{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:DS2JGPYYHLLWFTM365XC37XFRV","short_pith_number":"pith:DS2JGPYY","canonical_record":{"source":{"id":"2606.07361","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.NE","submitted_at":"2026-06-05T15:07:12Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"ba3cf28c60a64100e20130d0bf765ce4115e4f205e7a7952e0bdee0b960a8cbc","abstract_canon_sha256":"b10f0ca6885253f4834624f0ef397baa215fa04b52846470043f15fe66d6eea5"},"schema_version":"1.0"},"canonical_sha256":"1cb4933f183ad762cd9bf76e2dfee58d4f50a6c8999b180f6f0d2b718d50286f","source":{"kind":"arxiv","id":"2606.07361","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.07361","created_at":"2026-06-08T01:05:22Z"},{"alias_kind":"arxiv_version","alias_value":"2606.07361v1","created_at":"2026-06-08T01:05:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.07361","created_at":"2026-06-08T01:05:22Z"},{"alias_kind":"pith_short_12","alias_value":"DS2JGPYYHLLW","created_at":"2026-06-08T01:05:22Z"},{"alias_kind":"pith_short_16","alias_value":"DS2JGPYYHLLWFTM3","created_at":"2026-06-08T01:05:22Z"},{"alias_kind":"pith_short_8","alias_value":"DS2JGPYY","created_at":"2026-06-08T01:05:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:DS2JGPYYHLLWFTM365XC37XFRV","target":"record","payload":{"canonical_record":{"source":{"id":"2606.07361","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.NE","submitted_at":"2026-06-05T15:07:12Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"ba3cf28c60a64100e20130d0bf765ce4115e4f205e7a7952e0bdee0b960a8cbc","abstract_canon_sha256":"b10f0ca6885253f4834624f0ef397baa215fa04b52846470043f15fe66d6eea5"},"schema_version":"1.0"},"canonical_sha256":"1cb4933f183ad762cd9bf76e2dfee58d4f50a6c8999b180f6f0d2b718d50286f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-08T01:05:22.034884Z","signature_b64":"3CeYvxpUxA6m4YxbChzcMhYxa2WmUEi/Zm832SAs5y1RfNMLHlBVQIItMa6yayfE6/xqFegrUTXEH20GBsZ+AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1cb4933f183ad762cd9bf76e2dfee58d4f50a6c8999b180f6f0d2b718d50286f","last_reissued_at":"2026-06-08T01:05:22.034078Z","signature_status":"signed_v1","first_computed_at":"2026-06-08T01:05:22.034078Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.07361","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":"2026-06-08T01:05:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/H8ptSsVMiT1SwP3dtPzoZA0tNnLLlEfnp9SIcqwz3/sUpPkNy1Q9fDcaTA39knNqh+Dh5kQfz2dMttqLR9eAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T22:25:27.825990Z"},"content_sha256":"ca7ab7a9f79fec299aa7fc99e37d46f864d9030a2f6294931acb97482047df14","schema_version":"1.0","event_id":"sha256:ca7ab7a9f79fec299aa7fc99e37d46f864d9030a2f6294931acb97482047df14"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:DS2JGPYYHLLWFTM365XC37XFRV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Combinatorial Landscape Analysis for Dominating Set and Vertex Coloring","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.NE","authors_text":"Antonia Heinen, Felix Kn\\\"ofel, Johanna Gasse, Maxim Stanko, Timo K\\\"otzing","submitted_at":"2026-06-05T15:07:12Z","abstract_excerpt":"We analyze the two combinatorial problems of Dominating Set and Vertex Coloring regarding what kind of local optima are present for various instances. For a variety of graph classes each, we determine whether the induced landscapes are unimodal, plateau-unimodal (all optima are just one plateau), equimodal (all local optima are global) or truly multimodal. We do this for two different neighborhood operators, one based on making only a single change and one also allowing swaps (interchanging two parts of the solution)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.07361","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/2606.07361/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":"2026-06-08T01:05:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kz2QbpvzJelH5pe7O3+OStbPzdZSkmk7GGtZjJZ3O8/I3Xd1cOfPaKRVs1OIj2XaWwRatWWEHjpZg8Uixh2UBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T22:25:27.826379Z"},"content_sha256":"e0f1d4324434ff0e8a4de3f48dc2536b75851173fc6d4f5764bf1a4db98db93b","schema_version":"1.0","event_id":"sha256:e0f1d4324434ff0e8a4de3f48dc2536b75851173fc6d4f5764bf1a4db98db93b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DS2JGPYYHLLWFTM365XC37XFRV/bundle.json","state_url":"https://pith.science/pith/DS2JGPYYHLLWFTM365XC37XFRV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DS2JGPYYHLLWFTM365XC37XFRV/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":"2026-06-20T22:25:27Z","links":{"resolver":"https://pith.science/pith/DS2JGPYYHLLWFTM365XC37XFRV","bundle":"https://pith.science/pith/DS2JGPYYHLLWFTM365XC37XFRV/bundle.json","state":"https://pith.science/pith/DS2JGPYYHLLWFTM365XC37XFRV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DS2JGPYYHLLWFTM365XC37XFRV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:DS2JGPYYHLLWFTM365XC37XFRV","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":"b10f0ca6885253f4834624f0ef397baa215fa04b52846470043f15fe66d6eea5","cross_cats_sorted":["cs.DM"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.NE","submitted_at":"2026-06-05T15:07:12Z","title_canon_sha256":"ba3cf28c60a64100e20130d0bf765ce4115e4f205e7a7952e0bdee0b960a8cbc"},"schema_version":"1.0","source":{"id":"2606.07361","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.07361","created_at":"2026-06-08T01:05:22Z"},{"alias_kind":"arxiv_version","alias_value":"2606.07361v1","created_at":"2026-06-08T01:05:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.07361","created_at":"2026-06-08T01:05:22Z"},{"alias_kind":"pith_short_12","alias_value":"DS2JGPYYHLLW","created_at":"2026-06-08T01:05:22Z"},{"alias_kind":"pith_short_16","alias_value":"DS2JGPYYHLLWFTM3","created_at":"2026-06-08T01:05:22Z"},{"alias_kind":"pith_short_8","alias_value":"DS2JGPYY","created_at":"2026-06-08T01:05:22Z"}],"graph_snapshots":[{"event_id":"sha256:e0f1d4324434ff0e8a4de3f48dc2536b75851173fc6d4f5764bf1a4db98db93b","target":"graph","created_at":"2026-06-08T01:05:22Z","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/2606.07361/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We analyze the two combinatorial problems of Dominating Set and Vertex Coloring regarding what kind of local optima are present for various instances. For a variety of graph classes each, we determine whether the induced landscapes are unimodal, plateau-unimodal (all optima are just one plateau), equimodal (all local optima are global) or truly multimodal. We do this for two different neighborhood operators, one based on making only a single change and one also allowing swaps (interchanging two parts of the solution).","authors_text":"Antonia Heinen, Felix Kn\\\"ofel, Johanna Gasse, Maxim Stanko, Timo K\\\"otzing","cross_cats":["cs.DM"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.NE","submitted_at":"2026-06-05T15:07:12Z","title":"Combinatorial Landscape Analysis for Dominating Set and Vertex Coloring"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.07361","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:ca7ab7a9f79fec299aa7fc99e37d46f864d9030a2f6294931acb97482047df14","target":"record","created_at":"2026-06-08T01:05:22Z","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":"b10f0ca6885253f4834624f0ef397baa215fa04b52846470043f15fe66d6eea5","cross_cats_sorted":["cs.DM"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.NE","submitted_at":"2026-06-05T15:07:12Z","title_canon_sha256":"ba3cf28c60a64100e20130d0bf765ce4115e4f205e7a7952e0bdee0b960a8cbc"},"schema_version":"1.0","source":{"id":"2606.07361","kind":"arxiv","version":1}},"canonical_sha256":"1cb4933f183ad762cd9bf76e2dfee58d4f50a6c8999b180f6f0d2b718d50286f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1cb4933f183ad762cd9bf76e2dfee58d4f50a6c8999b180f6f0d2b718d50286f","first_computed_at":"2026-06-08T01:05:22.034078Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-08T01:05:22.034078Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3CeYvxpUxA6m4YxbChzcMhYxa2WmUEi/Zm832SAs5y1RfNMLHlBVQIItMa6yayfE6/xqFegrUTXEH20GBsZ+AA==","signature_status":"signed_v1","signed_at":"2026-06-08T01:05:22.034884Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.07361","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca7ab7a9f79fec299aa7fc99e37d46f864d9030a2f6294931acb97482047df14","sha256:e0f1d4324434ff0e8a4de3f48dc2536b75851173fc6d4f5764bf1a4db98db93b"],"state_sha256":"9afbd0b6218fbeb8c8389573a5e0a9a0b2d88fa90dc2a6419a4bfe1986c6f432"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VeJ2o/pQs1bMDgpWIE8a+wjXI6Rrz5kc3rXjLtA/TPp+vEfiSkzspgt7FOV1nK+aqm+sHWnOwCkxA7VBSh9jDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T22:25:27.828366Z","bundle_sha256":"974965847b86f194c6a8aac38af12911286c01641579774e740d6f50edd0dbb8"}}