{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:JDRSJGJEUH7Q2KZ3CGGWQOCP6I","short_pith_number":"pith:JDRSJGJE","canonical_record":{"source":{"id":"1404.5548","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-04-22T16:34:50Z","cross_cats_sorted":[],"title_canon_sha256":"f44c772ae80f5744435ea70ed18300f5f6017ffe49019bbd5f8cff7ae137dc38","abstract_canon_sha256":"09dcb35ba3527a438d501280780293568193c29ce567b8849f5e056262856e7c"},"schema_version":"1.0"},"canonical_sha256":"48e3249924a1ff0d2b3b118d68384ff21f0c4aa424f743b6b93d20f422f7801b","source":{"kind":"arxiv","id":"1404.5548","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.5548","created_at":"2026-05-18T02:32:07Z"},{"alias_kind":"arxiv_version","alias_value":"1404.5548v2","created_at":"2026-05-18T02:32:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.5548","created_at":"2026-05-18T02:32:07Z"},{"alias_kind":"pith_short_12","alias_value":"JDRSJGJEUH7Q","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"JDRSJGJEUH7Q2KZ3","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"JDRSJGJE","created_at":"2026-05-18T12:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:JDRSJGJEUH7Q2KZ3CGGWQOCP6I","target":"record","payload":{"canonical_record":{"source":{"id":"1404.5548","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-04-22T16:34:50Z","cross_cats_sorted":[],"title_canon_sha256":"f44c772ae80f5744435ea70ed18300f5f6017ffe49019bbd5f8cff7ae137dc38","abstract_canon_sha256":"09dcb35ba3527a438d501280780293568193c29ce567b8849f5e056262856e7c"},"schema_version":"1.0"},"canonical_sha256":"48e3249924a1ff0d2b3b118d68384ff21f0c4aa424f743b6b93d20f422f7801b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:07.468822Z","signature_b64":"SLFCjDrrbJrXN/WZ3Em+i6F0BjNk2pzH8Rsxq5ON4mUG1csjQRsbTUstNk2toIGVKNyumCW9yP3wZUEW8jLCAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"48e3249924a1ff0d2b3b118d68384ff21f0c4aa424f743b6b93d20f422f7801b","last_reissued_at":"2026-05-18T02:32:07.468431Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:07.468431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.5548","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:32:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jbgqPGHpD5x05QZFpzvvzrxhsQ2JZvB8gcvTMNDGhU7tXX7AluT6q8Olc1W/yVWrEHs+vCcBWITehQWxZZ7LDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:44:36.904433Z"},"content_sha256":"3b404126ed7a50faa3543a17889dc48f61d19a0f7746ce459177ee7bececd847","schema_version":"1.0","event_id":"sha256:3b404126ed7a50faa3543a17889dc48f61d19a0f7746ce459177ee7bececd847"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:JDRSJGJEUH7Q2KZ3CGGWQOCP6I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Online Colored Bin Packing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Ji\\v{r}\\'i Sgall, Martin B\\\"ohm, Pavel Vesel\\'y","submitted_at":"2014-04-22T16:34:50Z","abstract_excerpt":"In the Colored Bin Packing problem a sequence of items of sizes up to $1$ arrives to be packed into bins of unit capacity. Each item has one of $c\\geq 2$ colors and an additional constraint is that we cannot pack two items of the same color next to each other in the same bin. The objective is to minimize the number of bins.\n  In the important special case when all items have size zero, we characterize the optimal value to be equal to color discrepancy. As our main result, we give an (asymptotically) 1.5-competitive algorithm which is optimal. In fact, the algorithm always uses at most $\\lceil1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5548","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:32:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qBXt8onAWLN52YZDgfFF/d7X68G1Vysz/i4ZDMytvUf+0kCDsjkUFKTQZmYstMcFJt/v9b9sxyzuP+dwMCI3Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:44:36.904795Z"},"content_sha256":"8217178eb777748f76444314a8c8e31f1ceb9c2a4ddfe78d8902aa983420f63d","schema_version":"1.0","event_id":"sha256:8217178eb777748f76444314a8c8e31f1ceb9c2a4ddfe78d8902aa983420f63d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JDRSJGJEUH7Q2KZ3CGGWQOCP6I/bundle.json","state_url":"https://pith.science/pith/JDRSJGJEUH7Q2KZ3CGGWQOCP6I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JDRSJGJEUH7Q2KZ3CGGWQOCP6I/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":"2026-05-27T14:44:36Z","links":{"resolver":"https://pith.science/pith/JDRSJGJEUH7Q2KZ3CGGWQOCP6I","bundle":"https://pith.science/pith/JDRSJGJEUH7Q2KZ3CGGWQOCP6I/bundle.json","state":"https://pith.science/pith/JDRSJGJEUH7Q2KZ3CGGWQOCP6I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JDRSJGJEUH7Q2KZ3CGGWQOCP6I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:JDRSJGJEUH7Q2KZ3CGGWQOCP6I","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":"09dcb35ba3527a438d501280780293568193c29ce567b8849f5e056262856e7c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-04-22T16:34:50Z","title_canon_sha256":"f44c772ae80f5744435ea70ed18300f5f6017ffe49019bbd5f8cff7ae137dc38"},"schema_version":"1.0","source":{"id":"1404.5548","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.5548","created_at":"2026-05-18T02:32:07Z"},{"alias_kind":"arxiv_version","alias_value":"1404.5548v2","created_at":"2026-05-18T02:32:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.5548","created_at":"2026-05-18T02:32:07Z"},{"alias_kind":"pith_short_12","alias_value":"JDRSJGJEUH7Q","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"JDRSJGJEUH7Q2KZ3","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"JDRSJGJE","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:8217178eb777748f76444314a8c8e31f1ceb9c2a4ddfe78d8902aa983420f63d","target":"graph","created_at":"2026-05-18T02:32:07Z","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 the Colored Bin Packing problem a sequence of items of sizes up to $1$ arrives to be packed into bins of unit capacity. Each item has one of $c\\geq 2$ colors and an additional constraint is that we cannot pack two items of the same color next to each other in the same bin. The objective is to minimize the number of bins.\n  In the important special case when all items have size zero, we characterize the optimal value to be equal to color discrepancy. As our main result, we give an (asymptotically) 1.5-competitive algorithm which is optimal. In fact, the algorithm always uses at most $\\lceil1","authors_text":"Ji\\v{r}\\'i Sgall, Martin B\\\"ohm, Pavel Vesel\\'y","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-04-22T16:34:50Z","title":"Online Colored Bin Packing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5548","kind":"arxiv","version":2},"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":"sha256:3b404126ed7a50faa3543a17889dc48f61d19a0f7746ce459177ee7bececd847","target":"record","created_at":"2026-05-18T02:32:07Z","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":"09dcb35ba3527a438d501280780293568193c29ce567b8849f5e056262856e7c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-04-22T16:34:50Z","title_canon_sha256":"f44c772ae80f5744435ea70ed18300f5f6017ffe49019bbd5f8cff7ae137dc38"},"schema_version":"1.0","source":{"id":"1404.5548","kind":"arxiv","version":2}},"canonical_sha256":"48e3249924a1ff0d2b3b118d68384ff21f0c4aa424f743b6b93d20f422f7801b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"48e3249924a1ff0d2b3b118d68384ff21f0c4aa424f743b6b93d20f422f7801b","first_computed_at":"2026-05-18T02:32:07.468431Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:32:07.468431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SLFCjDrrbJrXN/WZ3Em+i6F0BjNk2pzH8Rsxq5ON4mUG1csjQRsbTUstNk2toIGVKNyumCW9yP3wZUEW8jLCAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:32:07.468822Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.5548","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3b404126ed7a50faa3543a17889dc48f61d19a0f7746ce459177ee7bececd847","sha256:8217178eb777748f76444314a8c8e31f1ceb9c2a4ddfe78d8902aa983420f63d"],"state_sha256":"98716044cccd923ecff64869b3c8d675b6e4fee1a000d1aeb20521c194b4771c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C4ZzFtOMgIxJlqFCiit4o3F1uEf81pARZ7lDDaULByLA68V90kw3GUxxLZeFEqb5X55SWfZgtmZDz9e0Tp6KDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T14:44:36.906940Z","bundle_sha256":"24b7508c866b52e92fc6eb490d935c2547791b5a04e9940a905dd9499b82f98b"}}