{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:7B7A75IZNT56HK6PHUFS7DWAMW","short_pith_number":"pith:7B7A75IZ","canonical_record":{"source":{"id":"1504.08011","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"cs.DS","submitted_at":"2015-04-29T20:22:12Z","cross_cats_sorted":["cs.DM","math.CO","quant-ph"],"title_canon_sha256":"3a706fa1e622301ad587d9b691e6b847c07665ff32909b9c86bb340a496a0e2d","abstract_canon_sha256":"4dfef954e9943ef4ddfab1879c82daae1ec9cdd2cdc76f17d22f3d3345797bf8"},"schema_version":"1.0"},"canonical_sha256":"f87e0ff5196cfbe3abcf3d0b2f8ec06583dd24620889b4730e66ceed2a2446ff","source":{"kind":"arxiv","id":"1504.08011","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.08011","created_at":"2026-05-18T01:24:10Z"},{"alias_kind":"arxiv_version","alias_value":"1504.08011v2","created_at":"2026-05-18T01:24:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.08011","created_at":"2026-05-18T01:24:10Z"},{"alias_kind":"pith_short_12","alias_value":"7B7A75IZNT56","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"7B7A75IZNT56HK6P","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"7B7A75IZ","created_at":"2026-05-18T12:29:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:7B7A75IZNT56HK6PHUFS7DWAMW","target":"record","payload":{"canonical_record":{"source":{"id":"1504.08011","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"cs.DS","submitted_at":"2015-04-29T20:22:12Z","cross_cats_sorted":["cs.DM","math.CO","quant-ph"],"title_canon_sha256":"3a706fa1e622301ad587d9b691e6b847c07665ff32909b9c86bb340a496a0e2d","abstract_canon_sha256":"4dfef954e9943ef4ddfab1879c82daae1ec9cdd2cdc76f17d22f3d3345797bf8"},"schema_version":"1.0"},"canonical_sha256":"f87e0ff5196cfbe3abcf3d0b2f8ec06583dd24620889b4730e66ceed2a2446ff","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:10.863291Z","signature_b64":"j2zciF1DVNYF8L1GSABV4so4F4JvN/b+67DTiuGANiypdxgU6AGiAFF6qblM3xFxK9DIEmaitAcvciXP8MLHDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f87e0ff5196cfbe3abcf3d0b2f8ec06583dd24620889b4730e66ceed2a2446ff","last_reissued_at":"2026-05-18T01:24:10.862714Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:10.862714Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.08011","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":"2026-05-18T01:24:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wl8C2mYy+fGSIe018xUCryuahCYQWr/XFLn3ehxjJDKTbEaakfbNYJ2yA2KaIRYs6fYTRsnqLzMkbnFIkd1/Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T17:35:34.585745Z"},"content_sha256":"7b8749fd848fa26e2e4e4249bcb9a7e56c9679c340b68b43261ceb7a1607fff5","schema_version":"1.0","event_id":"sha256:7b8749fd848fa26e2e4e4249bcb9a7e56c9679c340b68b43261ceb7a1607fff5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:7B7A75IZNT56HK6PHUFS7DWAMW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Comparison of Approaches for Solving Hard Graph-Theoretic Problems","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["cs.DM","math.CO","quant-ph"],"primary_cat":"cs.DS","authors_text":"Stanley Bak, Steve Adachi, Victoria Horan","submitted_at":"2015-04-29T20:22:12Z","abstract_excerpt":"In order to formulate mathematical conjectures likely to be true, a number of base cases must be determined. However, many combinatorial problems are NP-hard and the computational complexity makes this research approach difficult using a standard brute force approach on a typical computer. One sample problem explored is that of finding a minimum identifying code. To work around the computational issues, a variety of methods are explored and consist of a parallel computing approach using Matlab, a quantum annealing approach using the D-Wave computer, and lastly using satisfiability modulo theor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.08011","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":"2026-05-18T01:24:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BNAx0GaxrGgilEAsxdCS+y8853y3pZLXIaSw7wlAs1Ah/b8H3apy9JSCXmOKFxKlAMpgHNJhI1iOgY7l8kEADQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T17:35:34.586101Z"},"content_sha256":"ec502fce2dfc6eea04819c6c9afc14830bae9d8a51c13c629bde3622668e396b","schema_version":"1.0","event_id":"sha256:ec502fce2dfc6eea04819c6c9afc14830bae9d8a51c13c629bde3622668e396b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7B7A75IZNT56HK6PHUFS7DWAMW/bundle.json","state_url":"https://pith.science/pith/7B7A75IZNT56HK6PHUFS7DWAMW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7B7A75IZNT56HK6PHUFS7DWAMW/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":"2026-06-03T17:35:34Z","links":{"resolver":"https://pith.science/pith/7B7A75IZNT56HK6PHUFS7DWAMW","bundle":"https://pith.science/pith/7B7A75IZNT56HK6PHUFS7DWAMW/bundle.json","state":"https://pith.science/pith/7B7A75IZNT56HK6PHUFS7DWAMW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7B7A75IZNT56HK6PHUFS7DWAMW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:7B7A75IZNT56HK6PHUFS7DWAMW","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":"4dfef954e9943ef4ddfab1879c82daae1ec9cdd2cdc76f17d22f3d3345797bf8","cross_cats_sorted":["cs.DM","math.CO","quant-ph"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"cs.DS","submitted_at":"2015-04-29T20:22:12Z","title_canon_sha256":"3a706fa1e622301ad587d9b691e6b847c07665ff32909b9c86bb340a496a0e2d"},"schema_version":"1.0","source":{"id":"1504.08011","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.08011","created_at":"2026-05-18T01:24:10Z"},{"alias_kind":"arxiv_version","alias_value":"1504.08011v2","created_at":"2026-05-18T01:24:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.08011","created_at":"2026-05-18T01:24:10Z"},{"alias_kind":"pith_short_12","alias_value":"7B7A75IZNT56","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"7B7A75IZNT56HK6P","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"7B7A75IZ","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:ec502fce2dfc6eea04819c6c9afc14830bae9d8a51c13c629bde3622668e396b","target":"graph","created_at":"2026-05-18T01:24:10Z","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":"In order to formulate mathematical conjectures likely to be true, a number of base cases must be determined. However, many combinatorial problems are NP-hard and the computational complexity makes this research approach difficult using a standard brute force approach on a typical computer. One sample problem explored is that of finding a minimum identifying code. To work around the computational issues, a variety of methods are explored and consist of a parallel computing approach using Matlab, a quantum annealing approach using the D-Wave computer, and lastly using satisfiability modulo theor","authors_text":"Stanley Bak, Steve Adachi, Victoria Horan","cross_cats":["cs.DM","math.CO","quant-ph"],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"cs.DS","submitted_at":"2015-04-29T20:22:12Z","title":"A Comparison of Approaches for Solving Hard Graph-Theoretic Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.08011","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":"sha256:7b8749fd848fa26e2e4e4249bcb9a7e56c9679c340b68b43261ceb7a1607fff5","target":"record","created_at":"2026-05-18T01:24:10Z","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":"4dfef954e9943ef4ddfab1879c82daae1ec9cdd2cdc76f17d22f3d3345797bf8","cross_cats_sorted":["cs.DM","math.CO","quant-ph"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"cs.DS","submitted_at":"2015-04-29T20:22:12Z","title_canon_sha256":"3a706fa1e622301ad587d9b691e6b847c07665ff32909b9c86bb340a496a0e2d"},"schema_version":"1.0","source":{"id":"1504.08011","kind":"arxiv","version":2}},"canonical_sha256":"f87e0ff5196cfbe3abcf3d0b2f8ec06583dd24620889b4730e66ceed2a2446ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f87e0ff5196cfbe3abcf3d0b2f8ec06583dd24620889b4730e66ceed2a2446ff","first_computed_at":"2026-05-18T01:24:10.862714Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:10.862714Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j2zciF1DVNYF8L1GSABV4so4F4JvN/b+67DTiuGANiypdxgU6AGiAFF6qblM3xFxK9DIEmaitAcvciXP8MLHDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:10.863291Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.08011","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7b8749fd848fa26e2e4e4249bcb9a7e56c9679c340b68b43261ceb7a1607fff5","sha256:ec502fce2dfc6eea04819c6c9afc14830bae9d8a51c13c629bde3622668e396b"],"state_sha256":"e15007128b2a2a5b599405b9c8390c77c124505fc763e50c86255f138d80c844"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sSSgAUzNspE91yCUosrd/PCnZb9cDaerbEW8jRjv19ze5B4ziRbQ83D1geiYE2K8p06WeuGagh86CgSGzneFBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T17:35:34.588071Z","bundle_sha256":"e90f0c1461b71ef248634acde4868c801721b39bd476921c14ad77a012e3c047"}}