{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:D4BOGEL37ZSNHZCR6AK2CIYG6F","short_pith_number":"pith:D4BOGEL3","canonical_record":{"source":{"id":"2502.06542","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2025-02-10T15:08:22Z","cross_cats_sorted":["cs.ET"],"title_canon_sha256":"0baeb1cf9a2d1d57d7bf5616dbf0fdcf002d27bc554005acd85fb9d91d31e0a7","abstract_canon_sha256":"2714477abf399e6c3b1336f2d13d5c1b2b8aa100cac28de5ce065b8469354607"},"schema_version":"1.0"},"canonical_sha256":"1f02e3117bfe64d3e451f015a12306f14fd5f6b4dd0ddca225259a885f0ae8d1","source":{"kind":"arxiv","id":"2502.06542","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.06542","created_at":"2026-07-05T11:48:22Z"},{"alias_kind":"arxiv_version","alias_value":"2502.06542v1","created_at":"2026-07-05T11:48:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.06542","created_at":"2026-07-05T11:48:22Z"},{"alias_kind":"pith_short_12","alias_value":"D4BOGEL37ZSN","created_at":"2026-07-05T11:48:22Z"},{"alias_kind":"pith_short_16","alias_value":"D4BOGEL37ZSNHZCR","created_at":"2026-07-05T11:48:22Z"},{"alias_kind":"pith_short_8","alias_value":"D4BOGEL3","created_at":"2026-07-05T11:48:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:D4BOGEL37ZSNHZCR6AK2CIYG6F","target":"record","payload":{"canonical_record":{"source":{"id":"2502.06542","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2025-02-10T15:08:22Z","cross_cats_sorted":["cs.ET"],"title_canon_sha256":"0baeb1cf9a2d1d57d7bf5616dbf0fdcf002d27bc554005acd85fb9d91d31e0a7","abstract_canon_sha256":"2714477abf399e6c3b1336f2d13d5c1b2b8aa100cac28de5ce065b8469354607"},"schema_version":"1.0"},"canonical_sha256":"1f02e3117bfe64d3e451f015a12306f14fd5f6b4dd0ddca225259a885f0ae8d1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:48:22.800003Z","signature_b64":"hSozeGsGp9J4zKipMChOTCo9LZqgXvKFu5pj+Uw8bozfw6zeK4mmNKtgVxQwTWqwhHI66+i/f0xF+zExJY7pAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f02e3117bfe64d3e451f015a12306f14fd5f6b4dd0ddca225259a885f0ae8d1","last_reissued_at":"2026-07-05T11:48:22.799476Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:48:22.799476Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2502.06542","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":"2026-07-05T11:48:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JPjKZwC2fGsLo3Y5FsL39KaP3qBf3YvYa5PCgnvdf+1WYnkdt4IuVcgUdbjM2yoL2slA7S8FPaillDnpbRG9BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T02:14:20.185112Z"},"content_sha256":"19de30cad956771aa76c0c97faaf50354a2618554901caa0b9a1e7405ec516f7","schema_version":"1.0","event_id":"sha256:19de30cad956771aa76c0c97faaf50354a2618554901caa0b9a1e7405ec516f7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:D4BOGEL37ZSNHZCR6AK2CIYG6F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hamiltonian formulations of centroid-based clustering","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.ET"],"primary_cat":"quant-ph","authors_text":"Daniel K. Park, Myeonghwan Seong","submitted_at":"2025-02-10T15:08:22Z","abstract_excerpt":"Clustering is a fundamental task in data science that aims to group data based on their similarities. However, defining similarity is often ambiguous, making it challenging to determine the most appropriate objective function for a given dataset. Traditional clustering methods, such as the $k$-means algorithm and weighted maximum $k$-cut, focus on specific objectives -- typically relying on average or pairwise characteristics of the data -- leading to performance that is highly data-dependent. Moreover, incorporating practical constraints into clustering objectives is not straightforward, and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.06542","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/2502.06542/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":"2026-07-05T11:48:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0RNNymzGXBr6X8zEBm3Ijf3fhHr5tFocCdCGwj+MHT9aw5LttC5gewAT1taH2l2FLGe9wAOe4HOARUp3snNMBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T02:14:20.185637Z"},"content_sha256":"4de02d8c1bf416fdaa4f7fb5af0ca3b72c638f65743e11b100bcd22f5a7327c8","schema_version":"1.0","event_id":"sha256:4de02d8c1bf416fdaa4f7fb5af0ca3b72c638f65743e11b100bcd22f5a7327c8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D4BOGEL37ZSNHZCR6AK2CIYG6F/bundle.json","state_url":"https://pith.science/pith/D4BOGEL37ZSNHZCR6AK2CIYG6F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D4BOGEL37ZSNHZCR6AK2CIYG6F/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":"2026-08-10T02:14:20Z","links":{"resolver":"https://pith.science/pith/D4BOGEL37ZSNHZCR6AK2CIYG6F","bundle":"https://pith.science/pith/D4BOGEL37ZSNHZCR6AK2CIYG6F/bundle.json","state":"https://pith.science/pith/D4BOGEL37ZSNHZCR6AK2CIYG6F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D4BOGEL37ZSNHZCR6AK2CIYG6F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:D4BOGEL37ZSNHZCR6AK2CIYG6F","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":"2714477abf399e6c3b1336f2d13d5c1b2b8aa100cac28de5ce065b8469354607","cross_cats_sorted":["cs.ET"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2025-02-10T15:08:22Z","title_canon_sha256":"0baeb1cf9a2d1d57d7bf5616dbf0fdcf002d27bc554005acd85fb9d91d31e0a7"},"schema_version":"1.0","source":{"id":"2502.06542","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.06542","created_at":"2026-07-05T11:48:22Z"},{"alias_kind":"arxiv_version","alias_value":"2502.06542v1","created_at":"2026-07-05T11:48:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.06542","created_at":"2026-07-05T11:48:22Z"},{"alias_kind":"pith_short_12","alias_value":"D4BOGEL37ZSN","created_at":"2026-07-05T11:48:22Z"},{"alias_kind":"pith_short_16","alias_value":"D4BOGEL37ZSNHZCR","created_at":"2026-07-05T11:48:22Z"},{"alias_kind":"pith_short_8","alias_value":"D4BOGEL3","created_at":"2026-07-05T11:48:22Z"}],"graph_snapshots":[{"event_id":"sha256:4de02d8c1bf416fdaa4f7fb5af0ca3b72c638f65743e11b100bcd22f5a7327c8","target":"graph","created_at":"2026-07-05T11:48:22Z","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/2502.06542/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Clustering is a fundamental task in data science that aims to group data based on their similarities. However, defining similarity is often ambiguous, making it challenging to determine the most appropriate objective function for a given dataset. Traditional clustering methods, such as the $k$-means algorithm and weighted maximum $k$-cut, focus on specific objectives -- typically relying on average or pairwise characteristics of the data -- leading to performance that is highly data-dependent. Moreover, incorporating practical constraints into clustering objectives is not straightforward, and ","authors_text":"Daniel K. Park, Myeonghwan Seong","cross_cats":["cs.ET"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2025-02-10T15:08:22Z","title":"Hamiltonian formulations of centroid-based clustering"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.06542","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":"sha256:19de30cad956771aa76c0c97faaf50354a2618554901caa0b9a1e7405ec516f7","target":"record","created_at":"2026-07-05T11:48:22Z","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":"2714477abf399e6c3b1336f2d13d5c1b2b8aa100cac28de5ce065b8469354607","cross_cats_sorted":["cs.ET"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2025-02-10T15:08:22Z","title_canon_sha256":"0baeb1cf9a2d1d57d7bf5616dbf0fdcf002d27bc554005acd85fb9d91d31e0a7"},"schema_version":"1.0","source":{"id":"2502.06542","kind":"arxiv","version":1}},"canonical_sha256":"1f02e3117bfe64d3e451f015a12306f14fd5f6b4dd0ddca225259a885f0ae8d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f02e3117bfe64d3e451f015a12306f14fd5f6b4dd0ddca225259a885f0ae8d1","first_computed_at":"2026-07-05T11:48:22.799476Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:48:22.799476Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hSozeGsGp9J4zKipMChOTCo9LZqgXvKFu5pj+Uw8bozfw6zeK4mmNKtgVxQwTWqwhHI66+i/f0xF+zExJY7pAA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:48:22.800003Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.06542","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:19de30cad956771aa76c0c97faaf50354a2618554901caa0b9a1e7405ec516f7","sha256:4de02d8c1bf416fdaa4f7fb5af0ca3b72c638f65743e11b100bcd22f5a7327c8"],"state_sha256":"9203fa721eaf05c1e1dd649a6384427d94543ccadb600b145c659f71b8ddd131"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cFJNGEZ5PeIe8jvAvSfSUaq3k15JKDginUJDQCVQ6ELqEEQT+xfNDxB+/1wjc102epWwvEhNRQK1HA3djFF5BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T02:14:20.190898Z","bundle_sha256":"3889c3d7db204d055775c713c09a12bb1aef2cb5178c78c5519c0f23e8d67ecc"}}