Grader parameters

Every number the grader uses, by the name grader_model gives it (names(), with_overrides(), use(); see src/pencilmark/grader_model.py). The difficulty prices share every value with the engine parameters except two weight vectors, so only those are listed under them. This page is generated by tools/gen_parameters_md.py; changing a shipped value is a deliberate commit with a golden rewrite.

Engine parameters (route)

Name	Value	Source
route.price.FullHouse	1	Base price of a technique (B), used only where the structural model does not price the move.
route.price.NakedSingle(direct)	1.697	″
route.price.HiddenSingle(direct)	0.9849	″
route.price.NakedSingle+Pointing(direct)	2.362	″
route.price.HiddenSingle+Pointing(direct)	1.514	″
route.price.TakeNotes	4.008	″
route.price.NakedSingle(notes)	0.6942	″
route.price.HiddenSingle(notes)	0.7778	″
route.price.LockedCandidates	1.315	″
route.price.NakedPair	4.999	″
route.price.HiddenPair	5.638	″
route.price.NakedTriple	6.451	″
route.price.HiddenTriple	6.988	″
route.price.NakedQuad	6.086	″
route.price.HiddenQuad	6.987	″
route.price.X-Wing	8.707	″
route.price.Swordfish	5.6	″
route.price.XY-Wing	4.192	″
route.price.XYZ-Wing	5.713	″
route.price.Coloring	6.151	″
route.price.PairwiseConstraint	1.858	″
route.price.Trial	5.176	″
route.price.Guess	6.219	″
route.price.Innie/Outie(direct)	1.939	″
route.price.CageCombination	1.975	″
route.price.Innie/Outie(notes)	2.867	″
route.price.SumCombination	1.8	″
route.price.ArrowCombination	2	″
route.price.SetCombination	2	″
route.price.EqualSumCombination	2.6	″
route.price.TableCombination	2.6	″
route.price.ComboLock	2.8	″
route.price.ConstraintSingle(direct)	2	″
route.price.Innie/Outie(sum)	3.2	″
route.price.FinnedFish	5.4	″
route.price.Jellyfish	6.4	″
route.price.X-Chain	5.2	″
route.price.XY-Chain	5.6	″
route.price.AIC	6.4	″
route.price.NiceLoop(discontinuous)	6.8	″
route.price.SandwichCombination	2.6	″
route.price.XSumCombination	2.6	″
route.price.SkyscraperCombination	2.6	″
route.price.LawOfLeftovers	3	″
route.price.ImpliedHouses	3	″
route.price.UniqueRectangle	4.6	″
route.price.BUG+1	5.6	″
route.price.ALS-XZ	6.6	″
route.price.ALS-XY-Wing	7	″
route.price.DeathBlossom	7.4	″
route.price.ALS-AIC	7.6	″
route.price.CanonicalEnumeration	1	″
route.price.CountCombination	2	″
route.price.LineSingle(direct)	1.6	″
route.price.LineRange	2	″
route.price.MentalSingle(direct)	2.4	″
route.price.ShortTrial	6.2	″
route.price.MentalChain(direct)	4	″
route.price.EitherWay	5.8	″
route.price.LineClass	1.6	″
route.price.DigitCount	4.6	″
route.price.EqualDigits	5	″
route.price.LineScan	1.8	″
route.price.ForcingChains	6	″
route.price.DynamicForcingChains	6.4	″
route.price.NestedForcingChains	6.6	″
route.price.3DMedusa	6.3	″
route.price.SumBound	1.5	″
route.price.ClassCount	2.4	″
route.price.Domino	2.2	″
route.price.ColourAlgebra	5.4	″
route.price.WXYZ-Wing	6.2	″
route.price.SueDeCoq	6.6	″
route.price.AlignedPairExclusion	6.8	″
route.price.ChuteRemotePairs	5.6	″
route.price.PatternOverlay	7.2	″
route.price.GurthSymmetry	5	″
route.price.NishioForcingNet	5.6	″
route.price.WhatIf	5.2	″
route.price.MentalNotesSingle	3	″
route.price.MultiColouring	5.9	″
route.price.RemotePairs	4.8	″
route.price.EmptyRectangle	4.6	″
route.price.RuleIntersection	5	″
route.price.SumAlgebra	6	″
route.price.SnyderMarks	1.5	″
route.price.SnyderSingle	2.3	″
route.price.BandLogic	6.6	″
route.price.Fireworks	6.988	″
route.price.CaseAnalysis	6.6	″
route.price.ComboPositions	6.988	″
route.price.CliqueHouse	6.988	″
route.price.LineSets	6.988	″
route.price.LineClues	6.988	″
route.price.WeightedSums	6.988	″
route.price.ClassColouring	5	″
route.K	list of 9	Engine parameters (data/params.json): the step-price model and the scan / note costs, fitted on human solve times; they also price the time effort and the band route's tie-breaks.
route.gamma	-0.6291	″
route.alpha	1	″
route.beta	0.5081	″
route.c	0.1152	″
route.t_place	2.89	″
route.t_mark	0.1677	″
route.t_erase	0.2061	″
route.t0	5.42	″
route.tau	0.15	″
route.ref_steps	55	″
route.meta_theta	list of 10	″
route.meta_exclude		″
route.meta_theta_arith_cells	0	″
route.meta_theta_full	list of 18	Structural step-price weights (18 features), fitted on human solve times.
route.meta_theta_interact	0.02882, 0.2858, 0.1108	Depth interaction weights of the step price (D6).
route.dc_lines	1	Engine parameters (data/params.json): the step-price model and the scan / note costs, fitted on human solve times; they also price the time effort and the band route's tie-breaks.
route.locality	0.4	″
route.case_rounds	3	″
route.case_light	1	″

Difficulty prices (price)

Name	Value	Source
price.meta_theta_full	list of 18	Card-fit structural weights: refitted so difficulty ranks puzzles like human times across sources (data/card_score.json price_weights).
price.meta_theta_interact	0.3114, 0.2262, -0.1723	Card-fit depth interactions (fitted with the weights above).

Card score (score)

Name	Value	Source
score.version	3	Version of the configuration format.
score.beta	4.583	Exponent of a step's price in its value (card fit).
score.enum_w	0.1	Weight of the cage-enumeration term (validated on two sources).
score.stat	per_cell	How step values combine: the average per empty cell.
score.beta_time	3.807	The same exponent for the time effort (time fit).
score.refute_w	2	Weight of the technique-free search effort.
score.map.form	A * w * softplus((r - r0) / w)	The smooth difficulty map: softplus slope A, knee r0 and width w; below 2 a gentler square-root rule.
score.map.A	0.8258	″
score.map.r0	2.117	″
score.map.w	0.3	″

Time model (time)

Name	Value	Source
time.const	-5.68	Time model (data/time_model.json), fitted on era-adjusted per-player solve times.
time.k_effort	0.2929	″
time.k_empty	0.7441	″
time.k_geometry.blob_cells	0.385	Scanning cost of irregular regions (jigsaw pieces, extra regions per cell).
time.k_geometry.extra_area_pc	1.108	″
time.t0	0.0408	Time model (data/time_model.json), fitted on era-adjusted per-player solve times.
time.compress.k	0.15	Long predictions grow more slowly (monotone compression).
time.compress.c	0.4	″
time.minutes_per_unit	11.8	The median time of a classic 9x9, in minutes (one time unit).
time.spread_note	solve times of one puzzle across today's players: log-nor...	Time model (data/time_model.json), fitted on era-adjusted per-player solve times.
time.size_curve.q	0.2148	Very large boards are slower per cell (hinge above about 92 empty cells, measured on three sources).
time.size_curve.c	4.52	″
time.size_curve_note	log t += q * max(0, ln(empty) - c)^2 after everything els...	″
time.spread_sigma_classic	0.79	Spread of players around the median (log-normal sigma), for time_pNN.
time.spread_sigma_variant	0.62	″
time.model_sigma_classic	0.33	The model's own error (log-normal sigma).
time.model_sigma_variant	0.48	″