{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2003:PN2SUN7ZFTXBSZL2MND4F767D3","short_pith_number":"pith:PN2SUN7Z","canonical_record":{"source":{"id":"math/0305369","kind":"arxiv","version":8},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2003-05-26T23:00:33Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"3d43e4be2bb14d30e2141f91a84707957102e6a0931cc4181bfd2efbcf03c84a","abstract_canon_sha256":"71b9783e6e09387734dc7e8615bd7e9acec9ef2cdb08de3970ebfe83157484d4"},"schema_version":"1.0"},"canonical_sha256":"7b752a37f92cee19657a6347c2ffdf1ed6b8d64de94cc2642443ccd8cbc9cf0c","source":{"kind":"arxiv","id":"math/0305369","version":8},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0305369","created_at":"2026-07-04T15:42:26Z"},{"alias_kind":"arxiv_version","alias_value":"math/0305369v8","created_at":"2026-07-04T15:42:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0305369","created_at":"2026-07-04T15:42:26Z"},{"alias_kind":"pith_short_12","alias_value":"PN2SUN7ZFTXB","created_at":"2026-07-04T15:42:26Z"},{"alias_kind":"pith_short_16","alias_value":"PN2SUN7ZFTXBSZL2","created_at":"2026-07-04T15:42:26Z"},{"alias_kind":"pith_short_8","alias_value":"PN2SUN7Z","created_at":"2026-07-04T15:42:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2003:PN2SUN7ZFTXBSZL2MND4F767D3","target":"record","payload":{"canonical_record":{"source":{"id":"math/0305369","kind":"arxiv","version":8},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2003-05-26T23:00:33Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"3d43e4be2bb14d30e2141f91a84707957102e6a0931cc4181bfd2efbcf03c84a","abstract_canon_sha256":"71b9783e6e09387734dc7e8615bd7e9acec9ef2cdb08de3970ebfe83157484d4"},"schema_version":"1.0"},"canonical_sha256":"7b752a37f92cee19657a6347c2ffdf1ed6b8d64de94cc2642443ccd8cbc9cf0c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:42:26.052511Z","signature_b64":"9xA3/uecEaO6bP3kc7QZphzlSeNdaMDuxJCqbuaaX1PQ3FqeAifNm/YDDRLMAHVRujozAriYSD8Oene3Z984DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7b752a37f92cee19657a6347c2ffdf1ed6b8d64de94cc2642443ccd8cbc9cf0c","last_reissued_at":"2026-07-04T15:42:26.052114Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:42:26.052114Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0305369","source_version":8,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T15:42:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"meCJGnOlniW02C5CaIO+xG9BnKD0tjuoUVvbnUsQZayU8c5sVl0QCKd8zjbAs2AMcsgkihrFObiXjoKC8fG6Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T02:23:23.497988Z"},"content_sha256":"3093b36d9dec7dde66d7cb5670905445f7265e23b7a6ccf18be15fe13ee9bfb2","schema_version":"1.0","event_id":"sha256:3093b36d9dec7dde66d7cb5670905445f7265e23b7a6ccf18be15fe13ee9bfb2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2003:PN2SUN7ZFTXBSZL2MND4F767D3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Zero-sum problems for abelian p-groups and covers of the integers by residue classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Zhi-Wei Sun","submitted_at":"2003-05-26T23:00:33Z","abstract_excerpt":"Zero-sum problems for abelian groups and covers of the integers by residue classes, are two different active topics initiated by P. Erdos more than 40 years ago and investigated by many researchers separately since then. In an earlier announcement [Electron. Res. Announc. Amer. Math. Soc. 9(2003), 51-60], the author claimed some surprising connections among these seemingly unrelated fascinating areas. In this paper we establish further connections between zero-sum problems for abelian p-groups and covers of the integers. For example, we extend the famous Erdos-Ginzburg-Ziv theorem in the follo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0305369","kind":"arxiv","version":8},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0305369/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T15:42:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c/Oz/4tmJAhR6aEw0IOBXZoyWL8Xtpj/NxlG9QWrInbyb6Kua33e7SPxTP1YDJ4giNL/aQrFzo1Lsen61uMUCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T02:23:23.498598Z"},"content_sha256":"42bfa0cf0663e565d51f6ab1abe1ba2ec968c9980513810f318c268f7027ba48","schema_version":"1.0","event_id":"sha256:42bfa0cf0663e565d51f6ab1abe1ba2ec968c9980513810f318c268f7027ba48"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PN2SUN7ZFTXBSZL2MND4F767D3/bundle.json","state_url":"https://pith.science/pith/PN2SUN7ZFTXBSZL2MND4F767D3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PN2SUN7ZFTXBSZL2MND4F767D3/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":"2026-08-04T02:23:23Z","links":{"resolver":"https://pith.science/pith/PN2SUN7ZFTXBSZL2MND4F767D3","bundle":"https://pith.science/pith/PN2SUN7ZFTXBSZL2MND4F767D3/bundle.json","state":"https://pith.science/pith/PN2SUN7ZFTXBSZL2MND4F767D3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PN2SUN7ZFTXBSZL2MND4F767D3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:PN2SUN7ZFTXBSZL2MND4F767D3","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":"71b9783e6e09387734dc7e8615bd7e9acec9ef2cdb08de3970ebfe83157484d4","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2003-05-26T23:00:33Z","title_canon_sha256":"3d43e4be2bb14d30e2141f91a84707957102e6a0931cc4181bfd2efbcf03c84a"},"schema_version":"1.0","source":{"id":"math/0305369","kind":"arxiv","version":8}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0305369","created_at":"2026-07-04T15:42:26Z"},{"alias_kind":"arxiv_version","alias_value":"math/0305369v8","created_at":"2026-07-04T15:42:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0305369","created_at":"2026-07-04T15:42:26Z"},{"alias_kind":"pith_short_12","alias_value":"PN2SUN7ZFTXB","created_at":"2026-07-04T15:42:26Z"},{"alias_kind":"pith_short_16","alias_value":"PN2SUN7ZFTXBSZL2","created_at":"2026-07-04T15:42:26Z"},{"alias_kind":"pith_short_8","alias_value":"PN2SUN7Z","created_at":"2026-07-04T15:42:26Z"}],"graph_snapshots":[{"event_id":"sha256:42bfa0cf0663e565d51f6ab1abe1ba2ec968c9980513810f318c268f7027ba48","target":"graph","created_at":"2026-07-04T15:42:26Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0305369/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Zero-sum problems for abelian groups and covers of the integers by residue classes, are two different active topics initiated by P. Erdos more than 40 years ago and investigated by many researchers separately since then. In an earlier announcement [Electron. Res. Announc. Amer. Math. Soc. 9(2003), 51-60], the author claimed some surprising connections among these seemingly unrelated fascinating areas. In this paper we establish further connections between zero-sum problems for abelian p-groups and covers of the integers. For example, we extend the famous Erdos-Ginzburg-Ziv theorem in the follo","authors_text":"Zhi-Wei Sun","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2003-05-26T23:00:33Z","title":"Zero-sum problems for abelian p-groups and covers of the integers by residue classes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0305369","kind":"arxiv","version":8},"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":"sha256:3093b36d9dec7dde66d7cb5670905445f7265e23b7a6ccf18be15fe13ee9bfb2","target":"record","created_at":"2026-07-04T15:42:26Z","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":"71b9783e6e09387734dc7e8615bd7e9acec9ef2cdb08de3970ebfe83157484d4","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2003-05-26T23:00:33Z","title_canon_sha256":"3d43e4be2bb14d30e2141f91a84707957102e6a0931cc4181bfd2efbcf03c84a"},"schema_version":"1.0","source":{"id":"math/0305369","kind":"arxiv","version":8}},"canonical_sha256":"7b752a37f92cee19657a6347c2ffdf1ed6b8d64de94cc2642443ccd8cbc9cf0c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7b752a37f92cee19657a6347c2ffdf1ed6b8d64de94cc2642443ccd8cbc9cf0c","first_computed_at":"2026-07-04T15:42:26.052114Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:42:26.052114Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9xA3/uecEaO6bP3kc7QZphzlSeNdaMDuxJCqbuaaX1PQ3FqeAifNm/YDDRLMAHVRujozAriYSD8Oene3Z984DA==","signature_status":"signed_v1","signed_at":"2026-07-04T15:42:26.052511Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0305369","source_kind":"arxiv","source_version":8}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3093b36d9dec7dde66d7cb5670905445f7265e23b7a6ccf18be15fe13ee9bfb2","sha256:42bfa0cf0663e565d51f6ab1abe1ba2ec968c9980513810f318c268f7027ba48"],"state_sha256":"cc2a236bf94da25b727ca940502af17317410f700f19125eeb0fa0cd39a17f0c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/cQS0SwiEW1CK01bu/xkHDxunCoch9BiZSe/RyDMgfzGwI4AQzizBUr84+/MMTBAYF+bWV05wsp+r3lxfjGoCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T02:23:23.502385Z","bundle_sha256":"34382ad6eadab0413ad826cdfc9f9a14d08972ffba32489352bc60d4e6ef928c"}}