297aadc99177d5cd84817c52aa","sha256:e8875ef51a5ed192be6da1ad413050b4fea9c4c9ce53c07586f0119d9a9a1f3c"],"state_sha256":"f71394cfc46cfdbe2d5b81b8af1832f87edb325d7a701e806ebe9faea8af8634"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u8ZFjrvDsVzHfNfyqVM5XeAdchPMlPauBBp07SmrNoIWIhujPE8P72BVjh5XBaNet/F3YAmRa/NanQA18l5OBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T18:23:13.499079Z","bundle_sha256":"33c138f9c36a3062f92c5bb63e93c40e4941e2f8014ae843e8914e096d87710a"}}