{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:UE35FAB2NQPFRDPDBLETQA2DAS","short_pith_number":"pith:UE35FAB2","canonical_record":{"source":{"id":"1510.05806","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2015-10-20T09:37:25Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"c2a7d1cc95ee76012bea99bc415a6732e8250f04588967d44745a36682716204","abstract_canon_sha256":"0a64e2bf412db219dd3b587f9339b321ab27a5c8f10ed10eaa093523d62d77d4"},"schema_version":"1.0"},"canonical_sha256":"a137d2803a6c1e588de30ac93803430492d0bcda9493415564a172e7926f3017","source":{"kind":"arxiv","id":"1510.05806","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.05806","created_at":"2026-05-18T01:28:37Z"},{"alias_kind":"arxiv_version","alias_value":"1510.05806v1","created_at":"2026-05-18T01:28:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.05806","created_at":"2026-05-18T01:28:37Z"},{"alias_kind":"pith_short_12","alias_value":"UE35FAB2NQPF","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UE35FAB2NQPFRDPD","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UE35FAB2","created_at":"2026-05-18T12:29:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:UE35FAB2NQPFRDPDBLETQA2DAS","target":"record","payload":{"canonical_record":{"source":{"id":"1510.05806","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2015-10-20T09:37:25Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"c2a7d1cc95ee76012bea99bc415a6732e8250f04588967d44745a36682716204","abstract_canon_sha256":"0a64e2bf412db219dd3b587f9339b321ab27a5c8f10ed10eaa093523d62d77d4"},"schema_version":"1.0"},"canonical_sha256":"a137d2803a6c1e588de30ac93803430492d0bcda9493415564a172e7926f3017","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:28:37.646058Z","signature_b64":"COrP1D4DI8VLOdYO2b7pDutwiqJ7x4MKuxiB0jvRoxHK7uTYGaJe5mwS9AnmYbcWwNgIe/2ssjxR4YUi3baCCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a137d2803a6c1e588de30ac93803430492d0bcda9493415564a172e7926f3017","last_reissued_at":"2026-05-18T01:28:37.645347Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:28:37.645347Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.05806","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":"2026-05-18T01:28:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IQSe2n55ThPzJS0ScVee3s2VL+xDjNeMmiuvTxK2N9zDrcb9w0Owf7/smMD4XBug5Yz1L7vI5OV1dQiAV68eBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T03:10:34.976106Z"},"content_sha256":"616f5a3aa1fcc6a6afe679550a6cf7b7746e2de4407bc4d0f8f9b5a30e2a121f","schema_version":"1.0","event_id":"sha256:616f5a3aa1fcc6a6afe679550a6cf7b7746e2de4407bc4d0f8f9b5a30e2a121f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:UE35FAB2NQPFRDPDBLETQA2DAS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Propagation dynamics of a light beam in fractional Schr\\\"odinger equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"physics.optics","authors_text":"Milivoj R. Beli\\'c, Min Xiao, Weiping Zhong, Xing Liu, Yanpeng Zhang, Yiqi Zhang","submitted_at":"2015-10-20T09:37:25Z","abstract_excerpt":"Dynamics of wavepackets in fractional Schrodinger equation is still an open problem. The difficulty stems from the fact that the fractional Laplacian derivative is essentially a nonlocal operator. We investigate analytically and numerically the propagation of optical beams in fractional Schr\\\"odinger equation with a harmonic potential. We find that the propagation of one- and two-dimensional (1D, 2D) input chirped Gaussian beams is not harmonic. In 1D, the beam propagates along a zigzag trajectory in the real space, which corresponds to a modulated anharmonic oscillation in the momentum spac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.05806","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":"2026-05-18T01:28:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T4tQrHB8eN52QlAvnc34mvJh2UkliMRBtoFmpqVkqqyZPJvursudUSXLPGHz/VYa8PoBzOmCqaXd4iX1VrvBBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T03:10:34.976840Z"},"content_sha256":"6a53f660f998b32a83d97ce9088c110a8d2240043136056dea72e957456f215d","schema_version":"1.0","event_id":"sha256:6a53f660f998b32a83d97ce9088c110a8d2240043136056dea72e957456f215d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UE35FAB2NQPFRDPDBLETQA2DAS/bundle.json","state_url":"https://pith.science/pith/UE35FAB2NQPFRDPDBLETQA2DAS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UE35FAB2NQPFRDPDBLETQA2DAS/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":"2026-05-31T03:10:34Z","links":{"resolver":"https://pith.science/pith/UE35FAB2NQPFRDPDBLETQA2DAS","bundle":"https://pith.science/pith/UE35FAB2NQPFRDPDBLETQA2DAS/bundle.json","state":"https://pith.science/pith/UE35FAB2NQPFRDPDBLETQA2DAS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UE35FAB2NQPFRDPDBLETQA2DAS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:UE35FAB2NQPFRDPDBLETQA2DAS","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":"0a64e2bf412db219dd3b587f9339b321ab27a5c8f10ed10eaa093523d62d77d4","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2015-10-20T09:37:25Z","title_canon_sha256":"c2a7d1cc95ee76012bea99bc415a6732e8250f04588967d44745a36682716204"},"schema_version":"1.0","source":{"id":"1510.05806","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.05806","created_at":"2026-05-18T01:28:37Z"},{"alias_kind":"arxiv_version","alias_value":"1510.05806v1","created_at":"2026-05-18T01:28:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.05806","created_at":"2026-05-18T01:28:37Z"},{"alias_kind":"pith_short_12","alias_value":"UE35FAB2NQPF","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UE35FAB2NQPFRDPD","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UE35FAB2","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:6a53f660f998b32a83d97ce9088c110a8d2240043136056dea72e957456f215d","target":"graph","created_at":"2026-05-18T01:28:37Z","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":"Dynamics of wavepackets in fractional Schrodinger equation is still an open problem. The difficulty stems from the fact that the fractional Laplacian derivative is essentially a nonlocal operator. We investigate analytically and numerically the propagation of optical beams in fractional Schr\\\"odinger equation with a harmonic potential. We find that the propagation of one- and two-dimensional (1D, 2D) input chirped Gaussian beams is not harmonic. In 1D, the beam propagates along a zigzag trajectory in the real space, which corresponds to a modulated anharmonic oscillation in the momentum spac","authors_text":"Milivoj R. Beli\\'c, Min Xiao, Weiping Zhong, Xing Liu, Yanpeng Zhang, Yiqi Zhang","cross_cats":["quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2015-10-20T09:37:25Z","title":"Propagation dynamics of a light beam in fractional Schr\\\"odinger equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.05806","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":"sha256:616f5a3aa1fcc6a6afe679550a6cf7b7746e2de4407bc4d0f8f9b5a30e2a121f","target":"record","created_at":"2026-05-18T01:28:37Z","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":"0a64e2bf412db219dd3b587f9339b321ab27a5c8f10ed10eaa093523d62d77d4","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2015-10-20T09:37:25Z","title_canon_sha256":"c2a7d1cc95ee76012bea99bc415a6732e8250f04588967d44745a36682716204"},"schema_version":"1.0","source":{"id":"1510.05806","kind":"arxiv","version":1}},"canonical_sha256":"a137d2803a6c1e588de30ac93803430492d0bcda9493415564a172e7926f3017","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a137d2803a6c1e588de30ac93803430492d0bcda9493415564a172e7926f3017","first_computed_at":"2026-05-18T01:28:37.645347Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:28:37.645347Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"COrP1D4DI8VLOdYO2b7pDutwiqJ7x4MKuxiB0jvRoxHK7uTYGaJe5mwS9AnmYbcWwNgIe/2ssjxR4YUi3baCCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:28:37.646058Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.05806","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:616f5a3aa1fcc6a6afe679550a6cf7b7746e2de4407bc4d0f8f9b5a30e2a121f","sha256:6a53f660f998b32a83d97ce9088c110a8d2240043136056dea72e957456f215d"],"state_sha256":"25a2c9ad6d599bb1873f315c90007b0382cbdd59d1eab17def8374b790f4851b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n+Aon7CN8VPGTgXXzwhYZRFKQxYS4gBYkiqa6ehLy5svp4zBd1qBYVrT2k31LS9eJQCS42LLwArU1IlrJi39AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T03:10:34.980637Z","bundle_sha256":"28a36e86f2c8a5a78f508291f557c081dc9964526b9c554d1dd32093b7533d78"}}