{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:I4T5JGP6QUWUT3WLFCADHIHFDU","short_pith_number":"pith:I4T5JGP6","schema_version":"1.0","canonical_sha256":"4727d499fe852d49eecb288033a0e51d0760f2f052122cc368b124b0e512d9d1","source":{"kind":"arxiv","id":"2606.30433","version":1},"attestation_state":"computed","paper":{"title":"Testing k-submodularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Diptaksho Palit, Themistoklis Haris","submitted_at":"2026-06-29T15:11:18Z","abstract_excerpt":"We initiate the study of property testing for $k$-submodular functions, a higher-dimensional analogue of submodular functions defined on partial partitions of a ground set. While $k$-submodularity retains the diminishing-returns flavor of ordinary submodularity, it also introduces a pairwise monotonicity constraint comparing competing assignments of the same element. This additional local structure makes the testing problem qualitatively different from the classical case.\n  Our results show a sharp contrast between distance regimes. In the $\\ell_p$ regime for $p \\geq 1$, we prove that every bo"},"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":"2606.30433","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-06-29T15:11:18Z","cross_cats_sorted":[],"title_canon_sha256":"62c5a62f7d09fd6fdf43dc2099c0b54458b16d25f565409458ab8f77ca2a62ac","abstract_canon_sha256":"8e63848a0a30340546d3bcb7483b339065953bd976945852de63325a2f86fa70"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-30T02:18:15.014224Z","signature_b64":"/qcvhACW99UUHP0z1sxl1+Wyo04cZKVyYRR64gngrLXbSUTO+C04c58G+F7Nt8jWku6Gr9fUD2+9HBbycwzFCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4727d499fe852d49eecb288033a0e51d0760f2f052122cc368b124b0e512d9d1","last_reissued_at":"2026-06-30T02:18:15.013615Z","signature_status":"signed_v1","first_computed_at":"2026-06-30T02:18:15.013615Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Testing k-submodularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Diptaksho Palit, Themistoklis Haris","submitted_at":"2026-06-29T15:11:18Z","abstract_excerpt":"We initiate the study of property testing for $k$-submodular functions, a higher-dimensional analogue of submodular functions defined on partial partitions of a ground set. While $k$-submodularity retains the diminishing-returns flavor of ordinary submodularity, it also introduces a pairwise monotonicity constraint comparing competing assignments of the same element. This additional local structure makes the testing problem qualitatively different from the classical case.\n  Our results show a sharp contrast between distance regimes. In the $\\ell_p$ regime for $p \\geq 1$, we prove that every bo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30433","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/2606.30433/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":"2606.30433","created_at":"2026-06-30T02:18:15.013704+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.30433v1","created_at":"2026-06-30T02:18:15.013704+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.30433","created_at":"2026-06-30T02:18:15.013704+00:00"},{"alias_kind":"pith_short_12","alias_value":"I4T5JGP6QUWU","created_at":"2026-06-30T02:18:15.013704+00:00"},{"alias_kind":"pith_short_16","alias_value":"I4T5JGP6QUWUT3WL","created_at":"2026-06-30T02:18:15.013704+00:00"},{"alias_kind":"pith_short_8","alias_value":"I4T5JGP6","created_at":"2026-06-30T02:18:15.013704+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/I4T5JGP6QUWUT3WLFCADHIHFDU","json":"https://pith.science/pith/I4T5JGP6QUWUT3WLFCADHIHFDU.json","graph_json":"https://pith.science/api/pith-number/I4T5JGP6QUWUT3WLFCADHIHFDU/graph.json","events_json":"https://pith.science/api/pith-number/I4T5JGP6QUWUT3WLFCADHIHFDU/events.json","paper":"https://pith.science/paper/I4T5JGP6"},"agent_actions":{"view_html":"https://pith.science/pith/I4T5JGP6QUWUT3WLFCADHIHFDU","download_json":"https://pith.science/pith/I4T5JGP6QUWUT3WLFCADHIHFDU.json","view_paper":"https://pith.science/paper/I4T5JGP6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.30433&json=true","fetch_graph":"https://pith.science/api/pith-number/I4T5JGP6QUWUT3WLFCADHIHFDU/graph.json","fetch_events":"https://pith.science/api/pith-number/I4T5JGP6QUWUT3WLFCADHIHFDU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I4T5JGP6QUWUT3WLFCADHIHFDU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I4T5JGP6QUWUT3WLFCADHIHFDU/action/storage_attestation","attest_author":"https://pith.science/pith/I4T5JGP6QUWUT3WLFCADHIHFDU/action/author_attestation","sign_citation":"https://pith.science/pith/I4T5JGP6QUWUT3WLFCADHIHFDU/action/citation_signature","submit_replication":"https://pith.science/pith/I4T5JGP6QUWUT3WLFCADHIHFDU/action/replication_record"}},"created_at":"2026-06-30T02:18:15.013704+00:00","updated_at":"2026-06-30T02:18:15.013704+00:00"}