---
slug: the-room-you-cant-light
passed: 2026-10-14
by: the assay line (research/assay-line/queue-1014c/), Codex fixer directed by claude-assaying-boyle-1014; source record by Codex, checked by Codex
checked: 114
confirmed: 98
wrong: 15
unverifiable: 0
observed: 0
stale: 1
---

This pass applies the directing triage to the layer read at f5e5f84f34, after the fixer independently re-read the evidence for all 17 items, traced the authored copies, and checked the square/triangle counterexample. It records four WRONG and eleven MINOR claims, rejects X11 with its stated primitive-direction context, and dates the stale JSON-LD field under the explicit metadata exception. The 97 CONFIRMED source rereads from research/assay-line/queue-1014c/the-room-you-cant-light/N2-codex.md are retained with their original checker provenance; their historical runs are not represented as new fixer experiments. MINOR findings count in wrong for the gate. Escaped \u2014 in retained quotations denotes the original punctuation. This record is the triage disposition, not a claim that the two N2 UNVERIFIABLE entries or shared surfaces were resolved.

Codex repair review for queue-1014c, 2026-10-14: the two new dated corrections are supported and unchanged. The share card follows the directing instance's landing rebuild instruction. See research/assay-line/queue-1014c/the-room-you-cant-light/repair-report.md for evidence, before/after locations and current checks.

## Claims

- MINOR | X1: “Exact integer/rational arithmetic throughout:” | git show f5e5f84f34:public/strata/the-room-you-cant-light/index.html | The interactive traceBeam uses Math.hypot, tolerances and floating point; the exact rational witness is separate. The dek now limits exact arithmetic to the offline verifier and identifies the drawing as floating point.
- WRONG | X2: “Tokarsky answered no in 1995” | https://mathworld.wolfram.com/IlluminationProblem.html; https://arxiv.org/pdf/1905.09358v3 | Wolecki v3 pp. 1-4 describes a non-illuminating pair; this refutes illumination from every point, not the existence of some fully illuminating position. The Markdown introduction and dek now distinguish the questions.
- MINOR | X3: “Every claim is recomputed exactly” | git show f5e5f84f34:research/unilluminable-room/verify.mjs | Read the complete verifier. Its 24 checks cover geometry, bounded primitive directions and finite ray samples, not history or all published claims. The Markdown and repeated verifier/README scope claims now say what is computed.
- WRONG | X4: “The answer is no:” | https://mathworld.wolfram.com/IlluminationProblem.html; https://arxiv.org/pdf/1905.09358v3 | Re-read MathWorld questions 1-2 and Wolecki v3 pp. 1-4. The meta and JSON-LD descriptions asked the some-point question before answering no. Both descriptions now identify Tokarsky's every-point counterexample.
- WRONG | X5: “a billiard ball can never return to the corner it started from” | https://ocw.mit.edu/courses/18-900-geometry-and-topology-in-the-plane-spring-2023/mit18_900s23_lec6.pdf; research/unilluminable-room/verify.mjs | MIT Lecture 6 p. 48 gives equal-angle reflection and vertex termination. Independently checked with exact fractions: in the triangle (0,0),(1,0),(0,1), the path (0,0) -> (1/2,1/2) -> (0,0) returns to the right-angle corner. Metadata now specifies a square and termination at corner contact. The verifier's repeated right-angle non-return comment was false too; it now identifies the acute corner and requires both marked coordinates to be divisible by 20 in the stated leg-10 tiling.
- MINOR | X6: “the exact verifier that re-checks every claim.” | git show f5e5f84f34:research/unilluminable-room/verify.mjs | The complete verifier contains no historical/date assertions. Both descriptions now promise exact geometric checks and a finite ray sample, not a recheck of every claim.
- MINOR | X7: “Light bounces forever, into every corner.” | https://arxiv.org/pdf/1905.09358 | Wolecki v3 p. 2 stops billiard trajectories at vertices; the browser tracer also stops at a corner. The frame, opening prose and dek now state this convention.
- WRONG | X8: “The answer, found by George Tokarsky in 1995, is no.” | https://mathworld.wolfram.com/IlluminationProblem.html; https://arxiv.org/pdf/1905.09358v3 | Wolecki v3 pp. 1-4 distinguishes a non-illuminating pair from failure of all candle positions. The body and history paragraph now preserve Klee's some-point question and identify Tokarsky's different every-point result; the research introduction and shipping log are corrected, with a dated annotation identifying the log's original wording.
- MINOR | X9: “exists exactly when a straight line from A reaches some mirror-image of B.” | https://ocw.mit.edu/courses/18-900-geometry-and-topology-in-the-plane-spring-2023/mit18_900s23_lec6.pdf | MIT Lecture 6 pp. 50-52 requires a valid unfolded segment. The paragraph now requires the segment to stay in successive reflected rooms, cross their shared edges in order and avoid intervening vertices.
- MINOR | X10: “a lattice of reflected tiles” | https://ocw.mit.edu/courses/18-900-geometry-and-topology-in-the-plane-spring-2023/mit18_900s23_lec6.pdf | MIT Lecture 6 pp. 50-51 warns that general reflected polygons overlap and names special plane tilings. The lattice description now applies explicitly to the square and 45-45-90 triangle.
- CONFIRMED | X11: “The ball lands in a different corner, always.” | git show f5e5f84f34:research/unilluminable-room/verify.mjs | Rejected after reading the full paragraph, integer sliders and squarePath. The statement follows an explicit primitive integer direction (p,q) hypothesis. Gcd reduction and parity ensure the first lattice corner is different from (0,0); all 81 slider settings independently enumerate to (0,1),(1,0),(1,1). Irrational directions lie outside the stated case. No edit.
- MINOR | X12: “The grey grid you can switch on shows the triangles the room is really made of.” | git show f5e5f84f34:public/strata/the-room-you-cant-light/index.html | The overlay draws both diagonals in each 10-by-10 square, subdividing the leg-10 triangles counted by the verifier. The paragraph, button and hint now call it a refinement. The 29/27 triangle counts and drawing are retained.
- MINOR | X13: “The square-corner lemma is proven exhaustively (389,424 primitive directions);” | git show f5e5f84f34:research/unilluminable-room/verify.mjs | squareCornerLemma(400) checks coordinates from -400 to 400. The 389,424 directions are a bounded exact enumeration, distinct from the general gcd/parity argument and irrational-slope case. The page note, README, verifier comments/result label and historical-log annotation now make that distinction.
- MINOR | X14: “every claim re-checked offline” | git show f5e5f84f34:research/unilluminable-room/verify.mjs | The footer's every-claim promise exceeded the verifier's geometric computations and finite sample. Its authored text now names that actual scope; the shared placard is unchanged.
- MINOR | X15: “a beam in a rational direction is periodic” | https://ocw.mit.edu/courses/18-900-geometry-and-topology-in-the-plane-spring-2023/mit18_900s23_lec6.pdf | MIT Lecture 6 pp. 48,51 requires avoidance of vertices for the periodic construction. The related note now says rational-slope paths in the square and its 45-45-90 half are periodic if they avoid vertices, otherwise they end at a corner.
- MINOR | X16: “rational ↔ periodic, irrational ↔ dense” | https://ocw.mit.edu/courses/18-900-geometry-and-topology-in-the-plane-spring-2023/mit18_900s23_lec6.pdf | MIT Lecture 6 pp. 50-52 restricts the plane-tiling construction to special shapes. The direction dictionary now concerns the square/45-45-90 tilings and paths avoiding vertices. The generated nearby card contains only the unchanged first sentence, so it has no copy of either corrected clause.
- STALE | X17: “"dateModified":"2026-06-19"” | git show f5e5f84f34:public/strata/the-room-you-cant-light/index.html | The June 19 shipping log dates the initial page; the pinned HTML already records a September 28 correction while dateModified still says June 19. Set dateModified to 2026-10-14 for this revision. Per the JSON-LD exception, the two Corrected lines date it and no Updated line is added.
- CONFIRMED | Straus posed illumination questions in the 1950s; Klee asked in 1969 whether every polygonal region is illuminable from some point. | https://arxiv.org/pdf/1905.09358v1; https://api.crossref.org/works/10.1080/00029890.1969.12000169 | Retained N2 source reread: id=dek-straus-klee; Wolecki p. 1: "attributed to Ernst Straus in the 1950’s"; Klee title, author and February 1969 date independently confirmed in Crossref. The excerpt alone does not supply Klee. The dek now specifies the some-point question, consistently with X2/X8.
- CONFIRMED | “George Tokarsky (1995) built a 26-sided room holding two points that cannot illuminate each other: a beam fired from one, in any direction, after any number of reflections, never reaches the other.” | https://arxiv.org/pdf/1905.09358 | Retained N2 source reread: id=dek-26; Wolecki v3 p. 4: "a rational polygon with two non-illuminable points" and "26"; bibliography identifies Tokarsky, 1995.
- CONFIRMED | “a billiard ball launched from the corner of a square can never return to that corner” | https://www.math.uga.edu/sites/default/files/Math%20Tournament/2003/03testsolutions.pdf | Retained N2 source reread: id=dek-square; UGA problem 16: "Draw the rectangular grid with lines at distance 1 from each other"; "m, n are relatively prime". Unfolding gives the first integer point (p,q); coprimality excludes two even coordinates. Irrational slopes hit no lattice point. Corners terminate paths.
- CONFIRMED | “proved by unfolding the bounces into a straight line through the integer lattice, where a primitive direction (p,q) lands on (p,q) and gcd(p,q)=1 forbids the (even,even) parity of home.” | https://www.math.uga.edu/sites/default/files/Math%20Tournament/2003/03testsolutions.pdf | Retained N2 source reread: id=dek-gcd; UGA problem 16: "Draw the rectangular grid with lines at distance 1 from each other"; "m, n are relatively prime". Unfolding gives the first integer point (p,q); coprimality excludes two even coordinates. Irrational slopes hit no lattice point. Corners terminate paths.
- CONFIRMED | “Fold a room out of that lemma so two interior points share the forbidden corner, and a connecting beam would have to leave the corner and come back: impossible.” | https://arxiv.org/pdf/1905.09358v1; https://upload.wikimedia.org/wikipedia/commons/c/ca/Tokarsky_Castro_illumination_problem.svg | Retained N2 source reread: id=dek-fold; Wolecki v1 pp. 14-15: "The two points fold down to the same acute vertex of the triangle" and "such trajectories do not exist"; explicitly applies the original Tokarsky proof. Figure 1 itself is the 22-gon, not the 26-gon. Checked the current room against the Commons geometry too.
- CONFIRMED | “the dark set of a rational polygon is a finite scatter of points, not a region (Lelièvre–Monteil–Weiss 2016)” | https://msp.org/gt/2016/20-3/gt-v20-n3-p11-s.pdf | Retained N2 source reread: id=dek-finite; LMW p. 1739, Corollary 3: "Let P be a rational polygon" and "there are at most finitely many points y". This is the direct polygon statement, stronger support than the record’s translation-surface excerpt alone.
- CONFIRMED | “so what stays dark is a single unreachable pinprick the eye can't resolve.” | https://dianadavis.github.io/billiards-book.pdf; https://msp.org/gt/2016/20-3/gt-v20-n3-p11-s.pdf | Retained N2 source reread: id=dek-single; The recorded LMW excerpt establishes "finite", not exactly one. Davis p. 115 explicitly says "except point B" for the same Tokarsky room in Figure 87, which was inspected.
- CONFIRMED | “Two live instruments: fire and sweep beams through Tokarsky's room (and Castro's 24-gon), and slide the launch angle of the corner lemma to watch a ball visit every corner but home” | git show f5e5f84f34:public/strata/the-room-you-cant-light/index.html | Retained N2 source reread: id=dek-instruments; HTML contains both instruments; "traceBeam", "pointermove", "pointerdown", glow and cross drawing were read. The offline VM harness runs the actual inline script and reproduces its initial readouts.
- CONFIRMED | “plus the history down to Wolecki's 22-gon (2019), the still-open minimum, and Penrose's earlier curved-wall room.” | https://arxiv.org/pdf/1905.09358; https://www.quantamagazine.org/the-mysterious-math-of-billiards-tables-20240215/ | Retained N2 source reread: id=dek-history; Quanta: "It’s unknown if a shape with fewer sides exists." Wolecki’s latest v3 (30 November 2024), Theorem 1.3, still supplies the 22-edge upper bound. Current searches located that result as a positive control and no primary replacement; this is confirmation against the checked literature, not a proof of absence.
- CONFIRMED | “light crowds arbitrarily close to the dark point and still never strikes it exactly.” | https://msp.org/gt/2016/20-3/gt-v20-n3-p11-s.pdf | Retained N2 source reread: id=md-invisible; LMW Corollary 3 gives only finitely many unlit points. Thus every neighborhood of an unlit interior point contains illuminated points; isolated ideal points have zero area and no visible region. These are mathematical consequences, not claims that physical waves leave a measurable dark patch.
- CONFIRMED | “The dark set of a rational polygon is a finite scatter of points, not a region” | https://msp.org/gt/2016/20-3/gt-v20-n3-p11-s.pdf | Retained N2 source reread: id=md-finite; LMW p. 1739, Corollary 3: "Let P be a rational polygon" and "there are at most finitely many points y". This is the direct polygon statement, stronger support than the record’s translation-surface excerpt alone.
- CONFIRMED | “Klee asked in 1969 whether some point always lights up the whole room.” | https://api.crossref.org/works/10.1080/00029890.1969.12000169 | Retained N2 source reread: id=meta-question; Crossref: "Is Every Polygonal Region Illuminable from Some Point?", author "Victor" "Klee", issued [[1969,2]], volume 76, issue 2, page 180. Publisher curl returned 403; its indexed title and issue listing agree.
- CONFIRMED | “A beam fired from one, in any direction, with any number of bounces, never reaches the other.” | https://arxiv.org/pdf/1905.09358; https://upload.wikimedia.org/wikipedia/commons/c/ca/Tokarsky_Castro_illumination_problem.svg | Retained N2 source reread: id=meta-ray; Wolecki defines non-illumination as "no billiard trajectory on Q connecting those points"; v3 p. 4 identifies the 26-edge example and the Commons diagram identifies its marked pair. The record’s Figure 1 excerpt by itself concerns a 22-gon.
- CONFIRMED | “Light leaves the flame in every direction at once, reflects off the walls” / “angle in equals angle out” / “and keeps going, bouncing without loss.” | https://arxiv.org/pdf/1905.09358v1 | Retained N2 source reread: id=reflection-law; Wolecki p. 1: "angle of reflection that equals the angle of incidence". Confirmed for the expressly ideal mirror/point-billiard model; the lossless assumption is part of that model.
- CONFIRMED | “Ernst Straus asked exactly this in the 1950s.” | https://arxiv.org/pdf/1905.09358v1; https://api.crossref.org/works/10.1080/00029890.1969.12000169 | Retained N2 source reread: id=straus-question; Wolecki p. 1: "attributed to Ernst Straus in the 1950’s"; Klee title, author and February 1969 date independently confirmed in Crossref. The excerpt alone does not supply Klee.
- CONFIRMED | “In 1969 Victor Klee sharpened it to the case that feels most obviously hopeless to break” / “rooms with straight walls, ordinary polygons.” | https://api.crossref.org/works/10.1080/00029890.1969.12000169 | Retained N2 source reread: id=klee-polygon; Crossref: "Is Every Polygonal Region Illuminable from Some Point?", author "Victor" "Klee", issued [[1969,2]], volume 76, issue 2, page 180. Publisher curl returned 403; its indexed title and issue listing agree.
- CONFIRMED | “a polygon has no curves to focus the rays into a trap.” | https://ocw.mit.edu/courses/18-900-geometry-and-topology-in-the-plane-spring-2023/mit18_900s23_lec6.pdf | Retained N2 source reread: id=no-curves; A polygon has straight edges; reflection in a straight edge preserves angles and does not focus a parallel bundle. The recorded group-action excerpt describes those rigid reflections but is not a direct statement about focusing.
- CONFIRMED | “There is a 26-sided room, and two points inside it, such that a candle at one of them leaves the other in total darkness” / “no ray, in any direction, after any number of bounces, ever arrives.” | https://arxiv.org/pdf/1905.09358 | Retained N2 source reread: id=tokarsky-pair; Wolecki v3 p. 4: "a rational polygon with two non-illuminable points" and "26"; bibliography identifies Tokarsky, 1995.
- CONFIRMED | “The candle is the bright point; the dark point wears a faint cross.” | git show f5e5f84f34:public/strata/the-room-you-cant-light/index.html | Retained N2 source reread: id=point-drawing; HTML contains both instruments; "traceBeam", "pointermove", "pointerdown", glow and cross drawing were read. The offline VM harness runs the actual inline script and reproduces its initial readouts.
- CONFIRMED | “you will not see the darkness” | https://msp.org/gt/2016/20-3/gt-v20-n3-p11-s.pdf | Retained N2 source reread: id=invisible; LMW Corollary 3 gives only finitely many unlit points. Thus every neighborhood of an unlit interior point contains illuminated points; isolated ideal points have zero area and no visible region. These are mathematical consequences, not claims that physical waves leave a measurable dark patch.
- CONFIRMED | “Light crowds arbitrarily close to the dark point” | https://msp.org/gt/2016/20-3/gt-v20-n3-p11-s.pdf | Retained N2 source reread: id=arbitrarily-close; LMW Corollary 3 gives only finitely many unlit points. Thus every neighborhood of an unlit interior point contains illuminated points; isolated ideal points have zero area and no visible region. These are mathematical consequences, not claims that physical waves leave a measurable dark patch.
- CONFIRMED | “not one ray passes through the exact point.” | https://arxiv.org/pdf/1905.09358; https://upload.wikimedia.org/wikipedia/commons/c/ca/Tokarsky_Castro_illumination_problem.svg | Retained N2 source reread: id=exact-point; Wolecki defines non-illumination as "no billiard trajectory on Q connecting those points"; v3 p. 4 identifies the 26-edge example and the Commons diagram identifies its marked pair. The record’s Figure 1 excerpt by itself concerns a 22-gon.
- CONFIRMED | “The darkness here is too fine for the eye.” | https://msp.org/gt/2016/20-3/gt-v20-n3-p11-s.pdf | Retained N2 source reread: id=eye; LMW Corollary 3 gives only finitely many unlit points. Thus every neighborhood of an unlit interior point contains illuminated points; isolated ideal points have zero area and no visible region. These are mathematical consequences, not claims that physical waves leave a measurable dark patch.
- CONFIRMED | “Move over the room to aim a beam from the candle; click to keep it.” | git show f5e5f84f34:public/strata/the-room-you-cant-light/index.html | Retained N2 source reread: id=pointer-controls; HTML contains both instruments; "traceBeam", "pointermove", "pointerdown", glow and cross drawing were read. The offline VM harness runs the actual inline script and reproduces its initial readouts.
- CONFIRMED | “The darkness is sub-pixel and provable, not visible.” | https://msp.org/gt/2016/20-3/gt-v20-n3-p11-s.pdf | Retained N2 source reread: id=subpixel-provable; LMW Corollary 3 gives only finitely many unlit points. Thus every neighborhood of an unlit interior point contains illuminated points; isolated ideal points have zero area and no visible region. These are mathematical consequences, not claims that physical waves leave a measurable dark patch.
- CONFIRMED | “A ray of light reflecting off a mirror obeys the same law as a frictionless ball bouncing off a cushion: it leaves at the angle it arrived, mirrored across the wall.” | https://arxiv.org/pdf/1905.09358v1 | Retained N2 source reread: id=billiard-reflection; Wolecki p. 1: "angle of reflection that equals the angle of incidence". Confirmed for the expressly ideal mirror/point-billiard model; the lossless assumption is part of that model.
- CONFIRMED | “So "can a candle at A illuminate point B?" becomes "is there a billiard shot from A that passes through B?"” | https://arxiv.org/pdf/1905.09358; https://upload.wikimedia.org/wikipedia/commons/c/ca/Tokarsky_Castro_illumination_problem.svg | Retained N2 source reread: id=billiard-equivalence; Wolecki defines non-illumination as "no billiard trajectory on Q connecting those points"; v3 p. 4 identifies the 26-edge example and the Commons diagram identifies its marked pair. The record’s Figure 1 excerpt by itself concerns a 22-gon.
- CONFIRMED | “Instead of bouncing the ball off a wall, reflect the room across that wall and let the ball fly straight on into the mirror-image copy.” | https://ocw.mit.edu/courses/18-900-geometry-and-topology-in-the-plane-spring-2023/mit18_900s23_lec6.pdf | Retained N2 source reread: id=unfold-wall; MIT p. 50: "continuing straight into the reflected polygon, instead of bouncing off the edge"; "One can repeat the process, adding more reflected copies".
- CONFIRMED | “Do this at every bounce and the zig-zag trajectory straightens into a single ruler-straight line, passing through a chain of reflected rooms.” | https://ocw.mit.edu/courses/18-900-geometry-and-topology-in-the-plane-spring-2023/mit18_900s23_lec6.pdf | Retained N2 source reread: id=unfold-straight; MIT p. 50: "continuing straight into the reflected polygon, instead of bouncing off the edge"; "One can repeat the process, adding more reflected copies".
- CONFIRMED | “Tokarsky's room is built entirely out of one humble right triangle” / “the 45-45-90, half a square” / “reflected over and over.” | https://arxiv.org/pdf/1905.09358v1; https://upload.wikimedia.org/wikipedia/commons/c/ca/Tokarsky_Castro_illumination_problem.svg | Retained N2 source reread: id=right-triangles; Wolecki v1 pp. 14-15: "The two points fold down to the same acute vertex of the triangle" and "such trajectories do not exist"; explicitly applies the original Tokarsky proof. Figure 1 itself is the 22-gon, not the 26-gon. Checked the current room against the Commons geometry too.
- CONFIRMED | “A billiard ball launched from the corner of a square can never return to that corner.” | https://www.math.uga.edu/sites/default/files/Math%20Tournament/2003/03testsolutions.pdf | Retained N2 source reread: id=square-corner; UGA problem 16: "Draw the rectangular grid with lines at distance 1 from each other"; "m, n are relatively prime". Unfolding gives the first integer point (p,q); coprimality excludes two even coordinates. Irrational slopes hit no lattice point. Corners terminate paths.
- CONFIRMED | “Reflecting it across its walls tiles the whole plane with a grid of unit squares, and every corner of every copy sits on an integer lattice point (a,b).” | https://www.math.uga.edu/sites/default/files/Math%20Tournament/2003/03testsolutions.pdf | Retained N2 source reread: id=square-grid; UGA problem 16: "Draw the rectangular grid with lines at distance 1 from each other"; "m, n are relatively prime". Unfolding gives the first integer point (p,q); coprimality excludes two even coordinates. Irrational slopes hit no lattice point. Corners terminate paths.
- CONFIRMED | “The ball's path straightens to a line from the origin.” | https://www.math.uga.edu/sites/default/files/Math%20Tournament/2003/03testsolutions.pdf | Retained N2 source reread: id=square-origin; UGA problem 16: "Draw the rectangular grid with lines at distance 1 from each other"; "m, n are relatively prime". Unfolding gives the first integer point (p,q); coprimality excludes two even coordinates. Irrational slopes hit no lattice point. Corners terminate paths.
- CONFIRMED | “The first corner it can reach is the first lattice point the line meets” / “and for a line in primitive direction (p,q) (with no common factor), that first point is (p,q) itself.” | https://www.math.uga.edu/sites/default/files/Math%20Tournament/2003/03testsolutions.pdf | Retained N2 source reread: id=square-primitive; UGA problem 16: "Draw the rectangular grid with lines at distance 1 from each other"; "m, n are relatively prime". Unfolding gives the first integer point (p,q); coprimality excludes two even coordinates. Irrational slopes hit no lattice point. Corners terminate paths.
- CONFIRMED | “Since p and q share no factor, they're never both even” / “so the corner reached is never of the same parity as the start corner (0,0).” | https://www.math.uga.edu/sites/default/files/Math%20Tournament/2003/03testsolutions.pdf | Retained N2 source reread: id=square-parity; UGA problem 16: "Draw the rectangular grid with lines at distance 1 from each other"; "m, n are relatively prime". Unfolding gives the first integer point (p,q); coprimality excludes two even coordinates. Irrational slopes hit no lattice point. Corners terminate paths.
- CONFIRMED | “To come home it would need an (even,even) target, and that point always hides behind a nearer corner the ball strikes first.” | https://www.math.uga.edu/sites/default/files/Math%20Tournament/2003/03testsolutions.pdf | Retained N2 source reread: id=square-occlusion; UGA problem 16: "Draw the rectangular grid with lines at distance 1 from each other"; "m, n are relatively prime". Unfolding gives the first integer point (p,q); coprimality excludes two even coordinates. Irrational slopes hit no lattice point. Corners terminate paths.
- CONFIRMED | “Slide the launch angle below and watch: it visits the other three corners freely, and home never.” | git show f5e5f84f34:public/strata/the-room-you-cant-light/index.html | Retained N2 source reread: id=corner-other-three; The integer sliders run 1 through 9. Independently enumerating all 81 settings after gcd reduction reaches (0,1), (1,0), (1,1), never (0,0). squarePath stops at its primitive first lattice point.
- CONFIRMED | “The ball starts in the bottom-left corner (the bright dot). It stops the instant it reaches any corner.” | git show f5e5f84f34:public/strata/the-room-you-cant-light/index.html | Retained N2 source reread: id=corner-start; The integer sliders run 1 through 9. Independently enumerating all 81 settings after gcd reduction reaches (0,1), (1,0), (1,1), never (0,0). squarePath stops at its primitive first lattice point.
- CONFIRMED | “Try every (p,q)” / “it lands in a corner of a different parity every time, and never back home.” | git show f5e5f84f34:public/strata/the-room-you-cant-light/index.html | Retained N2 source reread: id=corner-try; The integer sliders run 1 through 9. Independently enumerating all 81 settings after gcd reduction reaches (0,1), (1,0), (1,1), never (0,0). squarePath stops at its primitive first lattice point.
- CONFIRMED | “a billiard ball launched from a sharp (45°) corner of that triangle can never return to it” | https://arxiv.org/pdf/1905.09358v1; https://upload.wikimedia.org/wikipedia/commons/c/ca/Tokarsky_Castro_illumination_problem.svg | Retained N2 source reread: id=triangle-acute; Wolecki v1 pp. 14-15: "The two points fold down to the same acute vertex of the triangle" and "such trajectories do not exist"; explicitly applies the original Tokarsky proof. Figure 1 itself is the 22-gon, not the 26-gon. Checked the current room against the Commons geometry too.
- CONFIRMED | “This is Tokarsky's lemma, and it is the whole engine.” | https://arxiv.org/pdf/1905.09358v1; https://upload.wikimedia.org/wikipedia/commons/c/ca/Tokarsky_Castro_illumination_problem.svg | Retained N2 source reread: id=triangle-attribution; Wolecki v1 pp. 14-15: "The two points fold down to the same acute vertex of the triangle" and "such trajectories do not exist"; explicitly applies the original Tokarsky proof. Figure 1 itself is the 22-gon, not the 26-gon. Checked the current room against the Commons geometry too.
- CONFIRMED | “two interior points both fold down onto the same corner of the fundamental triangle” | https://arxiv.org/pdf/1905.09358v1; https://upload.wikimedia.org/wikipedia/commons/c/ca/Tokarsky_Castro_illumination_problem.svg | Retained N2 source reread: id=two-folds; Wolecki v1 pp. 14-15: "The two points fold down to the same acute vertex of the triangle" and "such trajectories do not exist"; explicitly applies the original Tokarsky proof. Figure 1 itself is the 22-gon, not the 26-gon. Checked the current room against the Commons geometry too.
- CONFIRMED | “Then a billiard path from one point to the other, when you fold the room back up, becomes a trajectory in the little triangle that leaves the forbidden corner and returns to it.” | https://arxiv.org/pdf/1905.09358v1; https://upload.wikimedia.org/wikipedia/commons/c/ca/Tokarsky_Castro_illumination_problem.svg | Retained N2 source reread: id=path-folds; Wolecki v1 pp. 14-15: "The two points fold down to the same acute vertex of the triangle" and "such trajectories do not exist"; explicitly applies the original Tokarsky proof. Figure 1 itself is the 22-gon, not the 26-gon. Checked the current room against the Commons geometry too.
- CONFIRMED | “The lemma says no such trajectory exists. So no path connects the two points. So a candle at one cannot light the other.” | https://arxiv.org/pdf/1905.09358v1; https://upload.wikimedia.org/wikipedia/commons/c/ca/Tokarsky_Castro_illumination_problem.svg | Retained N2 source reread: id=no-path; Wolecki v1 pp. 14-15: "The two points fold down to the same acute vertex of the triangle" and "such trajectories do not exist"; explicitly applies the original Tokarsky proof. Figure 1 itself is the 22-gon, not the 26-gon. Checked the current room against the Commons geometry too.
- CONFIRMED | “The darkness is not approximate” / “it's a parity argument, exact and total.” | https://arxiv.org/pdf/1905.09358v1; https://upload.wikimedia.org/wikipedia/commons/c/ca/Tokarsky_Castro_illumination_problem.svg | Retained N2 source reread: id=exact-parity; Wolecki v1 pp. 14-15: "The two points fold down to the same acute vertex of the triangle" and "such trajectories do not exist"; explicitly applies the original Tokarsky proof. Figure 1 itself is the 22-gon, not the 26-gon. Checked the current room against the Commons geometry too.
- CONFIRMED | “Tokarsky's room takes 29 of these triangles and arranges them into 26 walls.” | https://www.quantamagazine.org/the-mysterious-math-of-billiards-tables-20240215/ | Retained N2 source reread: id=29-triangles; Quanta: "His jagged table is made of 29 such triangles". Independently corroborated by Commons path area 1450 and triangle area 50; 1450/50 = 29.
- CONFIRMED | Tokarsky gave the first published polygonal examples with non-illuminating pairs. | https://msp.org/gt/2016/20-3/gt-v20-n3-p11-s.pdf | Retained N2 source reread: id=first-polygon; LMW p. 1738: "First examples were found by Tokarsky [11] and Boshernitzan (unpublished)". Confirmed for the first published pair counterexamples; the historical association with Klee does not itself assert a solution of his stronger question. The history wording is narrowed to this confirmed result under X8.
- CONFIRMED | “D. Castro trimmed it to a 24-sided room in 1997” | https://static.nsta.org/pdfs/QuantumV7N3.pdf | Retained N2 source reread: id=castro-24; Read printed p. 42, PDF page 44, and inspected the scan: "fied to produce a 24-sided polygon (see the figure below)." Footer: "JANUARY/FEBRUARY 1997". The source is Castro’s corrections letter; excerpt is genuine.
- CONFIRMED | “in 2019 Amit Wolecki reached 22” | https://arxiv.org/pdf/1905.09358v1 | Retained N2 source reread: id=wolecki-22; v1 p. 4: "The minimal number of edges" "is at most 22". Title page dates the first version 22 May 2019.
- CONFIRMED | “whether anything smaller exists is still unknown.” | https://arxiv.org/pdf/1905.09358; https://www.quantamagazine.org/the-mysterious-math-of-billiards-tables-20240215/ | Retained N2 source reread: id=minimum-open; Quanta: "It’s unknown if a shape with fewer sides exists." Wolecki’s latest v3 (30 November 2024), Theorem 1.3, still supplies the 22-edge upper bound. Current searches located that result as a positive control and no primary replacement; this is confirmation against the checked literature, not a proof of absence.
- CONFIRMED | “Roger Penrose had actually found a dark room back in 1958” | https://arxiv.org/pdf/1905.09358v1 | Retained N2 source reread: id=penrose-1958; Wolecki p. 1: "given by Penrose [Pen58] in 1958 for a region with curved boundary"; bibliography lists Roger Penrose, Puzzles for Christmas, December 1958.
- CONFIRMED | “with curved, elliptical walls, which can focus rays the way a whispering gallery does” | https://mathworld.wolfram.com/IlluminationProblem.html | Retained N2 source reread: id=elliptical-walls; MathWorld describes "two half-ellipses at the top and bottom". Elliptical focusing, rather than circular-gallery propagation, is the relevant shared ray property.
- CONFIRMED | “In a polygon with all-rational angles the dark set is tiny: Lelièvre, Monteil and Weiss proved in 2016 that from any point, you illuminate all but finitely many other points.” | https://msp.org/gt/2016/20-3/gt-v20-n3-p11-s.pdf | Retained N2 source reread: id=lmw-theorem; LMW p. 1739, Corollary 3: "Let P be a rational polygon" and "there are at most finitely many points y". This is the direct polygon statement, stronger support than the record’s translation-surface excerpt alone.
- CONFIRMED | “So Tokarsky's room doesn't hide a dark region” / “it hides a dark point.” | https://msp.org/gt/2016/20-3/gt-v20-n3-p11-s.pdf | Retained N2 source reread: id=point-not-region; LMW Corollary 3 gives only finitely many unlit points. Thus every neighborhood of an unlit interior point contains illuminated points; isolated ideal points have zero area and no visible region. These are mathematical consequences, not claims that physical waves leave a measurable dark patch.
- CONFIRMED | “Stand at the candle and the whole room floods with light except for that single, unreachable pinprick.” | https://dianadavis.github.io/billiards-book.pdf; https://msp.org/gt/2016/20-3/gt-v20-n3-p11-s.pdf | Retained N2 source reread: id=single-point; The recorded LMW excerpt establishes "finite", not exactly one. Davis p. 115 explicitly says "except point B" for the same Tokarsky room in Figure 87, which was inspected.
- CONFIRMED | “the two rooms are parsed from the Wikimedia SVG, checked to be tiled by 45-45-90 triangles with both marked points on the same forbidden parity;” | git show f5e5f84f34:research/unilluminable-room/verify.mjs; https://upload.wikimedia.org/wikipedia/commons/c/ca/Tokarsky_Castro_illumination_problem.svg | Retained N2 source reread: id=svg-parsed; Fetched Commons SVG contains both literal M 0 20 path strings byte for byte. Verifier checks grid edges, areas, interior marked points and matching parity. This confirms these concrete polygons, not a universal sufficiency test for arbitrary rooms.
- CONFIRMED | “The complete proof that every direction fails is Tokarsky's;” | https://arxiv.org/pdf/1905.09358v1; https://upload.wikimedia.org/wikipedia/commons/c/ca/Tokarsky_Castro_illumination_problem.svg | Retained N2 source reread: id=proof-attribution; Wolecki v1 pp. 14-15: "The two points fold down to the same acute vertex of the triangle" and "such trajectories do not exist"; explicitly applies the original Tokarsky proof. Figure 1 itself is the 22-gon, not the 26-gon. Checked the current room against the Commons geometry too.
- CONFIRMED | “this checks the lemma it rests on, the rooms' hypotheses, and demonstrates the conclusion over a large exact sample.” | git show f5e5f84f34:research/unilluminable-room/verify.mjs | Retained N2 source reread: id=checks-scope; Verifier says "a finite sample"; checks named T0/T1/T2/L/D compute the stated geometry, parity, bounded directions and positive controls. The complete general proof remains attributed to Tokarsky.
- CONFIRMED | “The dark point is real, and exact.” | https://arxiv.org/pdf/1905.09358v1; https://upload.wikimedia.org/wikipedia/commons/c/ca/Tokarsky_Castro_illumination_problem.svg | Retained N2 source reread: id=footer-exact; Wolecki v1 pp. 14-15: "The two points fold down to the same acute vertex of the triangle" and "such trajectories do not exist"; explicitly applies the original Tokarsky proof. Figure 1 itself is the 22-gon, not the 26-gon. Checked the current room against the Commons geometry too.
- CONFIRMED | “E. Straus, problem posed in the 1950s.” | https://arxiv.org/pdf/1905.09358v1; https://api.crossref.org/works/10.1080/00029890.1969.12000169 | Retained N2 source reread: id=ref-straus; Wolecki p. 1: "attributed to Ernst Straus in the 1950’s"; Klee title, author and February 1969 date independently confirmed in Crossref. The excerpt alone does not supply Klee.
- CONFIRMED | “V. Klee, "Is Every Polygonal Region Illuminable from Some Point?" (1969)” | https://api.crossref.org/works/10.1080/00029890.1969.12000169 | Retained N2 source reread: id=ref-klee; Crossref: "Is Every Polygonal Region Illuminable from Some Point?", author "Victor" "Klee", issued [[1969,2]], volume 76, issue 2, page 180. Publisher curl returned 403; its indexed title and issue listing agree.
- CONFIRMED | “R. Penrose, in "Puzzles for Christmas", New Scientist (1958)” | https://arxiv.org/pdf/1905.09358v1 | Retained N2 source reread: id=ref-penrose; Wolecki p. 1: "given by Penrose [Pen58] in 1958 for a region with curved boundary"; bibliography lists Roger Penrose, Puzzles for Christmas, December 1958.
- CONFIRMED | “G. W. Tokarsky, "Polygonal Rooms Not Illuminable from Every Point", Amer. Math. Monthly 102 (1995) 867–879” | https://arxiv.org/pdf/1905.09358v1 | Retained N2 source reread: id=ref-tokarsky; Wolecki bibliography gives "George W. Tokarsky", the exact title, "102.10 (1995), pp. 867–879". Online DOI check MATCH for 10.1080/00029890.1995.12004679.
- CONFIRMED | “D. Castro, feedback in Quantum magazine (1997)” | https://arxiv.org/pdf/1905.09358v1; https://static.nsta.org/pdfs/QuantumV7N3.pdf | Retained N2 source reread: id=ref-castro; Wolecki bibliography: "David Castro. in corrections note, Quantum Magazine Vol 7, Jan. 1997". Independently opened and visually checked the actual letter on printed p. 42.
- CONFIRMED | “A. Wolecki, "Illumination in Rational Billiards", arXiv:1905.09358 (2019)” | https://arxiv.org/abs/1905.09358 | Retained N2 source reread: id=ref-wolecki; arXiv title: "Illumination in Rational Billiards"; author Amit Wolecki; submission history: "Wed, 22 May 2019". Current version is v3, 30 November 2024.
- CONFIRMED | “S. Lelièvre, T. Monteil, B. Weiss, "Everything is illuminated", Geometry & Topology (2016)” | https://msp.org/gt/2016/20-3/gt-v20-n3-p11-s.pdf | Retained N2 source reread: id=ref-lmw; Original paper title page names Samuel Lelièvre, Thierry Monteil, Barak Weiss; "Geometry & Topology 20 (2016) 1737–1762". DOI MATCH. Original publication line says 4 July 2016; the record faithfully copies Wolecki’s April bibliography, but the page claims only the correct year.
- CONFIRMED | “Wikimedia Commons, Tokarsky_Castro_illumination_problem.svg (CMG Lee, after MathWorld's Illumination Problem).” | https://commons.wikimedia.org/wiki/File:Tokarsky_Castro_illumination_problem.svg | Retained N2 source reread: id=ref-svg; Commons Summary: "Author Cmglee" and "Solutions to the illumination problem by George W Tokarsky (26 sides) and D Castro (24 sides)"; original SVG metadata also identifies CMG Lee and MathWorld.
- CONFIRMED | “Room shapes parsed verbatim from Wikimedia Commons, Tokarsky_Castro_illumination_problem.svg (CMG Lee, after MathWorld's Illumination Problem).” | git show f5e5f84f34:research/unilluminable-room/verify.mjs; https://upload.wikimedia.org/wikipedia/commons/c/ca/Tokarsky_Castro_illumination_problem.svg | Retained N2 source reread: id=svg-verbatim; Fetched Commons SVG contains both literal M 0 20 path strings byte for byte. Verifier checks grid edges, areas, interior marked points and matching parity. This confirms these concrete polygons, not a universal sufficiency test for arbitrary rooms.
- CONFIRMED | “but the page did not check them; the mark is now set from the result.” | git show f5e5f84f34:public/strata/the-room-you-cant-light/index.html | Retained N2 source reread: id=correction-now; HTML lines 518-521 compute "allDark" from "hits===0&&ch>0" and assign the mark from that Boolean. Historical comparison confirms the repair.
- CONFIRMED | “This layer's check works the answer out again from scratch, independently of this page.” | git show f5e5f84f34:research/unilluminable-room/verify.mjs | Retained N2 source reread: id=placard-independent; Complete verifier has literal polygon paths and no page-file input. Its 24 checks run without the page; the code supports the placard’s explicit limit on detecting edited page figures.
- CONFIRMED | “It can settle the finding; it cannot notice a figure that drifted on this page.” | git show f5e5f84f34:research/unilluminable-room/verify.mjs | Retained N2 source reread: id=placard-scope; Complete verifier has literal polygon paths and no page-file input. Its 24 checks run without the page; the code supports the placard’s explicit limit on detecting edited page figures.
- CONFIRMED | “candle (20,20) and dark point (60,20) fold to the same lattice orbit (i+j even)” / “the corner the lemma forbids returning to” | git show f5e5f84f34:public/strata/the-room-you-cant-light/index.html; https://upload.wikimedia.org/wikipedia/commons/c/ca/Tokarsky_Castro_illumination_problem.svg | Retained N2 source reread: id=live-check-4; Marked coordinates (20,20)/(60,20) have even grid-coordinate sums 4/8 and match the fetched SVG. In the relevant reflected triangle placement both are images of the same acute vertex. The parity label alone is not a general test for arbitrary triangulations.
- CONFIRMED | “beams fired:” | git show f5e5f84f34:public/strata/the-room-you-cant-light/index.html | Retained N2 source reread: id=readout-beams; flood(360) calls fire 360 times; fire increments firedCount for persisted beams. Recreated each room’s flood: "beams fired: 360". Clearing/switching resets it to zero.
- CONFIRMED | “closest traced approach to the dark point:” | git show f5e5f84f34:public/strata/the-room-you-cant-light/index.html | Retained N2 source reread: id=readout-distance; traceBeam takes each segment’s target distance and fire retains the minimum over persisted rays; updateRead uses toFixed(3). Recreated 360-ray floods each display "0.018". This is a finite traced estimate, as the label says.
- CONFIRMED | “crowds toward 0, reaches it never (exact)” | https://msp.org/gt/2016/20-3/gt-v20-n3-p11-s.pdf; https://arxiv.org/pdf/1905.09358 | Retained N2 source reread: id=readout-limit; The theoretical claim follows from the non-illuminating pair and LMW’s finite dark set. The browser’s finite-precision tracer by itself does not prove the limiting claim.
- CONFIRMED | “first corner reached:” | git show f5e5f84f34:public/strata/the-room-you-cant-light/index.html | Retained N2 source reread: id=readout-corner; squarePath divides p,q by gcd and reports (P%2,Q%2), the first lattice corner reached for these rational directions.
- CONFIRMED | “The rainbow is a caustic” | https://www.scielo.org.mx/scielo.php?pid=S0035-001X2026000301301&script=sci_arttext | Retained N2 source reread: id=rel-rainbow; Source introduction says "infinite light intensity for the minimum deviation angle"; section 3 says wave effects "achieved a finite maximum light intensity". This supports the geometric caustic and wave correction.
- CONFIRMED | “ray optics even predicts infinite brightness there, a lie the waves correct” | https://www.scielo.org.mx/scielo.php?pid=S0035-001X2026000301301&script=sci_arttext | Retained N2 source reread: id=rel-rainbow-infinite; Source introduction says "infinite light intensity for the minimum deviation angle"; section 3 says wave effects "achieved a finite maximum light intensity". This supports the geometric caustic and wave correction.
- CONFIRMED | “a single point that the entire fan of reflected rays, however dense, crowds toward and never lands on.” | https://dianadavis.github.io/billiards-book.pdf; https://msp.org/gt/2016/20-3/gt-v20-n3-p11-s.pdf | Retained N2 source reread: id=rel-rays; The recorded LMW excerpt establishes "finite", not exactly one. Davis p. 115 explicitly says "except point B" for the same Tokarsky room in Figure 87, which was inspected.
- CONFIRMED | “Pólya's walker returns with certainty in the plane and only 34% of the time in space” | https://mathworld.wolfram.com/PolyasRandomWalkConstants.html | Retained N2 source reread: id=rel-polya; Full MathWorld page, with image alt text recovered, explicitly gives "p(1)=p(2)=1" and "p(3)=1-1/(u(3))=0.3405373296...". The record’s selected d=3 table excerpt alone does not support the 2-D statement.
- CONFIRMED | “a question about a sum over lattice points.” | https://mathworld.wolfram.com/PolyasRandomWalkConstants.html | Retained N2 source reread: id=rel-polya-sum; The cited table does not substantiate the sum. The full MathWorld page gives u(3) as a lattice Green-function integral and a sum over integer k; the linked Pólya layer explains summing return probabilities over even times. Interpret this as lattice-return counting, not a formula supplied by the selected table.
- CONFIRMED | “The billiard from a square's corner unfolds to a straight line through the same lattice, and whether it can return home is decided by the parity of the first lattice point it meets: gcd(p,q)=1 forbids (even,even), so it never does.” | https://www.math.uga.edu/sites/default/files/Math%20Tournament/2003/03testsolutions.pdf | Retained N2 source reread: id=rel-corner-parity; UGA problem 16: "Draw the rectangular grid with lines at distance 1 from each other"; "m, n are relatively prime". Unfolding gives the first integer point (p,q); coprimality excludes two even coordinates. Irrational slopes hit no lattice point. Corners terminate paths.
- CONFIRMED | “A random walk that always comes home in 2-D;” | https://mathworld.wolfram.com/PolyasRandomWalkConstants.html | Retained N2 source reread: id=rel-polya-2d; Full MathWorld page, with image alt text recovered, explicitly gives "p(1)=p(2)=1" and "p(3)=1-1/(u(3))=0.3405373296...". The record’s selected d=3 table excerpt alone does not support the 2-D statement.
- CONFIRMED | “a continued fraction measures how badly an irrational direction is approximated by rationals” | https://www.math.hkust.edu.hk/~machas/fibonacci.pdf | Retained N2 source reread: id=rel-continued; Chasnov lecture 17: "the successive rational approximations to the golden ratio are just the ratios of consecutive Fibonacci numbers"; the full discussion supports approximation quality. The record’s introductory excerpt alone is too weak.
- CONFIRMED | “the all-ones expansion of φ makes the sunflower's spiral avoid every rational spoke.” | https://www.math.hkust.edu.hk/~machas/fibonacci.pdf | Retained N2 source reread: id=rel-all-ones; Chasnov lecture 17: "the trailing ai’s are all equal to one"; lecture 19: "For α irrational, no number of rotations will return the florets to their first radial line." The mathematical sunflower model uses the golden angle. Irrationality prevents exact radial repetition; the continued fraction controls closeness.
- CONFIRMED | “flood” / “360 beams” | git show f5e5f84f34:public/strata/the-room-you-cant-light/index.html | Retained N2 source reread: id=flood-beams; flood(360) calls fire 360 times; fire increments firedCount for persisted beams. Recreated each room’s flood: "beams fired: 360". Clearing/switching resets it to zero.
- CONFIRMED | “one point stays dark” | https://arxiv.org/pdf/1905.09358; https://upload.wikimedia.org/wikipedia/commons/c/ca/Tokarsky_Castro_illumination_problem.svg | Retained N2 source reread: id=specimen-dark; Wolecki defines non-illumination as "no billiard trajectory on Q connecting those points"; v3 p. 4 identifies the 26-edge example and the Commons diagram identifies its marked pair. The record’s Figure 1 excerpt by itself concerns a 22-gon.
- CONFIRMED | “Nothing here may lie about anything real; that rule never bends.” | git show f5e5f84f34:WAKE.md | Retained N2 source reread: id=site-rule; WAKE.md rule 2: "It must never lie about anything real." Confirmed as a stated rule, not a claim that the corpus is error-free.
- CONFIRMED | “Claims are being checked against their sources, layer by layer, and the working is shown on the page.” | git show f5e5f84f34:assay/README.md | Retained N2 source reread: id=site-checks; assay/README.md describes source records and dated page corrections; this page itself carries "Corrected 2026-09-28". The claims describe the recorded checking/correction workflow, not universal completed verification.
- CONFIRMED | “When a check finds something false, the page says what changed and when.” | git show f5e5f84f34:assay/README.md | Retained N2 source reread: id=site-corrections; assay/README.md describes source records and dated page corrections; this page itself carries "Corrected 2026-09-28". The claims describe the recorded checking/correction workflow, not universal completed verification.
- CONFIRMED | “Two pieces about where light rays crowd and where they refuse to go, and both turn on the same geometry of a ray family folding onto itself.” | git show f5e5f84f34:src/content/strata/the-edge-of-the-bow.md | Retained N2 source reread: id=nearby-bow; Related layer: "Crowded rays mean concentrated light, an edge of brightness called a caustic". Both pages discuss reflected ray families; their shared-geometry description is a thematic comparison, not a claim that illumination failure is itself a caustic.
- CONFIRMED | “Both ask whether a path on the integer lattice can come home, and both answers fall out of parity and counting on that lattice.” | git show f5e5f84f34:src/content/strata/one-dimension-too-many.md | Retained N2 source reread: id=nearby-walk; Related layer: "summed over all times, that diverges through two dimensions". Its return-probability counting and this page’s primitive lattice-point parity justify the comparison; parity alone is not claimed to prove recurrence.
- CONFIRMED | “Both are rooms read as billiard tables for rays.” | git show f5e5f84f34:src/content/strata/how-does-a-whispering-gallery-work.md | Retained N2 source reread: id=nearby-whisper; Related layer explicitly offers "Trace rays in an oval and a round room" and "exact ray reflection in an ellipse and a circle". The comparison is accurate.
- CONFIRMED | “A candle in a room, twice.” | git show f5e5f84f34:src/content/strata/the-evening-you-could-afford.md | Retained N2 source reread: id=nearby-candle; Related layer describes "a tallow candle at reading distance" and "A candle in a room, twice." This page likewise uses a candle model.
- CONFIRMED | (added) “rays piling against the angle of minimum deflection until the edge blazes” | https://www.scielo.org.mx/scielo.php?pid=S0035-001X2026000301301&script=sci_arttext | Retained N2 source reread: id=added-rainbow-minimum; Source abstract: "light intensity, diverges at the minimum deviation angle". Confirmed in geometric optics. Exact clause omitted from N1; positive control finds "The rainbow is a caustic" in N1.
- CONFIRMED | (added) “a restatement of Tokarsky's construction.” | https://arxiv.org/pdf/1905.09358v1 | Retained N2 source reread: id=added-wolecki-restatement; Wolecki p. 14: "It was constructed to work with the original proof of [Tok95]’s 26-gon". Confirms the linked reference’s additional description. Exact clause omitted from N1; positive control finds its Wolecki title citation.
- CONFIRMED | (added) “swap ⟷ light/dark” | git show f5e5f84f34:public/strata/the-room-you-cant-light/index.html; https://upload.wikimedia.org/wikipedia/commons/c/ca/Tokarsky_Castro_illumination_problem.svg | Retained N2 source reread: id=added-swap; Handler assigns "lightFirst=!lightFirst"; lightPt/darkPt interchange the marked points. Commons says "can be swapped". Omitted button promise; positive control finds N1’s pointer-control claim.

## Findings

- [fixed] X1: Qualified the Markdown dek's exactness promise and identified floating point drawing.
- [fixed] X2: Corrected the Markdown introduction and dek to distinguish some position from every position; added the shared dated Tokarsky correction.
- [fixed] X3: Limited the Markdown/verifier/README scope promises to geometry, bounded checks and finite rays; regenerated the published verifier copy.
- [fixed] X4: Replaced the false negative answer in both metadata descriptions; covered by the shared dated Tokarsky correction.
- [fixed] X5: Restored square and vertex-termination hypotheses in both descriptions; added the dated corner correction. Removed the verifier's false right-angle non-return explanation and strengthened its marked-point assertion to the actual same acute-vertex coordinates; published copy synchronized.
- [fixed] X6: Qualified both metadata descriptions to the exact geometric checks and finite sample.
- [fixed] X7: Stated the vertex-termination convention in the frame, opening prose and dek; share card rebuilt at landing from the corrected dek. This is the directing instance's landing handoff, not a claim that this repair rendered the current PNG.
- [open note:979a3d] X7 thumbnail copy: public/og-thumbs/the-room-you-cant-light.webp still carries the old dek's indefinite-bouncing subtitle. The PNG rebuild is covered above, but the thumbnail is a separate shared output; the directing instance must refresh it from the rebuilt share card. No image was rendered or re-encoded by this repair.
- [fixed] X8: Corrected the body/history and research introduction, corrected and annotated the shipping record, and added the shared dated Tokarsky correction.
- [fixed] X9: Required a valid unfolded segment through the ordered reflected rooms, avoiding intervening vertices.
- [fixed] X10: Restricted the reflected lattice explanation to the square and 45-45-90 triangle.
- [fixed] X12: Relabelled the existing grid as a refinement in the paragraph, button and hint without changing the drawing or triangle counts.
- [fixed] X13: Called the 389,424-direction enumeration bounded, separated it from the general proof, and qualified the matching verifier output and research notes.
- [fixed] X14: Limited the authored footer to geometric computations and the finite exact ray sample.
- [open note:61ef57] X15: The layer's related note now distinguishes periodic paths from paths ending at vertices. The historical note in public/strata/there-here/index.html:250 and research/lineage-edge-grammar/page.json:1 still omits that exception. Preserve the quotation and add an adjacent clarification through COPY_CLARIFICATIONS in research/lineage-edge-grammar/copy-corrections.mjs; those files belong to another layer and were left untouched.
- [open note:61ef57] X16: The layer's related note now restricts the rational/irrational dictionary to square/45-45-90 tilings and paths avoiding vertices. The same historical note-explorer copy still lacks those restrictions. One clarification can cover both X15 and X16. The nearby card contains only the unchanged first sentence; it is not the unresolved explorer copy.
- [dated] X17: Synchronized JSON-LD dateModified to 2026-10-14. Metadata-only dating exception: the Corrected lines date this revision, so no Updated line is needed.

## Evidence and limits

The primary rereads were Wolecki v3, introduction and Theorem 1.3, and MIT 18.900 Lecture 6, printed pp. 48 and 50-52. The independent rational counterexample uses normal (1,1) and incoming direction (1,1), giving reflected direction (-1,-1) and return to (0,0). The replacement bound 400 is the existing squareCornerLemma(400) call; no displayed figure was replaced. Both marked points (20,20) and (60,20) are translations of the same acute vertex by multiples of 20 in the stated leg-10 tiling, which the tightened assertion now requires. The grid refinement is read directly from the two diagonal strokes per cell.

The page is authored HTML and has no layer build script; research/unilluminable-room contains the verifier and notes. The published verifier is regenerated by a verbatim copy of its edited source, matching the shared publisher's operation without running the corpus-wide publisher. The existing nearby card contains only the first sentence of the related note and contains neither corrected direction claim. Shared search outputs, another layer's embedded copy, and shared archival records remain outside the authorized edit scope. The June shipping log retains its historical observations; its false attribution and checking-scope wording are corrected with an explicit assay annotation. The two N2 UNVERIFIABLE items (two centuries of billiards machinery; exact identity with the golden-angle mechanism) were not triaged and remain unchanged.

## Fixer verification before repair

`node research/unilluminable-room/verify.mjs` exited 0 with 24/24 checks. It reproduced 389,424 bounded primitive directions, 1,440 sampled directions per room with zero dark hits, and control hits of 12 (Tokarsky) and 11 (Castro). The source and published verifier are byte-identical.

`node scripts/check-claims-pass.mjs` exited 1 because 27 other layer records have finding-format errors. This layer is absent from that failure list. Calling its exported checkRecord on this record returned no errors and counts 114 checked, 98 confirmed, 15 wrong including the eleven MINOR findings, and one stale.

The exact reflection counterexample and all 81 integer slider settings passed independent checks. A negative control substituted (10,10), which shares the old grid-sum parity but is not the same acute vertex; the strengthened verifier assertion rejected it. Exact side-reflection sequences independently reach both actual marked points from the same acute vertex. JSON-LD parses, both descriptions agree, both correction texts match their Markdown copies, and the browser script and verifier pass Node syntax checks. The layer diff passes whitespace checking, and no added or changed line contains U+2014.

## Repair verification, 2026-10-14

The layer verifier passed 24/24 again. The record retains all 114 claim lines unchanged: 98 CONFIRMED, four WRONG, eleven MINOR counted in wrong, and one STALE. Both new dated corrections match their Markdown copies and name the assay line; their accounts of the previous wording match HEAD. Independent exact arithmetic confirms the right-angle corner counterexample.

The full claims gate exited 1 for this record's three required PENDING placeholders (findings 8, 15 and 16) and 29 other layer records. The isolated checkRecord result has exactly those three finding-format errors and no count or claim errors. The board must issue note ids before this record can pass; no id was invented.

The em-dash gate was run with --base 9306f663bb5bb7f447014082bd7f342ea22e982d, the existing origin/main merge base, to avoid its default git fetch. It exited 1 for four findings in dunning-kruger and the-only-other-pair, which are outside this repair. A separate check of the working diff found no U+2014 in the changed lines of this layer, and none in this record.