{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:O7OIIHJFWPPNJGWMDB5GWQONCQ","short_pith_number":"pith:O7OIIHJF","canonical_record":{"source":{"id":"1901.04738","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2019-01-15T10:02:33Z","cross_cats_sorted":[],"title_canon_sha256":"53fde5c39a319ff1858d5abe8429aded961740ed4c793f8bbebf85c0a76b55fd","abstract_canon_sha256":"749dd25d79f06e52ab5285de80061d2d9144c6adb8666d92ec227b069511f15e"},"schema_version":"1.0"},"canonical_sha256":"77dc841d25b3ded49acc187a6b41cd142f48421ca930ba8c0abc283b497101c3","source":{"kind":"arxiv","id":"1901.04738","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.04738","created_at":"2026-05-17T23:56:21Z"},{"alias_kind":"arxiv_version","alias_value":"1901.04738v1","created_at":"2026-05-17T23:56:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.04738","created_at":"2026-05-17T23:56:21Z"},{"alias_kind":"pith_short_12","alias_value":"O7OIIHJFWPPN","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"O7OIIHJFWPPNJGWM","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"O7OIIHJF","created_at":"2026-05-18T12:33:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:O7OIIHJFWPPNJGWMDB5GWQONCQ","target":"record","payload":{"canonical_record":{"source":{"id":"1901.04738","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2019-01-15T10:02:33Z","cross_cats_sorted":[],"title_canon_sha256":"53fde5c39a319ff1858d5abe8429aded961740ed4c793f8bbebf85c0a76b55fd","abstract_canon_sha256":"749dd25d79f06e52ab5285de80061d2d9144c6adb8666d92ec227b069511f15e"},"schema_version":"1.0"},"canonical_sha256":"77dc841d25b3ded49acc187a6b41cd142f48421ca930ba8c0abc283b497101c3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:21.883856Z","signature_b64":"BSie4TqPCcv9agnJa4adMfve6dXXuFavMotRXJKy6zYO5uph0SWw3ro1FMw+byUrWi4PGQVu+QJRRNdT2mpxAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"77dc841d25b3ded49acc187a6b41cd142f48421ca930ba8c0abc283b497101c3","last_reissued_at":"2026-05-17T23:56:21.883223Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:21.883223Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1901.04738","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":"2026-05-17T23:56:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xdiAYUQ6nJ9+A0K30Mj/qFTcol05Fw0hN0ihq+i2nHoaK1CbvLLS93x4kRBcWP0vCOrnmzwfrieTmoJVUyIcAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T21:46:16.368446Z"},"content_sha256":"03de2c2ad9dfabad311a770703bbd24f347bba8973033d0b397d943b08c1d709","schema_version":"1.0","event_id":"sha256:03de2c2ad9dfabad311a770703bbd24f347bba8973033d0b397d943b08c1d709"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:O7OIIHJFWPPNJGWMDB5GWQONCQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Efficient Algorithms to Test Digital Convexity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Guilherme D. da Fonseca, Lo\\\"ic Crombez, Yan G\\'erard","submitted_at":"2019-01-15T10:02:33Z","abstract_excerpt":"A set $S \\subset \\mathbb{Z}^d$ is digital convex if $conv(S) \\cap \\mathbb{Z}^d = S$, where $conv(S)$ denotes the convex hull of $S$. In this paper, we consider the algorithmic problem of testing whether a given set $S$ of $n$ lattice points is digital convex. Although convex hull computation requires $\\Omega(n \\log n)$ time even for dimension $d = 2$, we provide an algorithm for testing the digital convexity of $S\\subset \\mathbb{Z}^2$ in $O(n + h \\log r)$ time, where $h$ is the number of edges of the convex hull and $r$ is the diameter of $S$. This main result is obtained by proving that if $S"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.04738","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":"2026-05-17T23:56:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nCTMDAwgE0TJ7iuGWi3ozUDJejy416uOlJM12migSQtUGf1Nze360lYkCQF5GLF0u09Bx82eBJlC6f0DwlxrAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T21:46:16.368797Z"},"content_sha256":"adff4b7bea3c7350ad26447cafbecc38e4d953af48c225a0df59e1a8dd51a318","schema_version":"1.0","event_id":"sha256:adff4b7bea3c7350ad26447cafbecc38e4d953af48c225a0df59e1a8dd51a318"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O7OIIHJFWPPNJGWMDB5GWQONCQ/bundle.json","state_url":"https://pith.science/pith/O7OIIHJFWPPNJGWMDB5GWQONCQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O7OIIHJFWPPNJGWMDB5GWQONCQ/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":"2026-07-02T21:46:16Z","links":{"resolver":"https://pith.science/pith/O7OIIHJFWPPNJGWMDB5GWQONCQ","bundle":"https://pith.science/pith/O7OIIHJFWPPNJGWMDB5GWQONCQ/bundle.json","state":"https://pith.science/pith/O7OIIHJFWPPNJGWMDB5GWQONCQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O7OIIHJFWPPNJGWMDB5GWQONCQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:O7OIIHJFWPPNJGWMDB5GWQONCQ","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":"749dd25d79f06e52ab5285de80061d2d9144c6adb8666d92ec227b069511f15e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2019-01-15T10:02:33Z","title_canon_sha256":"53fde5c39a319ff1858d5abe8429aded961740ed4c793f8bbebf85c0a76b55fd"},"schema_version":"1.0","source":{"id":"1901.04738","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.04738","created_at":"2026-05-17T23:56:21Z"},{"alias_kind":"arxiv_version","alias_value":"1901.04738v1","created_at":"2026-05-17T23:56:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.04738","created_at":"2026-05-17T23:56:21Z"},{"alias_kind":"pith_short_12","alias_value":"O7OIIHJFWPPN","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"O7OIIHJFWPPNJGWM","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"O7OIIHJF","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:adff4b7bea3c7350ad26447cafbecc38e4d953af48c225a0df59e1a8dd51a318","target":"graph","created_at":"2026-05-17T23:56:21Z","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":"A set $S \\subset \\mathbb{Z}^d$ is digital convex if $conv(S) \\cap \\mathbb{Z}^d = S$, where $conv(S)$ denotes the convex hull of $S$. In this paper, we consider the algorithmic problem of testing whether a given set $S$ of $n$ lattice points is digital convex. Although convex hull computation requires $\\Omega(n \\log n)$ time even for dimension $d = 2$, we provide an algorithm for testing the digital convexity of $S\\subset \\mathbb{Z}^2$ in $O(n + h \\log r)$ time, where $h$ is the number of edges of the convex hull and $r$ is the diameter of $S$. This main result is obtained by proving that if $S","authors_text":"Guilherme D. da Fonseca, Lo\\\"ic Crombez, Yan G\\'erard","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2019-01-15T10:02:33Z","title":"Efficient Algorithms to Test Digital Convexity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.04738","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":"sha256:03de2c2ad9dfabad311a770703bbd24f347bba8973033d0b397d943b08c1d709","target":"record","created_at":"2026-05-17T23:56:21Z","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":"749dd25d79f06e52ab5285de80061d2d9144c6adb8666d92ec227b069511f15e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CG","submitted_at":"2019-01-15T10:02:33Z","title_canon_sha256":"53fde5c39a319ff1858d5abe8429aded961740ed4c793f8bbebf85c0a76b55fd"},"schema_version":"1.0","source":{"id":"1901.04738","kind":"arxiv","version":1}},"canonical_sha256":"77dc841d25b3ded49acc187a6b41cd142f48421ca930ba8c0abc283b497101c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77dc841d25b3ded49acc187a6b41cd142f48421ca930ba8c0abc283b497101c3","first_computed_at":"2026-05-17T23:56:21.883223Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:21.883223Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BSie4TqPCcv9agnJa4adMfve6dXXuFavMotRXJKy6zYO5uph0SWw3ro1FMw+byUrWi4PGQVu+QJRRNdT2mpxAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:21.883856Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.04738","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:03de2c2ad9dfabad311a770703bbd24f347bba8973033d0b397d943b08c1d709","sha256:adff4b7bea3c7350ad26447cafbecc38e4d953af48c225a0df59e1a8dd51a318"],"state_sha256":"982d9849789953733dfee27f9368dd9a885bd36f72f657d0badc6666c5980dd4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9Leg1dpxG7fljruTSPS0OnPw/5HtPWU36xQREpm+8FBne5mSJGQd97T59L4M8d5v6F1HJnCTx6tiuOcf8uHnDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T21:46:16.370754Z","bundle_sha256":"9a86e4e8d35ceaa4cde50f38b5ada25221b3a9d85639d38882628bc34472ef94"}}