{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:KUUNUTWMPYUFC4RRFFETC2QDZQ","short_pith_number":"pith:KUUNUTWM","canonical_record":{"source":{"id":"1008.0763","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-08-04T12:24:07Z","cross_cats_sorted":[],"title_canon_sha256":"c49d06fda51fc2c2255751f08f71f260361bcd9ffa254c8d8723efbd708d10e0","abstract_canon_sha256":"967d87ea24916f105aea33faee8c9c7481834547b6a3985e6fc0a8be27c5b173"},"schema_version":"1.0"},"canonical_sha256":"5528da4ecc7e285172312949316a03cc3b51f8709c54316570624f6eae42f58b","source":{"kind":"arxiv","id":"1008.0763","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.0763","created_at":"2026-05-18T04:42:35Z"},{"alias_kind":"arxiv_version","alias_value":"1008.0763v1","created_at":"2026-05-18T04:42:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.0763","created_at":"2026-05-18T04:42:35Z"},{"alias_kind":"pith_short_12","alias_value":"KUUNUTWMPYUF","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"KUUNUTWMPYUFC4RR","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"KUUNUTWM","created_at":"2026-05-18T12:26:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:KUUNUTWMPYUFC4RRFFETC2QDZQ","target":"record","payload":{"canonical_record":{"source":{"id":"1008.0763","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-08-04T12:24:07Z","cross_cats_sorted":[],"title_canon_sha256":"c49d06fda51fc2c2255751f08f71f260361bcd9ffa254c8d8723efbd708d10e0","abstract_canon_sha256":"967d87ea24916f105aea33faee8c9c7481834547b6a3985e6fc0a8be27c5b173"},"schema_version":"1.0"},"canonical_sha256":"5528da4ecc7e285172312949316a03cc3b51f8709c54316570624f6eae42f58b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:42:35.670499Z","signature_b64":"5EQPyDVsDGRUHXx4PdVrKVlR6pg2bwD5iZ9anpSfSYdRg5zqd4T9mjfE6/IKubhqeAV/fJ+QdH7YyMqvI3R8DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5528da4ecc7e285172312949316a03cc3b51f8709c54316570624f6eae42f58b","last_reissued_at":"2026-05-18T04:42:35.669888Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:42:35.669888Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1008.0763","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":"2026-05-18T04:42:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZfmZjo+6XqPzqdivVvaUFOB+cgC0mMs60NzvroTfYwGtydn6eIhaAl3uiV2E+RJzogQTvgxnWOlu9jP8UgSiCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T06:59:52.470060Z"},"content_sha256":"6ca13b3d503604ce8ac09b5824c82be87ecf4f6ae3db78cb55e1709888ffa4a9","schema_version":"1.0","event_id":"sha256:6ca13b3d503604ce8ac09b5824c82be87ecf4f6ae3db78cb55e1709888ffa4a9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:KUUNUTWMPYUFC4RRFFETC2QDZQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Olson and the Strong Davenport constants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Andreas Philipp, Irene Santos, Oscar Ordaz, Wolfgang A. Schmid","submitted_at":"2010-08-04T12:24:07Z","abstract_excerpt":"A subset $S$ of a finite abelian group, written additively, is called zero-sumfree if the sum of the elements of each non-empty subset of $S$ is non-zero. We investigate the maximal cardinality of zero-sumfree sets, i.e., the (small) Olson constant. We determine the maximal cardinality of such sets for several new types of groups; in particular, $p$-groups with large rank relative to the exponent, including all groups with exponent at most five. These results are derived as consequences of more general results, establishing new lower bounds for the cardinality of zero-sumfree sets for various "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.0763","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":"2026-05-18T04:42:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VMbAu5n88N1UFbywrrpiJA0SbmQvcYJuGxmqNHG2IvHTrIQLqZGhGuHNctkZLt6E8EUmaCYlcLdslmM6jTuRBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T06:59:52.470706Z"},"content_sha256":"b9b95458e70b42a27825b88d82c7ec3349a229fe6968a0001a97b8018b462d15","schema_version":"1.0","event_id":"sha256:b9b95458e70b42a27825b88d82c7ec3349a229fe6968a0001a97b8018b462d15"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KUUNUTWMPYUFC4RRFFETC2QDZQ/bundle.json","state_url":"https://pith.science/pith/KUUNUTWMPYUFC4RRFFETC2QDZQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KUUNUTWMPYUFC4RRFFETC2QDZQ/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":"2026-05-27T06:59:52Z","links":{"resolver":"https://pith.science/pith/KUUNUTWMPYUFC4RRFFETC2QDZQ","bundle":"https://pith.science/pith/KUUNUTWMPYUFC4RRFFETC2QDZQ/bundle.json","state":"https://pith.science/pith/KUUNUTWMPYUFC4RRFFETC2QDZQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KUUNUTWMPYUFC4RRFFETC2QDZQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:KUUNUTWMPYUFC4RRFFETC2QDZQ","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":"967d87ea24916f105aea33faee8c9c7481834547b6a3985e6fc0a8be27c5b173","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-08-04T12:24:07Z","title_canon_sha256":"c49d06fda51fc2c2255751f08f71f260361bcd9ffa254c8d8723efbd708d10e0"},"schema_version":"1.0","source":{"id":"1008.0763","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.0763","created_at":"2026-05-18T04:42:35Z"},{"alias_kind":"arxiv_version","alias_value":"1008.0763v1","created_at":"2026-05-18T04:42:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.0763","created_at":"2026-05-18T04:42:35Z"},{"alias_kind":"pith_short_12","alias_value":"KUUNUTWMPYUF","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"KUUNUTWMPYUFC4RR","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"KUUNUTWM","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:b9b95458e70b42a27825b88d82c7ec3349a229fe6968a0001a97b8018b462d15","target":"graph","created_at":"2026-05-18T04:42:35Z","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":"A subset $S$ of a finite abelian group, written additively, is called zero-sumfree if the sum of the elements of each non-empty subset of $S$ is non-zero. We investigate the maximal cardinality of zero-sumfree sets, i.e., the (small) Olson constant. We determine the maximal cardinality of such sets for several new types of groups; in particular, $p$-groups with large rank relative to the exponent, including all groups with exponent at most five. These results are derived as consequences of more general results, establishing new lower bounds for the cardinality of zero-sumfree sets for various ","authors_text":"Andreas Philipp, Irene Santos, Oscar Ordaz, Wolfgang A. Schmid","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-08-04T12:24:07Z","title":"On the Olson and the Strong Davenport constants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.0763","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":"sha256:6ca13b3d503604ce8ac09b5824c82be87ecf4f6ae3db78cb55e1709888ffa4a9","target":"record","created_at":"2026-05-18T04:42:35Z","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":"967d87ea24916f105aea33faee8c9c7481834547b6a3985e6fc0a8be27c5b173","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-08-04T12:24:07Z","title_canon_sha256":"c49d06fda51fc2c2255751f08f71f260361bcd9ffa254c8d8723efbd708d10e0"},"schema_version":"1.0","source":{"id":"1008.0763","kind":"arxiv","version":1}},"canonical_sha256":"5528da4ecc7e285172312949316a03cc3b51f8709c54316570624f6eae42f58b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5528da4ecc7e285172312949316a03cc3b51f8709c54316570624f6eae42f58b","first_computed_at":"2026-05-18T04:42:35.669888Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:35.669888Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5EQPyDVsDGRUHXx4PdVrKVlR6pg2bwD5iZ9anpSfSYdRg5zqd4T9mjfE6/IKubhqeAV/fJ+QdH7YyMqvI3R8DA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:35.670499Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.0763","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6ca13b3d503604ce8ac09b5824c82be87ecf4f6ae3db78cb55e1709888ffa4a9","sha256:b9b95458e70b42a27825b88d82c7ec3349a229fe6968a0001a97b8018b462d15"],"state_sha256":"54889e333c8db921edd235351f117e95866580a2c10609af07cdf2d5cf5e7bd8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1+4NMPMR9pDHeaI6zp4d9uow9gQgK3TKGG2kXdYuRXUtR8ZoqAtGgvJBUEVwt0dURWuQB2rM61MB4swvuPSqBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T06:59:52.473907Z","bundle_sha256":"5a27542157ea32c273f7f0b1e112ca4f86339bf6739c71993c48c318828bd8f5"}}