{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:IMXX6DP3SMJCFMS2XVUF6ZANHH","short_pith_number":"pith:IMXX6DP3","canonical_record":{"source":{"id":"1604.05843","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2016-04-20T06:53:18Z","cross_cats_sorted":[],"title_canon_sha256":"cc6bb72d0e8416de9c9fbcf8ce6b0b9e59c5c4b305048d01cfcc35133087b8d9","abstract_canon_sha256":"12b8a682e654576bcbd4cee811eb0619ded586afe75c43af4ff6050822755de5"},"schema_version":"1.0"},"canonical_sha256":"432f7f0dfb931222b25abd685f640d39c360b83c5d89ca4b2b337a678b2e4d4b","source":{"kind":"arxiv","id":"1604.05843","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.05843","created_at":"2026-05-18T01:16:35Z"},{"alias_kind":"arxiv_version","alias_value":"1604.05843v1","created_at":"2026-05-18T01:16:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.05843","created_at":"2026-05-18T01:16:35Z"},{"alias_kind":"pith_short_12","alias_value":"IMXX6DP3SMJC","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IMXX6DP3SMJCFMS2","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IMXX6DP3","created_at":"2026-05-18T12:30:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:IMXX6DP3SMJCFMS2XVUF6ZANHH","target":"record","payload":{"canonical_record":{"source":{"id":"1604.05843","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2016-04-20T06:53:18Z","cross_cats_sorted":[],"title_canon_sha256":"cc6bb72d0e8416de9c9fbcf8ce6b0b9e59c5c4b305048d01cfcc35133087b8d9","abstract_canon_sha256":"12b8a682e654576bcbd4cee811eb0619ded586afe75c43af4ff6050822755de5"},"schema_version":"1.0"},"canonical_sha256":"432f7f0dfb931222b25abd685f640d39c360b83c5d89ca4b2b337a678b2e4d4b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:35.330411Z","signature_b64":"u7F/MtDwh76DBYj4G7M4tJJ5FwIvI8alDyS2s3HI3wyqAxvBBIy863iOa/xQb3Opt8jSYkVJIUMoQdOCFqWjCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"432f7f0dfb931222b25abd685f640d39c360b83c5d89ca4b2b337a678b2e4d4b","last_reissued_at":"2026-05-18T01:16:35.329862Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:35.329862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.05843","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":"2026-05-18T01:16:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3zNiADTF45B0T1YDN8LmZY2ijNoXSCuI9cGZR8aHRwILwTmAMfKJ0MrSVXhoZ+YgW/Q7ZaaP/UYRxpJ2GV6oCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T11:09:33.752100Z"},"content_sha256":"af52eb503ef62d0a31f064d1487136ab5e937aec397dcb3a7041d870f66ed85b","schema_version":"1.0","event_id":"sha256:af52eb503ef62d0a31f064d1487136ab5e937aec397dcb3a7041d870f66ed85b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:IMXX6DP3SMJCFMS2XVUF6ZANHH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Order-Invariance of Two-Variable Logic is Decidable","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Frederik Harwath, Thomas Zeume","submitted_at":"2016-04-20T06:53:18Z","abstract_excerpt":"It is shown that order-invariance of two-variable first-logic is decidable in the finite. This is an immediate consequence of a decision procedure obtained for the finite satisfiability problem for existential second-order logic with two first-order variables ($\\mathrm{ESO}^2$) on structures with two linear orders and one induced successor. We also show that finite satisfiability is decidable on structures with two successors and one induced linear order. In both cases, so far only decidability for monadic $\\mathrm{ESO}^2$ has been known. In addition, the finite satisfiability problem for $\\ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.05843","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":"2026-05-18T01:16:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IStCe0K19Vf/wPnRaMxvz7QVi6owhLtVHMpYNQFqX27dW+5Nf6fS3j6peX2NYcySSY80kMLMAiM/1ebw9iccCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T11:09:33.752463Z"},"content_sha256":"54245dfdfd10d4093183a7118ff67c24f3f2146a55f66d9a06c4f775fed091e8","schema_version":"1.0","event_id":"sha256:54245dfdfd10d4093183a7118ff67c24f3f2146a55f66d9a06c4f775fed091e8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IMXX6DP3SMJCFMS2XVUF6ZANHH/bundle.json","state_url":"https://pith.science/pith/IMXX6DP3SMJCFMS2XVUF6ZANHH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IMXX6DP3SMJCFMS2XVUF6ZANHH/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":"2026-05-28T11:09:33Z","links":{"resolver":"https://pith.science/pith/IMXX6DP3SMJCFMS2XVUF6ZANHH","bundle":"https://pith.science/pith/IMXX6DP3SMJCFMS2XVUF6ZANHH/bundle.json","state":"https://pith.science/pith/IMXX6DP3SMJCFMS2XVUF6ZANHH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IMXX6DP3SMJCFMS2XVUF6ZANHH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:IMXX6DP3SMJCFMS2XVUF6ZANHH","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":"12b8a682e654576bcbd4cee811eb0619ded586afe75c43af4ff6050822755de5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2016-04-20T06:53:18Z","title_canon_sha256":"cc6bb72d0e8416de9c9fbcf8ce6b0b9e59c5c4b305048d01cfcc35133087b8d9"},"schema_version":"1.0","source":{"id":"1604.05843","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.05843","created_at":"2026-05-18T01:16:35Z"},{"alias_kind":"arxiv_version","alias_value":"1604.05843v1","created_at":"2026-05-18T01:16:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.05843","created_at":"2026-05-18T01:16:35Z"},{"alias_kind":"pith_short_12","alias_value":"IMXX6DP3SMJC","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IMXX6DP3SMJCFMS2","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IMXX6DP3","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:54245dfdfd10d4093183a7118ff67c24f3f2146a55f66d9a06c4f775fed091e8","target":"graph","created_at":"2026-05-18T01:16:35Z","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":"It is shown that order-invariance of two-variable first-logic is decidable in the finite. This is an immediate consequence of a decision procedure obtained for the finite satisfiability problem for existential second-order logic with two first-order variables ($\\mathrm{ESO}^2$) on structures with two linear orders and one induced successor. We also show that finite satisfiability is decidable on structures with two successors and one induced linear order. In both cases, so far only decidability for monadic $\\mathrm{ESO}^2$ has been known. In addition, the finite satisfiability problem for $\\ma","authors_text":"Frederik Harwath, Thomas Zeume","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2016-04-20T06:53:18Z","title":"Order-Invariance of Two-Variable Logic is Decidable"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.05843","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:af52eb503ef62d0a31f064d1487136ab5e937aec397dcb3a7041d870f66ed85b","target":"record","created_at":"2026-05-18T01:16:35Z","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":"12b8a682e654576bcbd4cee811eb0619ded586afe75c43af4ff6050822755de5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2016-04-20T06:53:18Z","title_canon_sha256":"cc6bb72d0e8416de9c9fbcf8ce6b0b9e59c5c4b305048d01cfcc35133087b8d9"},"schema_version":"1.0","source":{"id":"1604.05843","kind":"arxiv","version":1}},"canonical_sha256":"432f7f0dfb931222b25abd685f640d39c360b83c5d89ca4b2b337a678b2e4d4b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"432f7f0dfb931222b25abd685f640d39c360b83c5d89ca4b2b337a678b2e4d4b","first_computed_at":"2026-05-18T01:16:35.329862Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:35.329862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u7F/MtDwh76DBYj4G7M4tJJ5FwIvI8alDyS2s3HI3wyqAxvBBIy863iOa/xQb3Opt8jSYkVJIUMoQdOCFqWjCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:35.330411Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.05843","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:af52eb503ef62d0a31f064d1487136ab5e937aec397dcb3a7041d870f66ed85b","sha256:54245dfdfd10d4093183a7118ff67c24f3f2146a55f66d9a06c4f775fed091e8"],"state_sha256":"f4510a43b10332db98907d91e4abd365a414ccafa32ec4e9db64224989c573a5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kNnUC2zW0sKzJ0JU+M92TwGZBsj7eldDLZ11MFruhOLQ1/tXDogXD1FeAqHCm7lelfLAtgg0wRDPak5GM1CkBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T11:09:33.754404Z","bundle_sha256":"b120bcfdb0607017ed4c2e1983c750d454e0b3627c38abb30dffdbc9ad77f1ee"}}