{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:KOJV2GN4YEM3WTO4GH4JUEHYQT","short_pith_number":"pith:KOJV2GN4","canonical_record":{"source":{"id":"1707.04089","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-07-12T02:53:36Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"a194696863925b9bad89274806efcbca9e49ed8e459d193372d699ee54fc9ab9","abstract_canon_sha256":"d6914bd7eacc12d027fbb777237a457a94644c5a8e0da7c7a9c930e7fc77a53c"},"schema_version":"1.0"},"canonical_sha256":"53935d19bcc119bb4ddc31f89a10f884e04fed2493f836cdac921e2e46cf34b6","source":{"kind":"arxiv","id":"1707.04089","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.04089","created_at":"2026-05-18T00:40:22Z"},{"alias_kind":"arxiv_version","alias_value":"1707.04089v1","created_at":"2026-05-18T00:40:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.04089","created_at":"2026-05-18T00:40:22Z"},{"alias_kind":"pith_short_12","alias_value":"KOJV2GN4YEM3","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"KOJV2GN4YEM3WTO4","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"KOJV2GN4","created_at":"2026-05-18T12:31:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:KOJV2GN4YEM3WTO4GH4JUEHYQT","target":"record","payload":{"canonical_record":{"source":{"id":"1707.04089","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-07-12T02:53:36Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"a194696863925b9bad89274806efcbca9e49ed8e459d193372d699ee54fc9ab9","abstract_canon_sha256":"d6914bd7eacc12d027fbb777237a457a94644c5a8e0da7c7a9c930e7fc77a53c"},"schema_version":"1.0"},"canonical_sha256":"53935d19bcc119bb4ddc31f89a10f884e04fed2493f836cdac921e2e46cf34b6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:22.676944Z","signature_b64":"uC2XY5lIz65nvq/ZxdBEV9I2veC5rENEV0KQgSc7l7c0XhqkCihnArQ1jcuevHxZb0a5MvGt8yrQIwgDSERZAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"53935d19bcc119bb4ddc31f89a10f884e04fed2493f836cdac921e2e46cf34b6","last_reissued_at":"2026-05-18T00:40:22.676313Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:22.676313Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.04089","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:40:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FClBiKlfDqlN9Is8xX1qnt0F4DUbyUX1KyWQDEWllrzT3xiS2Kvc9ZgpU3kv2RhYXuArLD5UnOFWpyPFAG3XBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T12:47:01.022829Z"},"content_sha256":"1f3f0d5f51e29d000d315fd2db44d52f1a058447f3d8b10ae9c60f88d1e4222b","schema_version":"1.0","event_id":"sha256:1f3f0d5f51e29d000d315fd2db44d52f1a058447f3d8b10ae9c60f88d1e4222b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:KOJV2GN4YEM3WTO4GH4JUEHYQT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bound states in the continuum of fractional Schr\\\"odinger equation in the Earth's gravitational field and their effects in the presence of a minimal length: applications to distinguish ultralight particles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Bo Yang, Chaozhen Wei, Maokang Luo, Xiao Zhang","submitted_at":"2017-07-12T02:53:36Z","abstract_excerpt":"In this paper, the influence of the fractional dimensions of the L\\'evy path under the Earth's gravitational field is studied, and the phase transitions of energy and wave functions are obtained: the energy changes from discrete to continuous and wave functions change from non-degenerate to degenerate when dimension of L\\'evy path becomes from integer to non-integer. By analyzing the phase transitions, we solve two popular problems. First, we find an exotic way to produce the bound states in the continuum (BICs), our approach only needs a simple potential, and does not depend on interactions b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.04089","kind":"arxiv","version":1},"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":"2026-05-18T00:40:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QPhJAg96KGXKVOnAolHYEM38bmEN/zjtiCIEkXuFng9b9OHt87CG7nXMihlqu0QstpbMRxTewM0XkgArtThlBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T12:47:01.023192Z"},"content_sha256":"d10f53d3474effa57fe2838ad05d7ea5155a26d67e02b06f18fae470d636454a","schema_version":"1.0","event_id":"sha256:d10f53d3474effa57fe2838ad05d7ea5155a26d67e02b06f18fae470d636454a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KOJV2GN4YEM3WTO4GH4JUEHYQT/bundle.json","state_url":"https://pith.science/pith/KOJV2GN4YEM3WTO4GH4JUEHYQT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KOJV2GN4YEM3WTO4GH4JUEHYQT/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":"2026-06-09T12:47:01Z","links":{"resolver":"https://pith.science/pith/KOJV2GN4YEM3WTO4GH4JUEHYQT","bundle":"https://pith.science/pith/KOJV2GN4YEM3WTO4GH4JUEHYQT/bundle.json","state":"https://pith.science/pith/KOJV2GN4YEM3WTO4GH4JUEHYQT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KOJV2GN4YEM3WTO4GH4JUEHYQT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:KOJV2GN4YEM3WTO4GH4JUEHYQT","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":"d6914bd7eacc12d027fbb777237a457a94644c5a8e0da7c7a9c930e7fc77a53c","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-07-12T02:53:36Z","title_canon_sha256":"a194696863925b9bad89274806efcbca9e49ed8e459d193372d699ee54fc9ab9"},"schema_version":"1.0","source":{"id":"1707.04089","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.04089","created_at":"2026-05-18T00:40:22Z"},{"alias_kind":"arxiv_version","alias_value":"1707.04089v1","created_at":"2026-05-18T00:40:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.04089","created_at":"2026-05-18T00:40:22Z"},{"alias_kind":"pith_short_12","alias_value":"KOJV2GN4YEM3","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"KOJV2GN4YEM3WTO4","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"KOJV2GN4","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:d10f53d3474effa57fe2838ad05d7ea5155a26d67e02b06f18fae470d636454a","target":"graph","created_at":"2026-05-18T00:40:22Z","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, the influence of the fractional dimensions of the L\\'evy path under the Earth's gravitational field is studied, and the phase transitions of energy and wave functions are obtained: the energy changes from discrete to continuous and wave functions change from non-degenerate to degenerate when dimension of L\\'evy path becomes from integer to non-integer. By analyzing the phase transitions, we solve two popular problems. First, we find an exotic way to produce the bound states in the continuum (BICs), our approach only needs a simple potential, and does not depend on interactions b","authors_text":"Bo Yang, Chaozhen Wei, Maokang Luo, Xiao Zhang","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-07-12T02:53:36Z","title":"Bound states in the continuum of fractional Schr\\\"odinger equation in the Earth's gravitational field and their effects in the presence of a minimal length: applications to distinguish ultralight particles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.04089","kind":"arxiv","version":1},"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":"sha256:1f3f0d5f51e29d000d315fd2db44d52f1a058447f3d8b10ae9c60f88d1e4222b","target":"record","created_at":"2026-05-18T00:40:22Z","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":"d6914bd7eacc12d027fbb777237a457a94644c5a8e0da7c7a9c930e7fc77a53c","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-07-12T02:53:36Z","title_canon_sha256":"a194696863925b9bad89274806efcbca9e49ed8e459d193372d699ee54fc9ab9"},"schema_version":"1.0","source":{"id":"1707.04089","kind":"arxiv","version":1}},"canonical_sha256":"53935d19bcc119bb4ddc31f89a10f884e04fed2493f836cdac921e2e46cf34b6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"53935d19bcc119bb4ddc31f89a10f884e04fed2493f836cdac921e2e46cf34b6","first_computed_at":"2026-05-18T00:40:22.676313Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:22.676313Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uC2XY5lIz65nvq/ZxdBEV9I2veC5rENEV0KQgSc7l7c0XhqkCihnArQ1jcuevHxZb0a5MvGt8yrQIwgDSERZAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:22.676944Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.04089","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f3f0d5f51e29d000d315fd2db44d52f1a058447f3d8b10ae9c60f88d1e4222b","sha256:d10f53d3474effa57fe2838ad05d7ea5155a26d67e02b06f18fae470d636454a"],"state_sha256":"9e6e903644fbc380b1e64cb64f625cf8d6da40b72cf6762244a7f9bb6c71dead"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RERkgznQ9uql0FgXvyFL+OQHpaGiaav1fS210lfSf8jfHXLr19njmjs18Xg27LKxLtkeLzBcfUMPxqjBynXVAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T12:47:01.025740Z","bundle_sha256":"68585fbbe97c0c746de1895b23d11e984218029ee237f856c10a0bd605f80c7b"}}