{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:2E2L5HL46NXMS7POPG3YFF6XXQ","short_pith_number":"pith:2E2L5HL4","schema_version":"1.0","canonical_sha256":"d134be9d7cf36ec97dee79b78297d7bc1cd9d0c384546f9b4402c17081783b19","source":{"kind":"arxiv","id":"1502.02414","version":3},"attestation_state":"computed","paper":{"title":"Tractability and Decompositions of Global Cost Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.AI","authors_text":"Christian Bessiere, David Allouche, Jean-Philippe M\\'etivier, Jimmy H.M. Lee, Kam Lun Leung, Patrice Boizumault, Patricia Gutierrez, Samir Loudni, Simon de Givry, Thomas Schiex, Yi Wu","submitted_at":"2015-02-09T10:09:35Z","abstract_excerpt":"Enforcing local consistencies in cost function networks is performed by applying so-called Equivalent Preserving Transformations (EPTs) to the cost functions. As EPTs transform the cost functions, they may break the property that was making local consistency enforcement tractable on a global cost function. A global cost function is called tractable projection-safe when applying an EPT to it is tractable and does not break the tractability property. In this paper, we prove that depending on the size r of the smallest scopes used for performing EPTs, the tractability of global cost functions can"},"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":"1502.02414","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2015-02-09T10:09:35Z","cross_cats_sorted":[],"title_canon_sha256":"e4ab8f30a0c884d08ffc2c7c10c9bc6c4908ecfb7ecc410183a5cf2173b04dd3","abstract_canon_sha256":"e917178ddd62b8ff82e9deb6dc0c708792a18b6c34e4442fa2dec1d4afa7c9df"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:20.426690Z","signature_b64":"uj3nozM616ZfiLdipa8UT2gDreDB2bspxLmCFqFbFDDE90lJkaZ3vLw+n5m3GxOVBva83TvPM0ksgACyJ+/6BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d134be9d7cf36ec97dee79b78297d7bc1cd9d0c384546f9b4402c17081783b19","last_reissued_at":"2026-05-18T01:10:20.426043Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:20.426043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tractability and Decompositions of Global Cost Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.AI","authors_text":"Christian Bessiere, David Allouche, Jean-Philippe M\\'etivier, Jimmy H.M. Lee, Kam Lun Leung, Patrice Boizumault, Patricia Gutierrez, Samir Loudni, Simon de Givry, Thomas Schiex, Yi Wu","submitted_at":"2015-02-09T10:09:35Z","abstract_excerpt":"Enforcing local consistencies in cost function networks is performed by applying so-called Equivalent Preserving Transformations (EPTs) to the cost functions. As EPTs transform the cost functions, they may break the property that was making local consistency enforcement tractable on a global cost function. A global cost function is called tractable projection-safe when applying an EPT to it is tractable and does not break the tractability property. In this paper, we prove that depending on the size r of the smallest scopes used for performing EPTs, the tractability of global cost functions can"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02414","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1502.02414","created_at":"2026-05-18T01:10:20.426142+00:00"},{"alias_kind":"arxiv_version","alias_value":"1502.02414v3","created_at":"2026-05-18T01:10:20.426142+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.02414","created_at":"2026-05-18T01:10:20.426142+00:00"},{"alias_kind":"pith_short_12","alias_value":"2E2L5HL46NXM","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_16","alias_value":"2E2L5HL46NXMS7PO","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_8","alias_value":"2E2L5HL4","created_at":"2026-05-18T12:28:59.999130+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/2E2L5HL46NXMS7POPG3YFF6XXQ","json":"https://pith.science/pith/2E2L5HL46NXMS7POPG3YFF6XXQ.json","graph_json":"https://pith.science/api/pith-number/2E2L5HL46NXMS7POPG3YFF6XXQ/graph.json","events_json":"https://pith.science/api/pith-number/2E2L5HL46NXMS7POPG3YFF6XXQ/events.json","paper":"https://pith.science/paper/2E2L5HL4"},"agent_actions":{"view_html":"https://pith.science/pith/2E2L5HL46NXMS7POPG3YFF6XXQ","download_json":"https://pith.science/pith/2E2L5HL46NXMS7POPG3YFF6XXQ.json","view_paper":"https://pith.science/paper/2E2L5HL4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1502.02414&json=true","fetch_graph":"https://pith.science/api/pith-number/2E2L5HL46NXMS7POPG3YFF6XXQ/graph.json","fetch_events":"https://pith.science/api/pith-number/2E2L5HL46NXMS7POPG3YFF6XXQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2E2L5HL46NXMS7POPG3YFF6XXQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2E2L5HL46NXMS7POPG3YFF6XXQ/action/storage_attestation","attest_author":"https://pith.science/pith/2E2L5HL46NXMS7POPG3YFF6XXQ/action/author_attestation","sign_citation":"https://pith.science/pith/2E2L5HL46NXMS7POPG3YFF6XXQ/action/citation_signature","submit_replication":"https://pith.science/pith/2E2L5HL46NXMS7POPG3YFF6XXQ/action/replication_record"}},"created_at":"2026-05-18T01:10:20.426142+00:00","updated_at":"2026-05-18T01:10:20.426142+00:00"}