{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:SQ7GHEZ2NARK7EMJ5C6NNHGZT3","short_pith_number":"pith:SQ7GHEZ2","schema_version":"1.0","canonical_sha256":"943e63933a6822af9189e8bcd69cd99ec689e51423e5e835e9e1857c6a17a0e7","source":{"kind":"arxiv","id":"2507.10569","version":1},"attestation_state":"computed","paper":{"title":"Metrics on Permutation Families Defined by a Restriction Graph","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Danylo Tymoshenko, Leonhard Nagel","submitted_at":"2025-07-08T22:00:05Z","abstract_excerpt":"Understanding the metric structure of permutation families is fundamental to combinatorics and has applications in social choice theory, bioinformatics, and coding theory. We study permutation families defined by restriction graphs--oriented graphs that constrain the relative order of elements in valid permutations. For any restriction graph $G$, we determine the maximum distance achievable by two permutations under the $\\ell_\\infty$-metric and provide an explicit algorithm that constructs optimal permutation pairs. Our main contribution characterizes when the Kendall-Tau metric achieves its c"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2507.10569","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"cs.DM","submitted_at":"2025-07-08T22:00:05Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"9be8883ca220f3a278f497ad485a0ec1ef4429b7a36018c3ddf5d4b9876dd7b0","abstract_canon_sha256":"a74b6e7f83d99766f2cc2c80bb536298aa7847a66c56909087a8d36e86170d3f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:36:56.769180Z","signature_b64":"IT6e5lFwnXyNsXafCMM4hLrd8A7EqMzUrQzR4p/oNFaOIxP+Tgic3IDdPYQRaeucadX6hmB12B+ZtSqXFcc4Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"943e63933a6822af9189e8bcd69cd99ec689e51423e5e835e9e1857c6a17a0e7","last_reissued_at":"2026-07-05T11:36:56.768646Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:36:56.768646Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Metrics on Permutation Families Defined by a Restriction Graph","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Danylo Tymoshenko, Leonhard Nagel","submitted_at":"2025-07-08T22:00:05Z","abstract_excerpt":"Understanding the metric structure of permutation families is fundamental to combinatorics and has applications in social choice theory, bioinformatics, and coding theory. We study permutation families defined by restriction graphs--oriented graphs that constrain the relative order of elements in valid permutations. For any restriction graph $G$, we determine the maximum distance achievable by two permutations under the $\\ell_\\infty$-metric and provide an explicit algorithm that constructs optimal permutation pairs. Our main contribution characterizes when the Kendall-Tau metric achieves its c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.10569","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/2507.10569/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2507.10569","created_at":"2026-07-05T11:36:56.768709+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.10569v1","created_at":"2026-07-05T11:36:56.768709+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.10569","created_at":"2026-07-05T11:36:56.768709+00:00"},{"alias_kind":"pith_short_12","alias_value":"SQ7GHEZ2NARK","created_at":"2026-07-05T11:36:56.768709+00:00"},{"alias_kind":"pith_short_16","alias_value":"SQ7GHEZ2NARK7EMJ","created_at":"2026-07-05T11:36:56.768709+00:00"},{"alias_kind":"pith_short_8","alias_value":"SQ7GHEZ2","created_at":"2026-07-05T11:36:56.768709+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2504.18690","citing_title":"Black hole mimickers as relativistic stars calculated from the Tolman-Oppenheimer-Volkoff equations","ref_index":31,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/SQ7GHEZ2NARK7EMJ5C6NNHGZT3","json":"https://pith.science/pith/SQ7GHEZ2NARK7EMJ5C6NNHGZT3.json","graph_json":"https://pith.science/api/pith-number/SQ7GHEZ2NARK7EMJ5C6NNHGZT3/graph.json","events_json":"https://pith.science/api/pith-number/SQ7GHEZ2NARK7EMJ5C6NNHGZT3/events.json","paper":"https://pith.science/paper/SQ7GHEZ2"},"agent_actions":{"view_html":"https://pith.science/pith/SQ7GHEZ2NARK7EMJ5C6NNHGZT3","download_json":"https://pith.science/pith/SQ7GHEZ2NARK7EMJ5C6NNHGZT3.json","view_paper":"https://pith.science/paper/SQ7GHEZ2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.10569&json=true","fetch_graph":"https://pith.science/api/pith-number/SQ7GHEZ2NARK7EMJ5C6NNHGZT3/graph.json","fetch_events":"https://pith.science/api/pith-number/SQ7GHEZ2NARK7EMJ5C6NNHGZT3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SQ7GHEZ2NARK7EMJ5C6NNHGZT3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SQ7GHEZ2NARK7EMJ5C6NNHGZT3/action/storage_attestation","attest_author":"https://pith.science/pith/SQ7GHEZ2NARK7EMJ5C6NNHGZT3/action/author_attestation","sign_citation":"https://pith.science/pith/SQ7GHEZ2NARK7EMJ5C6NNHGZT3/action/citation_signature","submit_replication":"https://pith.science/pith/SQ7GHEZ2NARK7EMJ5C6NNHGZT3/action/replication_record"}},"created_at":"2026-07-05T11:36:56.768709+00:00","updated_at":"2026-07-05T11:36:56.768709+00:00"}