{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:5BWW63OEW4BSI64VLBWXY3CK7T","short_pith_number":"pith:5BWW63OE","canonical_record":{"source":{"id":"1206.4462","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-06-20T11:32:35Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"74527571e2770d1364c8a5997b53f29c9a8f4517336691b4903b609764d903dc","abstract_canon_sha256":"0f94bb5668205bd910740cdd5f238a7e4f3e9eaaec90ccd2426969a06e40bdf2"},"schema_version":"1.0"},"canonical_sha256":"e86d6f6dc4b703247b95586d7c6c4afcc1717bc2c3da1906143033d9212dc7fe","source":{"kind":"arxiv","id":"1206.4462","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.4462","created_at":"2026-05-18T01:32:35Z"},{"alias_kind":"arxiv_version","alias_value":"1206.4462v5","created_at":"2026-05-18T01:32:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.4462","created_at":"2026-05-18T01:32:35Z"},{"alias_kind":"pith_short_12","alias_value":"5BWW63OEW4BS","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"5BWW63OEW4BSI64V","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"5BWW63OE","created_at":"2026-05-18T12:26:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:5BWW63OEW4BSI64VLBWXY3CK7T","target":"record","payload":{"canonical_record":{"source":{"id":"1206.4462","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-06-20T11:32:35Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"74527571e2770d1364c8a5997b53f29c9a8f4517336691b4903b609764d903dc","abstract_canon_sha256":"0f94bb5668205bd910740cdd5f238a7e4f3e9eaaec90ccd2426969a06e40bdf2"},"schema_version":"1.0"},"canonical_sha256":"e86d6f6dc4b703247b95586d7c6c4afcc1717bc2c3da1906143033d9212dc7fe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:35.208577Z","signature_b64":"K2A2faWzhQ8iMLU11IyhOBX80oJphTCCSg3oJIDv1AJTrVKnQzEy4fRZhz53Pn0rJnUsBBU9Mug354v6+UY/CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e86d6f6dc4b703247b95586d7c6c4afcc1717bc2c3da1906143033d9212dc7fe","last_reissued_at":"2026-05-18T01:32:35.208212Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:35.208212Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.4462","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:32:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wmge2hHGu/Hhq4lt9KzbT+itKFBwh4pUMyJAxsSh6wcV5K2bYsqkP0zSlVkt1+CrdBlvvzm6DcoPoTp+pcOUCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T02:31:26.102465Z"},"content_sha256":"dd296a15224b2d6d0e353a00b561a6bfb4eda4449f65cd1f8eefac43c808fa5a","schema_version":"1.0","event_id":"sha256:dd296a15224b2d6d0e353a00b561a6bfb4eda4449f65cd1f8eefac43c808fa5a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:5BWW63OEW4BSI64VLBWXY3CK7T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Remark on Littlewood-Paley projections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Younghun Hong","submitted_at":"2012-06-20T11:32:35Z","abstract_excerpt":"We establish the kernel estimates for the Littlewood-Paley projections associated with a Schr\\\"odinger operator H=-\\Delta+V in \\mathbb{R}^3 for a large class of short-range potentials V(x). As a corollary, we prove the homogeneous Sobolev inequality."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.4462","kind":"arxiv","version":5},"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":"2026-05-18T01:32:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CApgoEQqSQNcfUHgFdUxIImaQQhvJg1SFpN65BmQ/8EKmSU2hzPK32XwUv5cpOTA7/2/98BluMRzVeFcYn2WBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T02:31:26.102811Z"},"content_sha256":"bc64399704f65c1a1b26ddca98b229a2692586b1596f95a92cce53a62b130a9b","schema_version":"1.0","event_id":"sha256:bc64399704f65c1a1b26ddca98b229a2692586b1596f95a92cce53a62b130a9b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5BWW63OEW4BSI64VLBWXY3CK7T/bundle.json","state_url":"https://pith.science/pith/5BWW63OEW4BSI64VLBWXY3CK7T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5BWW63OEW4BSI64VLBWXY3CK7T/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":"2026-05-28T02:31:26Z","links":{"resolver":"https://pith.science/pith/5BWW63OEW4BSI64VLBWXY3CK7T","bundle":"https://pith.science/pith/5BWW63OEW4BSI64VLBWXY3CK7T/bundle.json","state":"https://pith.science/pith/5BWW63OEW4BSI64VLBWXY3CK7T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5BWW63OEW4BSI64VLBWXY3CK7T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:5BWW63OEW4BSI64VLBWXY3CK7T","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":"0f94bb5668205bd910740cdd5f238a7e4f3e9eaaec90ccd2426969a06e40bdf2","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-06-20T11:32:35Z","title_canon_sha256":"74527571e2770d1364c8a5997b53f29c9a8f4517336691b4903b609764d903dc"},"schema_version":"1.0","source":{"id":"1206.4462","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.4462","created_at":"2026-05-18T01:32:35Z"},{"alias_kind":"arxiv_version","alias_value":"1206.4462v5","created_at":"2026-05-18T01:32:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.4462","created_at":"2026-05-18T01:32:35Z"},{"alias_kind":"pith_short_12","alias_value":"5BWW63OEW4BS","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"5BWW63OEW4BSI64V","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"5BWW63OE","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:bc64399704f65c1a1b26ddca98b229a2692586b1596f95a92cce53a62b130a9b","target":"graph","created_at":"2026-05-18T01:32:35Z","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":"We establish the kernel estimates for the Littlewood-Paley projections associated with a Schr\\\"odinger operator H=-\\Delta+V in \\mathbb{R}^3 for a large class of short-range potentials V(x). As a corollary, we prove the homogeneous Sobolev inequality.","authors_text":"Younghun Hong","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-06-20T11:32:35Z","title":"A Remark on Littlewood-Paley projections"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.4462","kind":"arxiv","version":5},"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:dd296a15224b2d6d0e353a00b561a6bfb4eda4449f65cd1f8eefac43c808fa5a","target":"record","created_at":"2026-05-18T01:32:35Z","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":"0f94bb5668205bd910740cdd5f238a7e4f3e9eaaec90ccd2426969a06e40bdf2","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-06-20T11:32:35Z","title_canon_sha256":"74527571e2770d1364c8a5997b53f29c9a8f4517336691b4903b609764d903dc"},"schema_version":"1.0","source":{"id":"1206.4462","kind":"arxiv","version":5}},"canonical_sha256":"e86d6f6dc4b703247b95586d7c6c4afcc1717bc2c3da1906143033d9212dc7fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e86d6f6dc4b703247b95586d7c6c4afcc1717bc2c3da1906143033d9212dc7fe","first_computed_at":"2026-05-18T01:32:35.208212Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:35.208212Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K2A2faWzhQ8iMLU11IyhOBX80oJphTCCSg3oJIDv1AJTrVKnQzEy4fRZhz53Pn0rJnUsBBU9Mug354v6+UY/CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:35.208577Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.4462","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd296a15224b2d6d0e353a00b561a6bfb4eda4449f65cd1f8eefac43c808fa5a","sha256:bc64399704f65c1a1b26ddca98b229a2692586b1596f95a92cce53a62b130a9b"],"state_sha256":"8273ea1436153cfb464f7d82cb0a54d49dacee9c367a6f3801ebc3304b7bfa82"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iDlLjEyiIFEv5ysh31v5Jx8EdHq9bum8+YQMXVY7uxLxAIpAlI8jwF4m8VGlBH3y+0YwVeadeMhHrAGbwt6MDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T02:31:26.104934Z","bundle_sha256":"82284adb505b8125aafc1c264a622482683665fcbb16cc7655ce1e2e8d7a3548"}}