{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:C32WQBNKJEVDXQFZ25ZMJD7R5R","short_pith_number":"pith:C32WQBNK","canonical_record":{"source":{"id":"1705.05393","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-05-15T18:01:52Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"fb603e11fbdb605eb4068381b7877aafbac999df033444d2ad8dbf3db6254c74","abstract_canon_sha256":"46799003125dff92c06803ffa8066bfe822c047a28d0ab25f31fa1bc55fe7802"},"schema_version":"1.0"},"canonical_sha256":"16f56805aa492a3bc0b9d772c48ff1ec60fd2ca48a4580dea580f9bc3667d2bc","source":{"kind":"arxiv","id":"1705.05393","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.05393","created_at":"2026-05-17T23:43:07Z"},{"alias_kind":"arxiv_version","alias_value":"1705.05393v2","created_at":"2026-05-17T23:43:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.05393","created_at":"2026-05-17T23:43:07Z"},{"alias_kind":"pith_short_12","alias_value":"C32WQBNKJEVD","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"C32WQBNKJEVDXQFZ","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"C32WQBNK","created_at":"2026-05-18T12:31:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:C32WQBNKJEVDXQFZ25ZMJD7R5R","target":"record","payload":{"canonical_record":{"source":{"id":"1705.05393","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-05-15T18:01:52Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"fb603e11fbdb605eb4068381b7877aafbac999df033444d2ad8dbf3db6254c74","abstract_canon_sha256":"46799003125dff92c06803ffa8066bfe822c047a28d0ab25f31fa1bc55fe7802"},"schema_version":"1.0"},"canonical_sha256":"16f56805aa492a3bc0b9d772c48ff1ec60fd2ca48a4580dea580f9bc3667d2bc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:07.272378Z","signature_b64":"6T6OIvXaPz58Z5UBWXMq/6ThlgITOlWDfyXisi+NNYEdmclUF0DEGMhi6gqh4YE9bPAxGRUvPiKalb5yRa40DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"16f56805aa492a3bc0b9d772c48ff1ec60fd2ca48a4580dea580f9bc3667d2bc","last_reissued_at":"2026-05-17T23:43:07.271952Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:07.271952Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.05393","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":"2026-05-17T23:43:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VupL11WsNsjShVJtplA0Ex6SttaZ6yRB/dua4TQWou6yTYhk5ufdnrgeO1bndpBVJgJn/Zp3Vh6s+d0uPQR7Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T15:34:36.931329Z"},"content_sha256":"f1ebfb618655c1be4caacfb0869df9df8bf41abf2b03416a89554435a64ba6a6","schema_version":"1.0","event_id":"sha256:f1ebfb618655c1be4caacfb0869df9df8bf41abf2b03416a89554435a64ba6a6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:C32WQBNKJEVDXQFZ25ZMJD7R5R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A class of exponential neighbourhoods for the quadratic travelling salesman problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"cs.DM","authors_text":"Abraham Punnen, Brad Woods","submitted_at":"2017-05-15T18:01:52Z","abstract_excerpt":"The Quadratic Travelling Salesman Problem (QTSP) is to find a least-cost Hamiltonian cycle in an edge-weighted graph, where costs are defined on all pairs of edges such that each edge in the pair is contained in the Hamiltonian cycle. This is a more general version than the one that appears in the literature as the QTSP, denoted here as the \\emph{adjacent quadratic} TSP, which only considers costs for pairs of adjacent edges. Major directions of research work on the linear TSP include exact algorithms, heuristics, approximation algorithms, polynomially solvable special cases and exponential ne"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.05393","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":"2026-05-17T23:43:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NPUcJhsZ12YcRbhJcfIWOImdRS4hQGoNI210SJCpmz4m2VRKxMJRGbcQ/AQxzbqdyB1sHuT3FsGoD4y8aYRSDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T15:34:36.931683Z"},"content_sha256":"a0972bd544fc7bb9ad00a34d506c99e9cd8ddf6596c5403da8aebc2c334dcdce","schema_version":"1.0","event_id":"sha256:a0972bd544fc7bb9ad00a34d506c99e9cd8ddf6596c5403da8aebc2c334dcdce"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C32WQBNKJEVDXQFZ25ZMJD7R5R/bundle.json","state_url":"https://pith.science/pith/C32WQBNKJEVDXQFZ25ZMJD7R5R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C32WQBNKJEVDXQFZ25ZMJD7R5R/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":"2026-06-22T15:34:36Z","links":{"resolver":"https://pith.science/pith/C32WQBNKJEVDXQFZ25ZMJD7R5R","bundle":"https://pith.science/pith/C32WQBNKJEVDXQFZ25ZMJD7R5R/bundle.json","state":"https://pith.science/pith/C32WQBNKJEVDXQFZ25ZMJD7R5R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C32WQBNKJEVDXQFZ25ZMJD7R5R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:C32WQBNKJEVDXQFZ25ZMJD7R5R","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":"46799003125dff92c06803ffa8066bfe822c047a28d0ab25f31fa1bc55fe7802","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-05-15T18:01:52Z","title_canon_sha256":"fb603e11fbdb605eb4068381b7877aafbac999df033444d2ad8dbf3db6254c74"},"schema_version":"1.0","source":{"id":"1705.05393","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.05393","created_at":"2026-05-17T23:43:07Z"},{"alias_kind":"arxiv_version","alias_value":"1705.05393v2","created_at":"2026-05-17T23:43:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.05393","created_at":"2026-05-17T23:43:07Z"},{"alias_kind":"pith_short_12","alias_value":"C32WQBNKJEVD","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"C32WQBNKJEVDXQFZ","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"C32WQBNK","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:a0972bd544fc7bb9ad00a34d506c99e9cd8ddf6596c5403da8aebc2c334dcdce","target":"graph","created_at":"2026-05-17T23:43:07Z","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":"The Quadratic Travelling Salesman Problem (QTSP) is to find a least-cost Hamiltonian cycle in an edge-weighted graph, where costs are defined on all pairs of edges such that each edge in the pair is contained in the Hamiltonian cycle. This is a more general version than the one that appears in the literature as the QTSP, denoted here as the \\emph{adjacent quadratic} TSP, which only considers costs for pairs of adjacent edges. Major directions of research work on the linear TSP include exact algorithms, heuristics, approximation algorithms, polynomially solvable special cases and exponential ne","authors_text":"Abraham Punnen, Brad Woods","cross_cats":["cs.CC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-05-15T18:01:52Z","title":"A class of exponential neighbourhoods for the quadratic travelling salesman problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.05393","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:f1ebfb618655c1be4caacfb0869df9df8bf41abf2b03416a89554435a64ba6a6","target":"record","created_at":"2026-05-17T23:43:07Z","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":"46799003125dff92c06803ffa8066bfe822c047a28d0ab25f31fa1bc55fe7802","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-05-15T18:01:52Z","title_canon_sha256":"fb603e11fbdb605eb4068381b7877aafbac999df033444d2ad8dbf3db6254c74"},"schema_version":"1.0","source":{"id":"1705.05393","kind":"arxiv","version":2}},"canonical_sha256":"16f56805aa492a3bc0b9d772c48ff1ec60fd2ca48a4580dea580f9bc3667d2bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"16f56805aa492a3bc0b9d772c48ff1ec60fd2ca48a4580dea580f9bc3667d2bc","first_computed_at":"2026-05-17T23:43:07.271952Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:07.271952Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6T6OIvXaPz58Z5UBWXMq/6ThlgITOlWDfyXisi+NNYEdmclUF0DEGMhi6gqh4YE9bPAxGRUvPiKalb5yRa40DA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:07.272378Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.05393","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f1ebfb618655c1be4caacfb0869df9df8bf41abf2b03416a89554435a64ba6a6","sha256:a0972bd544fc7bb9ad00a34d506c99e9cd8ddf6596c5403da8aebc2c334dcdce"],"state_sha256":"8e20b91caf4f8839bfd5cc10c351db5bde584b7cb65cd49a95414eeb0bc8f604"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dYjeU1DxvUW6njcVCGXMxLqodjUcnfuxLt+4WNzuBADaXCZuBdHeEPPAKGk7Jfvr3SGUnEXdW+o5KGCrKubdCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T15:34:36.933645Z","bundle_sha256":"ca67c4df5dc677b3cb0b52b6a22d10d4da74ef9ec7f64635047008ec6f789eec"}}