datenvertrag.halowerk.com

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• POST/transaction-fragment-rank-audit$0.003Check a supplied multi-collection CDC transaction fragment set against END event counts and coupled global/per-collection ordinal positions before downstream assembly. Caller groups normalized fragments first;raw BEGIN/END IDs are never inferred. Missing evidence remains unknown;known rank/count contradictions take precedence. Schema-valid unknown has the same fixed price;invalid input requires nativeHTTP400 before settlement.
• POST/graph-burning-optimal-sequence-inventory$0.003For an original simple undirected labelled graph on0..6vertices, return its minimum number of burning rounds and ALLoptimal ordered sourcevertex sequences in numeric lexicographic order. Eachround chooses one vertex unburned at START of round, while vertices burned in preceding rounds spread to neighbors; the justselected source does not spread until next round. Originaledges require0<=u<v<n,no duplicates. Emptygraph convention number0 andoneemptysequence. Disconnectedgraphs accepted.
• POST/cartesian-graph-factorization-family$0.003For a fully captured simple undirected graph on original labels0..n-1,n1..6, edge_mask bits are lexicographic unordered pairs(0,1),(0,2),...,(n-2,n-1). Synthesize ALL decompositions G=A square B into TWO connected simple factors with2<=a<=b and a*b=n. Product adjacency holds exactly when one coordinate agrees and the other factor has an edge. Return decompositions records{a,b,mask_a,mask_b,grid},count,decomposable. Factor masks use their own lexicographic unordered pairs.
• POST/minimum-sorting-network-family$0.003For a supplied wire count n0..4, synthesize EVERY minimum-COMPARATOR fixed sorting network. A comparator(i,j),i<j, sends min to lower-index wire and max to higher-index wire; the same entire sequence must sort EVERY input, not one permutation. Return the canonical lexicographic comparator-pair inventory, ALL minimum sequences as comparator-index arrays in numeric lexicographic order, minimum_comparators, count, and aligned unsorted_histories.
• POST/geodesic-seed-hull-ledger$0.003Construct the COMPLETE GEODESIC CONVEX HULL H_G(S) of ONE independently supplied original seed vertex set S in a connected simple undirected labelled graph G. Original n=1..4, labels0..n-1, edge_mask uses lexicographic pairs(0,1),(0,2),...,(n-2,n-1); seed_mask bitv denotes original vertexv. H is the smallest superset of S closed under EVERY vertex on EVERY shortest path between EACH pair of its vertices; apply closure to fixedpoint, not arbitrary single shortest paths.
• POST/boolean-npn-orbit-stabilizer$0.003For n1..3 and a fully captured single-output Boolean truth-table mask f, reconstruct ALL equivalent masks under input permutation, input negations and output negation. Truth bit a evaluates x_i=(a>>i)&1. Exact own action: y_i=x_permutation[i] XOR input_negation_mask[i], transformed(x)=f(y) XOR output_negation. Mask-bit i denotes the negation of source argument y_i. Return numerically sorted truth_masks, smallest canonical_truth, orbit_size, all original stabilizers, and group_order=n!*2^(n+1).
• POST/finite-group-class-sum-algebra$0.003For a complete valid1..6element finite group Cayleytable on labels0..n-1 with identity at ANYlabel, derive its integral center basis of conjugacy-class sums and ALL multiplication structure constants c[i][j][k] in Ki*Kj=sum_k c[i][j][k]Kk. Classes/members are ordered by numeric leastlabel/ascendinglabel. Coefficients count pairs with product a FIXED element of outputclass, not totalpairs in that class; equivalently total divided by outputclasssize.
• POST/latin-square-orthogonal-mate-family$0.003For a fully captured Latin square of order1..4 on labels0..n-1, construct ALL Latin squares B for which every ordered pair (original[r][c],B[r][c]) occurs exactly once. Return every mate as a flat row-major value array in numeric lexicographic order, aligned pair_codes[r*n+c]=n*original[r][c]+B[r][c], and count. Retain every symbol-labelled mate; no symmetry quotient. A valid square without mates has a known empty family. n1 admits its single square as its mate.
• POST/partition-hook-multiset-inverse-family$0.003Given an original multiset of0..20positive hooklengths each1..20, reconstruct EVERY integer partition of that cellcount whose English Ferrers diagram has exactly that hookmultiset. Hook counts self plus cells strictlyright and strictlybelow. Return all shapes in numeric lexicographic order, complete rowaligned hooktableau for each shape, exact familycount.
• POST/finite-chained-glyph-lookup-audit$0.003A font/layout fixture maintainer checks whole output glyphs and execution-event claims against original logical glyphs, ordered context rules and nested Single or first internal2-to-1 Ligature records. Own nonexpanding normalized HarfBuzz10.4.0 reader profile, commit3ef8709829a5884517ad91a97b32b9435b2f20d1. Flags0 and neutral metadata; no mark skipping, font download, general OpenType/HarfBuzz conformance or rendering judgment. Missing capture stays unknown; known counterclaims dominate.
• POST/latin-bitrade-switch-family$0.003For two fully captured Latin squares LEFT and RIGHT of the SAME order n1..4, reconstruct EVERY NONEMPTY cellmask on which replacing LEFT entries by RIGHT preserves a Latin square. Each original is a flat rowmajor n*n array with symbols0..n-1, each symbol once per row/column; LEFT is REDUCED: its first row AND first column must be0..n-1. RIGHT need not be reduced. ORIGINAL labels are retained; no automatic relabelling. A switchmask may select ONLY cells where left differs from right, bit(r*n+c).
• POST/scd2-validity-ledger$0.003Check a bounded corrected dimension history before a data agent publishes it. Caller-supplied pseudonyms/hashes only; no external identity claim. Conflicting selected hashes yield not_observed; missing coverage yields unknown. A schema-valid unknown is a successful result at the same fixed price. Invalid input must raise native HTTP 400 before settlement.
• POST/line-mass-transport-audit$0.003For two strictly position-sorted positive-integer mass histograms with1..8bins, coordinates-32..32 and equal totalmass1..32, construct the full canonical monotone quantile coupling matrix. Return raw mass-times-distance L1cost, reduced rational normalized W1 and every interval of the absolute-CDF-imbalance cost witness. Compare the whole supplied canonical artifact by fieldname with ordered matrix/segment arrays.
• POST/invert-sequence-prefix$0.003Apply the forward INVERT transform to a fully captured signed integer sequence a1,...,aN. The result b1,...,bN is defined by 1+B(x)=1/(1-A(x)), where A(x)=a1*x+...+aN*x^N and coefficients are retained through degree N. Equivalently, b_n is the sum, over all ordered compositions of n, of the product of the corresponding input entries. For example, [1,1,1,1] maps to [1,2,4,8], and [-1,0,0] maps to [-1,1,-1].
• POST/literal-like-pattern-witness$0.003Decide whole-string LIKE membership for caller-supplied nonnull text, pattern and explicit escape, returning parsed tokens and a deterministic shortest-percent-span witness. Bounded Unicode scalar codepoint literal equality profile: underscore consumes exactly one codepoint, percent consumes zero or more. No ILIKE, locale/nondeterministic collation, SQL literal parser, database execution or vendor conformance assertion.
• POST/minimum-string-attractor-family$0.003For one FULLY CAPTURED binary word of length0..8 represented by its original ordered0/1tokens, synthesize EVERY minimum-CARDINALITY STRING ATTRACTOR. A positionset Gamma is an attractor iff EACH DISTINCT NONEMPTY CONTIGUOUS SUBSTRING has at least ONE occurrence whose inclusive positioninterval contains at least one element of Gamma. Other occurrences of that substring need NOT cross Gamma. Original positions are zero-based; bitp of a mask selects positionp.
• POST/finite-field-quadratic-witt-decomposition$0.003For a symmetric n by n Gram matrix A, n=1..4, over the prime field p=3 or5, use q(x)=x A x^T. Return row basis B, G=B A B^T, hyperbolic_planes h, anisotropic_dimension a and radical_dimension r. Basis order consists of h adjacent hyperbolic pairs with Gram [[0,1],[1,0]], then an anisotropic block, then radical basis. All cross blocks are zero; n=2h+a+r. Exhaustive lexicographic vector enumeration and rank extension fix the witness.
• POST/classical-pattern-avoiding-permutation-family$0.003For length n0..5 and one original permutation pattern of length1..4 on0..m-1, generate EVERY permutation of0..n-1 with no increasing index subsequence whose selected values have that pattern relative order. Gaps are allowed; this is classical, not consecutive pattern avoidance. Return all full permutations in numeric lexicographic order, count, and inversion_histogram indexed0..n*(n-1)/2 including zero bins.
• POST/delta-dv-replacement-precondition$0.003Check the two named atomic logical-file replacement preconditions before a data writer proposes a new deletion-vector identity for an existing physical file. Checks only per-path action multiplicity and exact prior-DV retirement; observed is not full Delta commit validity. Pseudonym metadata only,no file access or changes. Schema-valid unknown is successful at the same fixed price;invalid input requires native400 before settlement.
• POST/gaussian-euclidean-trace-audit$0.003Reconstruct the entire exact Euclidean division trace for two Gaussian integers, including every quotient/remainder/norm, canonical first-quadrant gcd and unit-rotated Bezout coefficients. Coordinates -128..128; componentwise nearest quotient with half ties toward positive infinity; nonzero canonical gcd real>0,imag>=0, deterministic zero-zero convention. Compare the whole supplied claimed artifact, independent of object-key order.
• POST/exact-bezier-subdivision-audit$0.003Subdivide one planar Bezier curve with2..6integercontrolpoints[-20,20] at explicit rational t0..1 numerator0..denominator<=8. Return normalizedparameter,every intermediate deCasteljau triangle coordinate,and complete same-degree left/right child controlpolygons oriented from original start to split and split to original end. Every coordinate is an exact reduced signed-numerator/positive-denominator decimal-string pair;split point included.
• POST/binary-automaton-reset-word-ledger$0.003Given the original total binary transition table of a deterministic automaton with 1..4 states, reconstruct every reachable state subset and labelled transition, the minimum reset-word length, the exact number of shortest binary words, the lexicographically first word and its full image trace. Distinct symbol words remain distinct when they reach the same subset. A one-state automaton resets by the empty word. Claim -1 means no reset word; null claim or missing table remains unknown.
• POST/binary-necklace-orbit-inventory-audit$0.003For a supplied length1..10 generate ALL binary necklaces under cyclic rotation, represented by lexicographically least0/1word, in increasing lexical order. Return each full word, its least positive cyclic period and orbit size; total necklaces, primitive necklaces with period=n and ascending divisor-period class histogram including zero bins. Sum of orbit sizes covers all2^n binary words. No reflection quotient, color relabeling or density restriction.

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Showing 23 of 23 listed endpoints.