{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:3BGOOTBA5374FFTMGKAJHLN25R","short_pith_number":"pith:3BGOOTBA","canonical_record":{"source":{"id":"1902.10511","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-02-27T13:15:04Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"d7ab99fb2f4a147e4097f9e8e5d6f76533b858079d66d412f08d148f6c8d6ccf","abstract_canon_sha256":"5a45abcc7bff3fda2e5e4d04046f05c8ff95dd658545fa0cbac377bf3d5c8718"},"schema_version":"1.0"},"canonical_sha256":"d84ce74c20eeffc2966c328093adbaec752439c1ab52f2f5e3540b32eb3c560f","source":{"kind":"arxiv","id":"1902.10511","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.10511","created_at":"2026-05-17T23:52:30Z"},{"alias_kind":"arxiv_version","alias_value":"1902.10511v1","created_at":"2026-05-17T23:52:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.10511","created_at":"2026-05-17T23:52:30Z"},{"alias_kind":"pith_short_12","alias_value":"3BGOOTBA5374","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"3BGOOTBA5374FFTM","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"3BGOOTBA","created_at":"2026-05-18T12:33:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:3BGOOTBA5374FFTMGKAJHLN25R","target":"record","payload":{"canonical_record":{"source":{"id":"1902.10511","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-02-27T13:15:04Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"d7ab99fb2f4a147e4097f9e8e5d6f76533b858079d66d412f08d148f6c8d6ccf","abstract_canon_sha256":"5a45abcc7bff3fda2e5e4d04046f05c8ff95dd658545fa0cbac377bf3d5c8718"},"schema_version":"1.0"},"canonical_sha256":"d84ce74c20eeffc2966c328093adbaec752439c1ab52f2f5e3540b32eb3c560f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:30.682582Z","signature_b64":"gHp1RftWSK3rMQx4aPLwamVxGm2p8HojtKZLimC4OB17d5vGJnUjD4fr4Kj1dBGPYA1mC5uWaZW2b0EM/qriBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d84ce74c20eeffc2966c328093adbaec752439c1ab52f2f5e3540b32eb3c560f","last_reissued_at":"2026-05-17T23:52:30.682096Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:30.682096Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.10511","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":"2026-05-17T23:52:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U+pfzuqxDZKZKIHL/KbmxwrsDaFiMT2n9zlSWEjlBoNaLg4sq8Gh/1+wk4jZ1Q0xFYzQMSgDwwlsKrsvp2x7AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:00:35.188873Z"},"content_sha256":"974362837508ee39177df00ddc5e16c09325e302dbab505fb963d51468350008","schema_version":"1.0","event_id":"sha256:974362837508ee39177df00ddc5e16c09325e302dbab505fb963d51468350008"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:3BGOOTBA5374FFTMGKAJHLN25R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Tenth Hilbert Problem-like Result: The Decidability of MLS with Unordered Cartesian Product","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.CO","authors_text":"Pietro Ursino","submitted_at":"2019-02-27T13:15:04Z","abstract_excerpt":"Using the technique of formative processes, I solve the decidability problem of MLS with unordered cartesian product in the positive. Moreover I give a pure combinatorial description of the satisfiable MLS with unordered cartesian product-formulas for a given number of variables."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.10511","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":"2026-05-17T23:52:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FxCDrKz90nUcUXpKHziecovdSx7Kug+HuMe3SOgPV4m09RNQ4JGT74ZF9cLcsfa6iQl2rrvAwAm45nFuoindDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:00:35.189222Z"},"content_sha256":"740c4a2bc851a79ef55da0cd76da8c6d624343d9149e36a0c8a15d8d475f39e7","schema_version":"1.0","event_id":"sha256:740c4a2bc851a79ef55da0cd76da8c6d624343d9149e36a0c8a15d8d475f39e7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3BGOOTBA5374FFTMGKAJHLN25R/bundle.json","state_url":"https://pith.science/pith/3BGOOTBA5374FFTMGKAJHLN25R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3BGOOTBA5374FFTMGKAJHLN25R/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":"2026-06-06T16:00:35Z","links":{"resolver":"https://pith.science/pith/3BGOOTBA5374FFTMGKAJHLN25R","bundle":"https://pith.science/pith/3BGOOTBA5374FFTMGKAJHLN25R/bundle.json","state":"https://pith.science/pith/3BGOOTBA5374FFTMGKAJHLN25R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3BGOOTBA5374FFTMGKAJHLN25R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:3BGOOTBA5374FFTMGKAJHLN25R","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":"5a45abcc7bff3fda2e5e4d04046f05c8ff95dd658545fa0cbac377bf3d5c8718","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-02-27T13:15:04Z","title_canon_sha256":"d7ab99fb2f4a147e4097f9e8e5d6f76533b858079d66d412f08d148f6c8d6ccf"},"schema_version":"1.0","source":{"id":"1902.10511","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.10511","created_at":"2026-05-17T23:52:30Z"},{"alias_kind":"arxiv_version","alias_value":"1902.10511v1","created_at":"2026-05-17T23:52:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.10511","created_at":"2026-05-17T23:52:30Z"},{"alias_kind":"pith_short_12","alias_value":"3BGOOTBA5374","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"3BGOOTBA5374FFTM","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"3BGOOTBA","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:740c4a2bc851a79ef55da0cd76da8c6d624343d9149e36a0c8a15d8d475f39e7","target":"graph","created_at":"2026-05-17T23:52:30Z","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":"Using the technique of formative processes, I solve the decidability problem of MLS with unordered cartesian product in the positive. Moreover I give a pure combinatorial description of the satisfiable MLS with unordered cartesian product-formulas for a given number of variables.","authors_text":"Pietro Ursino","cross_cats":["math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-02-27T13:15:04Z","title":"A Tenth Hilbert Problem-like Result: The Decidability of MLS with Unordered Cartesian Product"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.10511","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":"sha256:974362837508ee39177df00ddc5e16c09325e302dbab505fb963d51468350008","target":"record","created_at":"2026-05-17T23:52:30Z","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":"5a45abcc7bff3fda2e5e4d04046f05c8ff95dd658545fa0cbac377bf3d5c8718","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-02-27T13:15:04Z","title_canon_sha256":"d7ab99fb2f4a147e4097f9e8e5d6f76533b858079d66d412f08d148f6c8d6ccf"},"schema_version":"1.0","source":{"id":"1902.10511","kind":"arxiv","version":1}},"canonical_sha256":"d84ce74c20eeffc2966c328093adbaec752439c1ab52f2f5e3540b32eb3c560f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d84ce74c20eeffc2966c328093adbaec752439c1ab52f2f5e3540b32eb3c560f","first_computed_at":"2026-05-17T23:52:30.682096Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:30.682096Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gHp1RftWSK3rMQx4aPLwamVxGm2p8HojtKZLimC4OB17d5vGJnUjD4fr4Kj1dBGPYA1mC5uWaZW2b0EM/qriBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:30.682582Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.10511","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:974362837508ee39177df00ddc5e16c09325e302dbab505fb963d51468350008","sha256:740c4a2bc851a79ef55da0cd76da8c6d624343d9149e36a0c8a15d8d475f39e7"],"state_sha256":"61645f52a592a1bc3f20ebb0db8ecbc0ac89c85b0227b82643755cbd5e0bd86c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0i9fkg4KpFCbUE9F/0loyeZosBHYlaDBYPjOu+5jTyy+ooObFYrB08db7t+jLXd6xdWPX8bpzXZi8ySH2+GpCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T16:00:35.191346Z","bundle_sha256":"3e1826c669ef2f39b5ae174b1457cd3f5824ff95c49abd639251b7ff724c2696"}}