{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:R52VP6NQQN6IZVZFGYV3H6WOI2","short_pith_number":"pith:R52VP6NQ","canonical_record":{"source":{"id":"1506.03201","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-06-10T07:54:37Z","cross_cats_sorted":[],"title_canon_sha256":"9a0913a77f3d1b494943830733b3317926e4d50769e1c0cf5efd4bc0e663b9fc","abstract_canon_sha256":"dda43efc24529efb015638e82bed2a0abf1a19d504242a96d05c70dc19700eae"},"schema_version":"1.0"},"canonical_sha256":"8f7557f9b0837c8cd725362bb3face46970324d0061043787a8e5c28beb8773b","source":{"kind":"arxiv","id":"1506.03201","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.03201","created_at":"2026-05-18T01:55:31Z"},{"alias_kind":"arxiv_version","alias_value":"1506.03201v1","created_at":"2026-05-18T01:55:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.03201","created_at":"2026-05-18T01:55:31Z"},{"alias_kind":"pith_short_12","alias_value":"R52VP6NQQN6I","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"R52VP6NQQN6IZVZF","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"R52VP6NQ","created_at":"2026-05-18T12:29:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:R52VP6NQQN6IZVZFGYV3H6WOI2","target":"record","payload":{"canonical_record":{"source":{"id":"1506.03201","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-06-10T07:54:37Z","cross_cats_sorted":[],"title_canon_sha256":"9a0913a77f3d1b494943830733b3317926e4d50769e1c0cf5efd4bc0e663b9fc","abstract_canon_sha256":"dda43efc24529efb015638e82bed2a0abf1a19d504242a96d05c70dc19700eae"},"schema_version":"1.0"},"canonical_sha256":"8f7557f9b0837c8cd725362bb3face46970324d0061043787a8e5c28beb8773b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:55:31.272060Z","signature_b64":"0onnpiLoh5hU8Bj8rr6yt4nf5NtAIavHGKpFxgP+2Lr4Ulvjjq5r00YFROsyNwzG7RC/8W4qbb+hy5XXigNVCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f7557f9b0837c8cd725362bb3face46970324d0061043787a8e5c28beb8773b","last_reissued_at":"2026-05-18T01:55:31.271415Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:55:31.271415Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.03201","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":"2026-05-18T01:55:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"turjrPIas2oIrD2q1lzo4hlyryrr6kE2hDgGgL1EGHRVywyQswp3Ubh8P83zjUZiIEIZ7rbLI36ACNhGvKyzAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T05:07:34.945287Z"},"content_sha256":"ec4167bb92a90eee2b90d698ba591b1ed73da717d5f30f041d3a27149e4400ee","schema_version":"1.0","event_id":"sha256:ec4167bb92a90eee2b90d698ba591b1ed73da717d5f30f041d3a27149e4400ee"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:R52VP6NQQN6IZVZFGYV3H6WOI2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Construction algorithms for plane nets in base $b$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Friedrich Pillichshammer, Gunther Leobacher, Thomas Schell","submitted_at":"2015-06-10T07:54:37Z","abstract_excerpt":"The class of $(0,m,s)$-nets in base $b$ has been introduced by Niederreiter as examples of point sets in the $s$-dimensional unit cube with excellent uniform distribution properties. In particular such nets have been proved to have very low discrepancy. This property is essential for the use of nets in quasi-Monte Carlo rules for numerical integration. In this short note we propose two algorithms for the construction of plane $(0,m,2)$-nets in base~$b$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03201","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":"2026-05-18T01:55:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w4sJRJ1oJJ1rUFPd/Q4WL9sAymIx35zf2iE6rnGyyJfpXH9zPIIDz/2ZMcmHtsnP6kJllEkUp9KzQFNn0H0yCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T05:07:34.945654Z"},"content_sha256":"ed2dd3de3c675712ffc6f829d4075b813071a0f8f212ce630fb4bfe7c1d15693","schema_version":"1.0","event_id":"sha256:ed2dd3de3c675712ffc6f829d4075b813071a0f8f212ce630fb4bfe7c1d15693"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R52VP6NQQN6IZVZFGYV3H6WOI2/bundle.json","state_url":"https://pith.science/pith/R52VP6NQQN6IZVZFGYV3H6WOI2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R52VP6NQQN6IZVZFGYV3H6WOI2/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":"2026-05-28T05:07:34Z","links":{"resolver":"https://pith.science/pith/R52VP6NQQN6IZVZFGYV3H6WOI2","bundle":"https://pith.science/pith/R52VP6NQQN6IZVZFGYV3H6WOI2/bundle.json","state":"https://pith.science/pith/R52VP6NQQN6IZVZFGYV3H6WOI2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R52VP6NQQN6IZVZFGYV3H6WOI2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:R52VP6NQQN6IZVZFGYV3H6WOI2","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":"dda43efc24529efb015638e82bed2a0abf1a19d504242a96d05c70dc19700eae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-06-10T07:54:37Z","title_canon_sha256":"9a0913a77f3d1b494943830733b3317926e4d50769e1c0cf5efd4bc0e663b9fc"},"schema_version":"1.0","source":{"id":"1506.03201","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.03201","created_at":"2026-05-18T01:55:31Z"},{"alias_kind":"arxiv_version","alias_value":"1506.03201v1","created_at":"2026-05-18T01:55:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.03201","created_at":"2026-05-18T01:55:31Z"},{"alias_kind":"pith_short_12","alias_value":"R52VP6NQQN6I","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"R52VP6NQQN6IZVZF","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"R52VP6NQ","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:ed2dd3de3c675712ffc6f829d4075b813071a0f8f212ce630fb4bfe7c1d15693","target":"graph","created_at":"2026-05-18T01:55:31Z","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 class of $(0,m,s)$-nets in base $b$ has been introduced by Niederreiter as examples of point sets in the $s$-dimensional unit cube with excellent uniform distribution properties. In particular such nets have been proved to have very low discrepancy. This property is essential for the use of nets in quasi-Monte Carlo rules for numerical integration. In this short note we propose two algorithms for the construction of plane $(0,m,2)$-nets in base~$b$.","authors_text":"Friedrich Pillichshammer, Gunther Leobacher, Thomas Schell","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-06-10T07:54:37Z","title":"Construction algorithms for plane nets in base $b$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03201","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:ec4167bb92a90eee2b90d698ba591b1ed73da717d5f30f041d3a27149e4400ee","target":"record","created_at":"2026-05-18T01:55:31Z","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":"dda43efc24529efb015638e82bed2a0abf1a19d504242a96d05c70dc19700eae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-06-10T07:54:37Z","title_canon_sha256":"9a0913a77f3d1b494943830733b3317926e4d50769e1c0cf5efd4bc0e663b9fc"},"schema_version":"1.0","source":{"id":"1506.03201","kind":"arxiv","version":1}},"canonical_sha256":"8f7557f9b0837c8cd725362bb3face46970324d0061043787a8e5c28beb8773b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f7557f9b0837c8cd725362bb3face46970324d0061043787a8e5c28beb8773b","first_computed_at":"2026-05-18T01:55:31.271415Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:55:31.271415Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0onnpiLoh5hU8Bj8rr6yt4nf5NtAIavHGKpFxgP+2Lr4Ulvjjq5r00YFROsyNwzG7RC/8W4qbb+hy5XXigNVCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:55:31.272060Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.03201","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ec4167bb92a90eee2b90d698ba591b1ed73da717d5f30f041d3a27149e4400ee","sha256:ed2dd3de3c675712ffc6f829d4075b813071a0f8f212ce630fb4bfe7c1d15693"],"state_sha256":"1c6df79bd063eef897d543357d496c2bd8604cc2306e4a3359ffa2474034f6a1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3Jg8a9rw+KQyWoylt6PbgZTL2LcoAAVzobI+T991Ttua63EUwuz3+JssZ6cEXjDQEA46T5IkxJuZRtWtyHmAAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T05:07:34.948015Z","bundle_sha256":"ecb16e0394e1d68d654f40170f9da97c101d30ba42ca18e5a92bd3f406b60433"}}