{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:24J2W2K77HBQYTKB6BGUQNAPWU","short_pith_number":"pith:24J2W2K7","canonical_record":{"source":{"id":"1601.06689","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-01-25T17:36:00Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"6c032acfa5f8e35f0978d3ed667c00553997f9982d253a015d2174ddb5922820","abstract_canon_sha256":"8e0e8ab43f6971709f33819646e7bac567bf4c3e15195a11aca1611ca08f354c"},"schema_version":"1.0"},"canonical_sha256":"d713ab695ff9c30c4d41f04d48340fb53e87e879b01af22ba697c32ee466ca3c","source":{"kind":"arxiv","id":"1601.06689","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.06689","created_at":"2026-05-18T01:22:03Z"},{"alias_kind":"arxiv_version","alias_value":"1601.06689v1","created_at":"2026-05-18T01:22:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.06689","created_at":"2026-05-18T01:22:03Z"},{"alias_kind":"pith_short_12","alias_value":"24J2W2K77HBQ","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"24J2W2K77HBQYTKB","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"24J2W2K7","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:24J2W2K77HBQYTKB6BGUQNAPWU","target":"record","payload":{"canonical_record":{"source":{"id":"1601.06689","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-01-25T17:36:00Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"6c032acfa5f8e35f0978d3ed667c00553997f9982d253a015d2174ddb5922820","abstract_canon_sha256":"8e0e8ab43f6971709f33819646e7bac567bf4c3e15195a11aca1611ca08f354c"},"schema_version":"1.0"},"canonical_sha256":"d713ab695ff9c30c4d41f04d48340fb53e87e879b01af22ba697c32ee466ca3c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:03.935687Z","signature_b64":"IVZZWK3PRSvYP+NETwc8uBBNaWDpWYbj2kMUOyKxhscbmDWTPe7QPuwg5jUx3qsH6DPU40dZGCsTeesr1LPWAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d713ab695ff9c30c4d41f04d48340fb53e87e879b01af22ba697c32ee466ca3c","last_reissued_at":"2026-05-18T01:22:03.935169Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:03.935169Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.06689","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":"2026-05-18T01:22:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oSAB74am/IyqYJHCi4QFvkLhJwzU3DWuq1zcGOICsx9yVBqDkKHsybwi7YHZHQxHaCbSqtWSoMQ4S6PC1S7jBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T15:57:26.524179Z"},"content_sha256":"e2bfcc83de01c7099fd1d535ed98bfd587f91360d7fce940d5acb09fc8c55611","schema_version":"1.0","event_id":"sha256:e2bfcc83de01c7099fd1d535ed98bfd587f91360d7fce940d5acb09fc8c55611"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:24J2W2K77HBQYTKB6BGUQNAPWU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A class of index coding problems with rate 1/3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Prasad Krishnan, V. Lalitha","submitted_at":"2016-01-25T17:36:00Z","abstract_excerpt":"An index coding problem with $n$ messages has symmetric rate $R$ if all $n$ messages can be conveyed at rate $R$. In a recent work, a class of index coding problems for which symmetric rate $\\frac{1}{3}$ is achievable was characterised using special properties of the side-information available at the receivers. In this paper, we show a larger class of index coding problems (which includes the previous class of problems) for which symmetric rate $\\frac{1}{3}$ is achievable. In the process, we also obtain a stricter necessary condition for rate $\\frac{1}{3}$ feasibility than what is known in lit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.06689","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":"2026-05-18T01:22:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lg7XMxRp4iMLEXX7dVHwO78X+7DdxH0Ie3iuchkNbtks27Ie6zbF4biAtW1dX5qsWd4TTfAaPyzPtuXzhgi/Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T15:57:26.524549Z"},"content_sha256":"7c48ff3b41924b085e9324320bc7851df672e70175eacea6f5de85868df1eb68","schema_version":"1.0","event_id":"sha256:7c48ff3b41924b085e9324320bc7851df672e70175eacea6f5de85868df1eb68"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/24J2W2K77HBQYTKB6BGUQNAPWU/bundle.json","state_url":"https://pith.science/pith/24J2W2K77HBQYTKB6BGUQNAPWU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/24J2W2K77HBQYTKB6BGUQNAPWU/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":"2026-06-23T15:57:26Z","links":{"resolver":"https://pith.science/pith/24J2W2K77HBQYTKB6BGUQNAPWU","bundle":"https://pith.science/pith/24J2W2K77HBQYTKB6BGUQNAPWU/bundle.json","state":"https://pith.science/pith/24J2W2K77HBQYTKB6BGUQNAPWU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/24J2W2K77HBQYTKB6BGUQNAPWU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:24J2W2K77HBQYTKB6BGUQNAPWU","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":"8e0e8ab43f6971709f33819646e7bac567bf4c3e15195a11aca1611ca08f354c","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-01-25T17:36:00Z","title_canon_sha256":"6c032acfa5f8e35f0978d3ed667c00553997f9982d253a015d2174ddb5922820"},"schema_version":"1.0","source":{"id":"1601.06689","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.06689","created_at":"2026-05-18T01:22:03Z"},{"alias_kind":"arxiv_version","alias_value":"1601.06689v1","created_at":"2026-05-18T01:22:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.06689","created_at":"2026-05-18T01:22:03Z"},{"alias_kind":"pith_short_12","alias_value":"24J2W2K77HBQ","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"24J2W2K77HBQYTKB","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"24J2W2K7","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:7c48ff3b41924b085e9324320bc7851df672e70175eacea6f5de85868df1eb68","target":"graph","created_at":"2026-05-18T01:22:03Z","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":"An index coding problem with $n$ messages has symmetric rate $R$ if all $n$ messages can be conveyed at rate $R$. In a recent work, a class of index coding problems for which symmetric rate $\\frac{1}{3}$ is achievable was characterised using special properties of the side-information available at the receivers. In this paper, we show a larger class of index coding problems (which includes the previous class of problems) for which symmetric rate $\\frac{1}{3}$ is achievable. In the process, we also obtain a stricter necessary condition for rate $\\frac{1}{3}$ feasibility than what is known in lit","authors_text":"Prasad Krishnan, V. Lalitha","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-01-25T17:36:00Z","title":"A class of index coding problems with rate 1/3"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.06689","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:e2bfcc83de01c7099fd1d535ed98bfd587f91360d7fce940d5acb09fc8c55611","target":"record","created_at":"2026-05-18T01:22:03Z","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":"8e0e8ab43f6971709f33819646e7bac567bf4c3e15195a11aca1611ca08f354c","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-01-25T17:36:00Z","title_canon_sha256":"6c032acfa5f8e35f0978d3ed667c00553997f9982d253a015d2174ddb5922820"},"schema_version":"1.0","source":{"id":"1601.06689","kind":"arxiv","version":1}},"canonical_sha256":"d713ab695ff9c30c4d41f04d48340fb53e87e879b01af22ba697c32ee466ca3c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d713ab695ff9c30c4d41f04d48340fb53e87e879b01af22ba697c32ee466ca3c","first_computed_at":"2026-05-18T01:22:03.935169Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:03.935169Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IVZZWK3PRSvYP+NETwc8uBBNaWDpWYbj2kMUOyKxhscbmDWTPe7QPuwg5jUx3qsH6DPU40dZGCsTeesr1LPWAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:03.935687Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.06689","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e2bfcc83de01c7099fd1d535ed98bfd587f91360d7fce940d5acb09fc8c55611","sha256:7c48ff3b41924b085e9324320bc7851df672e70175eacea6f5de85868df1eb68"],"state_sha256":"d8dbf2465d8096faf215d789e54ec94d802e7de5a4e8ec5bcbc867b6d42f0efe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z8MwUBwlMjZUZpk2V79yC8RxaogaCqFKd73ndrTxFo79RcOJl6MoqkRQUBQ2FSIDAexedtsPnqSxCM7a7QVOAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T15:57:26.527389Z","bundle_sha256":"30653d288d144a1f368f58ca0c4ba0e107971d3ef0824c7b9f286cf63d57537a"}}