{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:TWJYYGYIJSFC7QFZO37ECO5AB6","short_pith_number":"pith:TWJYYGYI","canonical_record":{"source":{"id":"1501.04843","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2015-01-20T15:16:12Z","cross_cats_sorted":[],"title_canon_sha256":"45309d16492cf122c1a7a968f546a22ece050f1fefb64f9648014a2d01e9c96e","abstract_canon_sha256":"8e32429aa8509a466c3ce387126f3d837aea882284c84cfe6bab76f0f12fee7e"},"schema_version":"1.0"},"canonical_sha256":"9d938c1b084c8a2fc0b976fe413ba00fb5303015f5ca27c2a49707200b037b1d","source":{"kind":"arxiv","id":"1501.04843","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.04843","created_at":"2026-05-18T02:29:02Z"},{"alias_kind":"arxiv_version","alias_value":"1501.04843v1","created_at":"2026-05-18T02:29:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.04843","created_at":"2026-05-18T02:29:02Z"},{"alias_kind":"pith_short_12","alias_value":"TWJYYGYIJSFC","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TWJYYGYIJSFC7QFZ","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TWJYYGYI","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:TWJYYGYIJSFC7QFZO37ECO5AB6","target":"record","payload":{"canonical_record":{"source":{"id":"1501.04843","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2015-01-20T15:16:12Z","cross_cats_sorted":[],"title_canon_sha256":"45309d16492cf122c1a7a968f546a22ece050f1fefb64f9648014a2d01e9c96e","abstract_canon_sha256":"8e32429aa8509a466c3ce387126f3d837aea882284c84cfe6bab76f0f12fee7e"},"schema_version":"1.0"},"canonical_sha256":"9d938c1b084c8a2fc0b976fe413ba00fb5303015f5ca27c2a49707200b037b1d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:02.128987Z","signature_b64":"aY+6rRb07dW+WOLjG3BJsWND7M7V19wAzq5UBGqMln6oZIjE7ea/dp5Wy9qLbdKcc100MS1OH1GZneG2uu8kAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d938c1b084c8a2fc0b976fe413ba00fb5303015f5ca27c2a49707200b037b1d","last_reissued_at":"2026-05-18T02:29:02.128393Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:02.128393Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.04843","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":"2026-05-18T02:29:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lydVW9CsKvqk/A/zSlVMTj6jSfesfgUWzvP6UxQ9ODSYP2blG16rD/URb1PwuknQ9qf8y3LXqhIhe+AoaHGmDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T07:33:54.552662Z"},"content_sha256":"529dda69b2bc45d850f80643ff6f2397e7536d175aa2c5a77093537a09f8a869","schema_version":"1.0","event_id":"sha256:529dda69b2bc45d850f80643ff6f2397e7536d175aa2c5a77093537a09f8a869"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:TWJYYGYIJSFC7QFZO37ECO5AB6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Discrete Voronoi Games and $\\epsilon$-Nets, in Two and Three Dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Anil Maheshwari, Aritra Banik, Jean-Lou De Carufel, Michiel Smid","submitted_at":"2015-01-20T15:16:12Z","abstract_excerpt":"The one-round discrete Voronoi game, with respect to a $n$-point user set $U$, consists of two players Player 1 ($\\mathcal{P}_1$) and Player 2 ($\\mathcal{P}_2$). At first, $\\mathcal{P}_1$ chooses a set of facilities $F_1$ following which $\\mathcal{P}_2$ chooses another set of facilities $F_2$, disjoint from $F_1$. The payoff of $\\mathcal{P}_2$ is defined as the cardinality of the set of points in $U$ which are closer to a facility in $F_2$ than to every facility in $F_1$, and the payoff of $\\mathcal{P}_1$ is the difference between the number of users in $U$ and the payoff of $\\mathcal{P}_2$. T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04843","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":"2026-05-18T02:29:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pi1/IN1LVIOetvXxQRIiS4tJx6lR6N7EWQ1HD4nbt5s+NsOkl3tfPGuLx9TyVH5H5IPLo1SI8LtRKnf93vsECQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T07:33:54.553033Z"},"content_sha256":"57a00bf7ce6d38c76493bc09e08a21ac150efbbafb978986eb7ea2f3c1a17087","schema_version":"1.0","event_id":"sha256:57a00bf7ce6d38c76493bc09e08a21ac150efbbafb978986eb7ea2f3c1a17087"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TWJYYGYIJSFC7QFZO37ECO5AB6/bundle.json","state_url":"https://pith.science/pith/TWJYYGYIJSFC7QFZO37ECO5AB6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TWJYYGYIJSFC7QFZO37ECO5AB6/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":"2026-05-27T07:33:54Z","links":{"resolver":"https://pith.science/pith/TWJYYGYIJSFC7QFZO37ECO5AB6","bundle":"https://pith.science/pith/TWJYYGYIJSFC7QFZO37ECO5AB6/bundle.json","state":"https://pith.science/pith/TWJYYGYIJSFC7QFZO37ECO5AB6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TWJYYGYIJSFC7QFZO37ECO5AB6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:TWJYYGYIJSFC7QFZO37ECO5AB6","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":"8e32429aa8509a466c3ce387126f3d837aea882284c84cfe6bab76f0f12fee7e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2015-01-20T15:16:12Z","title_canon_sha256":"45309d16492cf122c1a7a968f546a22ece050f1fefb64f9648014a2d01e9c96e"},"schema_version":"1.0","source":{"id":"1501.04843","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.04843","created_at":"2026-05-18T02:29:02Z"},{"alias_kind":"arxiv_version","alias_value":"1501.04843v1","created_at":"2026-05-18T02:29:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.04843","created_at":"2026-05-18T02:29:02Z"},{"alias_kind":"pith_short_12","alias_value":"TWJYYGYIJSFC","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TWJYYGYIJSFC7QFZ","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TWJYYGYI","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:57a00bf7ce6d38c76493bc09e08a21ac150efbbafb978986eb7ea2f3c1a17087","target":"graph","created_at":"2026-05-18T02:29:02Z","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 one-round discrete Voronoi game, with respect to a $n$-point user set $U$, consists of two players Player 1 ($\\mathcal{P}_1$) and Player 2 ($\\mathcal{P}_2$). At first, $\\mathcal{P}_1$ chooses a set of facilities $F_1$ following which $\\mathcal{P}_2$ chooses another set of facilities $F_2$, disjoint from $F_1$. The payoff of $\\mathcal{P}_2$ is defined as the cardinality of the set of points in $U$ which are closer to a facility in $F_2$ than to every facility in $F_1$, and the payoff of $\\mathcal{P}_1$ is the difference between the number of users in $U$ and the payoff of $\\mathcal{P}_2$. T","authors_text":"Anil Maheshwari, Aritra Banik, Jean-Lou De Carufel, Michiel Smid","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2015-01-20T15:16:12Z","title":"Discrete Voronoi Games and $\\epsilon$-Nets, in Two and Three Dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04843","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":"sha256:529dda69b2bc45d850f80643ff6f2397e7536d175aa2c5a77093537a09f8a869","target":"record","created_at":"2026-05-18T02:29:02Z","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":"8e32429aa8509a466c3ce387126f3d837aea882284c84cfe6bab76f0f12fee7e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2015-01-20T15:16:12Z","title_canon_sha256":"45309d16492cf122c1a7a968f546a22ece050f1fefb64f9648014a2d01e9c96e"},"schema_version":"1.0","source":{"id":"1501.04843","kind":"arxiv","version":1}},"canonical_sha256":"9d938c1b084c8a2fc0b976fe413ba00fb5303015f5ca27c2a49707200b037b1d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9d938c1b084c8a2fc0b976fe413ba00fb5303015f5ca27c2a49707200b037b1d","first_computed_at":"2026-05-18T02:29:02.128393Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:02.128393Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aY+6rRb07dW+WOLjG3BJsWND7M7V19wAzq5UBGqMln6oZIjE7ea/dp5Wy9qLbdKcc100MS1OH1GZneG2uu8kAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:02.128987Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.04843","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:529dda69b2bc45d850f80643ff6f2397e7536d175aa2c5a77093537a09f8a869","sha256:57a00bf7ce6d38c76493bc09e08a21ac150efbbafb978986eb7ea2f3c1a17087"],"state_sha256":"2225bd4a268a1f949a23b97a0673fd1e54af2aaa6afc5057a0b5801fbdc72ded"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pX5v4Cn2wJMFG+lqS07zjGZuV2J/L+XguAuz1TlMKHvZRlPwKXMiCpaUtciDNq+IPp4H4Dz26Cxi33SumQ8OAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T07:33:54.555283Z","bundle_sha256":"6c1068650702b9c5f7a3cc0a7c4e371a7d04f397cb047235f7332dae5ffbf788"}}