{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:L46LB5K7V64AMDIFCMG72MD7U4","short_pith_number":"pith:L46LB5K7","canonical_record":{"source":{"id":"1208.1152","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-08-06T12:51:54Z","cross_cats_sorted":["math.CA","math.LO"],"title_canon_sha256":"462d11d612e930fd589d57dca06a35d9f62445068e26041cac98b5fb95f2d526","abstract_canon_sha256":"41d8f94ca0b7693d47d4055ae66cb2ff67a8e182d845b05c8174ed46851c33f1"},"schema_version":"1.0"},"canonical_sha256":"5f3cb0f55fafb8060d05130dfd307fa72570016ca2c7c2e8364fd6537fbd0237","source":{"kind":"arxiv","id":"1208.1152","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.1152","created_at":"2026-05-18T02:54:21Z"},{"alias_kind":"arxiv_version","alias_value":"1208.1152v2","created_at":"2026-05-18T02:54:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.1152","created_at":"2026-05-18T02:54:21Z"},{"alias_kind":"pith_short_12","alias_value":"L46LB5K7V64A","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"L46LB5K7V64AMDIF","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"L46LB5K7","created_at":"2026-05-18T12:27:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:L46LB5K7V64AMDIFCMG72MD7U4","target":"record","payload":{"canonical_record":{"source":{"id":"1208.1152","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-08-06T12:51:54Z","cross_cats_sorted":["math.CA","math.LO"],"title_canon_sha256":"462d11d612e930fd589d57dca06a35d9f62445068e26041cac98b5fb95f2d526","abstract_canon_sha256":"41d8f94ca0b7693d47d4055ae66cb2ff67a8e182d845b05c8174ed46851c33f1"},"schema_version":"1.0"},"canonical_sha256":"5f3cb0f55fafb8060d05130dfd307fa72570016ca2c7c2e8364fd6537fbd0237","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:21.765609Z","signature_b64":"0Myn/4QY/GtE1fYq+B/0dKmCzHxWtRiSWimPGzUKnKoUhyLVjS8Ig4tEYsn2etMCGWkRIEYm8UtEr9HFx6AkAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f3cb0f55fafb8060d05130dfd307fa72570016ca2c7c2e8364fd6537fbd0237","last_reissued_at":"2026-05-18T02:54:21.765159Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:21.765159Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.1152","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":"2026-05-18T02:54:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rm/ehZzoVuIqGvQS9kvZqYpA3668Phtg8If1s46c72DIO8OJztax2hPbLHQ+4FUTn6skSm2DOBDWt6y/eqA6Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T03:57:22.993201Z"},"content_sha256":"50fcd5942bead88e82f36a32b26909cf64c8f93b48ac742a166d1ee0c313837d","schema_version":"1.0","event_id":"sha256:50fcd5942bead88e82f36a32b26909cf64c8f93b48ac742a166d1ee0c313837d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:L46LB5K7V64AMDIFCMG72MD7U4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Computing Constraint Sets for Differential Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.LO"],"primary_cat":"math.AC","authors_text":"Alexey Ovchinnikov, Dmitry Trushin, Russell Miller","submitted_at":"2012-08-06T12:51:54Z","abstract_excerpt":"Kronecker's Theorem and Rabin's Theorem are fundamental results about computable fields F and the decidability of the set of irreducible polynomials over F. We adapt these theorems to the setting of differential fields K, with constrained pairs of differential polynomials over K assuming the role of the irreducible polynomials. We prove that two of the three basic aspects of Kronecker's Theorem remain true here, and that the reducibility in one direction (but not the other) from Rabin's Theorem also continues to hold."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1152","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":"2026-05-18T02:54:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IJVzk+FSkSeOVQxKtAJoRtA45jyvqPT950iDOixB5nyo1VOMyfBaN9zMqcVajKCvYPwicfzXqmCY18O5EhRMBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T03:57:22.993559Z"},"content_sha256":"06a13b37b06bf6357e4d89c72c6cc2cc467ccacd273409d71812a2b90544db12","schema_version":"1.0","event_id":"sha256:06a13b37b06bf6357e4d89c72c6cc2cc467ccacd273409d71812a2b90544db12"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L46LB5K7V64AMDIFCMG72MD7U4/bundle.json","state_url":"https://pith.science/pith/L46LB5K7V64AMDIFCMG72MD7U4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L46LB5K7V64AMDIFCMG72MD7U4/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":"2026-06-23T03:57:22Z","links":{"resolver":"https://pith.science/pith/L46LB5K7V64AMDIFCMG72MD7U4","bundle":"https://pith.science/pith/L46LB5K7V64AMDIFCMG72MD7U4/bundle.json","state":"https://pith.science/pith/L46LB5K7V64AMDIFCMG72MD7U4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L46LB5K7V64AMDIFCMG72MD7U4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:L46LB5K7V64AMDIFCMG72MD7U4","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":"41d8f94ca0b7693d47d4055ae66cb2ff67a8e182d845b05c8174ed46851c33f1","cross_cats_sorted":["math.CA","math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-08-06T12:51:54Z","title_canon_sha256":"462d11d612e930fd589d57dca06a35d9f62445068e26041cac98b5fb95f2d526"},"schema_version":"1.0","source":{"id":"1208.1152","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.1152","created_at":"2026-05-18T02:54:21Z"},{"alias_kind":"arxiv_version","alias_value":"1208.1152v2","created_at":"2026-05-18T02:54:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.1152","created_at":"2026-05-18T02:54:21Z"},{"alias_kind":"pith_short_12","alias_value":"L46LB5K7V64A","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"L46LB5K7V64AMDIF","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"L46LB5K7","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:06a13b37b06bf6357e4d89c72c6cc2cc467ccacd273409d71812a2b90544db12","target":"graph","created_at":"2026-05-18T02:54:21Z","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":"Kronecker's Theorem and Rabin's Theorem are fundamental results about computable fields F and the decidability of the set of irreducible polynomials over F. We adapt these theorems to the setting of differential fields K, with constrained pairs of differential polynomials over K assuming the role of the irreducible polynomials. We prove that two of the three basic aspects of Kronecker's Theorem remain true here, and that the reducibility in one direction (but not the other) from Rabin's Theorem also continues to hold.","authors_text":"Alexey Ovchinnikov, Dmitry Trushin, Russell Miller","cross_cats":["math.CA","math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-08-06T12:51:54Z","title":"Computing Constraint Sets for Differential Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1152","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":"sha256:50fcd5942bead88e82f36a32b26909cf64c8f93b48ac742a166d1ee0c313837d","target":"record","created_at":"2026-05-18T02:54:21Z","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":"41d8f94ca0b7693d47d4055ae66cb2ff67a8e182d845b05c8174ed46851c33f1","cross_cats_sorted":["math.CA","math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-08-06T12:51:54Z","title_canon_sha256":"462d11d612e930fd589d57dca06a35d9f62445068e26041cac98b5fb95f2d526"},"schema_version":"1.0","source":{"id":"1208.1152","kind":"arxiv","version":2}},"canonical_sha256":"5f3cb0f55fafb8060d05130dfd307fa72570016ca2c7c2e8364fd6537fbd0237","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5f3cb0f55fafb8060d05130dfd307fa72570016ca2c7c2e8364fd6537fbd0237","first_computed_at":"2026-05-18T02:54:21.765159Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:21.765159Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0Myn/4QY/GtE1fYq+B/0dKmCzHxWtRiSWimPGzUKnKoUhyLVjS8Ig4tEYsn2etMCGWkRIEYm8UtEr9HFx6AkAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:21.765609Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.1152","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:50fcd5942bead88e82f36a32b26909cf64c8f93b48ac742a166d1ee0c313837d","sha256:06a13b37b06bf6357e4d89c72c6cc2cc467ccacd273409d71812a2b90544db12"],"state_sha256":"c7fed0107116861fc605eb40b352a2eb34936d9ac14a6ef33d2975f9662f0ec6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JAIlkGTuoLdxSKCc2OgZlunrIKdgn6I1NgNSfx8TKCJHQGdqzrFUnm0VStQACLuTQxA9GgWll6U7hpaJ65LtDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T03:57:22.995453Z","bundle_sha256":"4c476affd5d2e70abe993240bd6e7ba94a6cf31fa89bd97f6deb40910d5c5fc7"}}