{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:TIP72PRFL5XKFOQXJTUYT5FZQO","short_pith_number":"pith:TIP72PRF","canonical_record":{"source":{"id":"1801.09488","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-01-29T13:06:44Z","cross_cats_sorted":[],"title_canon_sha256":"a6260e727aa4903cc24ca3850acf0530f75962a940fa7c91cf7d00d265a971c4","abstract_canon_sha256":"154339098ce85008a63ad5f8a353278ae749b590dda22668e11cbc5d727fc889"},"schema_version":"1.0"},"canonical_sha256":"9a1ffd3e255f6ea2ba174ce989f4b98398afc72fab15189021879b5648973b99","source":{"kind":"arxiv","id":"1801.09488","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.09488","created_at":"2026-05-18T00:24:57Z"},{"alias_kind":"arxiv_version","alias_value":"1801.09488v1","created_at":"2026-05-18T00:24:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.09488","created_at":"2026-05-18T00:24:57Z"},{"alias_kind":"pith_short_12","alias_value":"TIP72PRFL5XK","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"TIP72PRFL5XKFOQX","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"TIP72PRF","created_at":"2026-05-18T12:32:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:TIP72PRFL5XKFOQXJTUYT5FZQO","target":"record","payload":{"canonical_record":{"source":{"id":"1801.09488","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-01-29T13:06:44Z","cross_cats_sorted":[],"title_canon_sha256":"a6260e727aa4903cc24ca3850acf0530f75962a940fa7c91cf7d00d265a971c4","abstract_canon_sha256":"154339098ce85008a63ad5f8a353278ae749b590dda22668e11cbc5d727fc889"},"schema_version":"1.0"},"canonical_sha256":"9a1ffd3e255f6ea2ba174ce989f4b98398afc72fab15189021879b5648973b99","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:57.283533Z","signature_b64":"KAuAQGclGqk/SyLby5UCMhqzHeNzCbgerYaWSKOZE5zS4aZNNk3VCZdAI20qGQJne3dq65Or/6uWlvU/wdTVBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a1ffd3e255f6ea2ba174ce989f4b98398afc72fab15189021879b5648973b99","last_reissued_at":"2026-05-18T00:24:57.282864Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:57.282864Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.09488","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":"2026-05-18T00:24:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"elJb7tQErEUvk27GF3yOwoznhnvIYvZWFv+LlnKuXvKdEata+FKgTE2G1WeW97CzxLCF2Zujs4Q7ZspItmyECA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T21:29:28.402380Z"},"content_sha256":"571d8b4b7720f8d4c6761e1ce9f2b3965d9b93e2c44be7d353c0fdc0d9ffead8","schema_version":"1.0","event_id":"sha256:571d8b4b7720f8d4c6761e1ce9f2b3965d9b93e2c44be7d353c0fdc0d9ffead8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:TIP72PRFL5XKFOQXJTUYT5FZQO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Which NP-Hard SAT and CSP Problems Admit Exponentially Improved Algorithms?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Magnus Wahlstr\\\"om, Victor Lagerkvist","submitted_at":"2018-01-29T13:06:44Z","abstract_excerpt":"We study the complexity of SAT($\\Gamma$) problems for potentially infinite languages $\\Gamma$ closed under variable negation (sign-symmetric languages). Via an algebraic connection, this reduces to the study of restricted partial polymorphisms of $\\Gamma$ we refer to as \\emph{pSDI-operations} (for partial, self-dual and idempotent). First, we study the language classes themselves. We classify the structure of the least restrictive pSDI-operations, corresponding to the most powerful languages $\\Gamma$, and find that these operations can be divided into \\emph{levels}, corresponding to a rough no"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.09488","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":"2026-05-18T00:24:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j8LCYSAda0xnUtoTXgmKzt8OLCJE5HMHGWQ9m5vgEo/EZbonbQP2QqBVUZBp5RbRM/nPZBv1f/gwZd/a7u1sDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T21:29:28.402723Z"},"content_sha256":"3ceb736946afda6cbd13bb5c20b398e6011db9d801a6bfc4acbd2a3ab9ba0fd7","schema_version":"1.0","event_id":"sha256:3ceb736946afda6cbd13bb5c20b398e6011db9d801a6bfc4acbd2a3ab9ba0fd7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TIP72PRFL5XKFOQXJTUYT5FZQO/bundle.json","state_url":"https://pith.science/pith/TIP72PRFL5XKFOQXJTUYT5FZQO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TIP72PRFL5XKFOQXJTUYT5FZQO/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":"2026-05-19T21:29:28Z","links":{"resolver":"https://pith.science/pith/TIP72PRFL5XKFOQXJTUYT5FZQO","bundle":"https://pith.science/pith/TIP72PRFL5XKFOQXJTUYT5FZQO/bundle.json","state":"https://pith.science/pith/TIP72PRFL5XKFOQXJTUYT5FZQO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TIP72PRFL5XKFOQXJTUYT5FZQO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:TIP72PRFL5XKFOQXJTUYT5FZQO","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":"154339098ce85008a63ad5f8a353278ae749b590dda22668e11cbc5d727fc889","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-01-29T13:06:44Z","title_canon_sha256":"a6260e727aa4903cc24ca3850acf0530f75962a940fa7c91cf7d00d265a971c4"},"schema_version":"1.0","source":{"id":"1801.09488","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.09488","created_at":"2026-05-18T00:24:57Z"},{"alias_kind":"arxiv_version","alias_value":"1801.09488v1","created_at":"2026-05-18T00:24:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.09488","created_at":"2026-05-18T00:24:57Z"},{"alias_kind":"pith_short_12","alias_value":"TIP72PRFL5XK","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"TIP72PRFL5XKFOQX","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"TIP72PRF","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:3ceb736946afda6cbd13bb5c20b398e6011db9d801a6bfc4acbd2a3ab9ba0fd7","target":"graph","created_at":"2026-05-18T00:24:57Z","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 study the complexity of SAT($\\Gamma$) problems for potentially infinite languages $\\Gamma$ closed under variable negation (sign-symmetric languages). Via an algebraic connection, this reduces to the study of restricted partial polymorphisms of $\\Gamma$ we refer to as \\emph{pSDI-operations} (for partial, self-dual and idempotent). First, we study the language classes themselves. We classify the structure of the least restrictive pSDI-operations, corresponding to the most powerful languages $\\Gamma$, and find that these operations can be divided into \\emph{levels}, corresponding to a rough no","authors_text":"Magnus Wahlstr\\\"om, Victor Lagerkvist","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-01-29T13:06:44Z","title":"Which NP-Hard SAT and CSP Problems Admit Exponentially Improved Algorithms?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.09488","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":"sha256:571d8b4b7720f8d4c6761e1ce9f2b3965d9b93e2c44be7d353c0fdc0d9ffead8","target":"record","created_at":"2026-05-18T00:24:57Z","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":"154339098ce85008a63ad5f8a353278ae749b590dda22668e11cbc5d727fc889","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-01-29T13:06:44Z","title_canon_sha256":"a6260e727aa4903cc24ca3850acf0530f75962a940fa7c91cf7d00d265a971c4"},"schema_version":"1.0","source":{"id":"1801.09488","kind":"arxiv","version":1}},"canonical_sha256":"9a1ffd3e255f6ea2ba174ce989f4b98398afc72fab15189021879b5648973b99","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a1ffd3e255f6ea2ba174ce989f4b98398afc72fab15189021879b5648973b99","first_computed_at":"2026-05-18T00:24:57.282864Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:57.282864Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KAuAQGclGqk/SyLby5UCMhqzHeNzCbgerYaWSKOZE5zS4aZNNk3VCZdAI20qGQJne3dq65Or/6uWlvU/wdTVBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:57.283533Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.09488","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:571d8b4b7720f8d4c6761e1ce9f2b3965d9b93e2c44be7d353c0fdc0d9ffead8","sha256:3ceb736946afda6cbd13bb5c20b398e6011db9d801a6bfc4acbd2a3ab9ba0fd7"],"state_sha256":"9163e03c7fe0dc57942c59413783dfb715aa0764c2c577aab2f2627e45f3ef5a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"00oDQLU9eTaACaIivTB8OtC0lZm5pPSOwfgmao74UTAcQ85tZgYjXS5MimBqJhLTotEBD7tBrQiD4JFROZwDBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-19T21:29:28.404575Z","bundle_sha256":"d3a99a56a2fa592be330c486093c6f90b60a63faf8eee3139b927e77e89eb0a1"}}