{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:CEJXHPDBSHJ4ZMKMEIQ6W4OFHG","short_pith_number":"pith:CEJXHPDB","canonical_record":{"source":{"id":"1304.6838","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-04-25T09:12:30Z","cross_cats_sorted":[],"title_canon_sha256":"404ac7e4181e92c46780981009348f85381b22b9d204096410208cead2f943eb","abstract_canon_sha256":"2cc20098c1e273c41db1fb316eb35ace43ee8efa2e1181792e3bcaff802f518b"},"schema_version":"1.0"},"canonical_sha256":"111373bc6191d3ccb14c2221eb71c539b97a874e81ef667a31f0ba3d21bfeabe","source":{"kind":"arxiv","id":"1304.6838","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.6838","created_at":"2026-05-18T03:27:10Z"},{"alias_kind":"arxiv_version","alias_value":"1304.6838v1","created_at":"2026-05-18T03:27:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.6838","created_at":"2026-05-18T03:27:10Z"},{"alias_kind":"pith_short_12","alias_value":"CEJXHPDBSHJ4","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"CEJXHPDBSHJ4ZMKM","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"CEJXHPDB","created_at":"2026-05-18T12:27:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:CEJXHPDBSHJ4ZMKMEIQ6W4OFHG","target":"record","payload":{"canonical_record":{"source":{"id":"1304.6838","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-04-25T09:12:30Z","cross_cats_sorted":[],"title_canon_sha256":"404ac7e4181e92c46780981009348f85381b22b9d204096410208cead2f943eb","abstract_canon_sha256":"2cc20098c1e273c41db1fb316eb35ace43ee8efa2e1181792e3bcaff802f518b"},"schema_version":"1.0"},"canonical_sha256":"111373bc6191d3ccb14c2221eb71c539b97a874e81ef667a31f0ba3d21bfeabe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:10.983613Z","signature_b64":"OcsfpsHWQYHE0NTw2BhvG2bnNqh7Is9u8ejbkYjCVB9TepMiqVim6AiATyo+YVYcGs5jfIMXXcGqMQBx1fksDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"111373bc6191d3ccb14c2221eb71c539b97a874e81ef667a31f0ba3d21bfeabe","last_reissued_at":"2026-05-18T03:27:10.982918Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:10.982918Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.6838","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":"2026-05-18T03:27:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ODzv0pchtSCtEB+y9xEFIimDNpR7Sk7G0CJmONp5hRbAZXmUHs6u2sxPRHhLVMJLLrH1E2vF1An249BpJHPNBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T13:00:11.852377Z"},"content_sha256":"70fa3f2758e460e8fe9cf74adc14a3129cc5e13f8b790275220c64112482aab5","schema_version":"1.0","event_id":"sha256:70fa3f2758e460e8fe9cf74adc14a3129cc5e13f8b790275220c64112482aab5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:CEJXHPDBSHJ4ZMKMEIQ6W4OFHG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On additive complement of a finite set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Csaba S\\'andor, Eszter Rozgonyi, S\\'andor Z. Kiss","submitted_at":"2013-04-25T09:12:30Z","abstract_excerpt":"We say the sets of nonnegative integers A and B are additive complements if their sum contains all sufficiently large integers. In this paper we prove a conjecture of Chen and Fang about additive complement of a finite set."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.6838","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":"2026-05-18T03:27:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m20S1R2OJoj9+4l4oJ20eFZ9JQlCjPY9DvCO4YisOOAipmTqov4NSRwmKppLZptt8r98NLlu1bi2sAWennlsAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T13:00:11.852726Z"},"content_sha256":"fab0d561df7ee4a3c00dcabc6867aae75e5db7c1bee8cfdfa8dafdc1aa2ebf0d","schema_version":"1.0","event_id":"sha256:fab0d561df7ee4a3c00dcabc6867aae75e5db7c1bee8cfdfa8dafdc1aa2ebf0d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CEJXHPDBSHJ4ZMKMEIQ6W4OFHG/bundle.json","state_url":"https://pith.science/pith/CEJXHPDBSHJ4ZMKMEIQ6W4OFHG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CEJXHPDBSHJ4ZMKMEIQ6W4OFHG/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":"2026-06-22T13:00:11Z","links":{"resolver":"https://pith.science/pith/CEJXHPDBSHJ4ZMKMEIQ6W4OFHG","bundle":"https://pith.science/pith/CEJXHPDBSHJ4ZMKMEIQ6W4OFHG/bundle.json","state":"https://pith.science/pith/CEJXHPDBSHJ4ZMKMEIQ6W4OFHG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CEJXHPDBSHJ4ZMKMEIQ6W4OFHG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:CEJXHPDBSHJ4ZMKMEIQ6W4OFHG","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":"2cc20098c1e273c41db1fb316eb35ace43ee8efa2e1181792e3bcaff802f518b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-04-25T09:12:30Z","title_canon_sha256":"404ac7e4181e92c46780981009348f85381b22b9d204096410208cead2f943eb"},"schema_version":"1.0","source":{"id":"1304.6838","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.6838","created_at":"2026-05-18T03:27:10Z"},{"alias_kind":"arxiv_version","alias_value":"1304.6838v1","created_at":"2026-05-18T03:27:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.6838","created_at":"2026-05-18T03:27:10Z"},{"alias_kind":"pith_short_12","alias_value":"CEJXHPDBSHJ4","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"CEJXHPDBSHJ4ZMKM","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"CEJXHPDB","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:fab0d561df7ee4a3c00dcabc6867aae75e5db7c1bee8cfdfa8dafdc1aa2ebf0d","target":"graph","created_at":"2026-05-18T03:27:10Z","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":"We say the sets of nonnegative integers A and B are additive complements if their sum contains all sufficiently large integers. In this paper we prove a conjecture of Chen and Fang about additive complement of a finite set.","authors_text":"Csaba S\\'andor, Eszter Rozgonyi, S\\'andor Z. Kiss","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-04-25T09:12:30Z","title":"On additive complement of a finite set"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.6838","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":"sha256:70fa3f2758e460e8fe9cf74adc14a3129cc5e13f8b790275220c64112482aab5","target":"record","created_at":"2026-05-18T03:27:10Z","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":"2cc20098c1e273c41db1fb316eb35ace43ee8efa2e1181792e3bcaff802f518b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-04-25T09:12:30Z","title_canon_sha256":"404ac7e4181e92c46780981009348f85381b22b9d204096410208cead2f943eb"},"schema_version":"1.0","source":{"id":"1304.6838","kind":"arxiv","version":1}},"canonical_sha256":"111373bc6191d3ccb14c2221eb71c539b97a874e81ef667a31f0ba3d21bfeabe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"111373bc6191d3ccb14c2221eb71c539b97a874e81ef667a31f0ba3d21bfeabe","first_computed_at":"2026-05-18T03:27:10.982918Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:27:10.982918Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OcsfpsHWQYHE0NTw2BhvG2bnNqh7Is9u8ejbkYjCVB9TepMiqVim6AiATyo+YVYcGs5jfIMXXcGqMQBx1fksDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:27:10.983613Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.6838","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:70fa3f2758e460e8fe9cf74adc14a3129cc5e13f8b790275220c64112482aab5","sha256:fab0d561df7ee4a3c00dcabc6867aae75e5db7c1bee8cfdfa8dafdc1aa2ebf0d"],"state_sha256":"20705ac13b56a504fab19ebc8536cbc0432044f525695451c5e19222e482d987"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NowmjjGVS4OOiLAqeQ/aKgBTxdxF9OFGnurezWmSs1M33b8p1+ilzZiMGWmckGYvBhYPrMiXNrlpWp76xmEeCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T13:00:11.854661Z","bundle_sha256":"55a29eeecbc8240116e4430b8dcdc1b059688ee2959433eb903f1427998f363f"}}