{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:TEF3AUXFOJZVU5UZI3PKC4JCDO","short_pith_number":"pith:TEF3AUXF","canonical_record":{"source":{"id":"2607.26690","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DM","submitted_at":"2026-07-29T09:39:19Z","cross_cats_sorted":[],"title_canon_sha256":"5544424634ef3d9a379f47ba261211e9067b948411a4d20d9c771bc8c4e0425e","abstract_canon_sha256":"20f17261d2fbc70e0a89849da59c43df1c6559a7d27e1c7b59c6cbb2a68a073b"},"schema_version":"1.0"},"canonical_sha256":"990bb052e572735a769946dea171221bbb8de27948e25d197d15dca33e9c2324","source":{"kind":"arxiv","id":"2607.26690","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.26690","created_at":"2026-07-30T01:21:56Z"},{"alias_kind":"arxiv_version","alias_value":"2607.26690v1","created_at":"2026-07-30T01:21:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.26690","created_at":"2026-07-30T01:21:56Z"},{"alias_kind":"pith_short_12","alias_value":"TEF3AUXFOJZV","created_at":"2026-07-30T01:21:56Z"},{"alias_kind":"pith_short_16","alias_value":"TEF3AUXFOJZVU5UZ","created_at":"2026-07-30T01:21:56Z"},{"alias_kind":"pith_short_8","alias_value":"TEF3AUXF","created_at":"2026-07-30T01:21:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:TEF3AUXFOJZVU5UZI3PKC4JCDO","target":"record","payload":{"canonical_record":{"source":{"id":"2607.26690","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DM","submitted_at":"2026-07-29T09:39:19Z","cross_cats_sorted":[],"title_canon_sha256":"5544424634ef3d9a379f47ba261211e9067b948411a4d20d9c771bc8c4e0425e","abstract_canon_sha256":"20f17261d2fbc70e0a89849da59c43df1c6559a7d27e1c7b59c6cbb2a68a073b"},"schema_version":"1.0"},"canonical_sha256":"990bb052e572735a769946dea171221bbb8de27948e25d197d15dca33e9c2324","receipt":{"kind":"pith_receipt","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"990bb052e572735a769946dea171221bbb8de27948e25d197d15dca33e9c2324","last_reissued_at":"2026-07-30T01:21:56.831495Z","signature_status":"unsigned_v0","first_computed_at":"2026-07-30T01:21:56.831495Z"},"source_kind":"arxiv","source_id":"2607.26690","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":"2026-07-30T01:21:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SOtDBrBCQ3j/qKuelbxq3l1tr1/bl8B6hMNA9lMnmMugwHNs5tZ4+yNd7VJcNkDXYymilFUh/jzTLDdmLsLjDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T06:56:19.242442Z"},"content_sha256":"86dc502e98c8da115bb3b2a097e6aace1c71ac4e31b46797643339ed29fb24ff","schema_version":"1.0","event_id":"sha256:86dc502e98c8da115bb3b2a097e6aace1c71ac4e31b46797643339ed29fb24ff"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:TEF3AUXFOJZVU5UZI3PKC4JCDO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tournaments determined by three and five voters","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Ararat Harutyunyan, Leonid Chindelevitch","submitted_at":"2026-07-29T09:39:19Z","abstract_excerpt":"The Kemeny median problem asks for a linear order minimizing the total pairwise disagreement with $m$ given rankings of $n$ options; it is NP-hard for every even $m \\ge 4$ and every odd $m \\ge 7$, while $m = 3$ and $m = 5$ remain open. Weighting each arc of the majority tournament by its margin reduces the problem to minimum-weight feedback arc set (FAS). The fewest voters inducing a tournament is its McGarvey number, and its predictability $\\alpha^{*}(T)$ is the largest supermajority threshold at which $T$ is inducible.\n  We refute three conjectures on inducibility. (i) In any tournament, eve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.26690","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.26690/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":"2026-07-30T01:21:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HWh0wC7UAm/wXxbB3hAdX68ozlbnBdV3eEAq9bxNr6Y8qmlvt1SsnAMSNyMQtyuFAGzquoZRuAS/7ArTpWShAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T06:56:19.242944Z"},"content_sha256":"76c12c21117fe03e7972f7721bcdb94d3cb7dcf6da46f9e59bd972a7c63c5b5d","schema_version":"1.0","event_id":"sha256:76c12c21117fe03e7972f7721bcdb94d3cb7dcf6da46f9e59bd972a7c63c5b5d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TEF3AUXFOJZVU5UZI3PKC4JCDO/bundle.json","state_url":"https://pith.science/pith/TEF3AUXFOJZVU5UZI3PKC4JCDO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TEF3AUXFOJZVU5UZI3PKC4JCDO/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":"2026-08-04T06:56:19Z","links":{"resolver":"https://pith.science/pith/TEF3AUXFOJZVU5UZI3PKC4JCDO","bundle":"https://pith.science/pith/TEF3AUXFOJZVU5UZI3PKC4JCDO/bundle.json","state":"https://pith.science/pith/TEF3AUXFOJZVU5UZI3PKC4JCDO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TEF3AUXFOJZVU5UZI3PKC4JCDO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:TEF3AUXFOJZVU5UZI3PKC4JCDO","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":"20f17261d2fbc70e0a89849da59c43df1c6559a7d27e1c7b59c6cbb2a68a073b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DM","submitted_at":"2026-07-29T09:39:19Z","title_canon_sha256":"5544424634ef3d9a379f47ba261211e9067b948411a4d20d9c771bc8c4e0425e"},"schema_version":"1.0","source":{"id":"2607.26690","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.26690","created_at":"2026-07-30T01:21:56Z"},{"alias_kind":"arxiv_version","alias_value":"2607.26690v1","created_at":"2026-07-30T01:21:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.26690","created_at":"2026-07-30T01:21:56Z"},{"alias_kind":"pith_short_12","alias_value":"TEF3AUXFOJZV","created_at":"2026-07-30T01:21:56Z"},{"alias_kind":"pith_short_16","alias_value":"TEF3AUXFOJZVU5UZ","created_at":"2026-07-30T01:21:56Z"},{"alias_kind":"pith_short_8","alias_value":"TEF3AUXF","created_at":"2026-07-30T01:21:56Z"}],"graph_snapshots":[{"event_id":"sha256:76c12c21117fe03e7972f7721bcdb94d3cb7dcf6da46f9e59bd972a7c63c5b5d","target":"graph","created_at":"2026-07-30T01:21:56Z","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/2607.26690/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Kemeny median problem asks for a linear order minimizing the total pairwise disagreement with $m$ given rankings of $n$ options; it is NP-hard for every even $m \\ge 4$ and every odd $m \\ge 7$, while $m = 3$ and $m = 5$ remain open. Weighting each arc of the majority tournament by its margin reduces the problem to minimum-weight feedback arc set (FAS). The fewest voters inducing a tournament is its McGarvey number, and its predictability $\\alpha^{*}(T)$ is the largest supermajority threshold at which $T$ is inducible.\n  We refute three conjectures on inducibility. (i) In any tournament, eve","authors_text":"Ararat Harutyunyan, Leonid Chindelevitch","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DM","submitted_at":"2026-07-29T09:39:19Z","title":"Tournaments determined by three and five voters"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.26690","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":"sha256:86dc502e98c8da115bb3b2a097e6aace1c71ac4e31b46797643339ed29fb24ff","target":"record","created_at":"2026-07-30T01:21:56Z","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":"20f17261d2fbc70e0a89849da59c43df1c6559a7d27e1c7b59c6cbb2a68a073b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DM","submitted_at":"2026-07-29T09:39:19Z","title_canon_sha256":"5544424634ef3d9a379f47ba261211e9067b948411a4d20d9c771bc8c4e0425e"},"schema_version":"1.0","source":{"id":"2607.26690","kind":"arxiv","version":1}},"canonical_sha256":"990bb052e572735a769946dea171221bbb8de27948e25d197d15dca33e9c2324","receipt":{"builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"990bb052e572735a769946dea171221bbb8de27948e25d197d15dca33e9c2324","first_computed_at":"2026-07-30T01:21:56.831495Z","kind":"pith_receipt","last_reissued_at":"2026-07-30T01:21:56.831495Z","receipt_version":"0.3","signature_status":"unsigned_v0"},"source_id":"2607.26690","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:86dc502e98c8da115bb3b2a097e6aace1c71ac4e31b46797643339ed29fb24ff","sha256:76c12c21117fe03e7972f7721bcdb94d3cb7dcf6da46f9e59bd972a7c63c5b5d"],"state_sha256":"e17e37081c3f70340e60f45b603d0ec1cb93c93f4f26a32009704d4fdea61d91"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vEw0qumrHM7TQgGtC4eJ/l/TV3PBzOCeC+W2OfmSNs8455Ro6XeEv6k84opJ+Krv9W6i+/f+YK0j1M+UIVZeBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T06:56:19.247840Z","bundle_sha256":"6aeb877878cc953ab081aaf398ce158cc21c55611046572ffd1a991351be48f4"}}