{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:WJ6LBPLS2YHMQXELM2WR2GVXIT","short_pith_number":"pith:WJ6LBPLS","canonical_record":{"source":{"id":"1502.06149","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-02-21T22:37:04Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"92c2ae328f3ce069b13bf402dd5530aaa1e6601afae53730509f10ce2618463c","abstract_canon_sha256":"64fa6b648e16a127f11d7dbc2fe33d2451eb636b0a5a9a3ad6e13cdf19ff71f4"},"schema_version":"1.0"},"canonical_sha256":"b27cb0bd72d60ec85c8b66ad1d1ab744fa4c833532d4ca36e8a66ae4ed2ef007","source":{"kind":"arxiv","id":"1502.06149","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.06149","created_at":"2026-05-18T02:26:37Z"},{"alias_kind":"arxiv_version","alias_value":"1502.06149v1","created_at":"2026-05-18T02:26:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.06149","created_at":"2026-05-18T02:26:37Z"},{"alias_kind":"pith_short_12","alias_value":"WJ6LBPLS2YHM","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WJ6LBPLS2YHMQXEL","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WJ6LBPLS","created_at":"2026-05-18T12:29:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:WJ6LBPLS2YHMQXELM2WR2GVXIT","target":"record","payload":{"canonical_record":{"source":{"id":"1502.06149","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-02-21T22:37:04Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"92c2ae328f3ce069b13bf402dd5530aaa1e6601afae53730509f10ce2618463c","abstract_canon_sha256":"64fa6b648e16a127f11d7dbc2fe33d2451eb636b0a5a9a3ad6e13cdf19ff71f4"},"schema_version":"1.0"},"canonical_sha256":"b27cb0bd72d60ec85c8b66ad1d1ab744fa4c833532d4ca36e8a66ae4ed2ef007","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:26:37.952816Z","signature_b64":"vGLkpN5X3HoA/FgpdbBFM0UE+liWA07ZSVVzYeZ5rvNHTZQ7/qhudNqmPapjV1VYY5FSM+AsJHKRBF1jDsBCAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b27cb0bd72d60ec85c8b66ad1d1ab744fa4c833532d4ca36e8a66ae4ed2ef007","last_reissued_at":"2026-05-18T02:26:37.952409Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:26:37.952409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.06149","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":"2026-05-18T02:26:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DM/X3dPau9cjYrSM5KnhMDU0fgzvUoG6VOZQRQvd86/ClGaemMAq2j36/phBhDecG6IzhZdvOstUmDwAJU8bBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T13:48:50.473579Z"},"content_sha256":"4a084f51001c8c10395de892e3230fffe44ac5b9c3fd014aa79c993b31359bc3","schema_version":"1.0","event_id":"sha256:4a084f51001c8c10395de892e3230fffe44ac5b9c3fd014aa79c993b31359bc3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:WJ6LBPLS2YHMQXELM2WR2GVXIT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Efficient Algorithms for the Data Exchange Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Kannan Ramchandran, Michael Gastpar, Nebojsa Milosavljevic, Salim El Rouayheb, Sameer Pawar","submitted_at":"2015-02-21T22:37:04Z","abstract_excerpt":"In this paper we study the data exchange problem where a set of users is interested in gaining access to a common file, but where each has only partial knowledge about it as side-information. Assuming that the file is broken into packets, the side-information considered is in the form of linear combinations of the file packets. Given that the collective information of all the users is sufficient to allow recovery of the entire file, the goal is for each user to gain access to the file while minimizing some communication cost. We assume that users can communicate over a noiseless broadcast chan"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06149","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":"2026-05-18T02:26:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"juaZbRukOtwo/moxilM3PgY5mjifzdmf6dvIgx9B/SpROsjKbU+BxCYXZfjZg38CaiEX+mrZjhd20SScKV4dBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T13:48:50.473927Z"},"content_sha256":"061815979923d0069868501c56acb30a2e59795017931ec3a7767defc14be6db","schema_version":"1.0","event_id":"sha256:061815979923d0069868501c56acb30a2e59795017931ec3a7767defc14be6db"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WJ6LBPLS2YHMQXELM2WR2GVXIT/bundle.json","state_url":"https://pith.science/pith/WJ6LBPLS2YHMQXELM2WR2GVXIT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WJ6LBPLS2YHMQXELM2WR2GVXIT/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":"2026-05-28T13:48:50Z","links":{"resolver":"https://pith.science/pith/WJ6LBPLS2YHMQXELM2WR2GVXIT","bundle":"https://pith.science/pith/WJ6LBPLS2YHMQXELM2WR2GVXIT/bundle.json","state":"https://pith.science/pith/WJ6LBPLS2YHMQXELM2WR2GVXIT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WJ6LBPLS2YHMQXELM2WR2GVXIT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:WJ6LBPLS2YHMQXELM2WR2GVXIT","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":"64fa6b648e16a127f11d7dbc2fe33d2451eb636b0a5a9a3ad6e13cdf19ff71f4","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-02-21T22:37:04Z","title_canon_sha256":"92c2ae328f3ce069b13bf402dd5530aaa1e6601afae53730509f10ce2618463c"},"schema_version":"1.0","source":{"id":"1502.06149","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.06149","created_at":"2026-05-18T02:26:37Z"},{"alias_kind":"arxiv_version","alias_value":"1502.06149v1","created_at":"2026-05-18T02:26:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.06149","created_at":"2026-05-18T02:26:37Z"},{"alias_kind":"pith_short_12","alias_value":"WJ6LBPLS2YHM","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WJ6LBPLS2YHMQXEL","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WJ6LBPLS","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:061815979923d0069868501c56acb30a2e59795017931ec3a7767defc14be6db","target":"graph","created_at":"2026-05-18T02:26:37Z","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":"In this paper we study the data exchange problem where a set of users is interested in gaining access to a common file, but where each has only partial knowledge about it as side-information. Assuming that the file is broken into packets, the side-information considered is in the form of linear combinations of the file packets. Given that the collective information of all the users is sufficient to allow recovery of the entire file, the goal is for each user to gain access to the file while minimizing some communication cost. We assume that users can communicate over a noiseless broadcast chan","authors_text":"Kannan Ramchandran, Michael Gastpar, Nebojsa Milosavljevic, Salim El Rouayheb, Sameer Pawar","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-02-21T22:37:04Z","title":"Efficient Algorithms for the Data Exchange Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06149","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":"sha256:4a084f51001c8c10395de892e3230fffe44ac5b9c3fd014aa79c993b31359bc3","target":"record","created_at":"2026-05-18T02:26:37Z","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":"64fa6b648e16a127f11d7dbc2fe33d2451eb636b0a5a9a3ad6e13cdf19ff71f4","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-02-21T22:37:04Z","title_canon_sha256":"92c2ae328f3ce069b13bf402dd5530aaa1e6601afae53730509f10ce2618463c"},"schema_version":"1.0","source":{"id":"1502.06149","kind":"arxiv","version":1}},"canonical_sha256":"b27cb0bd72d60ec85c8b66ad1d1ab744fa4c833532d4ca36e8a66ae4ed2ef007","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b27cb0bd72d60ec85c8b66ad1d1ab744fa4c833532d4ca36e8a66ae4ed2ef007","first_computed_at":"2026-05-18T02:26:37.952409Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:26:37.952409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vGLkpN5X3HoA/FgpdbBFM0UE+liWA07ZSVVzYeZ5rvNHTZQ7/qhudNqmPapjV1VYY5FSM+AsJHKRBF1jDsBCAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:26:37.952816Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.06149","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a084f51001c8c10395de892e3230fffe44ac5b9c3fd014aa79c993b31359bc3","sha256:061815979923d0069868501c56acb30a2e59795017931ec3a7767defc14be6db"],"state_sha256":"23679d8d529073725d90749fe1242ab1f348fbcbe0711aa59452d918db4a6618"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lJx5OFFZIpkwlJh5L23W5znpk7TsJpJiI/Ed8w0pTxwFyFPYaHWpFQVS2w4OLyyXKBFHAUassHXUeyKFppWHCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T13:48:50.475897Z","bundle_sha256":"a53c984e8b514acc74a85b37254ccb7e62f3ce5862e6747f3105ae5bde570504"}}