{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:4TN354345NSO6QIPDESM6AH442","short_pith_number":"pith:4TN35434","canonical_record":{"source":{"id":"1702.07922","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.FL","submitted_at":"2017-02-25T17:05:35Z","cross_cats_sorted":[],"title_canon_sha256":"361d6eea952db130e2cc34e54c9cc488ebdf10f96d8118c9d1de3decb3851ef9","abstract_canon_sha256":"33efaf1f845234a14697aa6440fe23fd7b11cabb6c9a02b7d2e18dc0dd2a9460"},"schema_version":"1.0"},"canonical_sha256":"e4dbbef37ceb64ef410f1924cf00fce6a7427dd99a33cf567945f72572f4a0b4","source":{"kind":"arxiv","id":"1702.07922","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.07922","created_at":"2026-05-18T00:49:50Z"},{"alias_kind":"arxiv_version","alias_value":"1702.07922v2","created_at":"2026-05-18T00:49:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.07922","created_at":"2026-05-18T00:49:50Z"},{"alias_kind":"pith_short_12","alias_value":"4TN354345NSO","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"4TN354345NSO6QIP","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"4TN35434","created_at":"2026-05-18T12:31:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:4TN354345NSO6QIPDESM6AH442","target":"record","payload":{"canonical_record":{"source":{"id":"1702.07922","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.FL","submitted_at":"2017-02-25T17:05:35Z","cross_cats_sorted":[],"title_canon_sha256":"361d6eea952db130e2cc34e54c9cc488ebdf10f96d8118c9d1de3decb3851ef9","abstract_canon_sha256":"33efaf1f845234a14697aa6440fe23fd7b11cabb6c9a02b7d2e18dc0dd2a9460"},"schema_version":"1.0"},"canonical_sha256":"e4dbbef37ceb64ef410f1924cf00fce6a7427dd99a33cf567945f72572f4a0b4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:50.583723Z","signature_b64":"qhioVu0aG1mSpBrd+UoVQn5nm9SixP1EEWUcYTNawqL+IQDKydx3u7hbALmRh34UQMI+7M3IS1oti42jvu/qCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4dbbef37ceb64ef410f1924cf00fce6a7427dd99a33cf567945f72572f4a0b4","last_reissued_at":"2026-05-18T00:49:50.583213Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:50.583213Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.07922","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":"2026-05-18T00:49:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ry61Ltq9smUrKca1omkJC264xOuPJxVJtg5CiS0ZopMdfCA0CbYRs9WeYavQT+OuvErGdStie4Eri4R7WpFMAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T23:02:36.133889Z"},"content_sha256":"2db6499b47547e8573b96b18e347e8806a73e5b3c204e8700e48d488c4728f63","schema_version":"1.0","event_id":"sha256:2db6499b47547e8573b96b18e347e8806a73e5b3c204e8700e48d488c4728f63"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:4TN354345NSO6QIPDESM6AH442","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Hardness of Solving Simple Word Equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.FL","authors_text":"Dirk Nowotka, Florin Manea, Joel D. Day","submitted_at":"2017-02-25T17:05:35Z","abstract_excerpt":"We investigate the class of regular-ordered word equations. In such equations, each variable occurs at most once in each side and the order of the variables occurring in both sides is the preserved (the variables can be, however, separated by potentially distinct constant factors). Surprisingly, we obtain that solving such simple equations, even when the sides contain exactly the same variables, is NP-hard. By considerations regarding the combinatorial structure of the minimal solutions of the more general quadratic equations we obtain that the satisfiability problem for regular-ordered equati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.07922","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":"2026-05-18T00:49:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LJPpZJBvtx0oxKnjpzrqyY04AsxniELUfmCHB/usTxXsUeMTjEgDeEVclG1D6Mz9RBPqY2OFg2giW+TD7EhiDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T23:02:36.134603Z"},"content_sha256":"fac0f53a6cf2fff89e08326d0c25ad0e5a068c77eef3e60b66f15fa3534f7b83","schema_version":"1.0","event_id":"sha256:fac0f53a6cf2fff89e08326d0c25ad0e5a068c77eef3e60b66f15fa3534f7b83"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4TN354345NSO6QIPDESM6AH442/bundle.json","state_url":"https://pith.science/pith/4TN354345NSO6QIPDESM6AH442/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4TN354345NSO6QIPDESM6AH442/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":"2026-06-10T23:02:36Z","links":{"resolver":"https://pith.science/pith/4TN354345NSO6QIPDESM6AH442","bundle":"https://pith.science/pith/4TN354345NSO6QIPDESM6AH442/bundle.json","state":"https://pith.science/pith/4TN354345NSO6QIPDESM6AH442/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4TN354345NSO6QIPDESM6AH442/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:4TN354345NSO6QIPDESM6AH442","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":"33efaf1f845234a14697aa6440fe23fd7b11cabb6c9a02b7d2e18dc0dd2a9460","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.FL","submitted_at":"2017-02-25T17:05:35Z","title_canon_sha256":"361d6eea952db130e2cc34e54c9cc488ebdf10f96d8118c9d1de3decb3851ef9"},"schema_version":"1.0","source":{"id":"1702.07922","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.07922","created_at":"2026-05-18T00:49:50Z"},{"alias_kind":"arxiv_version","alias_value":"1702.07922v2","created_at":"2026-05-18T00:49:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.07922","created_at":"2026-05-18T00:49:50Z"},{"alias_kind":"pith_short_12","alias_value":"4TN354345NSO","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"4TN354345NSO6QIP","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"4TN35434","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:fac0f53a6cf2fff89e08326d0c25ad0e5a068c77eef3e60b66f15fa3534f7b83","target":"graph","created_at":"2026-05-18T00:49:50Z","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":"We investigate the class of regular-ordered word equations. In such equations, each variable occurs at most once in each side and the order of the variables occurring in both sides is the preserved (the variables can be, however, separated by potentially distinct constant factors). Surprisingly, we obtain that solving such simple equations, even when the sides contain exactly the same variables, is NP-hard. By considerations regarding the combinatorial structure of the minimal solutions of the more general quadratic equations we obtain that the satisfiability problem for regular-ordered equati","authors_text":"Dirk Nowotka, Florin Manea, Joel D. Day","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.FL","submitted_at":"2017-02-25T17:05:35Z","title":"The Hardness of Solving Simple Word Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.07922","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":"sha256:2db6499b47547e8573b96b18e347e8806a73e5b3c204e8700e48d488c4728f63","target":"record","created_at":"2026-05-18T00:49:50Z","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":"33efaf1f845234a14697aa6440fe23fd7b11cabb6c9a02b7d2e18dc0dd2a9460","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.FL","submitted_at":"2017-02-25T17:05:35Z","title_canon_sha256":"361d6eea952db130e2cc34e54c9cc488ebdf10f96d8118c9d1de3decb3851ef9"},"schema_version":"1.0","source":{"id":"1702.07922","kind":"arxiv","version":2}},"canonical_sha256":"e4dbbef37ceb64ef410f1924cf00fce6a7427dd99a33cf567945f72572f4a0b4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e4dbbef37ceb64ef410f1924cf00fce6a7427dd99a33cf567945f72572f4a0b4","first_computed_at":"2026-05-18T00:49:50.583213Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:50.583213Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qhioVu0aG1mSpBrd+UoVQn5nm9SixP1EEWUcYTNawqL+IQDKydx3u7hbALmRh34UQMI+7M3IS1oti42jvu/qCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:50.583723Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.07922","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2db6499b47547e8573b96b18e347e8806a73e5b3c204e8700e48d488c4728f63","sha256:fac0f53a6cf2fff89e08326d0c25ad0e5a068c77eef3e60b66f15fa3534f7b83"],"state_sha256":"9b0cf84c56666c5e74bbd51314aa897510f25830ccfd565635d22411b86f98f0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RPllyudhUOxo8QPZKMVzJCoCGMRDywqqTWA8goynl6hyX+lLr9F8M4CLHxGYtflm4Ce+A27o4+99ZpFHnjdBDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T23:02:36.138521Z","bundle_sha256":"9db299dfe4e00928a129a0c9dc6c2522652728487e81003b355f3dde668fa053"}}