{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:ELBN2KRC5JLKSS5U4NAZDZWRLS","short_pith_number":"pith:ELBN2KRC","canonical_record":{"source":{"id":"2206.08805","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.CC","submitted_at":"2022-06-17T14:35:40Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"b90ec264e16ec1e3bcbcd792b9366224c816647ad8c80bb54f2e17b5bf7c4f0a","abstract_canon_sha256":"ed69ac3c439d4be1c9a26c014d20ca1d4a3e32760ef70678519a3bb7ae8bbf97"},"schema_version":"1.0"},"canonical_sha256":"22c2dd2a22ea56a94bb4e34191e6d15ca8a2a438d49d4d57dd5317fd09793fce","source":{"kind":"arxiv","id":"2206.08805","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2206.08805","created_at":"2026-07-05T04:32:43Z"},{"alias_kind":"arxiv_version","alias_value":"2206.08805v1","created_at":"2026-07-05T04:32:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.08805","created_at":"2026-07-05T04:32:43Z"},{"alias_kind":"pith_short_12","alias_value":"ELBN2KRC5JLK","created_at":"2026-07-05T04:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"ELBN2KRC5JLKSS5U","created_at":"2026-07-05T04:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"ELBN2KRC","created_at":"2026-07-05T04:32:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:ELBN2KRC5JLKSS5U4NAZDZWRLS","target":"record","payload":{"canonical_record":{"source":{"id":"2206.08805","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.CC","submitted_at":"2022-06-17T14:35:40Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"b90ec264e16ec1e3bcbcd792b9366224c816647ad8c80bb54f2e17b5bf7c4f0a","abstract_canon_sha256":"ed69ac3c439d4be1c9a26c014d20ca1d4a3e32760ef70678519a3bb7ae8bbf97"},"schema_version":"1.0"},"canonical_sha256":"22c2dd2a22ea56a94bb4e34191e6d15ca8a2a438d49d4d57dd5317fd09793fce","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:32:43.542185Z","signature_b64":"PIKDTG+LNYmwMoi7MLk3Ztp3RjEJ0LFkOxMNl43RAHJzUYNZ3GRqyV/YsrdDpc33paSd5o6EOC54SZs5oWCzAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"22c2dd2a22ea56a94bb4e34191e6d15ca8a2a438d49d4d57dd5317fd09793fce","last_reissued_at":"2026-07-05T04:32:43.541784Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:32:43.541784Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2206.08805","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":"2026-07-05T04:32:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3PStyX1RFOuSOf/30Qk7YNV80TcJ32Ei2kQGxS4xRCnCa9kHbmkQE4Obo4vMwi+K9p0rBEyBte0UG3nvelqDDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T10:06:16.915378Z"},"content_sha256":"4f94c45655adb5e6f985831d43c1c772cc213ef316e74b5f3cc1b08bbc6bc15f","schema_version":"1.0","event_id":"sha256:4f94c45655adb5e6f985831d43c1c772cc213ef316e74b5f3cc1b08bbc6bc15f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:ELBN2KRC5JLKSS5U4NAZDZWRLS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Complexity of the Multiobjective Spanner Problem","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.CC","authors_text":"Fritz B\\\"okler, Henning Jasper","submitted_at":"2022-06-17T14:35:40Z","abstract_excerpt":"In this paper, we take an in-depth look at the complexity of a hitherto unexplored Multiobjective Spanner (MSp) problem. The MSp is a multiobjective generalization of the well-studied Minimum t-Spanner problem. This multiobjective approach allows us to find solutions that offer a viable compromise between cost and utility. Thus, the MSp can be a powerful modeling tool when it comes to the planning of, e.g., infrastructure. We show that for degree-3 bounded outerplanar instances the MSp is intractable and computing the non-dominated set is BUCO-hard. Additionally, we prove that if P != NP, neit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.08805","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2206.08805/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T04:32:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I2KG3FlYDqEdqdWsYLhDc4UPxTpWfKRczh8NO6NO/Am6cgJJRJHKYNYfcTaORKuC10S134JBc5T9kt/4DHh9AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T10:06:16.916271Z"},"content_sha256":"dc9bf5d5d6b507ce3ba5ef8e548c6d44d0304e70f46b356fce3e1f29d31eaf1a","schema_version":"1.0","event_id":"sha256:dc9bf5d5d6b507ce3ba5ef8e548c6d44d0304e70f46b356fce3e1f29d31eaf1a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ELBN2KRC5JLKSS5U4NAZDZWRLS/bundle.json","state_url":"https://pith.science/pith/ELBN2KRC5JLKSS5U4NAZDZWRLS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ELBN2KRC5JLKSS5U4NAZDZWRLS/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":"2026-08-20T10:06:16Z","links":{"resolver":"https://pith.science/pith/ELBN2KRC5JLKSS5U4NAZDZWRLS","bundle":"https://pith.science/pith/ELBN2KRC5JLKSS5U4NAZDZWRLS/bundle.json","state":"https://pith.science/pith/ELBN2KRC5JLKSS5U4NAZDZWRLS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ELBN2KRC5JLKSS5U4NAZDZWRLS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:ELBN2KRC5JLKSS5U4NAZDZWRLS","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":"ed69ac3c439d4be1c9a26c014d20ca1d4a3e32760ef70678519a3bb7ae8bbf97","cross_cats_sorted":["math.OC"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.CC","submitted_at":"2022-06-17T14:35:40Z","title_canon_sha256":"b90ec264e16ec1e3bcbcd792b9366224c816647ad8c80bb54f2e17b5bf7c4f0a"},"schema_version":"1.0","source":{"id":"2206.08805","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2206.08805","created_at":"2026-07-05T04:32:43Z"},{"alias_kind":"arxiv_version","alias_value":"2206.08805v1","created_at":"2026-07-05T04:32:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.08805","created_at":"2026-07-05T04:32:43Z"},{"alias_kind":"pith_short_12","alias_value":"ELBN2KRC5JLK","created_at":"2026-07-05T04:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"ELBN2KRC5JLKSS5U","created_at":"2026-07-05T04:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"ELBN2KRC","created_at":"2026-07-05T04:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:dc9bf5d5d6b507ce3ba5ef8e548c6d44d0304e70f46b356fce3e1f29d31eaf1a","target":"graph","created_at":"2026-07-05T04:32:43Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2206.08805/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we take an in-depth look at the complexity of a hitherto unexplored Multiobjective Spanner (MSp) problem. The MSp is a multiobjective generalization of the well-studied Minimum t-Spanner problem. This multiobjective approach allows us to find solutions that offer a viable compromise between cost and utility. Thus, the MSp can be a powerful modeling tool when it comes to the planning of, e.g., infrastructure. We show that for degree-3 bounded outerplanar instances the MSp is intractable and computing the non-dominated set is BUCO-hard. Additionally, we prove that if P != NP, neit","authors_text":"Fritz B\\\"okler, Henning Jasper","cross_cats":["math.OC"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.CC","submitted_at":"2022-06-17T14:35:40Z","title":"Complexity of the Multiobjective Spanner Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.08805","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":"sha256:4f94c45655adb5e6f985831d43c1c772cc213ef316e74b5f3cc1b08bbc6bc15f","target":"record","created_at":"2026-07-05T04:32:43Z","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":"ed69ac3c439d4be1c9a26c014d20ca1d4a3e32760ef70678519a3bb7ae8bbf97","cross_cats_sorted":["math.OC"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.CC","submitted_at":"2022-06-17T14:35:40Z","title_canon_sha256":"b90ec264e16ec1e3bcbcd792b9366224c816647ad8c80bb54f2e17b5bf7c4f0a"},"schema_version":"1.0","source":{"id":"2206.08805","kind":"arxiv","version":1}},"canonical_sha256":"22c2dd2a22ea56a94bb4e34191e6d15ca8a2a438d49d4d57dd5317fd09793fce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"22c2dd2a22ea56a94bb4e34191e6d15ca8a2a438d49d4d57dd5317fd09793fce","first_computed_at":"2026-07-05T04:32:43.541784Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:32:43.541784Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PIKDTG+LNYmwMoi7MLk3Ztp3RjEJ0LFkOxMNl43RAHJzUYNZ3GRqyV/YsrdDpc33paSd5o6EOC54SZs5oWCzAw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:32:43.542185Z","signed_message":"canonical_sha256_bytes"},"source_id":"2206.08805","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4f94c45655adb5e6f985831d43c1c772cc213ef316e74b5f3cc1b08bbc6bc15f","sha256:dc9bf5d5d6b507ce3ba5ef8e548c6d44d0304e70f46b356fce3e1f29d31eaf1a"],"state_sha256":"56ffc407ae3e39b20e12233a3d5db5917314fc97220e5fbecc5b586249b39a81"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t/9S6W6AIXhx+ItbWsWAB5Jq4HoRqQtfLfXITLbCPy//bO6vbhGZyeHJFV1uV2ig3xDA6IRM0rOpEBnOyb2KBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-20T10:06:16.920802Z","bundle_sha256":"84bdcce48cc0eeefab062d30b2f0b59b41ceb741f245ff3b353c5a138c43107d"}}