{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:PFSW6AVK2UGVHLKNFWOPXWYVSJ","short_pith_number":"pith:PFSW6AVK","canonical_record":{"source":{"id":"1510.05536","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2015-10-19T15:41:17Z","cross_cats_sorted":["cond-mat.mes-hall"],"title_canon_sha256":"4b32ae424f22f03788d18359858b00e383219bf00df6987f4d3e7fff3af0e341","abstract_canon_sha256":"e9a1173aecba3c88fc19377e59eecada3ef3f6a47be504741292f0f05584c397"},"schema_version":"1.0"},"canonical_sha256":"79656f02aad50d53ad4d2d9cfbdb15924dde46b244f0a4724d984cec6045811a","source":{"kind":"arxiv","id":"1510.05536","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.05536","created_at":"2026-05-18T01:22:35Z"},{"alias_kind":"arxiv_version","alias_value":"1510.05536v2","created_at":"2026-05-18T01:22:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.05536","created_at":"2026-05-18T01:22:35Z"},{"alias_kind":"pith_short_12","alias_value":"PFSW6AVK2UGV","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PFSW6AVK2UGVHLKN","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PFSW6AVK","created_at":"2026-05-18T12:29:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:PFSW6AVK2UGVHLKNFWOPXWYVSJ","target":"record","payload":{"canonical_record":{"source":{"id":"1510.05536","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2015-10-19T15:41:17Z","cross_cats_sorted":["cond-mat.mes-hall"],"title_canon_sha256":"4b32ae424f22f03788d18359858b00e383219bf00df6987f4d3e7fff3af0e341","abstract_canon_sha256":"e9a1173aecba3c88fc19377e59eecada3ef3f6a47be504741292f0f05584c397"},"schema_version":"1.0"},"canonical_sha256":"79656f02aad50d53ad4d2d9cfbdb15924dde46b244f0a4724d984cec6045811a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:35.242466Z","signature_b64":"gxs0hnvo3W9j/hPE1gasE5IS9s6uBf0FR3ZbEO7gB6tYtI7Cp9ax+pVDpp5uZ4LONXZbjncSSo/H/U3t0qIUBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"79656f02aad50d53ad4d2d9cfbdb15924dde46b244f0a4724d984cec6045811a","last_reissued_at":"2026-05-18T01:22:35.242010Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:35.242010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.05536","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":"2026-05-18T01:22:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IzMtCD5yWb2aXWroLT8mKeA46giO5Afjc4U5jVrGMP6URHYTIGJzRF7d3yXNRY/NSwkhV2c5RZfc/xAqNctkDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T07:53:14.268704Z"},"content_sha256":"24509822d239c9c8bd360ae0aa15e0d2e8af178d5866ca83ef56b06defe20fc7","schema_version":"1.0","event_id":"sha256:24509822d239c9c8bd360ae0aa15e0d2e8af178d5866ca83ef56b06defe20fc7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:PFSW6AVK2UGVHLKNFWOPXWYVSJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonlinear optical response of a two-dimensional atomic crystal","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mes-hall"],"primary_cat":"physics.optics","authors_text":"Michele Merano","submitted_at":"2015-10-19T15:41:17Z","abstract_excerpt":"The theory of Bloembergen and Pershan for the light waves at the boundary of nonlinear media is extended to a nonlinear two-dimensional atomic crystal, i.e. a single planar atomic lattice, placed in between linear bulk media. The crystal is treated as a zero-thickness interface, a real two-dimensional system. Harmonic waves emanate from it. Generalization of the laws of reflection and refraction give the direction and the intensity of the harmonic waves. As a particular case that contains all the essential physical features, second order harmonic generation is considered. The theory, due to it"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.05536","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":"2026-05-18T01:22:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nn1I/1/bVtEeQYr2oDJaDUbEiCWNm1vTzhZMX96YtAwQvVrSUIuPv+lGhuFnTwpe9RQJ56E9pxuG0Et7G6i3Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T07:53:14.269132Z"},"content_sha256":"66d6b7a2b5b704f9bf52a65eb75e19f06a4336c09360eae2323b637ec62d0593","schema_version":"1.0","event_id":"sha256:66d6b7a2b5b704f9bf52a65eb75e19f06a4336c09360eae2323b637ec62d0593"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PFSW6AVK2UGVHLKNFWOPXWYVSJ/bundle.json","state_url":"https://pith.science/pith/PFSW6AVK2UGVHLKNFWOPXWYVSJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PFSW6AVK2UGVHLKNFWOPXWYVSJ/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":"2026-06-12T07:53:14Z","links":{"resolver":"https://pith.science/pith/PFSW6AVK2UGVHLKNFWOPXWYVSJ","bundle":"https://pith.science/pith/PFSW6AVK2UGVHLKNFWOPXWYVSJ/bundle.json","state":"https://pith.science/pith/PFSW6AVK2UGVHLKNFWOPXWYVSJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PFSW6AVK2UGVHLKNFWOPXWYVSJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:PFSW6AVK2UGVHLKNFWOPXWYVSJ","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":"e9a1173aecba3c88fc19377e59eecada3ef3f6a47be504741292f0f05584c397","cross_cats_sorted":["cond-mat.mes-hall"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2015-10-19T15:41:17Z","title_canon_sha256":"4b32ae424f22f03788d18359858b00e383219bf00df6987f4d3e7fff3af0e341"},"schema_version":"1.0","source":{"id":"1510.05536","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.05536","created_at":"2026-05-18T01:22:35Z"},{"alias_kind":"arxiv_version","alias_value":"1510.05536v2","created_at":"2026-05-18T01:22:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.05536","created_at":"2026-05-18T01:22:35Z"},{"alias_kind":"pith_short_12","alias_value":"PFSW6AVK2UGV","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PFSW6AVK2UGVHLKN","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PFSW6AVK","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:66d6b7a2b5b704f9bf52a65eb75e19f06a4336c09360eae2323b637ec62d0593","target":"graph","created_at":"2026-05-18T01:22:35Z","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 theory of Bloembergen and Pershan for the light waves at the boundary of nonlinear media is extended to a nonlinear two-dimensional atomic crystal, i.e. a single planar atomic lattice, placed in between linear bulk media. The crystal is treated as a zero-thickness interface, a real two-dimensional system. Harmonic waves emanate from it. Generalization of the laws of reflection and refraction give the direction and the intensity of the harmonic waves. As a particular case that contains all the essential physical features, second order harmonic generation is considered. The theory, due to it","authors_text":"Michele Merano","cross_cats":["cond-mat.mes-hall"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2015-10-19T15:41:17Z","title":"Nonlinear optical response of a two-dimensional atomic crystal"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.05536","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":"sha256:24509822d239c9c8bd360ae0aa15e0d2e8af178d5866ca83ef56b06defe20fc7","target":"record","created_at":"2026-05-18T01:22:35Z","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":"e9a1173aecba3c88fc19377e59eecada3ef3f6a47be504741292f0f05584c397","cross_cats_sorted":["cond-mat.mes-hall"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2015-10-19T15:41:17Z","title_canon_sha256":"4b32ae424f22f03788d18359858b00e383219bf00df6987f4d3e7fff3af0e341"},"schema_version":"1.0","source":{"id":"1510.05536","kind":"arxiv","version":2}},"canonical_sha256":"79656f02aad50d53ad4d2d9cfbdb15924dde46b244f0a4724d984cec6045811a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"79656f02aad50d53ad4d2d9cfbdb15924dde46b244f0a4724d984cec6045811a","first_computed_at":"2026-05-18T01:22:35.242010Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:35.242010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gxs0hnvo3W9j/hPE1gasE5IS9s6uBf0FR3ZbEO7gB6tYtI7Cp9ax+pVDpp5uZ4LONXZbjncSSo/H/U3t0qIUBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:35.242466Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.05536","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:24509822d239c9c8bd360ae0aa15e0d2e8af178d5866ca83ef56b06defe20fc7","sha256:66d6b7a2b5b704f9bf52a65eb75e19f06a4336c09360eae2323b637ec62d0593"],"state_sha256":"f0c6ed2ffd2e1067906a7a06ea577d6c98d2adf182f0ee5e2f8552abcd4a60b2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oPZdkpzZXARmpszGBlPJpfF/jq6qX36mey3tTPoOq1j8mTkiCea97sDHayn93x6BVU80A8LK6+FPtxjztIMaBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T07:53:14.271468Z","bundle_sha256":"4ea3409d9a0dacc1d28f9e3c2c5b6baa0140cd61abc65b0bd373fafc9e30d63e"}}