{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:COGQMENAH3WULBXWVDKFYDETCQ","short_pith_number":"pith:COGQMENA","canonical_record":{"source":{"id":"1308.3316","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-08-15T06:17:02Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"ba3845cde7ab2cb7d7fc2f5f0cb6c95343876ca3c5bca6596ea3e6387b4c580f","abstract_canon_sha256":"5d50915558c6a656a52b3296d21e4f22c6070fd5e94862aac8a081f556f094f2"},"schema_version":"1.0"},"canonical_sha256":"138d0611a03eed4586f6a8d45c0c93143b27e8df4eb39710df0865556832fdf7","source":{"kind":"arxiv","id":"1308.3316","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.3316","created_at":"2026-05-18T03:15:55Z"},{"alias_kind":"arxiv_version","alias_value":"1308.3316v1","created_at":"2026-05-18T03:15:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.3316","created_at":"2026-05-18T03:15:55Z"},{"alias_kind":"pith_short_12","alias_value":"COGQMENAH3WU","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"COGQMENAH3WULBXW","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"COGQMENA","created_at":"2026-05-18T12:27:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:COGQMENAH3WULBXWVDKFYDETCQ","target":"record","payload":{"canonical_record":{"source":{"id":"1308.3316","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-08-15T06:17:02Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"ba3845cde7ab2cb7d7fc2f5f0cb6c95343876ca3c5bca6596ea3e6387b4c580f","abstract_canon_sha256":"5d50915558c6a656a52b3296d21e4f22c6070fd5e94862aac8a081f556f094f2"},"schema_version":"1.0"},"canonical_sha256":"138d0611a03eed4586f6a8d45c0c93143b27e8df4eb39710df0865556832fdf7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:15:55.064727Z","signature_b64":"9/11LHwj8MNtZWpHrrq0UG8nkgafRv5ok+RH/cblOY5GEiAL7sUL/+sKVj637MGBdkEl4mdRTRAzN7olef3oAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"138d0611a03eed4586f6a8d45c0c93143b27e8df4eb39710df0865556832fdf7","last_reissued_at":"2026-05-18T03:15:55.063997Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:15:55.063997Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.3316","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":"2026-05-18T03:15:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2g1TgTQeDQrmUQarZ5kpJ3uJO4h4rWIylFoMoJWT8ERnIUfcK22tp3KSccA8ksGADrmDZgvrOsxuqZ2/9MypBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T13:27:06.235356Z"},"content_sha256":"b777b851e91055f9a9747347a219b13503185966a241f223909ae835cb8c5b64","schema_version":"1.0","event_id":"sha256:b777b851e91055f9a9747347a219b13503185966a241f223909ae835cb8c5b64"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:COGQMENAH3WULBXWVDKFYDETCQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Remarks on the plus-minus weighted Davenport constant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Luz Elimar Marchan, Oscar Ordaz, Wolfgang Schmid (LAGA)","submitted_at":"2013-08-15T06:17:02Z","abstract_excerpt":"For $(G,+)$ a finite abelian group the plus-minus weighted Davenport constant, denoted $\\mathsf{D}_{\\pm}(G)$, is the smallest $\\ell$ such that each sequence $g_1 ... g_{\\ell}$ over $G$ has a weighted zero-subsum with weights +1 and -1, i.e., there is a non-empty subset $I \\subset \\{1,..., \\ell\\}$ such that $\\sum_{i \\in I} a_i g_i =0$ for $a_i \\in \\{+1,-1\\}$. We present new bounds for this constant, mainly lower bounds, and also obtain the exact value of this constant for various additional types of groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.3316","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":"2026-05-18T03:15:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K1WE6/bDPcLW4W+JpPVH7XmlfinX7w1EePDr5mC7Yyv+aC8BR5TAdU2t4T5wsDQMtFdAGQTdnXpgLjFkV1yzBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T13:27:06.236079Z"},"content_sha256":"8586a0127d14197beaf4338dc025fc00993d0804bf37d9e6f50c7b04efd57633","schema_version":"1.0","event_id":"sha256:8586a0127d14197beaf4338dc025fc00993d0804bf37d9e6f50c7b04efd57633"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/COGQMENAH3WULBXWVDKFYDETCQ/bundle.json","state_url":"https://pith.science/pith/COGQMENAH3WULBXWVDKFYDETCQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/COGQMENAH3WULBXWVDKFYDETCQ/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":"2026-05-27T13:27:06Z","links":{"resolver":"https://pith.science/pith/COGQMENAH3WULBXWVDKFYDETCQ","bundle":"https://pith.science/pith/COGQMENAH3WULBXWVDKFYDETCQ/bundle.json","state":"https://pith.science/pith/COGQMENAH3WULBXWVDKFYDETCQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/COGQMENAH3WULBXWVDKFYDETCQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:COGQMENAH3WULBXWVDKFYDETCQ","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":"5d50915558c6a656a52b3296d21e4f22c6070fd5e94862aac8a081f556f094f2","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-08-15T06:17:02Z","title_canon_sha256":"ba3845cde7ab2cb7d7fc2f5f0cb6c95343876ca3c5bca6596ea3e6387b4c580f"},"schema_version":"1.0","source":{"id":"1308.3316","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.3316","created_at":"2026-05-18T03:15:55Z"},{"alias_kind":"arxiv_version","alias_value":"1308.3316v1","created_at":"2026-05-18T03:15:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.3316","created_at":"2026-05-18T03:15:55Z"},{"alias_kind":"pith_short_12","alias_value":"COGQMENAH3WU","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"COGQMENAH3WULBXW","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"COGQMENA","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:8586a0127d14197beaf4338dc025fc00993d0804bf37d9e6f50c7b04efd57633","target":"graph","created_at":"2026-05-18T03:15:55Z","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":"For $(G,+)$ a finite abelian group the plus-minus weighted Davenport constant, denoted $\\mathsf{D}_{\\pm}(G)$, is the smallest $\\ell$ such that each sequence $g_1 ... g_{\\ell}$ over $G$ has a weighted zero-subsum with weights +1 and -1, i.e., there is a non-empty subset $I \\subset \\{1,..., \\ell\\}$ such that $\\sum_{i \\in I} a_i g_i =0$ for $a_i \\in \\{+1,-1\\}$. We present new bounds for this constant, mainly lower bounds, and also obtain the exact value of this constant for various additional types of groups.","authors_text":"Luz Elimar Marchan, Oscar Ordaz, Wolfgang Schmid (LAGA)","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-08-15T06:17:02Z","title":"Remarks on the plus-minus weighted Davenport constant"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.3316","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:b777b851e91055f9a9747347a219b13503185966a241f223909ae835cb8c5b64","target":"record","created_at":"2026-05-18T03:15:55Z","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":"5d50915558c6a656a52b3296d21e4f22c6070fd5e94862aac8a081f556f094f2","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-08-15T06:17:02Z","title_canon_sha256":"ba3845cde7ab2cb7d7fc2f5f0cb6c95343876ca3c5bca6596ea3e6387b4c580f"},"schema_version":"1.0","source":{"id":"1308.3316","kind":"arxiv","version":1}},"canonical_sha256":"138d0611a03eed4586f6a8d45c0c93143b27e8df4eb39710df0865556832fdf7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"138d0611a03eed4586f6a8d45c0c93143b27e8df4eb39710df0865556832fdf7","first_computed_at":"2026-05-18T03:15:55.063997Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:15:55.063997Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9/11LHwj8MNtZWpHrrq0UG8nkgafRv5ok+RH/cblOY5GEiAL7sUL/+sKVj637MGBdkEl4mdRTRAzN7olef3oAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:15:55.064727Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.3316","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b777b851e91055f9a9747347a219b13503185966a241f223909ae835cb8c5b64","sha256:8586a0127d14197beaf4338dc025fc00993d0804bf37d9e6f50c7b04efd57633"],"state_sha256":"ad725c5e688d57ed11e35bcd2bfac40380c51b7c04e574b2ee977bb31d06fa36"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kOKBbJmBgNY1RRgNyvir9xb09XQndj7eDDWnGEFPYRuoNyQ1mO5nhGSF7khQjtoo8v4gQTB9tINA4Oo27tfdBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T13:27:06.239895Z","bundle_sha256":"52ba7e607b284c7b790edcf0b5627fcbed5dbf3f1bc71829484789477e7116de"}}