{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:PCQQRAACHFA2DQV4VUN7MBFJDE","short_pith_number":"pith:PCQQRAAC","schema_version":"1.0","canonical_sha256":"78a10880023941a1c2bcad1bf604a91937f7dcb22168c5d96ad7d5b66b541399","source":{"kind":"arxiv","id":"1608.03689","version":2},"attestation_state":"computed","paper":{"title":"Generalized Lexicographic Products and the Index Coding Capacity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Fatemeh Arbabjolfaei, Young-Han Kim","submitted_at":"2016-08-12T06:45:31Z","abstract_excerpt":"The index coding problem studies the fundamental limit on broadcasting multiple messages to their respective receivers with different sets of side information that are represented by a directed graph. The generalized lexicographic product structure in the side information graph is introduced as a natural condition under which the corresponding index coding problem can be decomposed into multiple interacting subproblems. The capacity region is characterized in terms of the subproblem capacity regions combined in the same product structure. The proof is based on dual uses of random coding---one "},"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":"1608.03689","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-08-12T06:45:31Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"6152f4cab861552364fd24d4732d08dcab5e1f7506a91aca03b52f66ff11e959","abstract_canon_sha256":"83ce48953c9a56fbcb8ea5fdc1dcb39a4dab25850507215fa77b4a4b8c14a3df"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:32.764371Z","signature_b64":"xKoXzFdT4CzeeDNMzGku6WXQ/HQKWIHsIG4JNYzZV3ygNq+jTsJ/3alWc/QjDwsKto+dfCRHH8V8fqJrp2r/BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78a10880023941a1c2bcad1bf604a91937f7dcb22168c5d96ad7d5b66b541399","last_reissued_at":"2026-05-18T00:04:32.763922Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:32.763922Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Generalized Lexicographic Products and the Index Coding Capacity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Fatemeh Arbabjolfaei, Young-Han Kim","submitted_at":"2016-08-12T06:45:31Z","abstract_excerpt":"The index coding problem studies the fundamental limit on broadcasting multiple messages to their respective receivers with different sets of side information that are represented by a directed graph. The generalized lexicographic product structure in the side information graph is introduced as a natural condition under which the corresponding index coding problem can be decomposed into multiple interacting subproblems. The capacity region is characterized in terms of the subproblem capacity regions combined in the same product structure. The proof is based on dual uses of random coding---one "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.03689","kind":"arxiv","version":2},"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":"1608.03689","created_at":"2026-05-18T00:04:32.763990+00:00"},{"alias_kind":"arxiv_version","alias_value":"1608.03689v2","created_at":"2026-05-18T00:04:32.763990+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.03689","created_at":"2026-05-18T00:04:32.763990+00:00"},{"alias_kind":"pith_short_12","alias_value":"PCQQRAACHFA2","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_16","alias_value":"PCQQRAACHFA2DQV4","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_8","alias_value":"PCQQRAAC","created_at":"2026-05-18T12:30:39.010887+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/PCQQRAACHFA2DQV4VUN7MBFJDE","json":"https://pith.science/pith/PCQQRAACHFA2DQV4VUN7MBFJDE.json","graph_json":"https://pith.science/api/pith-number/PCQQRAACHFA2DQV4VUN7MBFJDE/graph.json","events_json":"https://pith.science/api/pith-number/PCQQRAACHFA2DQV4VUN7MBFJDE/events.json","paper":"https://pith.science/paper/PCQQRAAC"},"agent_actions":{"view_html":"https://pith.science/pith/PCQQRAACHFA2DQV4VUN7MBFJDE","download_json":"https://pith.science/pith/PCQQRAACHFA2DQV4VUN7MBFJDE.json","view_paper":"https://pith.science/paper/PCQQRAAC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1608.03689&json=true","fetch_graph":"https://pith.science/api/pith-number/PCQQRAACHFA2DQV4VUN7MBFJDE/graph.json","fetch_events":"https://pith.science/api/pith-number/PCQQRAACHFA2DQV4VUN7MBFJDE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PCQQRAACHFA2DQV4VUN7MBFJDE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PCQQRAACHFA2DQV4VUN7MBFJDE/action/storage_attestation","attest_author":"https://pith.science/pith/PCQQRAACHFA2DQV4VUN7MBFJDE/action/author_attestation","sign_citation":"https://pith.science/pith/PCQQRAACHFA2DQV4VUN7MBFJDE/action/citation_signature","submit_replication":"https://pith.science/pith/PCQQRAACHFA2DQV4VUN7MBFJDE/action/replication_record"}},"created_at":"2026-05-18T00:04:32.763990+00:00","updated_at":"2026-05-18T00:04:32.763990+00:00"}