{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:R4QEQL3KMDNPD6J7PDHWIRQLZF","short_pith_number":"pith:R4QEQL3K","canonical_record":{"source":{"id":"1806.05878","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-06-15T10:03:42Z","cross_cats_sorted":["cs.DM","math.IT"],"title_canon_sha256":"d8a059d980a1999a34e3a5a749b09b99476105237b996dea33914b5b59b51840","abstract_canon_sha256":"6af933656900f6e77596d358f21921ed253002fd1b4ccfd3069e9b94d39cf4d8"},"schema_version":"1.0"},"canonical_sha256":"8f20482f6a60daf1f93f78cf64460bc9710712942487b9eb29f9839f158e3ba7","source":{"kind":"arxiv","id":"1806.05878","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.05878","created_at":"2026-05-18T00:13:09Z"},{"alias_kind":"arxiv_version","alias_value":"1806.05878v1","created_at":"2026-05-18T00:13:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.05878","created_at":"2026-05-18T00:13:09Z"},{"alias_kind":"pith_short_12","alias_value":"R4QEQL3KMDNP","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"R4QEQL3KMDNPD6J7","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"R4QEQL3K","created_at":"2026-05-18T12:32:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:R4QEQL3KMDNPD6J7PDHWIRQLZF","target":"record","payload":{"canonical_record":{"source":{"id":"1806.05878","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-06-15T10:03:42Z","cross_cats_sorted":["cs.DM","math.IT"],"title_canon_sha256":"d8a059d980a1999a34e3a5a749b09b99476105237b996dea33914b5b59b51840","abstract_canon_sha256":"6af933656900f6e77596d358f21921ed253002fd1b4ccfd3069e9b94d39cf4d8"},"schema_version":"1.0"},"canonical_sha256":"8f20482f6a60daf1f93f78cf64460bc9710712942487b9eb29f9839f158e3ba7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:09.170201Z","signature_b64":"6Q2xGLKVXEjvJ6CXvahZQH7NsAheeCbL2qKtLyeF7a5V36avm2C7zj508VDfmsIHZOSgsjXJNLgXterC7v6nBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f20482f6a60daf1f93f78cf64460bc9710712942487b9eb29f9839f158e3ba7","last_reissued_at":"2026-05-18T00:13:09.169511Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:09.169511Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.05878","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":"2026-05-18T00:13:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5lxoJdmT5Bqj6wqkCr4zZoSL5asPG8+mop9oOAvnoEc6getrXbfMUreDCtsAb49n9ByNcJaLKXubwqDCwbP0Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T00:18:40.020832Z"},"content_sha256":"f9df831e36db116787f1a3016bea0234e0911dcc62f12f1e82e5fdd373ef0d0b","schema_version":"1.0","event_id":"sha256:f9df831e36db116787f1a3016bea0234e0911dcc62f12f1e82e5fdd373ef0d0b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:R4QEQL3KMDNPD6J7PDHWIRQLZF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Landscape Boolean Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.IT"],"primary_cat":"cs.IT","authors_text":"Constanza Riera, Pantelimon Stanica","submitted_at":"2018-06-15T10:03:42Z","abstract_excerpt":"In this paper we define a class of Boolean and generalized Boolean functions defined on $\\mathbb{F}_2^n$ with values in $\\mathbb{Z}_q$ (mostly, we consider $q=2^k$), which we call landscape functions (whose class containing generalized bent, semibent, and plateaued) and find their complete characterization in terms of their components. In particular, we show that the previously published characterizations of generalized bent and plateaued Boolean functions are in fact particular cases of this more general setting. Furthermore, we provide an inductive construction of landscape functions, having"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.05878","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":"2026-05-18T00:13:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pvI7hTdElowbJ9i171H+2iJjGBdUUlcd1HcV+956SXnqDSba+9xFdAw9kW154MdV0WRWF0YzLVkHAFwoMKMGDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T00:18:40.021184Z"},"content_sha256":"f785d44103088f15e0240c96de2b07513598e1508b2a152c3a713560098828ee","schema_version":"1.0","event_id":"sha256:f785d44103088f15e0240c96de2b07513598e1508b2a152c3a713560098828ee"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R4QEQL3KMDNPD6J7PDHWIRQLZF/bundle.json","state_url":"https://pith.science/pith/R4QEQL3KMDNPD6J7PDHWIRQLZF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R4QEQL3KMDNPD6J7PDHWIRQLZF/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":"2026-06-03T00:18:40Z","links":{"resolver":"https://pith.science/pith/R4QEQL3KMDNPD6J7PDHWIRQLZF","bundle":"https://pith.science/pith/R4QEQL3KMDNPD6J7PDHWIRQLZF/bundle.json","state":"https://pith.science/pith/R4QEQL3KMDNPD6J7PDHWIRQLZF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R4QEQL3KMDNPD6J7PDHWIRQLZF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:R4QEQL3KMDNPD6J7PDHWIRQLZF","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":"6af933656900f6e77596d358f21921ed253002fd1b4ccfd3069e9b94d39cf4d8","cross_cats_sorted":["cs.DM","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-06-15T10:03:42Z","title_canon_sha256":"d8a059d980a1999a34e3a5a749b09b99476105237b996dea33914b5b59b51840"},"schema_version":"1.0","source":{"id":"1806.05878","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.05878","created_at":"2026-05-18T00:13:09Z"},{"alias_kind":"arxiv_version","alias_value":"1806.05878v1","created_at":"2026-05-18T00:13:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.05878","created_at":"2026-05-18T00:13:09Z"},{"alias_kind":"pith_short_12","alias_value":"R4QEQL3KMDNP","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"R4QEQL3KMDNPD6J7","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"R4QEQL3K","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:f785d44103088f15e0240c96de2b07513598e1508b2a152c3a713560098828ee","target":"graph","created_at":"2026-05-18T00:13:09Z","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 define a class of Boolean and generalized Boolean functions defined on $\\mathbb{F}_2^n$ with values in $\\mathbb{Z}_q$ (mostly, we consider $q=2^k$), which we call landscape functions (whose class containing generalized bent, semibent, and plateaued) and find their complete characterization in terms of their components. In particular, we show that the previously published characterizations of generalized bent and plateaued Boolean functions are in fact particular cases of this more general setting. Furthermore, we provide an inductive construction of landscape functions, having","authors_text":"Constanza Riera, Pantelimon Stanica","cross_cats":["cs.DM","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-06-15T10:03:42Z","title":"Landscape Boolean Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.05878","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:f9df831e36db116787f1a3016bea0234e0911dcc62f12f1e82e5fdd373ef0d0b","target":"record","created_at":"2026-05-18T00:13:09Z","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":"6af933656900f6e77596d358f21921ed253002fd1b4ccfd3069e9b94d39cf4d8","cross_cats_sorted":["cs.DM","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-06-15T10:03:42Z","title_canon_sha256":"d8a059d980a1999a34e3a5a749b09b99476105237b996dea33914b5b59b51840"},"schema_version":"1.0","source":{"id":"1806.05878","kind":"arxiv","version":1}},"canonical_sha256":"8f20482f6a60daf1f93f78cf64460bc9710712942487b9eb29f9839f158e3ba7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f20482f6a60daf1f93f78cf64460bc9710712942487b9eb29f9839f158e3ba7","first_computed_at":"2026-05-18T00:13:09.169511Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:09.169511Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6Q2xGLKVXEjvJ6CXvahZQH7NsAheeCbL2qKtLyeF7a5V36avm2C7zj508VDfmsIHZOSgsjXJNLgXterC7v6nBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:09.170201Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.05878","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f9df831e36db116787f1a3016bea0234e0911dcc62f12f1e82e5fdd373ef0d0b","sha256:f785d44103088f15e0240c96de2b07513598e1508b2a152c3a713560098828ee"],"state_sha256":"f1829d1a057f8bb13e558d09bdfbd016132a550b0792465c27785fa22fdb3021"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fkAmfb0QHoGFO5Tj8uysp6bleL573Si9wmOvxzIC5pTEwq2qdJ717iqhziKU0YoIbasKK2duwvRfXHg6j6PMBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T00:18:40.023156Z","bundle_sha256":"b9935670837b1b6b9825fb33c497f5307f08708b74289bc5aa8ad4664b1f8e1b"}}