{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:K6FTQAKBDZOW5K4CA3D2ZN2KJX","short_pith_number":"pith:K6FTQAKB","canonical_record":{"source":{"id":"1706.04840","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-15T12:24:47Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"7350d2640e180658dff10bc6741aaf9619da162ecaface0f9ea0683bba5193bf","abstract_canon_sha256":"ec56e0fb10a657f20f8945cafc63d4547c29336bc092dc9badd3c789f763a4d9"},"schema_version":"1.0"},"canonical_sha256":"578b3801411e5d6eab8206c7acb74a4dcd70a96eae719acdd2cf122d542ef6b6","source":{"kind":"arxiv","id":"1706.04840","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.04840","created_at":"2026-05-17T23:39:42Z"},{"alias_kind":"arxiv_version","alias_value":"1706.04840v2","created_at":"2026-05-17T23:39:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.04840","created_at":"2026-05-17T23:39:42Z"},{"alias_kind":"pith_short_12","alias_value":"K6FTQAKBDZOW","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"K6FTQAKBDZOW5K4C","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"K6FTQAKB","created_at":"2026-05-18T12:31:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:K6FTQAKBDZOW5K4CA3D2ZN2KJX","target":"record","payload":{"canonical_record":{"source":{"id":"1706.04840","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-15T12:24:47Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"7350d2640e180658dff10bc6741aaf9619da162ecaface0f9ea0683bba5193bf","abstract_canon_sha256":"ec56e0fb10a657f20f8945cafc63d4547c29336bc092dc9badd3c789f763a4d9"},"schema_version":"1.0"},"canonical_sha256":"578b3801411e5d6eab8206c7acb74a4dcd70a96eae719acdd2cf122d542ef6b6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:42.209158Z","signature_b64":"awopeddj8k2/MAoHX5uul+2qHaTMSjXs8fBIDDDMAqC6SlLacfngt2qIFRaMJGnIliyL17kqS5hlumgUbU8MCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"578b3801411e5d6eab8206c7acb74a4dcd70a96eae719acdd2cf122d542ef6b6","last_reissued_at":"2026-05-17T23:39:42.208573Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:42.208573Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.04840","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":"2026-05-17T23:39:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2CIZS1muEIsV9bciYpb/CENRpAGKdABtZe7RtiIH7vprt+suInauknwtGFXkEkcMlnIR56InlJTFVYeDCoMtAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T18:16:07.965333Z"},"content_sha256":"cd6699c719361d8b22264ce8253e00bcca2571de20697c6720d09023ada7ece5","schema_version":"1.0","event_id":"sha256:cd6699c719361d8b22264ce8253e00bcca2571de20697c6720d09023ada7ece5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:K6FTQAKBDZOW5K4CA3D2ZN2KJX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On large potential perturbations of the Schr\\\"odinger, wave and Klein--Gordon equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Piero D'Ancona","submitted_at":"2017-06-15T12:24:47Z","abstract_excerpt":"We prove a sharp resolvent estimate in scale invariant norms of Amgon--H\\\"{o}rmander type for a magnetic Schr\\\"{o}dinger operator on $\\mathbb{R}^{n}$, $n\\ge3$\\begin{equation*} L=-(\\partial+iA)^{2}+V \\end{equation*}with large potentials $A,V$ of almost critical decay and regularity.\n  The estimate is applied to prove sharp smoothing and Strichartz estimates for the Schr\\\"{o}dinger, wave and Klein--Gordon flows associated to $L$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.04840","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":"2026-05-17T23:39:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XrChhAMWFJSIFaX0x/yzdwxq/ApHAKOq2q9UXZCdcqbL89dH+Kg7w2YfJ8Ha9p2SpF5Gq5zHlcDCGxUhIsU0Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T18:16:07.966029Z"},"content_sha256":"3a91c112e52d97308530ff0bb18e6d7c30f36f7103474a67995ba6ffa1f9d032","schema_version":"1.0","event_id":"sha256:3a91c112e52d97308530ff0bb18e6d7c30f36f7103474a67995ba6ffa1f9d032"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K6FTQAKBDZOW5K4CA3D2ZN2KJX/bundle.json","state_url":"https://pith.science/pith/K6FTQAKBDZOW5K4CA3D2ZN2KJX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K6FTQAKBDZOW5K4CA3D2ZN2KJX/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":"2026-05-29T18:16:07Z","links":{"resolver":"https://pith.science/pith/K6FTQAKBDZOW5K4CA3D2ZN2KJX","bundle":"https://pith.science/pith/K6FTQAKBDZOW5K4CA3D2ZN2KJX/bundle.json","state":"https://pith.science/pith/K6FTQAKBDZOW5K4CA3D2ZN2KJX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K6FTQAKBDZOW5K4CA3D2ZN2KJX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:K6FTQAKBDZOW5K4CA3D2ZN2KJX","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":"ec56e0fb10a657f20f8945cafc63d4547c29336bc092dc9badd3c789f763a4d9","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-15T12:24:47Z","title_canon_sha256":"7350d2640e180658dff10bc6741aaf9619da162ecaface0f9ea0683bba5193bf"},"schema_version":"1.0","source":{"id":"1706.04840","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.04840","created_at":"2026-05-17T23:39:42Z"},{"alias_kind":"arxiv_version","alias_value":"1706.04840v2","created_at":"2026-05-17T23:39:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.04840","created_at":"2026-05-17T23:39:42Z"},{"alias_kind":"pith_short_12","alias_value":"K6FTQAKBDZOW","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"K6FTQAKBDZOW5K4C","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"K6FTQAKB","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:3a91c112e52d97308530ff0bb18e6d7c30f36f7103474a67995ba6ffa1f9d032","target":"graph","created_at":"2026-05-17T23:39:42Z","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 prove a sharp resolvent estimate in scale invariant norms of Amgon--H\\\"{o}rmander type for a magnetic Schr\\\"{o}dinger operator on $\\mathbb{R}^{n}$, $n\\ge3$\\begin{equation*} L=-(\\partial+iA)^{2}+V \\end{equation*}with large potentials $A,V$ of almost critical decay and regularity.\n  The estimate is applied to prove sharp smoothing and Strichartz estimates for the Schr\\\"{o}dinger, wave and Klein--Gordon flows associated to $L$.","authors_text":"Piero D'Ancona","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-15T12:24:47Z","title":"On large potential perturbations of the Schr\\\"odinger, wave and Klein--Gordon equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.04840","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:cd6699c719361d8b22264ce8253e00bcca2571de20697c6720d09023ada7ece5","target":"record","created_at":"2026-05-17T23:39:42Z","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":"ec56e0fb10a657f20f8945cafc63d4547c29336bc092dc9badd3c789f763a4d9","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-15T12:24:47Z","title_canon_sha256":"7350d2640e180658dff10bc6741aaf9619da162ecaface0f9ea0683bba5193bf"},"schema_version":"1.0","source":{"id":"1706.04840","kind":"arxiv","version":2}},"canonical_sha256":"578b3801411e5d6eab8206c7acb74a4dcd70a96eae719acdd2cf122d542ef6b6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"578b3801411e5d6eab8206c7acb74a4dcd70a96eae719acdd2cf122d542ef6b6","first_computed_at":"2026-05-17T23:39:42.208573Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:42.208573Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"awopeddj8k2/MAoHX5uul+2qHaTMSjXs8fBIDDDMAqC6SlLacfngt2qIFRaMJGnIliyL17kqS5hlumgUbU8MCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:42.209158Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.04840","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd6699c719361d8b22264ce8253e00bcca2571de20697c6720d09023ada7ece5","sha256:3a91c112e52d97308530ff0bb18e6d7c30f36f7103474a67995ba6ffa1f9d032"],"state_sha256":"78a3e486dbaaa14b1cf02ae34a036c21237ee6df858a3aaabd1e2ad97f24393a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nVfS4K+oyrz6FoHDoizxYPGBK4GsOFAeYW97h31OPan1NVlOolpCGxeTSY7PhFgUQrMX9vAk36hIzHSgu3CdDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T18:16:07.969937Z","bundle_sha256":"34ff35ebbb56fa77822b65ebf31d0b0251cd486f881f8a7b9895a0b96236aba8"}}