{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:HH4C5XW37MYOCFCHG24WKERVHI","short_pith_number":"pith:HH4C5XW3","canonical_record":{"source":{"id":"1102.3393","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-02-16T18:32:07Z","cross_cats_sorted":[],"title_canon_sha256":"a1f8ab737808ac12dd2e1c8626ea1bba351696a61d9cd294409ea84f49861a6e","abstract_canon_sha256":"9e3a0c6913748532619b13787a6c5f4714474277818e101b6aa03ca11504ba88"},"schema_version":"1.0"},"canonical_sha256":"39f82ededbfb30e1144736b96512353a0095c71da679d3c35bfbc3f8983f66cd","source":{"kind":"arxiv","id":"1102.3393","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.3393","created_at":"2026-05-18T04:28:30Z"},{"alias_kind":"arxiv_version","alias_value":"1102.3393v1","created_at":"2026-05-18T04:28:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.3393","created_at":"2026-05-18T04:28:30Z"},{"alias_kind":"pith_short_12","alias_value":"HH4C5XW37MYO","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HH4C5XW37MYOCFCH","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HH4C5XW3","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:HH4C5XW37MYOCFCHG24WKERVHI","target":"record","payload":{"canonical_record":{"source":{"id":"1102.3393","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-02-16T18:32:07Z","cross_cats_sorted":[],"title_canon_sha256":"a1f8ab737808ac12dd2e1c8626ea1bba351696a61d9cd294409ea84f49861a6e","abstract_canon_sha256":"9e3a0c6913748532619b13787a6c5f4714474277818e101b6aa03ca11504ba88"},"schema_version":"1.0"},"canonical_sha256":"39f82ededbfb30e1144736b96512353a0095c71da679d3c35bfbc3f8983f66cd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:28:30.325995Z","signature_b64":"fw7fXDFbUolgO/V122iFZeDVO/jp73IhzNIj2ubaGmjLN1ENECSBd0uV7Om4rDyTX2RHRrzK61k8H/7rc44xCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"39f82ededbfb30e1144736b96512353a0095c71da679d3c35bfbc3f8983f66cd","last_reissued_at":"2026-05-18T04:28:30.325423Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:28:30.325423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.3393","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":"2026-05-18T04:28:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7tsi2dCuF1u2IIV5hZCcBxd03BTo4T3had7fxvg5LtmqPlEaMaZFsoXIBVD4n80CL5dySpT5QKfRWQlfE2MMDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T05:26:01.600041Z"},"content_sha256":"929db1ce829c194a6f3f5af68d9afd14cbb9101f101e14db0248db20c089c1f5","schema_version":"1.0","event_id":"sha256:929db1ce829c194a6f3f5af68d9afd14cbb9101f101e14db0248db20c089c1f5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:HH4C5XW37MYOCFCHG24WKERVHI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Better Bounds for Incremental Frequency Allocation in Bipartite Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Ji\\v{r}\\'i Sgall, {\\L}ukasz Je\\.z, Marek Chrobak","submitted_at":"2011-02-16T18:32:07Z","abstract_excerpt":"We study frequency allocation in wireless networks. A wireless network is modeled by an undirected graph, with vertices corresponding to cells. In each vertex we have a certain number of requests, and each of those requests must be assigned a different frequency. Edges represent conflicts between cells, meaning that frequencies in adjacent vertices must be different as well. The objective is to minimize the total number of used frequencies.\n  The offline version of the problem is known to be NP-hard. In the incremental version, requests for frequencies arrive over time and the algorithm is req"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.3393","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":"2026-05-18T04:28:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WDFPHmr6g0tffvmguQYSZ8j9JokNXTdB2/fUTSFDFRAG5Ca1ljua8q1XBsc2qfNThPGEcwcCv0NFSFevJKOtCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T05:26:01.600405Z"},"content_sha256":"71eb6a06e3b5c295acdd34a8058820b3d5b6ed9d02eb8a045ddbc5b3be3dcd36","schema_version":"1.0","event_id":"sha256:71eb6a06e3b5c295acdd34a8058820b3d5b6ed9d02eb8a045ddbc5b3be3dcd36"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HH4C5XW37MYOCFCHG24WKERVHI/bundle.json","state_url":"https://pith.science/pith/HH4C5XW37MYOCFCHG24WKERVHI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HH4C5XW37MYOCFCHG24WKERVHI/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":"2026-05-28T05:26:01Z","links":{"resolver":"https://pith.science/pith/HH4C5XW37MYOCFCHG24WKERVHI","bundle":"https://pith.science/pith/HH4C5XW37MYOCFCHG24WKERVHI/bundle.json","state":"https://pith.science/pith/HH4C5XW37MYOCFCHG24WKERVHI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HH4C5XW37MYOCFCHG24WKERVHI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:HH4C5XW37MYOCFCHG24WKERVHI","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":"9e3a0c6913748532619b13787a6c5f4714474277818e101b6aa03ca11504ba88","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-02-16T18:32:07Z","title_canon_sha256":"a1f8ab737808ac12dd2e1c8626ea1bba351696a61d9cd294409ea84f49861a6e"},"schema_version":"1.0","source":{"id":"1102.3393","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.3393","created_at":"2026-05-18T04:28:30Z"},{"alias_kind":"arxiv_version","alias_value":"1102.3393v1","created_at":"2026-05-18T04:28:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.3393","created_at":"2026-05-18T04:28:30Z"},{"alias_kind":"pith_short_12","alias_value":"HH4C5XW37MYO","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HH4C5XW37MYOCFCH","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HH4C5XW3","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:71eb6a06e3b5c295acdd34a8058820b3d5b6ed9d02eb8a045ddbc5b3be3dcd36","target":"graph","created_at":"2026-05-18T04:28:30Z","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":"We study frequency allocation in wireless networks. A wireless network is modeled by an undirected graph, with vertices corresponding to cells. In each vertex we have a certain number of requests, and each of those requests must be assigned a different frequency. Edges represent conflicts between cells, meaning that frequencies in adjacent vertices must be different as well. The objective is to minimize the total number of used frequencies.\n  The offline version of the problem is known to be NP-hard. In the incremental version, requests for frequencies arrive over time and the algorithm is req","authors_text":"Ji\\v{r}\\'i Sgall, {\\L}ukasz Je\\.z, Marek Chrobak","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-02-16T18:32:07Z","title":"Better Bounds for Incremental Frequency Allocation in Bipartite Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.3393","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":"sha256:929db1ce829c194a6f3f5af68d9afd14cbb9101f101e14db0248db20c089c1f5","target":"record","created_at":"2026-05-18T04:28:30Z","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":"9e3a0c6913748532619b13787a6c5f4714474277818e101b6aa03ca11504ba88","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-02-16T18:32:07Z","title_canon_sha256":"a1f8ab737808ac12dd2e1c8626ea1bba351696a61d9cd294409ea84f49861a6e"},"schema_version":"1.0","source":{"id":"1102.3393","kind":"arxiv","version":1}},"canonical_sha256":"39f82ededbfb30e1144736b96512353a0095c71da679d3c35bfbc3f8983f66cd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"39f82ededbfb30e1144736b96512353a0095c71da679d3c35bfbc3f8983f66cd","first_computed_at":"2026-05-18T04:28:30.325423Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:28:30.325423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fw7fXDFbUolgO/V122iFZeDVO/jp73IhzNIj2ubaGmjLN1ENECSBd0uV7Om4rDyTX2RHRrzK61k8H/7rc44xCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:28:30.325995Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.3393","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:929db1ce829c194a6f3f5af68d9afd14cbb9101f101e14db0248db20c089c1f5","sha256:71eb6a06e3b5c295acdd34a8058820b3d5b6ed9d02eb8a045ddbc5b3be3dcd36"],"state_sha256":"f1ce6c87a0f2c2bd6179dbad9e2af59349241c9dc77c15757f64a3b4872460e8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l8vtsteLek+f947ySi3rnmp7lwMhEJPBKT9zkkjz6DI5SpBMlOgKLdlKSInt+AzkRocsn2TDG1aIYlV2Qr4uAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T05:26:01.602333Z","bundle_sha256":"3ef9ba72a4e604a4b255f78bb71c6dd3c80a650ccd9c9acf3bd430f48b4aa4ad"}}