{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:N2O2FI45PZ732NJ3WLI6K26GRR","short_pith_number":"pith:N2O2FI45","canonical_record":{"source":{"id":"1710.05099","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-10-13T23:19:39Z","cross_cats_sorted":["physics.optics"],"title_canon_sha256":"213d434fa6796b52c5c128188d11cdf1d04e119ce72068970b85f592b436ce02","abstract_canon_sha256":"94cc7f60fa8e520655b8cf69051b609965aceb9049157afb1b93273c96ccc8a9"},"schema_version":"1.0"},"canonical_sha256":"6e9da2a39d7e7fbd353bb2d1e56bc68c5a424c315463099f92151d9896ee26cf","source":{"kind":"arxiv","id":"1710.05099","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.05099","created_at":"2026-05-18T00:29:59Z"},{"alias_kind":"arxiv_version","alias_value":"1710.05099v2","created_at":"2026-05-18T00:29:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.05099","created_at":"2026-05-18T00:29:59Z"},{"alias_kind":"pith_short_12","alias_value":"N2O2FI45PZ73","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"N2O2FI45PZ732NJ3","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"N2O2FI45","created_at":"2026-05-18T12:31:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:N2O2FI45PZ732NJ3WLI6K26GRR","target":"record","payload":{"canonical_record":{"source":{"id":"1710.05099","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-10-13T23:19:39Z","cross_cats_sorted":["physics.optics"],"title_canon_sha256":"213d434fa6796b52c5c128188d11cdf1d04e119ce72068970b85f592b436ce02","abstract_canon_sha256":"94cc7f60fa8e520655b8cf69051b609965aceb9049157afb1b93273c96ccc8a9"},"schema_version":"1.0"},"canonical_sha256":"6e9da2a39d7e7fbd353bb2d1e56bc68c5a424c315463099f92151d9896ee26cf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:59.394619Z","signature_b64":"0cB5i3DLAwvTe9U45lJYlFD+ezj7w1ilJDI/SPpoGs9ZocuNqtw10YWTpECVlgU/eeYcs7CHidDpfvArCZG9DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6e9da2a39d7e7fbd353bb2d1e56bc68c5a424c315463099f92151d9896ee26cf","last_reissued_at":"2026-05-18T00:29:59.394160Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:59.394160Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.05099","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":"2026-05-18T00:29:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yplyI6MJgpNbTdGXGldR6ZzENoPIQe4OJE83xFjQ9+mQyd6c4yK68fKVjwt92Rg+TcS0P/eXPKJsM9+CU5ciAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T04:04:59.083441Z"},"content_sha256":"9b092c7825bcc04d138819ac9bf2597bdb731cf8199de641fc3b9156808c3dde","schema_version":"1.0","event_id":"sha256:9b092c7825bcc04d138819ac9bf2597bdb731cf8199de641fc3b9156808c3dde"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:N2O2FI45PZ732NJ3WLI6K26GRR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The second hyperpolarizability of systems described by the space-fractional Schrodinger equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.optics"],"primary_cat":"quant-ph","authors_text":"Moussa Kounta, Nathan J. Dawson, Onassis Nottage","submitted_at":"2017-10-13T23:19:39Z","abstract_excerpt":"The static second hyperpolarizability is derived from the space-fractional Schr\\\"{o}dinger equation in the particle-centric view. The Thomas-Reiche-Kuhn sum rule matrix elements and the three-level ansatz determines the maximum second hyperpolarizability for a space-fractional quantum system. The total oscillator strength is shown to decrease as the space-fractional parameter $\\alpha$ decreases, which reduces the optical response of a quantum system in the presence of an external field. This damped response is caused by the wavefunction dependent position and momentum commutation relation. Alt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.05099","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":"2026-05-18T00:29:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e57kc0jVmCVuTJNFUHdWIAsIMtargRknq2ixwsHZeuDZEHpCAQBooESnrH+H4TLZKG8UZNx2ghc0uNn4zNyeDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T04:04:59.084068Z"},"content_sha256":"42009d92f669b02ddd9724d75a6e35fb2eadb55eff1cdac3ad62688bf42fa884","schema_version":"1.0","event_id":"sha256:42009d92f669b02ddd9724d75a6e35fb2eadb55eff1cdac3ad62688bf42fa884"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N2O2FI45PZ732NJ3WLI6K26GRR/bundle.json","state_url":"https://pith.science/pith/N2O2FI45PZ732NJ3WLI6K26GRR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N2O2FI45PZ732NJ3WLI6K26GRR/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":"2026-06-06T04:04:59Z","links":{"resolver":"https://pith.science/pith/N2O2FI45PZ732NJ3WLI6K26GRR","bundle":"https://pith.science/pith/N2O2FI45PZ732NJ3WLI6K26GRR/bundle.json","state":"https://pith.science/pith/N2O2FI45PZ732NJ3WLI6K26GRR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N2O2FI45PZ732NJ3WLI6K26GRR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:N2O2FI45PZ732NJ3WLI6K26GRR","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":"94cc7f60fa8e520655b8cf69051b609965aceb9049157afb1b93273c96ccc8a9","cross_cats_sorted":["physics.optics"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-10-13T23:19:39Z","title_canon_sha256":"213d434fa6796b52c5c128188d11cdf1d04e119ce72068970b85f592b436ce02"},"schema_version":"1.0","source":{"id":"1710.05099","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.05099","created_at":"2026-05-18T00:29:59Z"},{"alias_kind":"arxiv_version","alias_value":"1710.05099v2","created_at":"2026-05-18T00:29:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.05099","created_at":"2026-05-18T00:29:59Z"},{"alias_kind":"pith_short_12","alias_value":"N2O2FI45PZ73","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"N2O2FI45PZ732NJ3","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"N2O2FI45","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:42009d92f669b02ddd9724d75a6e35fb2eadb55eff1cdac3ad62688bf42fa884","target":"graph","created_at":"2026-05-18T00:29:59Z","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":"The static second hyperpolarizability is derived from the space-fractional Schr\\\"{o}dinger equation in the particle-centric view. The Thomas-Reiche-Kuhn sum rule matrix elements and the three-level ansatz determines the maximum second hyperpolarizability for a space-fractional quantum system. The total oscillator strength is shown to decrease as the space-fractional parameter $\\alpha$ decreases, which reduces the optical response of a quantum system in the presence of an external field. This damped response is caused by the wavefunction dependent position and momentum commutation relation. Alt","authors_text":"Moussa Kounta, Nathan J. Dawson, Onassis Nottage","cross_cats":["physics.optics"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-10-13T23:19:39Z","title":"The second hyperpolarizability of systems described by the space-fractional Schrodinger equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.05099","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":"sha256:9b092c7825bcc04d138819ac9bf2597bdb731cf8199de641fc3b9156808c3dde","target":"record","created_at":"2026-05-18T00:29:59Z","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":"94cc7f60fa8e520655b8cf69051b609965aceb9049157afb1b93273c96ccc8a9","cross_cats_sorted":["physics.optics"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-10-13T23:19:39Z","title_canon_sha256":"213d434fa6796b52c5c128188d11cdf1d04e119ce72068970b85f592b436ce02"},"schema_version":"1.0","source":{"id":"1710.05099","kind":"arxiv","version":2}},"canonical_sha256":"6e9da2a39d7e7fbd353bb2d1e56bc68c5a424c315463099f92151d9896ee26cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e9da2a39d7e7fbd353bb2d1e56bc68c5a424c315463099f92151d9896ee26cf","first_computed_at":"2026-05-18T00:29:59.394160Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:59.394160Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0cB5i3DLAwvTe9U45lJYlFD+ezj7w1ilJDI/SPpoGs9ZocuNqtw10YWTpECVlgU/eeYcs7CHidDpfvArCZG9DA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:59.394619Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.05099","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9b092c7825bcc04d138819ac9bf2597bdb731cf8199de641fc3b9156808c3dde","sha256:42009d92f669b02ddd9724d75a6e35fb2eadb55eff1cdac3ad62688bf42fa884"],"state_sha256":"57722f744f13af3c9f3ff80368de08d7475da4ae26cfcf883bf436927d6a5ade"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qA3obeYG7U8mCvztyB29jXHCx9od6Omy1WdNga9XD47pDUFO3w5Of5ZMrtq2mG8h8yd/Rt1vvRRprwz269XCDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T04:04:59.087862Z","bundle_sha256":"44b8f8cd86631ad0e3524f2a51583d41021c78f0344991979bd489b8009ca916"}}