{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:IZ5IQD7YFDE55E54FPDAEPYHMR","short_pith_number":"pith:IZ5IQD7Y","canonical_record":{"source":{"id":"1004.0253","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-04-01T23:17:57Z","cross_cats_sorted":["math.GR","math.NT"],"title_canon_sha256":"218ffe09f20544cc30902fa44a2bc87d14c257aff0ab72da980ad8cb4835cd27","abstract_canon_sha256":"7f960e30d8a12450dd198b7e98eb01f760924de65773803643e00804f1f7f648"},"schema_version":"1.0"},"canonical_sha256":"467a880ff828c9de93bc2bc6023f07647b4ace5feb97571731f40b12e67c1d20","source":{"kind":"arxiv","id":"1004.0253","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.0253","created_at":"2026-05-18T04:23:35Z"},{"alias_kind":"arxiv_version","alias_value":"1004.0253v2","created_at":"2026-05-18T04:23:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.0253","created_at":"2026-05-18T04:23:35Z"},{"alias_kind":"pith_short_12","alias_value":"IZ5IQD7YFDE5","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"IZ5IQD7YFDE55E54","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"IZ5IQD7Y","created_at":"2026-05-18T12:26:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:IZ5IQD7YFDE55E54FPDAEPYHMR","target":"record","payload":{"canonical_record":{"source":{"id":"1004.0253","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-04-01T23:17:57Z","cross_cats_sorted":["math.GR","math.NT"],"title_canon_sha256":"218ffe09f20544cc30902fa44a2bc87d14c257aff0ab72da980ad8cb4835cd27","abstract_canon_sha256":"7f960e30d8a12450dd198b7e98eb01f760924de65773803643e00804f1f7f648"},"schema_version":"1.0"},"canonical_sha256":"467a880ff828c9de93bc2bc6023f07647b4ace5feb97571731f40b12e67c1d20","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:23:35.244820Z","signature_b64":"dBAgesq4a/5e79eQYMl7ZsrFMnFjKc1y9lt0E0edIzgEhq5pfKdL4t7RT3M48/FjID/gkXXovNHujgWmEFwYAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"467a880ff828c9de93bc2bc6023f07647b4ace5feb97571731f40b12e67c1d20","last_reissued_at":"2026-05-18T04:23:35.243979Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:23:35.243979Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1004.0253","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:23:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0XzrUqiQc8UoTz88Qv8SOA2Iv3gSopIcs3crrTLRP1SQfRDchPhlbgHEjHsX4+ECj2brmts/GWd1Mm6Qocv0CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:29:33.735816Z"},"content_sha256":"7a70f88b85f94e0293fe362743bff1c57be1e2b4a9e365396196b3f4c3d91653","schema_version":"1.0","event_id":"sha256:7a70f88b85f94e0293fe362743bff1c57be1e2b4a9e365396196b3f4c3d91653"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:IZ5IQD7YFDE55E54FPDAEPYHMR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Remarks to Arsovski's proof of Snevily's conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.NT"],"primary_cat":"math.CO","authors_text":"Gergely Harcos, G\\'eza K\\'os, Gyula K\\'arolyi","submitted_at":"2010-04-01T23:17:57Z","abstract_excerpt":"Based on the recent work of Arsovski, we confirm a conjecture of Feng, Sun, and Xiang, and we give a shortened proof of Snevily's conjecture."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.0253","kind":"arxiv","version":2},"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":"2026-05-18T04:23:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8tLC9Y62OxKhsBrByNuOjJz0Nrn3YHRyARmBGap/2J31HpULgkEh4e+adSEZPCzPgmbWv0v/5ygBaEmdroZ5AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:29:33.736451Z"},"content_sha256":"f73d9d4e4b5c79cff09f7d5f6e8147aa00ef8c2eb8796d54cf564ff166db30ba","schema_version":"1.0","event_id":"sha256:f73d9d4e4b5c79cff09f7d5f6e8147aa00ef8c2eb8796d54cf564ff166db30ba"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IZ5IQD7YFDE55E54FPDAEPYHMR/bundle.json","state_url":"https://pith.science/pith/IZ5IQD7YFDE55E54FPDAEPYHMR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IZ5IQD7YFDE55E54FPDAEPYHMR/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":"2026-05-30T08:29:33Z","links":{"resolver":"https://pith.science/pith/IZ5IQD7YFDE55E54FPDAEPYHMR","bundle":"https://pith.science/pith/IZ5IQD7YFDE55E54FPDAEPYHMR/bundle.json","state":"https://pith.science/pith/IZ5IQD7YFDE55E54FPDAEPYHMR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IZ5IQD7YFDE55E54FPDAEPYHMR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:IZ5IQD7YFDE55E54FPDAEPYHMR","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":"7f960e30d8a12450dd198b7e98eb01f760924de65773803643e00804f1f7f648","cross_cats_sorted":["math.GR","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-04-01T23:17:57Z","title_canon_sha256":"218ffe09f20544cc30902fa44a2bc87d14c257aff0ab72da980ad8cb4835cd27"},"schema_version":"1.0","source":{"id":"1004.0253","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.0253","created_at":"2026-05-18T04:23:35Z"},{"alias_kind":"arxiv_version","alias_value":"1004.0253v2","created_at":"2026-05-18T04:23:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.0253","created_at":"2026-05-18T04:23:35Z"},{"alias_kind":"pith_short_12","alias_value":"IZ5IQD7YFDE5","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"IZ5IQD7YFDE55E54","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"IZ5IQD7Y","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:f73d9d4e4b5c79cff09f7d5f6e8147aa00ef8c2eb8796d54cf564ff166db30ba","target":"graph","created_at":"2026-05-18T04:23:35Z","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":"Based on the recent work of Arsovski, we confirm a conjecture of Feng, Sun, and Xiang, and we give a shortened proof of Snevily's conjecture.","authors_text":"Gergely Harcos, G\\'eza K\\'os, Gyula K\\'arolyi","cross_cats":["math.GR","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-04-01T23:17:57Z","title":"Remarks to Arsovski's proof of Snevily's conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.0253","kind":"arxiv","version":2},"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":"sha256:7a70f88b85f94e0293fe362743bff1c57be1e2b4a9e365396196b3f4c3d91653","target":"record","created_at":"2026-05-18T04:23:35Z","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":"7f960e30d8a12450dd198b7e98eb01f760924de65773803643e00804f1f7f648","cross_cats_sorted":["math.GR","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-04-01T23:17:57Z","title_canon_sha256":"218ffe09f20544cc30902fa44a2bc87d14c257aff0ab72da980ad8cb4835cd27"},"schema_version":"1.0","source":{"id":"1004.0253","kind":"arxiv","version":2}},"canonical_sha256":"467a880ff828c9de93bc2bc6023f07647b4ace5feb97571731f40b12e67c1d20","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"467a880ff828c9de93bc2bc6023f07647b4ace5feb97571731f40b12e67c1d20","first_computed_at":"2026-05-18T04:23:35.243979Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:23:35.243979Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dBAgesq4a/5e79eQYMl7ZsrFMnFjKc1y9lt0E0edIzgEhq5pfKdL4t7RT3M48/FjID/gkXXovNHujgWmEFwYAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:23:35.244820Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.0253","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a70f88b85f94e0293fe362743bff1c57be1e2b4a9e365396196b3f4c3d91653","sha256:f73d9d4e4b5c79cff09f7d5f6e8147aa00ef8c2eb8796d54cf564ff166db30ba"],"state_sha256":"bfaa4d69c58228263c44c1ad791fee21f6d74ddf62014d504698e5fc1d0759f4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PHULfRevNO8w91FgheJUWB39RQnA/2pca7jUWzTs6qDl97etQ6q8BgG7onVafBdVlh2ZFwaOhbnG1ouq7FMvDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T08:29:33.739609Z","bundle_sha256":"e92823268bd8a02c19501a1bfdb60c32c4237266024841a2667085cfff13782f"}}