{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:JG6RJMHR57LIKWH4E5EC3VEHPA","short_pith_number":"pith:JG6RJMHR","canonical_record":{"source":{"id":"1904.12482","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-04-29T08:02:25Z","cross_cats_sorted":[],"title_canon_sha256":"8e090999e6aa30c7592f937fde8c13023360c95969f15e2a63be7469d587afea","abstract_canon_sha256":"01160008977cd303ad8e44d2f2d71a2bcb6233867544f697763106f388dc2258"},"schema_version":"1.0"},"canonical_sha256":"49bd14b0f1efd68558fc27482dd48778281eb516d7db300aff3c6b4f5350d799","source":{"kind":"arxiv","id":"1904.12482","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.12482","created_at":"2026-05-17T23:47:35Z"},{"alias_kind":"arxiv_version","alias_value":"1904.12482v1","created_at":"2026-05-17T23:47:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.12482","created_at":"2026-05-17T23:47:35Z"},{"alias_kind":"pith_short_12","alias_value":"JG6RJMHR57LI","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"JG6RJMHR57LIKWH4","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"JG6RJMHR","created_at":"2026-05-18T12:33:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:JG6RJMHR57LIKWH4E5EC3VEHPA","target":"record","payload":{"canonical_record":{"source":{"id":"1904.12482","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-04-29T08:02:25Z","cross_cats_sorted":[],"title_canon_sha256":"8e090999e6aa30c7592f937fde8c13023360c95969f15e2a63be7469d587afea","abstract_canon_sha256":"01160008977cd303ad8e44d2f2d71a2bcb6233867544f697763106f388dc2258"},"schema_version":"1.0"},"canonical_sha256":"49bd14b0f1efd68558fc27482dd48778281eb516d7db300aff3c6b4f5350d799","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:35.077050Z","signature_b64":"ARXiN5+LcBJAu7XefCf34fkFCGrjzXWJN6yHbWxZTzTWaC/58rxuqQAH5fgLGodq2uGV37FRXwLYf92CxWPqDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"49bd14b0f1efd68558fc27482dd48778281eb516d7db300aff3c6b4f5350d799","last_reissued_at":"2026-05-17T23:47:35.076561Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:35.076561Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.12482","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":"2026-05-17T23:47:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+GJVVIDQnvVKWXrHuET8ca6L6rNYgOfAHZIDrrYUfIP5RkUmfTXfuTqPjuxL96tyqh4s4wYdrw6qBbv95j9jDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T20:07:02.799160Z"},"content_sha256":"ac140284a4ea53bf6ce8bd4884a412c382731ff091abfeba83a91b0c15f2936c","schema_version":"1.0","event_id":"sha256:ac140284a4ea53bf6ce8bd4884a412c382731ff091abfeba83a91b0c15f2936c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:JG6RJMHR57LIKWH4E5EC3VEHPA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Aggregating Relational Structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Amit Kuber, Harshit Bisht","submitted_at":"2019-04-29T08:02:25Z","abstract_excerpt":"We generalize the Arrow's impossibility theorem--a key result in social choice theory--to the setting where the arity $k$ of the relation under consideration is greater than $2$. Some special but natural properties of $k$-ary relations are considered, as well as an analogue for such $k$-ary relations of Endriss and Grandi's result on graph aggregation is proved."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.12482","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":"2026-05-17T23:47:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e9E28DXwkqE7skrY6zRmF5E6uIaAA17q+NEDWaJdxsypfSltu3cHaSUjlFpA1HxBt4ep825BgOlQuu729Q6kBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T20:07:02.799513Z"},"content_sha256":"afb13c081bb225a1f5aa1a4110d24bae1727aaec5ff1cb00971b583bd4085fe9","schema_version":"1.0","event_id":"sha256:afb13c081bb225a1f5aa1a4110d24bae1727aaec5ff1cb00971b583bd4085fe9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JG6RJMHR57LIKWH4E5EC3VEHPA/bundle.json","state_url":"https://pith.science/pith/JG6RJMHR57LIKWH4E5EC3VEHPA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JG6RJMHR57LIKWH4E5EC3VEHPA/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":"2026-07-03T20:07:02Z","links":{"resolver":"https://pith.science/pith/JG6RJMHR57LIKWH4E5EC3VEHPA","bundle":"https://pith.science/pith/JG6RJMHR57LIKWH4E5EC3VEHPA/bundle.json","state":"https://pith.science/pith/JG6RJMHR57LIKWH4E5EC3VEHPA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JG6RJMHR57LIKWH4E5EC3VEHPA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:JG6RJMHR57LIKWH4E5EC3VEHPA","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":"01160008977cd303ad8e44d2f2d71a2bcb6233867544f697763106f388dc2258","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-04-29T08:02:25Z","title_canon_sha256":"8e090999e6aa30c7592f937fde8c13023360c95969f15e2a63be7469d587afea"},"schema_version":"1.0","source":{"id":"1904.12482","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.12482","created_at":"2026-05-17T23:47:35Z"},{"alias_kind":"arxiv_version","alias_value":"1904.12482v1","created_at":"2026-05-17T23:47:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.12482","created_at":"2026-05-17T23:47:35Z"},{"alias_kind":"pith_short_12","alias_value":"JG6RJMHR57LI","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"JG6RJMHR57LIKWH4","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"JG6RJMHR","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:afb13c081bb225a1f5aa1a4110d24bae1727aaec5ff1cb00971b583bd4085fe9","target":"graph","created_at":"2026-05-17T23:47:35Z","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":"We generalize the Arrow's impossibility theorem--a key result in social choice theory--to the setting where the arity $k$ of the relation under consideration is greater than $2$. Some special but natural properties of $k$-ary relations are considered, as well as an analogue for such $k$-ary relations of Endriss and Grandi's result on graph aggregation is proved.","authors_text":"Amit Kuber, Harshit Bisht","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-04-29T08:02:25Z","title":"Aggregating Relational Structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.12482","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:ac140284a4ea53bf6ce8bd4884a412c382731ff091abfeba83a91b0c15f2936c","target":"record","created_at":"2026-05-17T23:47:35Z","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":"01160008977cd303ad8e44d2f2d71a2bcb6233867544f697763106f388dc2258","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-04-29T08:02:25Z","title_canon_sha256":"8e090999e6aa30c7592f937fde8c13023360c95969f15e2a63be7469d587afea"},"schema_version":"1.0","source":{"id":"1904.12482","kind":"arxiv","version":1}},"canonical_sha256":"49bd14b0f1efd68558fc27482dd48778281eb516d7db300aff3c6b4f5350d799","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"49bd14b0f1efd68558fc27482dd48778281eb516d7db300aff3c6b4f5350d799","first_computed_at":"2026-05-17T23:47:35.076561Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:35.076561Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ARXiN5+LcBJAu7XefCf34fkFCGrjzXWJN6yHbWxZTzTWaC/58rxuqQAH5fgLGodq2uGV37FRXwLYf92CxWPqDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:35.077050Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.12482","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac140284a4ea53bf6ce8bd4884a412c382731ff091abfeba83a91b0c15f2936c","sha256:afb13c081bb225a1f5aa1a4110d24bae1727aaec5ff1cb00971b583bd4085fe9"],"state_sha256":"d76827b441409c2beb2e570ba55749ece8c47b0090273d767f3220b821d701a4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wi7P5UFdo30xPxpHvIOVYjcvMgz8tRk4WSgwY0LUqkljR2EG15RSbQR+svnmdXxOBE6kdgXnNQXc/FajrZXGBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T20:07:02.801401Z","bundle_sha256":"2bbd27f5d3f1a99b35f0a3e98ddae35f7900d778d8f9d830adbe3181f55a986a"}}