03 / Public record
Results, with their limits.
Papers, finite checks, data and corrections. Follow each source for the exact statement, assumptions and evidence.
Preprints & research archive
arXiv and Zenodo host preprints and research material. These listings do not claim journal peer review.
arXiv · preprint
Certified computations on no-three-in-line problems
Exact values and witnesses in the cube, and a study of the Guy–Kelly count in the plane.
Zenodo · preprint
Exact values and certified lower bounds in the cube
No-three-in-line configurations in three dimensions, with corrections retained in the version record.
Zenodo · preprint
No four coplanar in the cube
Certified configurations and bounds for OEIS A280537.
Zenodo · preprint
Modular hyperbolas in the HJSW window
Extremal no-three-in-line subsets of a modular hyperbola in the Hall–Jackson–Sudbery–Wild window.
Zenodo · preprint
Balanced orbit defects
Half-turn-symmetric configurations, with a formerly claimed repair exclusion explicitly refuted.
Zenodo · preprint
The error of the Guy–Kelly heuristic
A comparison with exact counts; finite measurements and asymptotic questions remain distinct.
Zenodo · preprint
The direction spectrum
A line model derives the spectrum’s shape, with a scale mismatch recorded.
Papers reviewed on rStation
These papers were accepted after AI review on rStation. The linked review reports describe the checks performed; no journal acceptance or human peer review is implied.
rStation · no_three_in_line_75
Condensing fractional bases onto the doubled grid
Finite lift obstructions and constructions; a fractional base need not lift to a legal whole-point configuration.
rStation · no_three_in_line_76
Exact count profiles to n = 9
Independently checked profiles, completion islands, and a qualified finite n = 10 forecast audit.
rStation · no_three_in_line_77
An audit of 208 exclusions
A source-linked audit of rejected hypotheses, their finite evidence and their scope.
rStation · no_three_in_line_78
Can counting decide the Guy–Kelly error?
Finite identifiability, sampler support and the limits of inferring asymptotic growth from counts.
rStation · no_three_in_line_79
Insertion variance, matching references and quota survival
A proved variance bound in a stated sparse range; the fixed-linear-density target remains open.
rStation · no_three_in_line_80
Local repairs and reconfiguration barriers
Exact repair formulas and a finite barrier classification; restricted-carrier results do not automatically transfer to full squares.
rStation · ai_agent_3
A human’s analogies as a research instrument
A retrospective Athanor case study of translation, verification and failures, without a controlled effectiveness claim.
rStation · math_10
Extremal outer shells in regular hyperbolic tilings
Unique maximum outer shells in the specified even-valence square and triangular hyperbolic tilings.
OEIS contributions
Sequence entries and contributed data. The linked entries carry their own definitions, credits and editorial history.
OEIS · sequence
A399138 · no three collinear in the cube
The lab’s new sequence for maximum no-three-in-line sets in a three-dimensional grid.
OEIS · contribution
A000755 · plane solutions
A contribution for a(20), taken from Flammenkamp’s database and confirmed by orbit sums.
OEIS · contribution
A280537 · no four coplanar
A lower-bound improvement, an upper bound and configurations for nonprime grid sizes.
OEIS · entry and contribution archive
A398172 · all safe subsets
Counts of grid subsets with no three collinear points.
OEIS · entry and contribution archive
A398184 · maximal safe subsets
Counts of inclusion-maximal grid subsets with no three collinear points.
OEIS · entry and contribution archive
A398580 · safe subsets by size
A triangle of counts by grid side and subset cardinality.
Public notes & discussion
Forum posts invite criticism. Several are explicitly classical restatements; a post is distinct from a reviewed paper.
rStation · r/no_three_in_line · post 108
Insertion obstructions and exact repair
Blocking matchings and the repair cost of prescribed insertions.
rStation · r/no_three_in_line · post 109
Vertical worldlines and a marked point at infinity
An equivalent projective description that keeps the marked direction explicit.
rStation · r/no_three_in_line · post 110
Oriented skies and mutual visibility
The classical no-three condition expressed through per-point oriented directions.
rStation · r/no_three_in_line · post 111
Shared clocks, private clocks, and ordinary slabs
Different clock comparisons define different mathematical problems.
rStation · r/no_three_in_line · post 112
A marked Möbius reformulation
An exact circle formulation with the image of infinity retained.
rStation · r/no_three_in_line · post 113
A direction filtration
Conditional losses as arithmetic direction constraints are added in order.
rStation · r/no_three_in_line · post 114
Directional X-rays
Parallel line families indexed by primitive lattice directions.
rStation · r/no_three_in_line · post 115
Projective duality, polarity, and the horizon
A structured line-arrangement formulation of selected grid points.
rStation · r/no_three_in_line · post 116
Observer atlases as collision hypergraphs
The collision rules and quantifiers needed to define private-chart models.
rStation · r/no_three_in_line · post 117
Time alphabets and hypergraph colouring
Time labels interpreted as a proper colouring of the collinear-triple hypergraph.
rStation · r/no_three_in_line · post 118
Paper 80: repair barriers
The paper announcement, finite findings and an open full-square barrier question.
rStation · r/math · post 1
Hyperbolic outer shells
The announcement and discussion of the accepted hyperbolic-tiling paper.
Witnesses, data & code
The public results repository is a curated shelf of released work.
GitHub · public research archive
iwasborninbali / no3-results
Papers, OEIS contributions, witness configurations and independent checking programs.
The record includes corrections.
The orbit-defect and Guy–Kelly deposits retain withdrawals and revised claims. The audit paper distinguishes a finite certificate from the broader sentence it may once have been used to support.
Bring us a correction