{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:67CCX3GI5S4ASFREOSHSQRLVZF","short_pith_number":"pith:67CCX3GI","canonical_record":{"source":{"id":"1507.05955","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-21T19:59:57Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"aa39967d6a919c0deecd9be375b60dd24e8632a74879bab96ede4905db302671","abstract_canon_sha256":"58c8bdfc6996fd7982e03c3d4ab2d40512b26f38e7544ba0d699f1c6a9e378a6"},"schema_version":"1.0"},"canonical_sha256":"f7c42becc8ecb8091624748f284575c969e5c5786c77e1b3904ac31873d69fc8","source":{"kind":"arxiv","id":"1507.05955","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.05955","created_at":"2026-05-18T01:36:32Z"},{"alias_kind":"arxiv_version","alias_value":"1507.05955v1","created_at":"2026-05-18T01:36:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.05955","created_at":"2026-05-18T01:36:32Z"},{"alias_kind":"pith_short_12","alias_value":"67CCX3GI5S4A","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"67CCX3GI5S4ASFRE","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"67CCX3GI","created_at":"2026-05-18T12:29:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:67CCX3GI5S4ASFREOSHSQRLVZF","target":"record","payload":{"canonical_record":{"source":{"id":"1507.05955","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-21T19:59:57Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"aa39967d6a919c0deecd9be375b60dd24e8632a74879bab96ede4905db302671","abstract_canon_sha256":"58c8bdfc6996fd7982e03c3d4ab2d40512b26f38e7544ba0d699f1c6a9e378a6"},"schema_version":"1.0"},"canonical_sha256":"f7c42becc8ecb8091624748f284575c969e5c5786c77e1b3904ac31873d69fc8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:32.056870Z","signature_b64":"9dQ3w4rAneozp6ZaXH0rAzQ4N9OnpFgeFriDDj/Oc9jmljfiW388KYFlAOWElRKDI2zvAvGblegHNjZPtNzYBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f7c42becc8ecb8091624748f284575c969e5c5786c77e1b3904ac31873d69fc8","last_reissued_at":"2026-05-18T01:36:32.056372Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:32.056372Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.05955","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":"2026-05-18T01:36:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fGa7gOct9ZmlggjBHKMYtqZyvgedjwSq4XyF/lhTc0SnlCE8qyL0HaCPoK5Wv6oOBRyzo13/YiSrJo6Fd0rnAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T13:56:58.826856Z"},"content_sha256":"73923fff0cb09b1cb50c088f99eeedd386390af844f15de74044ffbecbed6fec","schema_version":"1.0","event_id":"sha256:73923fff0cb09b1cb50c088f99eeedd386390af844f15de74044ffbecbed6fec"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:67CCX3GI5S4ASFREOSHSQRLVZF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sorting using non-binary comparisons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"math.CO","authors_text":"Gabor Meszaros, Richard A. B. Johnson","submitted_at":"2015-07-21T19:59:57Z","abstract_excerpt":"In this paper we investigate the problem of sorting a set of $n$ coins, each with distinct but unknown weights, using an unusual scale. The classical version of this problem, which has been well-studied, gives the user a binary scale, enabling them to determine which is the lighter/heavier of any two objects. We generalise this, considering a scale that accepts $k$ coins as input and returns the $t^{\\text{th}}$ lightest, for a fixed $k$ and $t$. We consider this in both an on-line and off-line setting, and exhibit algorithms in both settings that are best-possible in terms of the order of the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05955","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":"2026-05-18T01:36:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u+hiA2+Q4FksNryHV64ltqnhZ61JjOeTIuNNCxgMQJuXcbWXWw/9f3ipHqaOObRHbf2qq7t56nMmI3IyNnfSCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T13:56:58.827207Z"},"content_sha256":"42082bb06ffd2785460338b784db2f96aa3ceb30130cd5a28c10186a850b4b18","schema_version":"1.0","event_id":"sha256:42082bb06ffd2785460338b784db2f96aa3ceb30130cd5a28c10186a850b4b18"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/67CCX3GI5S4ASFREOSHSQRLVZF/bundle.json","state_url":"https://pith.science/pith/67CCX3GI5S4ASFREOSHSQRLVZF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/67CCX3GI5S4ASFREOSHSQRLVZF/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":"2026-06-22T13:56:58Z","links":{"resolver":"https://pith.science/pith/67CCX3GI5S4ASFREOSHSQRLVZF","bundle":"https://pith.science/pith/67CCX3GI5S4ASFREOSHSQRLVZF/bundle.json","state":"https://pith.science/pith/67CCX3GI5S4ASFREOSHSQRLVZF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/67CCX3GI5S4ASFREOSHSQRLVZF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:67CCX3GI5S4ASFREOSHSQRLVZF","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":"58c8bdfc6996fd7982e03c3d4ab2d40512b26f38e7544ba0d699f1c6a9e378a6","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-21T19:59:57Z","title_canon_sha256":"aa39967d6a919c0deecd9be375b60dd24e8632a74879bab96ede4905db302671"},"schema_version":"1.0","source":{"id":"1507.05955","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.05955","created_at":"2026-05-18T01:36:32Z"},{"alias_kind":"arxiv_version","alias_value":"1507.05955v1","created_at":"2026-05-18T01:36:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.05955","created_at":"2026-05-18T01:36:32Z"},{"alias_kind":"pith_short_12","alias_value":"67CCX3GI5S4A","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"67CCX3GI5S4ASFRE","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"67CCX3GI","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:42082bb06ffd2785460338b784db2f96aa3ceb30130cd5a28c10186a850b4b18","target":"graph","created_at":"2026-05-18T01:36:32Z","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":"In this paper we investigate the problem of sorting a set of $n$ coins, each with distinct but unknown weights, using an unusual scale. The classical version of this problem, which has been well-studied, gives the user a binary scale, enabling them to determine which is the lighter/heavier of any two objects. We generalise this, considering a scale that accepts $k$ coins as input and returns the $t^{\\text{th}}$ lightest, for a fixed $k$ and $t$. We consider this in both an on-line and off-line setting, and exhibit algorithms in both settings that are best-possible in terms of the order of the ","authors_text":"Gabor Meszaros, Richard A. B. Johnson","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-21T19:59:57Z","title":"Sorting using non-binary comparisons"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05955","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":"sha256:73923fff0cb09b1cb50c088f99eeedd386390af844f15de74044ffbecbed6fec","target":"record","created_at":"2026-05-18T01:36:32Z","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":"58c8bdfc6996fd7982e03c3d4ab2d40512b26f38e7544ba0d699f1c6a9e378a6","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-21T19:59:57Z","title_canon_sha256":"aa39967d6a919c0deecd9be375b60dd24e8632a74879bab96ede4905db302671"},"schema_version":"1.0","source":{"id":"1507.05955","kind":"arxiv","version":1}},"canonical_sha256":"f7c42becc8ecb8091624748f284575c969e5c5786c77e1b3904ac31873d69fc8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f7c42becc8ecb8091624748f284575c969e5c5786c77e1b3904ac31873d69fc8","first_computed_at":"2026-05-18T01:36:32.056372Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:32.056372Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9dQ3w4rAneozp6ZaXH0rAzQ4N9OnpFgeFriDDj/Oc9jmljfiW388KYFlAOWElRKDI2zvAvGblegHNjZPtNzYBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:32.056870Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.05955","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:73923fff0cb09b1cb50c088f99eeedd386390af844f15de74044ffbecbed6fec","sha256:42082bb06ffd2785460338b784db2f96aa3ceb30130cd5a28c10186a850b4b18"],"state_sha256":"6529144bb87f55d033213c129bdafb723dd501a07968dd3dd5aae45919a1b70d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H2jqDWVJDcKwo2tiO/WIBTSfXidWseyGKajkrJ0CzKg6d8sVKucA2od8UgCC3oGwvzZPYOoNIy49KoMhuJuBAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T13:56:58.829199Z","bundle_sha256":"c8b240b3204d5bcaf22727351e5bdd16885ee648c5ac2efe83ed2b7346e31aaf"}}