{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:I367ZGFIYXN5QXMOK7TGOHPJ6I","short_pith_number":"pith:I367ZGFI","canonical_record":{"source":{"id":"1312.2816","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-12-10T14:41:46Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"e45f94feca29210b4f27821cba1f612b203a1c20a7d43859fbda61f313476777","abstract_canon_sha256":"7c0c923b015c47db3709f43c27995bf7d214c306aa307f61dd4f70c82e025cb1"},"schema_version":"1.0"},"canonical_sha256":"46fdfc98a8c5dbd85d8e57e6671de9f21fcbc392d6c10706f58c6b740daf3450","source":{"kind":"arxiv","id":"1312.2816","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.2816","created_at":"2026-05-18T03:05:08Z"},{"alias_kind":"arxiv_version","alias_value":"1312.2816v1","created_at":"2026-05-18T03:05:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.2816","created_at":"2026-05-18T03:05:08Z"},{"alias_kind":"pith_short_12","alias_value":"I367ZGFIYXN5","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"I367ZGFIYXN5QXMO","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"I367ZGFI","created_at":"2026-05-18T12:27:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:I367ZGFIYXN5QXMOK7TGOHPJ6I","target":"record","payload":{"canonical_record":{"source":{"id":"1312.2816","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-12-10T14:41:46Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"e45f94feca29210b4f27821cba1f612b203a1c20a7d43859fbda61f313476777","abstract_canon_sha256":"7c0c923b015c47db3709f43c27995bf7d214c306aa307f61dd4f70c82e025cb1"},"schema_version":"1.0"},"canonical_sha256":"46fdfc98a8c5dbd85d8e57e6671de9f21fcbc392d6c10706f58c6b740daf3450","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:08.673849Z","signature_b64":"Gvm9x2InteqbT3Nflcgdw+T1BvJGseUx4BmAVjwkQn8Dm/4uKQzqQBDcQeX5Y3Tlmqmz+rGazw5miawmiGdkBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46fdfc98a8c5dbd85d8e57e6671de9f21fcbc392d6c10706f58c6b740daf3450","last_reissued_at":"2026-05-18T03:05:08.673197Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:08.673197Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.2816","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":"2026-05-18T03:05:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WEv/9MLoN/fln9qurfdpuiZpUWp81ASYkNmYjoYpLOdt+EL4UdwRy1IonF/bizZ4n6APWxqAB/D2sm3TIC8MDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T14:59:49.961189Z"},"content_sha256":"a8f6cbc68a0fdb83f67fc60c0077ef52b22d7a5035a657c7e0aa6846b3dd9c70","schema_version":"1.0","event_id":"sha256:a8f6cbc68a0fdb83f67fc60c0077ef52b22d7a5035a657c7e0aa6846b3dd9c70"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:I367ZGFIYXN5QXMOK7TGOHPJ6I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Complexity of Change","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Jan van den Heuvel","submitted_at":"2013-12-10T14:41:46Z","abstract_excerpt":"Many combinatorial problems can be formulated as \"Can I transform configuration 1 into configuration 2, if certain transformations only are allowed?\". An example of such a question is: given two k-colourings of a graph, can I transform the first k-colouring into the second one, by recolouring one vertex at a time, and always maintaining a proper k-colouring? Another example is: given two solutions of a SAT-instance, can I transform the first solution into the second one, by changing the truth value one variable at a time, and always maintaining a solution of the SAT-instance? Other examples ca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2816","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":""},"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":"2026-05-18T03:05:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"esB9wtxZQDHtu0Ix9NlRUxDUH5tOBiertbdLCDF98PEopwcco4knFSvX6UAxFWLt8nyN7QGUOJOsZzQEfVytBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T14:59:49.961924Z"},"content_sha256":"c35a998bfc6719fabe469201698cfe5df030df74ca74d452a6be06e8ffa575c3","schema_version":"1.0","event_id":"sha256:c35a998bfc6719fabe469201698cfe5df030df74ca74d452a6be06e8ffa575c3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I367ZGFIYXN5QXMOK7TGOHPJ6I/bundle.json","state_url":"https://pith.science/pith/I367ZGFIYXN5QXMOK7TGOHPJ6I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I367ZGFIYXN5QXMOK7TGOHPJ6I/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":"2026-06-11T14:59:49Z","links":{"resolver":"https://pith.science/pith/I367ZGFIYXN5QXMOK7TGOHPJ6I","bundle":"https://pith.science/pith/I367ZGFIYXN5QXMOK7TGOHPJ6I/bundle.json","state":"https://pith.science/pith/I367ZGFIYXN5QXMOK7TGOHPJ6I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I367ZGFIYXN5QXMOK7TGOHPJ6I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:I367ZGFIYXN5QXMOK7TGOHPJ6I","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":"7c0c923b015c47db3709f43c27995bf7d214c306aa307f61dd4f70c82e025cb1","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-12-10T14:41:46Z","title_canon_sha256":"e45f94feca29210b4f27821cba1f612b203a1c20a7d43859fbda61f313476777"},"schema_version":"1.0","source":{"id":"1312.2816","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.2816","created_at":"2026-05-18T03:05:08Z"},{"alias_kind":"arxiv_version","alias_value":"1312.2816v1","created_at":"2026-05-18T03:05:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.2816","created_at":"2026-05-18T03:05:08Z"},{"alias_kind":"pith_short_12","alias_value":"I367ZGFIYXN5","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"I367ZGFIYXN5QXMO","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"I367ZGFI","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:c35a998bfc6719fabe469201698cfe5df030df74ca74d452a6be06e8ffa575c3","target":"graph","created_at":"2026-05-18T03:05:08Z","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":"Many combinatorial problems can be formulated as \"Can I transform configuration 1 into configuration 2, if certain transformations only are allowed?\". An example of such a question is: given two k-colourings of a graph, can I transform the first k-colouring into the second one, by recolouring one vertex at a time, and always maintaining a proper k-colouring? Another example is: given two solutions of a SAT-instance, can I transform the first solution into the second one, by changing the truth value one variable at a time, and always maintaining a solution of the SAT-instance? Other examples ca","authors_text":"Jan van den Heuvel","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-12-10T14:41:46Z","title":"The Complexity of Change"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2816","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:a8f6cbc68a0fdb83f67fc60c0077ef52b22d7a5035a657c7e0aa6846b3dd9c70","target":"record","created_at":"2026-05-18T03:05:08Z","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":"7c0c923b015c47db3709f43c27995bf7d214c306aa307f61dd4f70c82e025cb1","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-12-10T14:41:46Z","title_canon_sha256":"e45f94feca29210b4f27821cba1f612b203a1c20a7d43859fbda61f313476777"},"schema_version":"1.0","source":{"id":"1312.2816","kind":"arxiv","version":1}},"canonical_sha256":"46fdfc98a8c5dbd85d8e57e6671de9f21fcbc392d6c10706f58c6b740daf3450","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"46fdfc98a8c5dbd85d8e57e6671de9f21fcbc392d6c10706f58c6b740daf3450","first_computed_at":"2026-05-18T03:05:08.673197Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:08.673197Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Gvm9x2InteqbT3Nflcgdw+T1BvJGseUx4BmAVjwkQn8Dm/4uKQzqQBDcQeX5Y3Tlmqmz+rGazw5miawmiGdkBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:08.673849Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.2816","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a8f6cbc68a0fdb83f67fc60c0077ef52b22d7a5035a657c7e0aa6846b3dd9c70","sha256:c35a998bfc6719fabe469201698cfe5df030df74ca74d452a6be06e8ffa575c3"],"state_sha256":"20b80a34cf1e3ef915b2c1ce4d2c096fc27bf2ed83da9d8fa4625b28994a795c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uZZYoSojx3GgL9pob8753fSbyeUc3TL59aZi9IorwtXk+ALgAKFOUTD8FN4wrZeSul5E/SeNgVoAysX7gG6vDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T14:59:49.965851Z","bundle_sha256":"716e56fed27629045be6ec5c1d690d1a974d1286112942873b768abb4a06a1c1"}}