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problem | problem:plane-constant-jacobian:v1 | Polynomial plane map with nonzero constant Jacobian | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | ["k is a field of characteristic zero.","p,q belong to k[x,y].","p_x q_y-p_y q_x belongs to k* (a nonzero constant)."] | null | null | ["The original user requested a complete affirmative proof surviving adversarial audit and diverse, dynamically managed subagent approaches.","The original user limited public search to ordinary background and standard named theorems; no exact-problem solution or status search.","The original user asked for at least ei... | null | null | null | ["math.polynomial_automorphisms","math.algebraic_geometry"] | problem:plane-constant-jacobian | null | null | null | null | null | {} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | prove | null | null | null | null | null | archive-extractor-batch-001 | model | null | null | null | {} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | extracted | [] | [{"record_id":"artifact:original-user-request-excerpt.txt:v1","selector":{"kind":"whole"}}] | null | null | null | null | null | null | null | null | null | null | null | 2026-09-14T06:16:08.885889+00:00 | null | 1 | null | null | 1.0.0 | null | null | null | null | null | null | null | null | math.plane-constant-jacobian | Let k be a field of characteristic zero and p,q in k[x,y]. If p_x q_y-p_y q_x is a nonzero constant, is F=(p,q):k^2 -> k^2 a polynomial automorphism? | null | null | null | null | null | null | A complete proof that every pair under the original hypotheses has a polynomial inverse over k, surviving the requested adversarial audit. Scoped results alone do not meet this criterion. | null | null | null | 1.0.0 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
branch | branch:rational-remainder:v1 | null | Rational remainder and finite pole defects | problem:plane-constant-jacobian:v1 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | branch:rational-remainder | null | null | null | null | null | {} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | ["valuation","elimination"] | ["math.rational_remainder"] | null | null | null | Determine the rational remainder degree and its finite pole budget in the actual s=1 primitive system. | null | null | [] | null | null | null | archive-extractor-batch-001 | model | null | null | null | null | null | null | null | null | inferred | null | inferred | inferred | null | null | null | null | null | null | null | Dataset grouping by mathematical objective. This does not reconstruct a historical assignment or imply an enacted branch state. | extracted | [] | [{"record_id":"artifact:rational-square-remainder-root-round599.md:v1","selector":{"kind":"line_range","start":1,"end":20}},{"record_id":"artifact:audit599-rational-remainder-defects-round600.md:v1","selector":{"kind":"line_range","start":109,"end":210}}] | null | null | null | null | null | null | null | null | null | null | null | 2026-09-14T06:16:08.885889+00:00 | null | 1 | null | null | 1.0.0 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | 1.0.0 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
branch | branch:primitive-countercontrols:v1 | null | Limits of primitive and norm constraints | problem:plane-constant-jacobian:v1 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | branch:primitive-countercontrols | null | null | null | null | null | {} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | ["countermodel","differential_operators"] | ["math.primitive_countercontrols"] | null | null | null | Separate partial primitive equations, full equations, source marks and actual nonsingularity by explicit controls. | null | null | [] | null | null | null | archive-extractor-batch-001 | model | null | null | null | null | null | null | null | null | inferred | null | inferred | inferred | null | null | null | null | null | null | null | Dataset grouping by mathematical objective. This does not reconstruct a historical assignment or imply an enacted branch state. | extracted | [] | [{"record_id":"artifact:audit599-rational-remainder-defects-round600.md:v1","selector":{"kind":"line_range","start":449,"end":507}}] | null | null | null | null | null | null | null | null | null | null | null | 2026-09-14T06:16:08.885889+00:00 | null | 1 | null | null | 1.0.0 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | 1.0.0 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
branch | branch:unmarked-block-base:v1 | null | Polynomial base for a given rational Hamiltonian block | problem:plane-constant-jacobian:v1 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | branch:unmarked-block-base | null | null | null | null | null | {} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | ["ramification","invariant_algebra","degree_counting"] | ["math.unmarked_block_base"] | null | null | null | Prove total ramification at source infinity under a given rational Hamiltonian block hypothesis. | null | null | [] | null | null | null | archive-extractor-batch-001 | model | null | null | null | null | null | null | null | null | inferred | null | inferred | inferred | null | null | null | null | null | null | null | Dataset grouping by mathematical objective. This does not reconstruct a historical assignment or imply an enacted branch state. | extracted | [] | [{"record_id":"artifact:unmarked-block-polynomial-base-root-round603.md:v1","selector":{"kind":"line_range","start":1,"end":18}}] | null | null | null | null | null | null | null | null | null | null | null | 2026-09-14T06:16:08.885889+00:00 | null | 1 | null | null | 1.0.0 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | 1.0.0 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
branch | branch:split-source:v1 | null | All-square source exclusion for s=1 | problem:plane-constant-jacobian:v1 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | branch:split-source | null | null | null | null | null | {} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | ["valuation","elimination","degree_counting"] | ["math.split_source"] | null | null | null | Exclude square discriminants in the actual s=1 source with its full primitive inputs. | null | null | [] | null | null | null | archive-extractor-batch-001 | model | null | null | null | null | null | null | null | null | inferred | null | inferred | inferred | null | null | null | null | null | null | null | Dataset grouping by mathematical objective. This does not reconstruct a historical assignment or imply an enacted branch state. | extracted | [] | [{"record_id":"artifact:split-discriminant-source-root-round605.md:v1","selector":{"kind":"line_range","start":1,"end":22}}] | null | null | null | null | null | null | null | null | null | null | null | 2026-09-14T06:16:08.885889+00:00 | null | 1 | null | null | 1.0.0 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | 1.0.0 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
branch | branch:direct-one-root:v1 | null | Direct one-root source singularity | problem:plane-constant-jacobian:v1 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | branch:direct-one-root | null | null | null | null | null | {} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | ["elimination","valuation","degree_counting"] | ["math.direct_one_root"] | null | null | null | Exclude one-root discriminants from the displayed actual source by the literal gradient and marked origin. | null | null | [] | null | null | null | archive-extractor-batch-001 | model | null | null | null | null | null | null | null | null | inferred | null | inferred | inferred | null | null | null | null | null | null | null | Dataset grouping by mathematical objective. This does not reconstruct a historical assignment or imply an enacted branch state. | extracted | [] | [{"record_id":"artifact:one-root-discriminant-direct-root-round609.md:v1","selector":{"kind":"line_range","start":1,"end":16}},{"record_id":"artifact:one-root-any-parity-source-root-round611.md:v1","selector":{"kind":"line_range","start":1,"end":16}}] | null | null | null | null | null | null | null | null | null | null | null | 2026-09-14T06:16:08.885889+00:00 | null | 1 | null | null | 1.0.0 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | 1.0.0 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
branch | branch:checker-repair:v1 | null | Independent checker repair and replay | problem:plane-constant-jacobian:v1 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | branch:checker-repair | null | null | null | null | null | {} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | ["finite_search"] | ["math.checker_repair"] | null | null | null | Repair and replay the saved round610 checker without changing the scoped mathematical argument. | null | null | [] | null | null | null | archive-extractor-batch-001 | model | null | null | null | null | null | null | null | null | inferred | null | inferred | inferred | null | null | null | null | null | null | null | Dataset grouping by mathematical objective. This does not reconstruct a historical assignment or imply an enacted branch state. | extracted | [] | [{"record_id":"artifact:audit609-610-614-root-closure.md:v1","selector":{"kind":"line_range","start":1,"end":30}}] | null | null | null | null | null | null | null | null | null | null | null | 2026-09-14T06:16:08.885889+00:00 | null | 1 | null | null | 1.0.0 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | 1.0.0 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
branch | branch:early-canonical-frame:v1 | null | Canonical derivations and truncation | problem:plane-constant-jacobian:v1 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | branch:early-canonical-frame | null | null | null | null | null | {} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | ["differential_operators","formal_expansion"] | ["math.early_canonical_frame"] | null | null | null | Extract the canonical commuting frame and the precise local-nilpotence or formal-truncation criteria. | null | null | [] | null | null | null | archive-extractor-batch-001 | model | null | null | null | null | null | null | null | null | inferred | null | inferred | inferred | null | null | null | null | null | null | null | Dataset grouping by mathematical objective. This does not reconstruct a historical assignment or imply an enacted branch state. | extracted | [] | [{"record_id":"artifact:algebra-initial.md:v1","selector":{"kind":"line_range","start":3,"end":83}}] | null | null | null | null | null | null | null | null | null | null | null | 2026-09-14T06:16:08.885889+00:00 | null | 1 | null | null | 1.0.0 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | 1.0.0 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
branch | branch:early-flow-countermodels:v1 | null | Limits of sliced and formal flows | problem:plane-constant-jacobian:v1 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | branch:early-flow-countermodels | null | null | null | null | null | {} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | ["countermodel","differential_operators"] | ["math.early_flow_countermodels"] | null | null | null | Test which source, divergence, and polynomial-slice assumptions are needed for flow completeness. | null | null | [] | null | null | null | archive-extractor-batch-001 | model | null | null | null | null | null | null | null | null | inferred | null | inferred | inferred | null | null | null | null | null | null | null | Dataset grouping by mathematical objective. This does not reconstruct a historical assignment or imply an enacted branch state. | extracted | [] | [{"record_id":"artifact:algebra-initial.md:v1","selector":{"kind":"line_range","start":85,"end":113}},{"record_id":"artifact:adversarial-initial.md:v1","selector":{"kind":"line_range","start":208,"end":230}}] | null | null | null | null | null | null | null | null | null | null | null | 2026-09-14T06:16:08.885889+00:00 | null | 1 | null | null | 1.0.0 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | 1.0.0 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
branch | branch:early-low-degree:v1 | null | Component degree at most two | problem:plane-constant-jacobian:v1 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | branch:early-low-degree | null | null | null | null | null | {} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | ["degree_counting","differential_operators"] | ["math.early_low_degree"] | null | null | null | Prove the original conclusion under a component-degree-at-most-two restriction. | null | null | [] | null | null | null | archive-extractor-batch-001 | model | null | null | null | null | null | null | null | null | inferred | null | inferred | inferred | null | null | null | null | null | null | null | Dataset grouping by mathematical objective. This does not reconstruct a historical assignment or imply an enacted branch state. | extracted | [] | [{"record_id":"artifact:algebra-initial.md:v1","selector":{"kind":"line_range","start":115,"end":133}}] | null | null | null | null | null | null | null | null | null | null | null | 2026-09-14T06:16:08.885889+00:00 | null | 1 | null | null | 1.0.0 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | 1.0.0 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
branch | branch:early-generic-fiber:v1 | null | Scalar descent and generic fiber geometry | problem:plane-constant-jacobian:v1 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | branch:early-generic-fiber | null | null | null | null | null | {} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | ["compactification","ramification","other"] | ["math.early_generic_fiber"] | null | null | null | Establish field descent and geometric generic-fiber properties while retaining the special-fiber distinction. | null | null | [] | null | null | null | archive-extractor-batch-001 | model | null | null | null | null | null | null | null | null | inferred | null | inferred | inferred | null | null | null | null | null | null | null | Dataset grouping by mathematical objective. This does not reconstruct a historical assignment or imply an enacted branch state. | extracted | [] | [{"record_id":"artifact:geometry-initial.md:v1","selector":{"kind":"line_range","start":9,"end":42}}] | null | null | null | null | null | null | null | null | null | null | null | 2026-09-14T06:16:08.885889+00:00 | null | 1 | null | null | 1.0.0 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | 1.0.0 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
branch | branch:early-boundary:v1 | null | Boundary identities and nonproper countermodels | problem:plane-constant-jacobian:v1 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | branch:early-boundary | null | null | null | null | null | {} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | ["ramification","compactification","countermodel"] | ["math.early_boundary"] | null | null | null | Quantify omitted finite-valued boundary points and test proposed ways to remove them. | null | null | [] | null | null | null | archive-extractor-batch-001 | model | null | null | null | null | null | null | null | null | inferred | null | inferred | inferred | null | null | null | null | null | null | null | Dataset grouping by mathematical objective. This does not reconstruct a historical assignment or imply an enacted branch state. | extracted | [] | [{"record_id":"artifact:geometry-initial.md:v1","selector":{"kind":"line_range","start":44,"end":105}},{"record_id":"artifact:geometry-initial.md:v1","selector":{"kind":"line_range","start":119,"end":133}}] | null | null | null | null | null | null | null | null | null | null | null | 2026-09-14T06:16:08.885889+00:00 | null | 1 | null | null | 1.0.0 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | 1.0.0 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
branch | branch:early-birational:v1 | null | Degree-one completion | problem:plane-constant-jacobian:v1 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | branch:early-birational | null | null | null | null | null | {} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | ["elimination","other"] | ["math.early_birational"] | null | null | null | Show by two distinct source proofs that birationality suffices for polynomial invertibility. | null | null | [] | null | null | null | archive-extractor-batch-001 | model | null | null | null | null | null | null | null | null | inferred | null | inferred | inferred | null | null | null | null | null | null | null | Dataset grouping by mathematical objective. This does not reconstruct a historical assignment or imply an enacted branch state. | extracted | [] | [{"record_id":"artifact:geometry-initial.md:v1","selector":{"kind":"line_range","start":107,"end":117}},{"record_id":"artifact:adversarial-initial.md:v1","selector":{"kind":"line_range","start":5,"end":47}}] | null | null | null | null | null | null | null | null | null | null | null | 2026-09-14T06:16:08.885889+00:00 | null | 1 | null | null | 1.0.0 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | 1.0.0 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
branch | branch:early-principal-parts:v1 | null | Compatibility of rational primitives | problem:plane-constant-jacobian:v1 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | branch:early-principal-parts | null | null | null | null | null | {} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | ["cohomology_periods","valuation","countermodel"] | ["math.early_principal_parts"] | null | null | null | Test whether a generic exact relative differential produces a global polynomial mate. | null | null | [] | null | null | null | archive-extractor-batch-001 | model | null | null | null | null | null | null | null | null | inferred | null | inferred | inferred | null | null | null | null | null | null | null | Dataset grouping by mathematical objective. This does not reconstruct a historical assignment or imply an enacted branch state. | extracted | [] | [{"record_id":"artifact:geometry-initial.md:v1","selector":{"kind":"line_range","start":135,"end":163}}] | null | null | null | null | null | null | null | null | null | null | null | 2026-09-14T06:16:08.885889+00:00 | null | 1 | null | null | 1.0.0 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | 1.0.0 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
branch | branch:early-homogeneous:v1 | null | Homogeneous layers and their interactions | problem:plane-constant-jacobian:v1 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | branch:early-homogeneous | null | null | null | null | null | {} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | ["degree_counting","countermodel"] | ["math.early_homogeneous"] | null | null | null | Prove the single nonlinear degree case and test extension to mixed homogeneous layers. | null | null | [] | null | null | null | archive-extractor-batch-001 | model | null | null | null | null | null | null | null | null | inferred | null | inferred | inferred | null | null | null | null | null | null | null | Dataset grouping by mathematical objective. This does not reconstruct a historical assignment or imply an enacted branch state. | extracted | [] | [{"record_id":"artifact:adversarial-initial.md:v1","selector":{"kind":"line_range","start":49,"end":139}}] | null | null | null | null | null | null | null | null | null | null | null | 2026-09-14T06:16:08.885889+00:00 | null | 1 | null | null | 1.0.0 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | 1.0.0 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
branch | branch:early-formal-inverse:v1 | null | Formal inverse versus polynomial truncation | problem:plane-constant-jacobian:v1 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | branch:early-formal-inverse | null | null | null | null | null | {} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | ["formal_expansion","countermodel"] | ["math.early_formal_inverse"] | null | null | null | Separate formal invertibility and algebraicity from polynomial truncation with an explicit weakened model. | null | null | [] | null | null | null | archive-extractor-batch-001 | model | null | null | null | null | null | null | null | null | inferred | null | inferred | inferred | null | null | null | null | null | null | null | Dataset grouping by mathematical objective. This does not reconstruct a historical assignment or imply an enacted branch state. | extracted | [] | [{"record_id":"artifact:adversarial-initial.md:v1","selector":{"kind":"line_range","start":141,"end":158}}] | null | null | null | null | null | null | null | null | null | null | null | 2026-09-14T06:16:08.885889+00:00 | null | 1 | null | null | 1.0.0 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | 1.0.0 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
branch | branch:early-degree-descent:v1 | null | Leading forms and finite cancellation | problem:plane-constant-jacobian:v1 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | branch:early-degree-descent | null | null | null | null | null | {} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | ["degree_counting","formal_expansion","countermodel"] | ["math.early_degree_descent"] | null | null | null | Determine what top-degree common powers and finite Jacobian agreement actually imply about degree descent. | null | null | [] | null | null | null | archive-extractor-batch-001 | model | null | null | null | null | null | null | null | null | inferred | null | inferred | inferred | null | null | null | null | null | null | null | Dataset grouping by mathematical objective. This does not reconstruct a historical assignment or imply an enacted branch state. | extracted | [] | [{"record_id":"artifact:adversarial-initial.md:v1","selector":{"kind":"line_range","start":160,"end":206}}] | null | null | null | null | null | null | null | null | null | null | null | 2026-09-14T06:16:08.885889+00:00 | null | 1 | null | null | 1.0.0 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | 1.0.0 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
branch | branch:reciprocal-ring:v1 | null | Polynomial invariants of reciprocal rational fields | problem:plane-constant-jacobian:v1 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | branch:reciprocal-ring | null | null | null | null | null | {} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | ["invariant_algebra","valuation","formal_expansion"] | ["math.reciprocal_ring"] | null | null | null | Classify the full original-plane polynomial intersection for t=x+1/x under stated noninvariant critical-pole hypotheses. | null | null | [] | null | null | null | archive-extractor-batch-001 | model | null | null | null | null | null | null | null | null | inferred | null | inferred | inferred | null | null | null | null | null | null | null | Dataset grouping by mathematical objective. This does not reconstruct a historical assignment or imply an enacted branch state. | extracted | [] | [{"record_id":"artifact:reciprocal-block-invariant-ring-round601.md:v1","selector":{"kind":"line_range","start":3,"end":21}},{"record_id":"artifact:arbitrary-reciprocal-invariants-round607.md:v1","selector":{"kind":"line_range","start":3,"end":15}}] | null | null | null | null | null | null | null | null | null | null | null | 2026-09-14T06:16:08.885889+00:00 | null | 1 | null | null | 1.0.0 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | 1.0.0 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
branch | branch:reciprocal-controls:v1 | null | Exact scope controls for reciprocal invariants | problem:plane-constant-jacobian:v1 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | branch:reciprocal-controls | null | null | null | null | null | {} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | ["countermodel","invariant_algebra"] | ["math.reciprocal_controls"] | null | null | null | Identify which pole, depression and distinct-center hypotheses are needed, and which rational gauges remain allowed. | null | null | [] | null | null | null | archive-extractor-batch-001 | model | null | null | null | null | null | null | null | null | inferred | null | inferred | inferred | null | null | null | null | null | null | null | Dataset grouping by mathematical objective. This does not reconstruct a historical assignment or imply an enacted branch state. | extracted | [] | [{"record_id":"artifact:reciprocal-block-invariant-ring-round601.md:v1","selector":{"kind":"line_range","start":174,"end":175}},{"record_id":"artifact:arbitrary-reciprocal-invariants-round607.md:v1","selector":{"kind":"line_range","start":201,"end":201}},{"record_id":"artifact:arbitrary-reciprocal-invariants-round607.m... | null | null | null | null | null | null | null | null | null | null | null | 2026-09-14T06:16:08.885889+00:00 | null | 1 | null | null | 1.0.0 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | 1.0.0 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
branch | branch:two-odd-pell:v1 | null | Polynomial normalization of the two-odd-root norm | problem:plane-constant-jacobian:v1 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | branch:two-odd-pell | null | null | null | null | null | {} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | ["ramification","elimination","degree_counting"] | ["math.two_odd_pell"] | null | null | null | Retain exact weights, delta, higher multiplicities and both normalization ends in the rational norm reduction. | null | null | [] | null | null | null | archive-extractor-batch-001 | model | null | null | null | null | null | null | null | null | inferred | null | inferred | inferred | null | null | null | null | null | null | null | Dataset grouping by mathematical objective. This does not reconstruct a historical assignment or imply an enacted branch state. | extracted | [] | [{"record_id":"artifact:two-odd-discriminant-normalization-round602.md:v1","selector":{"kind":"line_range","start":68,"end":168}}] | null | null | null | null | null | null | null | null | null | null | null | 2026-09-14T06:16:08.885889+00:00 | null | 1 | null | null | 1.0.0 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | 1.0.0 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
branch | branch:two-odd-connection:v1 | null | Finite linear connection system with two odd roots | problem:plane-constant-jacobian:v1 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | branch:two-odd-connection | null | null | null | null | null | {} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | ["elimination","differential_operators"] | ["math.two_odd_connection"] | null | null | null | Preserve the full rational connection beyond its norm and polar interface. | null | null | [] | null | null | null | archive-extractor-batch-001 | model | null | null | null | null | null | null | null | null | inferred | null | inferred | inferred | null | null | null | null | null | null | null | Dataset grouping by mathematical objective. This does not reconstruct a historical assignment or imply an enacted branch state. | extracted | [] | [{"record_id":"artifact:two-odd-discriminant-normalization-round602.md:v1","selector":{"kind":"line_range","start":170,"end":246}}] | null | null | null | null | null | null | null | null | null | null | null | 2026-09-14T06:16:08.885889+00:00 | null | 1 | null | null | 1.0.0 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | 1.0.0 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
branch | branch:two-odd-controls:v1 | null | Nonlifting norm and residue controls | problem:plane-constant-jacobian:v1 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | branch:two-odd-controls | null | null | null | null | null | {} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | ["countermodel","elimination"] | ["math.two_odd_controls"] | null | null | null | Test sufficiency of weighted Pell, exact degrees, eliminated rows and repeated-root polar conditions. | null | null | [] | null | null | null | archive-extractor-batch-001 | model | null | null | null | null | null | null | null | null | inferred | null | inferred | inferred | null | null | null | null | null | null | null | Dataset grouping by mathematical objective. This does not reconstruct a historical assignment or imply an enacted branch state. | extracted | [] | [{"record_id":"artifact:two-odd-discriminant-normalization-round602.md:v1","selector":{"kind":"line_range","start":248,"end":309}}] | null | null | null | null | null | null | null | null | null | null | null | 2026-09-14T06:16:08.885889+00:00 | null | 1 | null | null | 1.0.0 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | 1.0.0 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
branch | branch:quartic-full-rows:v1 | null | Quartic triple/simple complete-row exclusion | problem:plane-constant-jacobian:v1 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | branch:quartic-full-rows | null | null | null | null | null | {} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | ["elimination","degree_counting"] | ["math.quartic_full_rows"] | null | null | null | Exclude the bounded r=4,s=k=1 partition(3,1) primitive profile while retaining every coefficient branch. | null | null | [] | null | null | null | archive-extractor-batch-001 | model | null | null | null | null | null | null | null | null | inferred | null | inferred | inferred | null | null | null | null | null | null | null | Dataset grouping by mathematical objective. This does not reconstruct a historical assignment or imply an enacted branch state. | extracted | [] | [{"record_id":"artifact:quartic-triple-simple-primitive-round608.md:v1","selector":{"kind":"line_range","start":1,"end":13}}] | null | null | null | null | null | null | null | null | null | null | null | 2026-09-14T06:16:08.885889+00:00 | null | 1 | null | null | 1.0.0 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | 1.0.0 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
branch | branch:reciprocal-audit:v1 | null | Unfinished independent reciprocal-algebra challenge | problem:plane-constant-jacobian:v1 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | branch:reciprocal-audit | null | null | null | null | null | {} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | ["unknown"] | ["math.reciprocal_audit"] | null | null | null | Record the assigned independent612 challenge and interruption without inventing a review verdict. | null | null | [] | null | null | null | archive-extractor-batch-001 | model | null | null | null | null | null | null | null | null | inferred | null | inferred | inferred | null | null | null | null | null | null | null | Dataset grouping by mathematical objective. This does not reconstruct a historical assignment or imply an enacted branch state. | extracted | [] | [{"record_id":"artifact:audit607-root-review.md:v1","selector":{"kind":"line_range","start":3,"end":6}},{"record_id":"artifact:checkpoint-round605-614.md:v1","selector":{"kind":"line_range","start":93,"end":96}}] | null | null | null | null | null | null | null | null | null | null | null | 2026-09-14T06:16:08.885889+00:00 | null | 1 | null | null | 1.0.0 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | 1.0.0 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
branch | branch:quartic-audit:v1 | null | Unfinished independent quartic challenge | problem:plane-constant-jacobian:v1 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | branch:quartic-audit | null | null | null | null | null | {} | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | ["unknown"] | ["math.quartic_audit"] | null | null | null | Record the assigned independent613 challenge and interruption without inventing a review verdict. | null | null | [] | null | null | null | archive-extractor-batch-001 | model | null | null | null | null | null | null | null | null | inferred | null | inferred | inferred | null | null | null | null | null | null | null | Dataset grouping by mathematical objective. This does not reconstruct a historical assignment or imply an enacted branch state. | extracted | [] | [{"record_id":"artifact:audit608-root-review.md:v1","selector":{"kind":"line_range","start":3,"end":6}},{"record_id":"artifact:checkpoint-round605-614.md:v1","selector":{"kind":"line_range","start":109,"end":113}}] | null | null | null | null | null | null | null | null | null | null | null | 2026-09-14T06:16:08.885889+00:00 | null | 1 | null | null | 1.0.0 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | 1.0.0 | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
attempt | attempt:r599-remainder:v1 | Rational square remainder degree and defect bound | null | problem:plane-constant-jacobian:v1 | branch:rational-remainder:v1 | null | Determine E=b^2D-delta P^2 at infinity without discarding finite poles. | develop_argument | combined_report | completed | null | null | null | No reduction of arbitrary polynomial Keller pairs to the displayed source is supplied. The all-multiplicity pole and infinity inputs are imported; remaining nonsplit cases and s>1 are not eliminated by this remainder calculation. | null | historical-root | model | null | null | null | null | null | null | Scoped proposition, pending independent audit. | [{"id":"c1","kind":"identity","statement":"With N=P^2-b^2D, V=b(PD′/2-DP′)+PD b′, H=V-P and Ccal=D(N′/2+b)-alpha D′N/2, the complete rows give AH=Ccal and bV=PE′/2-EP′.","assumption_ids":["a1","a2","a3","a4","a5"],"scope_description":"Determine E=b^2D-delta P^2 at infinity without discarding finite poles.","evidence_re... | null | null | null | null | null | attempt:r599-remainder | null | ["artifact:rational-square-remainder-root-round599.md:v1","artifact:audit599-rational-remainder-defects-round600.md:v1","artifact:check_rational_square_remainder_round599.py:v1","artifact:rational-square-remainder-round599.json:v1"] | [] | null | Eliminate A′ using both rational rows, compare infinity degrees, then retain the finite pole divisor to bound the degree of the cleared remainder. | {} | null | null | null | null | null | null | null | null | null | null | [] | null | null | null | null | ["elimination","valuation"] | ["math.rational_remainder"] | null | null | null | null | null | null | null | null | null | null | archive-extractor-batch-001 | model | null | null | null | null | null | inferred | inferred | null | inferred | null | null | null | null | null | inferred | inferred | inferred | null | null | Extracted from retained reports. Original rendered input, generation settings and historical event time are unavailable. No mathematical verification was performed during extraction. | extracted | [] | [{"record_id":"artifact:rational-square-remainder-root-round599.md:v1","selector":{"kind":"line_range","start":1,"end":103}},{"record_id":"artifact:audit599-rational-remainder-defects-round600.md:v1","selector":{"kind":"line_range","start":24,"end":54}}] | [] | ["unknown"] | null | null | unknown | [] | ["unknown"] | null | null | null | null | 2026-09-14T06:16:08.885889+00:00 | null | 1 | null | null | 1.0.0 | [{"id":"a1","text":"Over an algebraic closure of characteristic zero, r>=2, k>=1, s=1, m=r+1, n=(r+1)k=e+k, e=rk, alpha=1/(r+1).","basis":"unproved_extra","evidence_refs":[{"record_id":"artifact:rational-square-remainder-root-round599.md:v1","selector":{"kind":"line_range","start":1,"end":103}},{"record_id":"artifact:a... | Determine E=b^2D-delta P^2 at infinity without discarding finite poles. | auxiliary_problem | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | 1.0.0 | null | null | null | [] | ["unknown"] | null | unknown | null | [] | [] | [] | null | null | null | null | null | null |
attempt | attempt:r600-pole-ledger:v1 | Exact pole-loss ledger for the remainder | null | problem:plane-constant-jacobian:v1 | branch:rational-remainder:v1 | null | Refine the remainder defect budget by the actual cancellation and finite-zero contributions. | develop_argument | combined_report | completed | null | null | null | No reduction of arbitrary polynomial Keller pairs to the displayed source is supplied. The all-multiplicity pole and infinity inputs are imported; remaining nonsplit cases and s>1 are not eliminated by this remainder calculation. | null | unknown-historical-actor | unknown | null | null | null | null | null | null | null | [{"id":"c1","kind":"lemma","statement":"Set J=product_{j_beta>=2}(t-beta)^(j_beta-2), q=deg(JE)=Delta_2+k+1-e/2. At an even canceled root j_beta=2v with a=v, branch orders ell>v and v, let d0=v-1+alpha v and d1=v-1+alpha ell. A pole loss occurs only at delta_beta=((d0+d1)/(d1-d0))^2; then tau_beta=(2v-2)+ord_beta E>=1.... | null | null | null | null | null | attempt:r600-pole-ledger | null | ["artifact:audit599-rational-remainder-defects-round600.md:v1","artifact:check_rational_remainder_defects_round600.py:v1","artifact:rational-remainder-defects-round600.json:v1"] | [] | null | Expand both local connection branches, retain the exceptional leading-ratio cancellation and add the forced zeros to the global rational divisor ledger. | {} | null | null | null | null | null | null | null | null | null | null | [] | null | null | null | null | ["valuation","formal_expansion"] | ["math.rational_remainder"] | null | null | null | null | null | null | null | null | null | null | archive-extractor-batch-001 | model | null | null | null | null | null | inferred | inferred | null | inferred | null | null | null | null | null | inferred | inferred | inferred | null | null | Extracted from retained reports. Original rendered input, generation settings and historical event time are unavailable. No mathematical verification was performed during extraction. | extracted | [] | [{"record_id":"artifact:audit599-rational-remainder-defects-round600.md:v1","selector":{"kind":"line_range","start":109,"end":210}},{"record_id":"artifact:audit599-rational-remainder-defects-round600.md:v1","selector":{"kind":"line_range","start":24,"end":108}}] | [] | ["unknown"] | null | null | unknown | [] | ["unknown"] | null | null | null | null | 2026-09-14T06:16:08.885889+00:00 | null | 1 | null | null | 1.0.0 | [{"id":"a1","text":"Over an algebraic closure of characteristic zero, r>=2, k>=1, s=1, m=r+1, n=(r+1)k=e+k, e=rk, alpha=1/(r+1).","basis":"unproved_extra","evidence_refs":[{"record_id":"artifact:audit599-rational-remainder-defects-round600.md:v1","selector":{"kind":"line_range","start":109,"end":210}},{"record_id":"art... | Refine the remainder defect budget by the actual cancellation and finite-zero contributions. | auxiliary_problem | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | 1.0.0 | null | null | null | ["attempt:r599-remainder:v1"] | ["strengthen_conclusion"] | Refines the aggregate pole bound in599 by charging exact pole losses and forced finite zeros. | deepen | null | [] | [] | [] | null | null | null | null | null | null |
attempt | attempt:r600-weighted-norm:v1 | Weighted polynomial norm after exact clearing | null | problem:plane-constant-jacobian:v1 | branch:rational-remainder:v1 | null | Translate the rational remainder into a polynomial identity while retaining simple and odd-root weights. | develop_argument | combined_report | completed | null | null | null | The weights S0 and O cannot be suppressed; polynomial Pell compatibility does not enforce both connection rows or actual nonsingularity. | null | unknown-historical-actor | unknown | null | null | null | null | null | null | null | [{"id":"c1","kind":"identity","statement":"Let S0 be the monic product of simple D-roots, O that of odd repeated D-roots, H_D=product_{j_beta>=2}(t-beta), J=I^2 O and D=d0 S0 H_D^2 J. Then P0=IP and b0=H_D J b are polynomials and JE=d0 S0 b0^2-delta O P0^2. The left side has degree q, while each term on the right has d... | null | null | null | null | null | attempt:r600-weighted-norm | null | ["artifact:audit599-rational-remainder-defects-round600.md:v1"] | [] | null | Use the separate pole bounds for the mean and anti-invariant coefficients. The resulting constant-right-side equation at q=0 is a weighted polynomial Pell equation, not an automatic obstruction. | {} | null | null | null | null | null | null | null | null | null | null | [] | null | null | null | null | ["elimination","valuation"] | ["math.rational_remainder"] | null | null | null | null | null | null | null | null | null | null | archive-extractor-batch-001 | model | null | null | null | null | null | inferred | inferred | null | inferred | null | null | null | null | null | inferred | inferred | inferred | null | null | Extracted from retained reports. Original rendered input, generation settings and historical event time are unavailable. No mathematical verification was performed during extraction. | extracted | [] | [{"record_id":"artifact:audit599-rational-remainder-defects-round600.md:v1","selector":{"kind":"line_range","start":212,"end":235}}] | [] | ["unknown"] | null | null | unknown | [] | ["unknown"] | null | null | null | null | 2026-09-14T06:16:08.885889+00:00 | null | 1 | null | null | 1.0.0 | [{"id":"a1","text":"Over an algebraic closure of characteristic zero, r>=2, k>=1, s=1, m=r+1, n=(r+1)k=e+k, e=rk, alpha=1/(r+1).","basis":"unproved_extra","evidence_refs":[{"record_id":"artifact:audit599-rational-remainder-defects-round600.md:v1","selector":{"kind":"line_range","start":212,"end":235}}]},{"id":"a2","tex... | Translate the rational remainder into a polynomial identity while retaining simple and odd-root weights. | auxiliary_problem | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | 1.0.0 | null | null | null | ["attempt:r599-remainder:v1"] | ["change_representation"] | Rewrites the already derived rational remainder with its actual clearing factors. | deepen | null | [] | [] | [] | null | null | null | null | null | null |
attempt | attempt:r600-split-factor:v1 | Square factorization forces at most one D-root | null | problem:plane-constant-jacobian:v1 | branch:split-source:v1 | null | Exclude square discriminants with at least two distinct roots using the exact cleared remainder degree. | develop_argument | combined_report | completed | null | null | null | The factorization itself leaves the one-root square case and all nonsplit cases. Source nonsingularity is a separate input. | null | unknown-historical-actor | unknown | null | null | null | null | null | null | null | [{"id":"c1","kind":"lemma","statement":"U=(L/H_D)P and V=c L(L/H_D)b are polynomials of degree K=k+h-M>=1. For eta^2=delta!=0,1, JE=(V-eta U)(V+eta U) has degree K+1-M. One factor has degree K and the other is nonzero, forcing M<=1.","assumption_ids":["a1","a2","a3","a4","a5","a6"],"scope_description":"Exclude square d... | null | null | null | null | null | attempt:r600-split-factor | null | ["artifact:audit599-rational-remainder-defects-round600.md:v1"] | [] | null | Factor the exact cleared remainder over the algebraic closure and compare polynomial degrees. | {} | null | null | null | null | null | null | null | null | null | null | [] | null | null | null | null | ["degree_counting","elimination"] | ["math.split_source"] | null | null | null | null | null | null | null | null | null | null | archive-extractor-batch-001 | model | null | null | null | null | null | inferred | inferred | null | inferred | null | null | null | null | null | inferred | inferred | inferred | null | null | Extracted from retained reports. Original rendered input, generation settings and historical event time are unavailable. No mathematical verification was performed during extraction. | extracted | [] | [{"record_id":"artifact:audit599-rational-remainder-defects-round600.md:v1","selector":{"kind":"line_range","start":237,"end":271}}] | [] | ["unknown"] | null | null | unknown | [] | ["unknown"] | null | null | null | null | 2026-09-14T06:16:08.885889+00:00 | null | 1 | null | null | 1.0.0 | [{"id":"a1","text":"Over an algebraic closure of characteristic zero, r>=2, k>=1, s=1, m=r+1, n=(r+1)k=e+k, e=rk, alpha=1/(r+1).","basis":"unproved_extra","evidence_refs":[{"record_id":"artifact:audit599-rational-remainder-defects-round600.md:v1","selector":{"kind":"line_range","start":237,"end":271}}]},{"id":"a2","tex... | Exclude square discriminants with at least two distinct roots using the exact cleared remainder degree. | auxiliary_problem | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | 1.0.0 | null | null | null | ["attempt:r600-weighted-norm:v1"] | ["specialize"] | Specializes the weighted norm to square D, so the root weights become trivial. | deepen | null | [] | [] | [] | null | null | null | null | null | null |
attempt | attempt:r600-one-root-interface:v1 | Surviving one-root full connection interface | null | problem:plane-constant-jacobian:v1 | branch:split-source:v1 | null | Record the equations that survive in the one-root square case before actual nonsingularity is used. | develop_argument | combined_report | completed | null | null | null | These equations and the origin mark do not imply actual source nonsingularity. No proof from these rows alone forces a=epsilon+C x^d. | null | unknown-historical-actor | unknown | null | null | null | null | null | null | null | [{"id":"c1","kind":"lemma","statement":"The Wronskian forces c C0=-1/K. Equal branch orders contradict alpha ell<k, so a=ord_beta A=h with a canceled branch. After choosing Y-sign, h<ell<n and eta=(2 a0 a1/K-a0-a1)/(a1-a0)<-1, where a0=h-1+alpha h and a1=h-1+alpha ell. This is a restriction, not a contradiction.","assu... | null | null | null | null | null | attempt:r600-one-root-interface | null | ["artifact:audit599-rational-remainder-defects-round600.md:v1"] | [] | null | Reconstruct the residual one-root branch constants and both branch equations; identify why the one eliminated row cannot replace the full system. | {} | null | null | null | null | null | null | null | null | null | null | [] | null | null | null | null | ["differential_operators","elimination","valuation"] | ["math.split_source"] | null | null | null | null | null | null | null | null | null | null | archive-extractor-batch-001 | model | null | null | null | null | null | inferred | inferred | null | inferred | null | null | null | null | null | inferred | inferred | inferred | null | null | Extracted from retained reports. Original rendered input, generation settings and historical event time are unavailable. No mathematical verification was performed during extraction. | extracted | [] | [{"record_id":"artifact:audit599-rational-remainder-defects-round600.md:v1","selector":{"kind":"line_range","start":273,"end":356}}] | [] | ["unknown"] | null | null | unknown | [] | ["unknown"] | null | null | null | null | 2026-09-14T06:16:08.885889+00:00 | null | 1 | null | null | 1.0.0 | [{"id":"a1","text":"Over an algebraic closure of characteristic zero, r>=2, k>=1, s=1, m=r+1, n=(r+1)k=e+k, e=rk, alpha=1/(r+1).","basis":"unproved_extra","evidence_refs":[{"record_id":"artifact:audit599-rational-remainder-defects-round600.md:v1","selector":{"kind":"line_range","start":273,"end":356}}]},{"id":"a2","tex... | Record the equations that survive in the one-root square case before actual nonsingularity is used. | auxiliary_problem | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | 1.0.0 | null | null | null | ["attempt:r600-split-factor:v1"] | ["specialize"] | Analyzes the single root left by the split factorization. | deepen | null | [] | [] | [] | null | null | null | null | null | null |
attempt | attempt:r600-first-row-control:v1 | Nonsplit equality satisfying only the first full row | null | problem:plane-constant-jacobian:v1 | branch:primitive-countercontrols:v1 | null | Test whether constant remainder numerator plus the first full row is already contradictory. | construct_example | combined_report | completed | null | null | null | This is neither a full primitive nor a marked source solution, and is not a counterexample to the original problem. | null | unknown-historical-actor | unknown | null | null | null | null | null | null | null | [{"id":"c1","kind":"counterexample","statement":"The displayed control satisfies the full first row, the r=4,k=1 infinity degrees and degree-two norm, with E=-25 and Delta_2=q=0. Its second residual is -x^2(-3a^2x^2+4a^2+20ax^3+75x^2+25)/(5a), never identically zero. Thus those retained conditions alone do not force a ... | null | null | null | null | null | attempt:r600-first-row-control | null | ["artifact:audit599-rational-remainder-defects-round600.md:v1"] | [] | null | Construct a rational-coefficient control and compute its two residuals, retaining the nonzero second row. | {} | null | null | null | null | null | null | null | null | null | null | [] | null | null | null | null | ["countermodel","differential_operators"] | ["math.primitive_countercontrols"] | null | null | null | null | null | null | null | null | null | null | archive-extractor-batch-001 | model | null | null | null | null | null | inferred | inferred | null | inferred | null | null | null | null | null | inferred | inferred | inferred | null | null | Extracted from retained reports. Original rendered input, generation settings and historical event time are unavailable. No mathematical verification was performed during extraction. | extracted | [] | [{"record_id":"artifact:audit599-rational-remainder-defects-round600.md:v1","selector":{"kind":"line_range","start":449,"end":471}}] | [] | ["unknown"] | null | null | unknown | [] | ["unknown"] | null | null | null | null | 2026-09-14T06:16:08.885889+00:00 | null | 1 | null | null | 1.0.0 | [{"id":"a1","text":"alpha=1/5, a!=0, a^2!=25; D=x^4-x^2, P=ax, b=5/x, A=x^5+5x^2/a, delta=25/a^2.","basis":"temporary_assumption","evidence_refs":[{"record_id":"artifact:audit599-rational-remainder-defects-round600.md:v1","selector":{"kind":"line_range","start":449,"end":471}}]}] | Test whether constant remainder numerator plus the first full row is already contradictory. | weakened_model | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | 1.0.0 | null | null | null | [] | ["unknown"] | null | unknown | null | [] | [] | [] | null | null | null | null | null | null |
attempt | attempt:r600-full-row-singular-control:v1 | Full marked primitive with a singular actual source | null | problem:plane-constant-jacobian:v1 | branch:primitive-countercontrols:v1 | null | Test whether both full primitive rows and source marks replace nonsingularity. | construct_example | combined_report | completed | null | null | null | The constructed source is singular and has no asserted polynomial Jacobian mate; it does not refute the source theorem or the original problem. | null | unknown-historical-actor | unknown | null | null | null | null | null | null | null | [{"id":"c1","kind":"counterexample","statement":"Both rows hold and F=t^2(t-1)^3(t+1), N=-9t(t+1), delta=25/9, E=15t-1. The actual source has r=2,s=k=1, monic A,C and A(0)=1/2, C(0)=-1, but is singular at t=zu=1/6, u^3=-25/108. Thus full rows plus the marks do not imply nonsingularity.","assumption_ids":["a1"],"scope_d... | null | null | null | null | null | attempt:r600-full-row-singular-control | null | ["artifact:audit599-rational-remainder-defects-round600.md:v1"] | [] | null | Retain both exact residual equations and reconstruct the actual source gradients at the algebraic control point. | {} | null | null | null | null | null | null | null | null | null | null | [] | null | null | null | null | ["countermodel","elimination"] | ["math.primitive_countercontrols"] | null | null | null | null | null | null | null | null | null | null | archive-extractor-batch-001 | model | null | null | null | null | null | inferred | inferred | null | inferred | null | null | null | null | null | inferred | inferred | inferred | null | null | Extracted from retained reports. Original rendered input, generation settings and historical event time are unavailable. No mathematical verification was performed during extraction. | extracted | [] | [{"record_id":"artifact:audit599-rational-remainder-defects-round600.md:v1","selector":{"kind":"line_range","start":473,"end":507}}] | [] | ["unknown"] | null | null | unknown | [] | ["unknown"] | null | null | null | null | 2026-09-14T06:16:08.885889+00:00 | null | 1 | null | null | 1.0.0 | [{"id":"a1","text":"alpha=1/3, A=t^3-t^2-t/2+1/2, D=(t-1)^2/4, P=(9t-3)/4, b=-15/2-9/(t-1).","basis":"temporary_assumption","evidence_refs":[{"record_id":"artifact:audit599-rational-remainder-defects-round600.md:v1","selector":{"kind":"line_range","start":473,"end":507}}]}] | Test whether both full primitive rows and source marks replace nonsingularity. | weakened_model | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | 1.0.0 | null | null | null | [] | ["unknown"] | null | unknown | null | [] | [] | [] | null | null | null | null | null | null |
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Jacobian research trajectory — batch 001
A flattened archival extraction of research attempts concerning polynomial maps in two variables with nonzero constant Jacobian determinant, using Research Trajectory Schema v1.0.0.
Contents
research_trajectory_flat.csv contains 207 records and 145 columns. Each row represents one canonical record: 1 problem, 24 branches, 55 attempts, 56 evaluations, 19 relations, 3 decisions, or 49 artifacts.
Nested object fields use dotted column names. Lists and empty objects are JSON-encoded within cells. Explicit null values are represented as null; empty cells denote absent fields. The file uses UTF-8 with a byte-order mark, quoted fields, and CRLF record separators. Quoted cells may contain line breaks.
Scope
This is a bounded extraction, not an exhaustive archive: 3,050 research files remain unprocessed. Mathematical proofs and checker outcomes are historical reports; this extraction did not rerun checkers or independently certify a solution to the original problem. Source references are retained as provenance, and local filesystem paths may not resolve on another computer.
File integrity
- Rows: 207
- Columns: 145
- Bytes: 908473
- SHA-256:
a085ed6f92a9adf2c36aade960548464043a77b00817e2b5a69813e4a063909f
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