{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:G5NOLUQS6NMQOK7DLUSYPT6TLK","short_pith_number":"pith:G5NOLUQS","canonical_record":{"source":{"id":"1406.3419","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-06-13T04:35:25Z","cross_cats_sorted":[],"title_canon_sha256":"f344e9c6b63d54867f0affcdbcdb7cc40722296efc56ae1d611c91af303c5bd1","abstract_canon_sha256":"80f8cb7013f63b1ca5f19b36d5688a63cc3363ff39c47658eed1ac7a05afa113"},"schema_version":"1.0"},"canonical_sha256":"375ae5d212f359072be35d2587cfd35ab4ab2db425535d9cdac0acd3306432f2","source":{"kind":"arxiv","id":"1406.3419","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.3419","created_at":"2026-05-18T01:35:32Z"},{"alias_kind":"arxiv_version","alias_value":"1406.3419v4","created_at":"2026-05-18T01:35:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.3419","created_at":"2026-05-18T01:35:32Z"},{"alias_kind":"pith_short_12","alias_value":"G5NOLUQS6NMQ","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"G5NOLUQS6NMQOK7D","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"G5NOLUQS","created_at":"2026-05-18T12:28:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:G5NOLUQS6NMQOK7DLUSYPT6TLK","target":"record","payload":{"canonical_record":{"source":{"id":"1406.3419","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-06-13T04:35:25Z","cross_cats_sorted":[],"title_canon_sha256":"f344e9c6b63d54867f0affcdbcdb7cc40722296efc56ae1d611c91af303c5bd1","abstract_canon_sha256":"80f8cb7013f63b1ca5f19b36d5688a63cc3363ff39c47658eed1ac7a05afa113"},"schema_version":"1.0"},"canonical_sha256":"375ae5d212f359072be35d2587cfd35ab4ab2db425535d9cdac0acd3306432f2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:32.956039Z","signature_b64":"RxZqQPzSDsfe/I0Q1gPenXG+peGqAFGHFKbAsU/CATY61QqdJK/9jxjMLHCcEYlKs3yG8tMkUCJErR0Z7b7xDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"375ae5d212f359072be35d2587cfd35ab4ab2db425535d9cdac0acd3306432f2","last_reissued_at":"2026-05-18T01:35:32.955510Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:32.955510Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.3419","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:35:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"molakpwHM/wA1BJyLwfr4KL4eCPlnRdfBBxLC+7cVfF9LN+asKqe9lOQ7/Juh7JhUPtT0rPV3FciqF4KBGuoAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T19:04:16.031771Z"},"content_sha256":"75915d04c2f53ce1ca4a0d21f8c557b741c0d57ceed91aabd45b4658a862ebf8","schema_version":"1.0","event_id":"sha256:75915d04c2f53ce1ca4a0d21f8c557b741c0d57ceed91aabd45b4658a862ebf8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:G5NOLUQS6NMQOK7DLUSYPT6TLK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On absolute continuity of the spectrum of periodic Schr\\\"odinger operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Ihyeok Seo","submitted_at":"2014-06-13T04:35:25Z","abstract_excerpt":"In this paper we find a new condition on a real periodic potential for which the self-adjoint Schr\\\"odinger operator may be defined by a quadratic form and the spectrum of the operator is purely absolutely continuous. This is based on resolvent estimates and spectral projection estimates in weighted $L^2$ spaces on the torus, and an oscillatory integral theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3419","kind":"arxiv","version":4},"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":"2026-05-18T01:35:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZvTwFJqe3SvTcp4Om/yqlKEk8ePKwvnOlzKfkA8F5NO5vN4w8PBvZT+cQ2vVOH4WXHzCTnJKDmhAAptHKm0ABQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T19:04:16.032123Z"},"content_sha256":"1c8a2ef644eb1187f4f3fc50687985ad6d58fc78d211378d1dfc44da0bc62157","schema_version":"1.0","event_id":"sha256:1c8a2ef644eb1187f4f3fc50687985ad6d58fc78d211378d1dfc44da0bc62157"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G5NOLUQS6NMQOK7DLUSYPT6TLK/bundle.json","state_url":"https://pith.science/pith/G5NOLUQS6NMQOK7DLUSYPT6TLK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G5NOLUQS6NMQOK7DLUSYPT6TLK/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":"2026-05-31T19:04:16Z","links":{"resolver":"https://pith.science/pith/G5NOLUQS6NMQOK7DLUSYPT6TLK","bundle":"https://pith.science/pith/G5NOLUQS6NMQOK7DLUSYPT6TLK/bundle.json","state":"https://pith.science/pith/G5NOLUQS6NMQOK7DLUSYPT6TLK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G5NOLUQS6NMQOK7DLUSYPT6TLK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:G5NOLUQS6NMQOK7DLUSYPT6TLK","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":"80f8cb7013f63b1ca5f19b36d5688a63cc3363ff39c47658eed1ac7a05afa113","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-06-13T04:35:25Z","title_canon_sha256":"f344e9c6b63d54867f0affcdbcdb7cc40722296efc56ae1d611c91af303c5bd1"},"schema_version":"1.0","source":{"id":"1406.3419","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.3419","created_at":"2026-05-18T01:35:32Z"},{"alias_kind":"arxiv_version","alias_value":"1406.3419v4","created_at":"2026-05-18T01:35:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.3419","created_at":"2026-05-18T01:35:32Z"},{"alias_kind":"pith_short_12","alias_value":"G5NOLUQS6NMQ","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"G5NOLUQS6NMQOK7D","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"G5NOLUQS","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:1c8a2ef644eb1187f4f3fc50687985ad6d58fc78d211378d1dfc44da0bc62157","target":"graph","created_at":"2026-05-18T01:35:32Z","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":"In this paper we find a new condition on a real periodic potential for which the self-adjoint Schr\\\"odinger operator may be defined by a quadratic form and the spectrum of the operator is purely absolutely continuous. This is based on resolvent estimates and spectral projection estimates in weighted $L^2$ spaces on the torus, and an oscillatory integral theorem.","authors_text":"Ihyeok Seo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-06-13T04:35:25Z","title":"On absolute continuity of the spectrum of periodic Schr\\\"odinger operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3419","kind":"arxiv","version":4},"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":"sha256:75915d04c2f53ce1ca4a0d21f8c557b741c0d57ceed91aabd45b4658a862ebf8","target":"record","created_at":"2026-05-18T01:35:32Z","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":"80f8cb7013f63b1ca5f19b36d5688a63cc3363ff39c47658eed1ac7a05afa113","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-06-13T04:35:25Z","title_canon_sha256":"f344e9c6b63d54867f0affcdbcdb7cc40722296efc56ae1d611c91af303c5bd1"},"schema_version":"1.0","source":{"id":"1406.3419","kind":"arxiv","version":4}},"canonical_sha256":"375ae5d212f359072be35d2587cfd35ab4ab2db425535d9cdac0acd3306432f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"375ae5d212f359072be35d2587cfd35ab4ab2db425535d9cdac0acd3306432f2","first_computed_at":"2026-05-18T01:35:32.955510Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:32.955510Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RxZqQPzSDsfe/I0Q1gPenXG+peGqAFGHFKbAsU/CATY61QqdJK/9jxjMLHCcEYlKs3yG8tMkUCJErR0Z7b7xDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:32.956039Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.3419","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:75915d04c2f53ce1ca4a0d21f8c557b741c0d57ceed91aabd45b4658a862ebf8","sha256:1c8a2ef644eb1187f4f3fc50687985ad6d58fc78d211378d1dfc44da0bc62157"],"state_sha256":"898f4f268476c8bdad89e48f88caf93b91405009a3ffb867e370711fd04dbe27"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yT4oVZcEOE5/1ByZGg01xCAskvnCwJg0yX4TkgeT1yItRzu98kzn1fCLiWneZnIOf4Ie9IIw75KJf18Zd7GBBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T19:04:16.034851Z","bundle_sha256":"1c451bea37377e1937fe0a60b9010ccf24ae29bde4a5a13fab69c039640092f8"}}