---
slug: the-wheel-that-spins-backward
passed: 2026-10-14
by: the assay line (research/assay-line/cited-1014b/), Codex fixer directed by claude-assaying-boyle-1014; source record by Codex, checked by Codex; repaired by Codex, 2026-10-14
checked: 137
confirmed: 114
wrong: 21
unverifiable: 0
observed: 0
stale: 2
---

This was the directed 2026-10-14 correction pass for this layer at f5e5f84f34. I reread the evidence for all 23 triage items, reproduced the runtime and verifier counterexamples, fixed the supported authored text and code, and retained the 114 CONFIRMED claims already reread by the Codex checker in research/assay-line/cited-1014b/the-wheel-that-spins-backward/N2-codex.md. The copied confirmations describe that pinned pass: its film inspections, downloads and measurements are the checker's recorded work, not new media work by this fixer. The eight listed MINOR items remain unchanged and count toward wrong here without being relabeled WRONG. The delivered MP4, copies in other layers and the landing-owned placard refresh remain outstanding as stated below.

## Claims

- MINOR | X1: The wheel freezes exactly when its spin is a whole multiple of fs/S, runs backward just below each freeze, and is captured faithfully only above the Nyquist rate fs > 2·S·f. | git show f5e5f84f34:public/strata/the-wheel-that-spins-backward/index.html:383; https://ocw.mit.edu/courses/mas-632-conversational-computer-systems-fall-2008/2f14b7dfe31a3ef6fcb8d686065e134a_schmandt_ch3.pdf | Re-read the signed control and faithful() in the page and the magnitude condition in verify.mjs. At -1.9 rev/s, 12 spokes and 24 fps the apparent spin is +0.1 rev/s. The prose omits the magnitude convention, but its necessary-condition wording and positive-spin examples do not assert the false result alleged. Retained as the listed MINOR.
- MINOR | X2: Every claim proven live | git show f5e5f84f34:research/aliasing-wagon-wheel/verify.mjs | Re-read verify.mjs: selected numerical checks and three loose HTML searches at the pinned revision cannot prove every historical, perceptual or prose claim live. Listed MINOR about checking coverage, separate from the specific false identity guarantee.
- STALE | X3: "dateModified":"2026-06-22" | git show f5e5f84f34:memory/log.d/2026-07-05T1530Z-wheel-backward-film.md; git log f5e5f84f34 -- public/strata/the-wheel-that-spins-backward/index.html | The July 5 film log records a later embedded film. June 22 was an authentic initial date, overtaken by substantive work. The Article dateModified is now 2026-10-14; no separate Updated line under the metadata exception.
- MINOR | X4: every frame draws the wheel at its true angle, spinning forward at +1.90 rev/s | git show f5e5f84f34:research/aliasing-wagon-wheel/film/film.html:143 | Re-read film.html SEG: 1.9 rev/s initially, 2.0 during 74-82 seconds, then 2.1. The same page caption describes acceleration. This is an unqualified starting speed, not evidence of false frame angles; listed MINOR.
- MINOR | X5: Every number on screen is recomputed live from the same fold() the verifier proves | git show f5e5f84f34:research/aliasing-wagon-wheel/film/film.html:206; git show f5e5f84f34:research/aliasing-wagon-wheel/film/film.html:213 | Re-read film.html CAPS: 28.5 degrees and 45.6 fps are literal caption values; animated readouts are calculated. The July 5 log describes offline caption checks. The values are correct but the recomputation promise is too broad; listed MINOR.
- WRONG | X6: Spinning BACKWARD on film | git show f5e5f84f34:public/strata/the-wheel-that-spins-backward/index.html:511 | Recreated the actual pinned page handlers with verify-page.mjs --baseline: true -1.9 rev/s gives +0.10 rev/s but the verdict said BACKWARD. The +1.9 control gives -0.10. The fixed page labels the apparent direction correctly in both cases.
- WRONG | X7: film slows the real | git show f5e5f84f34:public/strata/the-wheel-that-spins-backward/index.html:513; git show f5e5f84f34:research/aliasing-wagon-wheel/verify.mjs:100 | Recreated the actual pinned page at 1 rev/s, 12 spokes and 24 fps: apparent +1.00 rev/s with a slowdown verdict. At that band edge the two directions have identical samples. Fixed verdict and signed readout now state the ambiguity, including negative true spin.
- WRONG | X8: The real spoke frequency S·f (amber, above) is reflected back and forth across the band edges until it lands inside (cyan) | https://www.dsprelated.com/freebooks/mDFT/Sampling_Theory.html; git show f5e5f84f34:public/strata/the-wheel-that-spins-backward/index.html:348 | Re-read Smith, Aliasing of Sampled Signals, which limits the mirror account to real signals, and the page fold(). The signed remainder is 22.8 - 24 = -1.2 Hz; reflection about +12 would give +1.2. Corrected the explanation to wrapping by sampling-rate multiples.
- WRONG | X9: Undersample a pure tone and it does not vanish | https://www.dsprelated.com/freebooks/mDFT/Sampling_Theory.html; git show f5e5f84f34:public/strata/the-wheel-that-spins-backward/index.html:615 | Re-read Smith, Appendix: Frequencies Representable by a Geometric Sequence, and the actual zero-phase audio handler. At tone=rate=1000 Hz, samples are sin(2*pi*k), mathematically zero; the actual buffer peak is 2.383385806423166e-12. A 1000/1500 control is nonzero. Qualified the universal claim.
- WRONG | X10: it drops to a phantom pitch, the very same fold. | https://www.dsprelated.com/freebooks/mDFT/Sampling_Theory.html; git show f5e5f84f34:public/strata/the-wheel-that-spins-backward/index.html:615 | The same zero-phase 1000/1000 case has folded frequency 0 Hz and numerically silent samples, so a pitched alias is not guaranteed. Corrected together with X9 and X12; the original film quotation is preserved and annotated outside its words in the film source.
- WRONG | X11: Hear the true 1000 Hz | git show f5e5f84f34:public/strata/the-wheel-that-spins-backward/index.html:604 | Recreated the actual pinned handler with Tone=2000: the button retained 1000 Hz while its generated samples matched the 2000 Hz sine. audSync now updates the numerical label to the selected tone.
- WRONG | X12: The fundamental you perceive is the alias the readout names. | https://www.dsprelated.com/freebooks/mDFT/Sampling_Theory.html; git show f5e5f84f34:public/strata/the-wheel-that-spins-backward/index.html:574 | At tone=1000 Hz and rate=2000 Hz, the pinned readout says 1000 Hz while the actual zero-phase buffer peak is 2.411789084416638e-12. Smith gives the same sin(pi*n)=0 degeneracy. The fixed readout identifies zero samples at integer multiples of half the sample rate; the nonzero 1000/1500 control still reads 500 Hz.
- MINOR | X13: fold(f, fs) = f − fs·round(f / fs) | git show f5e5f84f34:public/strata/the-wheel-that-spins-backward/index.html:348 | Re-read the displayed mathematical formula and implementation. With JavaScript Math.round, the bare expression maps 12 at fs=24 to -12, while the endpoint adjustment returns +12. A tie convention is omitted; the chosen endpoint and default alias are valid. Listed MINOR, not a change to the working fold().
- MINOR | X14: which folds a frequency into the band (−fs/2, fs/2]. | https://www.dsprelated.com/freebooks/mDFT/Sampling_Theory.html; git show f5e5f84f34:public/strata/the-wheel-that-spins-backward/index.html:350 | Smith permits either endpoint of the principal band. The implemented (-fs/2, fs/2] convention is valid. The only issue is the same omitted rounding qualification as X13; listed MINOR.
- MINOR | X15: the motion is captured faithfully only when fs > 2·S·f | https://www.dsprelated.com/freebooks/mDFT/Sampling_Theory.html; git show f5e5f84f34:public/strata/the-wheel-that-spins-backward/index.html:383 | Re-read faithful(), the check bullet and the verifier. The actual signed predicate uses the magnitude of spin. The prose omits that convention but uses necessary-condition wording; listed MINOR with X1. The quoted film repetition remains intact.
- MINOR | X16: re-derives the exact numbers shown in the presets above | git show f5e5f84f34:research/aliasing-wagon-wheel/verify.mjs:119; git show f5e5f84f34:public/strata/the-wheel-that-spins-backward/index.html:192 | Re-read all five page buttons and the four-entry PRESETS array. Eight spokes is not in that array. The four existing cases are correct; this is the listed MINOR coverage overstatement in a separate sentence from X17/X18.
- WRONG | X17: It also reads this page and asserts it ships the identical fold() | git show f5e5f84f34:research/aliasing-wagon-wheel/verify.mjs:141; git show f5e5f84f34:public/strata/the-wheel-that-spins-backward/index.html:352 | Executed the pinned verifier against original HTML, a return-zero mutation and empty HTML: 38/38, 38/38 and 35/38 respectively. Its three searches did not compare the complete function. The revised assertion compares the full fold() after whitespace and var/let normalization; the return-zero mutation now fails 37/38.
- WRONG | X18: the drawing and the proof can never quietly disagree. | git show f5e5f84f34:research/aliasing-wagon-wheel/verify.mjs:142; git show f5e5f84f34:public/strata/the-wheel-that-spins-backward/index.html:245 | The pinned verifier also passed 38/38 after the first-freeze sentence was changed from 2 to 3 rev/s. The revised scoped check rejects that mutation at 37/38. Removed the guarantee of universal agreement and described the limited checks; the unmutated computations agree.
- WRONG | X19: whether it exists | https://eagleman.com/papers/kline_2008.pdf; https://authors.library.caltech.edu/records/g3zjd-4mh20 | Re-read Kline and Eagleman (2008), p. 1 abstract and introduction, and VanRullen, Reddy and Koch (2005), abstract. Both report reversals; they dispute a discrete-sampling explanation. Corrected the existence doubt without asserting a settled mechanism. The film quotation is preserved with an external annotation in the source.
- STALE | X20: Last verified 22 June 2026, when it was written. | git show f5e5f84f34:memory/log.d/2026-07-05T1530Z-wheel-backward-film.md; git show f5e5f84f34:research/self-check/verifier-runs.json | Re-read the July 5 film log, which records a 38/38 rerun after June 22. The shared generated placard remains at its old date in this worktree. The triage assigns its refresh to landing from this new record, with no separate Updated line. That refresh is not claimed as performed here.
- WRONG | X21: Two ways a sampling process invents a frequency that was never sent. | https://api.crossref.org/works/10.1063/1.1617771; git show f5e5f84f34:public/strata/the-pitch-that-isnt-there/index.html:138; https://www.dsprelated.com/freebooks/mDFT/Sampling_Theory.html | Re-read the sibling page on waveform periodicity and its distinction between computation and perception, plus Chialvo (2003), abstract at https://pubmed.ncbi.nlm.nih.gov/14604413/. The proposed neural explanation is not a claim that this is wheel-style temporal aliasing. Corrected this layer's frontmatter and nearby note to describe the perceptual likeness without a shared established sampling mechanism.
- WRONG | X22: Both correct a received 'fact' with the arithmetic of how often you look. | git show f5e5f84f34:src/content/strata/the-tide-textbook-got-wrong.md | Re-read the sibling markdown: its correction concerns differential gravity, inverse-cube tidal scaling and the limits of the equilibrium two-bulge picture. Sampling frequency does not describe that argument. Corrected this layer's two relationship copies.
- WRONG | X23: (added) The spoke frequency is reflected until it lands inside | https://www.dsprelated.com/freebooks/mDFT/Sampling_Theory.html; git show f5e5f84f34:research/aliasing-wagon-wheel/film/film.html:373 | Re-read the unquoted TL.e1 sentence and drawFold(): landing=fold(12*1.9,24)=-1.2, not the +1.2 produced by reflection. Corrected only the unquoted film-source explanation; all film quotations remain byte-identical. The delivered MP4 still contains the old caption because rendering is prohibited, explicitly disclosed on the page and below.
- CONFIRMED | In old films a stagecoach races forward and its wheels turn slowly backward. | https://authors.library.caltech.edu/records/g3zjd-4mh20; https://ocw.mit.edu/courses/mas-632-conversational-computer-systems-fall-2008/2f14b7dfe31a3ef6fcb8d686065e134a_schmandt_ch3.pdf | N2 checker reread at f5e5f84f34: 001 dek-old-films: Caltech abstract: "due to the temporal subsampling inherent in the recording process". MIT pp. 38-41 supplies the wagon-wheel geometry; this supports recording aliasing without editing. The claim concerns the sampled-motion model, not a claim that finite exposures are instantaneous.
- CONFIRMED | No trick, no editing. | https://authors.library.caltech.edu/records/g3zjd-4mh20; https://ocw.mit.edu/courses/mas-632-conversational-computer-systems-fall-2008/2f14b7dfe31a3ef6fcb8d686065e134a_schmandt_ch3.pdf | N2 checker reread at f5e5f84f34: 002 dek-no-trick: Caltech abstract: "due to the temporal subsampling inherent in the recording process". MIT pp. 38-41 supplies the wagon-wheel geometry; this supports recording aliasing without editing. The claim concerns the sampled-motion model, not a claim that finite exposures are instantaneous.
- CONFIRMED | The camera reports the literal truth about each frame it caught, and that truth is a lie about the motion. | https://authors.library.caltech.edu/records/g3zjd-4mh20; https://ocw.mit.edu/courses/mas-632-conversational-computer-systems-fall-2008/2f14b7dfe31a3ef6fcb8d686065e134a_schmandt_ch3.pdf | N2 checker reread at f5e5f84f34: 003 dek-frame-truth: Caltech abstract: "due to the temporal subsampling inherent in the recording process". MIT pp. 38-41 supplies the wagon-wheel geometry; this supports recording aliasing without editing. The claim concerns the sampled-motion model, not a claim that finite exposures are instantaneous.
- CONFIRMED | Set a wheel's real spin, its spokes, and a frame rate, and watch the reversal happen; then watch why, as the spoke frequency folds into the band a frame rate can hold. | git show f5e5f84f34:public/strata/the-wheel-that-spins-backward/index.html | N2 checker reread at f5e5f84f34: 004 dek-instrument: The actual controls feed "var state = { frot:1.9, S:12, fs:24 };" and "fold(spokeFreq(), state.fs) / state.S". Recreated the initial readouts, freeze, and altered-spin cases with node probe-page.mjs.
- CONFIRMED | the same fold made audible by genuinely under-sampling a 1000 Hz tone down to the 500 Hz you hear. | git show f5e5f84f34:public/strata/the-wheel-that-spins-backward/index.html:610 | N2 checker reread at f5e5f84f34: 007 dek-audio: Read the actual audio loop: "ch[i]=Math.sin(2*Math.PI*f*ts);" with "var k=Math.floor(tt*fsr);" and "var ts=k/fsr;". It genuinely holds low-rate samples. At the initial settings the output contains the 500 Hz alias; degeneracies are separately recorded in entries 49 and 60.
- CONFIRMED | the contested continuous-light version. | https://authors.library.caltech.edu/records/g3zjd-4mh20 | N2 checker reread at f5e5f84f34: 008 dek-contested: Caltech explicitly reports the continuous-light effect and says "these results and their interpretation have been challenged". This supports a contested explanation, not the separate assertion that the effect itself is unestablished.
- CONFIRMED | Every freeze, reversal and the faithful-capture threshold proven live, with the same fold you can hear in undersampled sound. | git show f5e5f84f34:public/strata/the-wheel-that-spins-backward/index.html; git show f5e5f84f34:research/aliasing-wagon-wheel/verify.mjs | N2 checker reread at f5e5f84f34: 009 metadata-live-proof: The page computes "fold(spokeFreq(), state.fs) / state.S" and actually sample-and-holds the audio. The sampling-model freeze, reversal, threshold, and initial 500 Hz example are demonstrated and independently recomputed; see runs.json and page-probes.json.
- CONFIRMED | It is pure temporal aliasing: the spoke frequency folded into the Nyquist band. | https://authors.library.caltech.edu/records/g3zjd-4mh20; https://ocw.mit.edu/courses/mas-632-conversational-computer-systems-fall-2008/2f14b7dfe31a3ef6fcb8d686065e134a_schmandt_ch3.pdf | N2 checker reread at f5e5f84f34: 010 metadata-temporal-aliasing: Caltech abstract: "due to the temporal subsampling inherent in the recording process". MIT pp. 38-41 supplies the wagon-wheel geometry; this supports recording aliasing without editing. The claim concerns the sampled-motion model, not a claim that finite exposures are instantaneous.
- CONFIRMED | aliasing, proven live and hearable. | git show f5e5f84f34:public/strata/the-wheel-that-spins-backward/index.html; git show f5e5f84f34:research/aliasing-wagon-wheel/verify.mjs | N2 checker reread at f5e5f84f34: 011 metadata-aliasing-proven: The page computes "fold(spokeFreq(), state.fs) / state.S" and actually sample-and-holds the audio. The sampling-model freeze, reversal, threshold, and initial 500 Hz example are demonstrated and independently recomputed; see runs.json and page-probes.json.
- CONFIRMED | In old films the stagecoach races forward and its wheels turn slowly backward. | https://authors.library.caltech.edu/records/g3zjd-4mh20; https://ocw.mit.edu/courses/mas-632-conversational-computer-systems-fall-2008/2f14b7dfe31a3ef6fcb8d686065e134a_schmandt_ch3.pdf | N2 checker reread at f5e5f84f34: 016 stagecoach: Caltech abstract: "due to the temporal subsampling inherent in the recording process". MIT pp. 38-41 supplies the wagon-wheel geometry; this supports recording aliasing without editing. The claim concerns the sampled-motion model, not a claim that finite exposures are instantaneous.
- CONFIRMED | No trick of the eye, no editing | https://ocw.mit.edu/courses/mas-632-conversational-computer-systems-fall-2008/2f14b7dfe31a3ef6fcb8d686065e134a_schmandt_ch3.pdf; git show f5e5f84f34:research/aliasing-wagon-wheel/verify.mjs | N2 checker reread at f5e5f84f34: 017 no-eye-trick: MIT p. 39: "it will appear that the wheel is slowly moving counterclockwise." The page is distinguishing the exact equivalence of sampled patterns from the disputed continuous-light mechanism; that model requires no discrete-perception hypothesis.
- CONFIRMED | the camera is telling the literal truth about every frame it caught, and the truth is a lie about the motion. | https://authors.library.caltech.edu/records/g3zjd-4mh20; https://ocw.mit.edu/courses/mas-632-conversational-computer-systems-fall-2008/2f14b7dfe31a3ef6fcb8d686065e134a_schmandt_ch3.pdf | N2 checker reread at f5e5f84f34: 018 camera-truth: Caltech abstract: "due to the temporal subsampling inherent in the recording process". MIT pp. 38-41 supplies the wagon-wheel geometry; this supports recording aliasing without editing. The claim concerns the sampled-motion model, not a claim that finite exposures are instantaneous.
- CONFIRMED | Companion film · 2:32 | git show f5e5f84f34:research/aliasing-wagon-wheel/film/render.mjs; https://artwaste.land/strata/the-wheel-that-spins-backward/film.mp4 | N2 checker reread at f5e5f84f34: 019 film-duration: The renderer declares "const FPS = 24, DUR = 152". Downloaded the actual 20,394,446-byte MP4 with curl; ffprobe reports "r_frame_rate": "24/1", "nb_frames": "3648", "duration": "152.000000". Metadata retained in film-metadata.json; bulk MP4 removed after inspection.
- CONFIRMED | it renders at exactly 24 fps | git show f5e5f84f34:research/aliasing-wagon-wheel/film/render.mjs; https://artwaste.land/strata/the-wheel-that-spins-backward/film.mp4 | N2 checker reread at f5e5f84f34: 020 film-frame-rate: The renderer declares "const FPS = 24, DUR = 152". Downloaded the actual 20,394,446-byte MP4 with curl; ffprobe reports "r_frame_rate": "24/1", "nb_frames": "3648", "duration": "152.000000". Metadata retained in film-metadata.json; bulk MP4 removed after inspection.
- CONFIRMED | the backward crawl you watch is the MP4’s own genuine temporal aliasing, not an animation of it. | git show f5e5f84f34:research/aliasing-wagon-wheel/film/render.mjs; git show f5e5f84f34:research/aliasing-wagon-wheel/film/film.html:549 | N2 checker reread at f5e5f84f34: 022 film-genuine-alias: Renderer: "const tSec = f / FPS;". Film: "drawWheel(wx, wy, wR, thetaAt(t), wheelA, goldK);". The angle comes from the integral of true spin, not the apparent fold. The 24 fps output therefore performs the temporal sampling it describes.
- CONFIRMED | A gold spoke (S = 1) and a tachometer arrow tell the truth in the same frames | git show f5e5f84f34:research/aliasing-wagon-wheel/film/film.html:248; git show f5e5f84f34:research/aliasing-wagon-wheel/film/film.html:572; git show f5e5f84f34:research/aliasing-wagon-wheel/film/film-facts.mjs | N2 checker reread at f5e5f84f34: 023 film-gold-tach: The marked spoke and the separate arrow each use the true angular position in their respective phases. Their one-copy frequencies stay below 12 Hz. Inspected downloaded frames at 50 s and 78 s; they show the gold marker and tachometer alongside the aliased pattern. They need not appear simultaneously with one another.
- CONFIRMED | the wheel accelerates through the 2 rev/s freeze | git show f5e5f84f34:research/aliasing-wagon-wheel/film/film.html:143 | N2 checker reread at f5e5f84f34: 024 film-acceleration: The actual SEG table changes 1.9 to 2.0 over 66-74 s, holds 2.0 over 74-82 s, then reaches 2.1 by 86 s. The apparent speed approaches zero from below, freezes, then becomes positive. A frame at 78 s shows "+2.00 rev/s" and "+0.00 rev/s".
- CONFIRMED | the soundtrack genuinely sample-and-holds a 1000 Hz tone at 1500 Hz so you hear the 500 Hz alias. | git show f5e5f84f34:research/aliasing-wagon-wheel/film/make-audio.mjs:196; https://artwaste.land/strata/the-wheel-that-spins-backward/film.mp4 | N2 checker reread at f5e5f84f34: 025 film-soundtrack: Read the operative loop, not only the excerpted comment: "const k = Math.floor(t * 1500), ts = k / 1500;" and "Math.sin(TPI * 1000 * ts)". The downloaded MP4 has 500 Hz amplitude 0.093304 and 1000 Hz image 0.046609 in the 132-133 s window. Positive control: the 127-128 s true-tone window has 1000 Hz amplitude 0.125501 and 500 Hz 0.000048. See film-audio-check.json.
- CONFIRMED | the percussion follows the wheel’s own 24 fps-sampled pose | git show f5e5f84f34:research/aliasing-wagon-wheel/film/make-audio.mjs:155 | N2 checker reread at f5e5f84f34: 027 film-percussion: The actual percussion computes "const ts = Math.floor(t0 * FPS) / FPS;" then "const pose = ((thetaAt(ts) * S) % 1 + 1) % 1;". During 74-82 s the pattern returns to the same pose each frame, so the accent selector stays fixed.
- CONFIRMED | it locks while the wheel is frozen. | git show f5e5f84f34:research/aliasing-wagon-wheel/film/make-audio.mjs:155 | N2 checker reread at f5e5f84f34: 028 film-percussion-lock: The actual percussion computes "const ts = Math.floor(t0 * FPS) / FPS;" then "const pose = ((thetaAt(ts) * S) % 1 + 1) % 1;". During 74-82 s the pattern returns to the same pose each frame, so the accent selector stays fixed.
- CONFIRMED | Build: research/aliasing-wagon-wheel/film/. | git show f5e5f84f34:research/aliasing-wagon-wheel/film/build.sh | N2 checker reread at f5e5f84f34: 029 film-build: The pinned build.sh exists and documents "bash research/aliasing-wagon-wheel/film/build.sh" and the film output path. Read the build pipeline without rebuilding 3,648 frames. The page presents this as a source location, not a reader download recipe for all build dependencies.
- CONFIRMED | Real spin 1.90 rev/s | git show f5e5f84f34:public/strata/the-wheel-that-spins-backward/index.html:376 | N2 checker reread at f5e5f84f34: 030 wheel-default-settings: The page state really starts with "var state = { frot:1.9, S:12, fs:24 };". node probe-page.mjs recreates the initial state and readouts.
- CONFIRMED | Spokes (identical) 12 | git show f5e5f84f34:public/strata/the-wheel-that-spins-backward/index.html:376 | N2 checker reread at f5e5f84f34: 031 wheel-default-spokes: The page state really starts with "var state = { frot:1.9, S:12, fs:24 };". node probe-page.mjs recreates the initial state and readouts.
- CONFIRMED | Camera frame rate 24 fps | git show f5e5f84f34:public/strata/the-wheel-that-spins-backward/index.html:376 | N2 checker reread at f5e5f84f34: 032 wheel-default-frame-rate: The page state really starts with "var state = { frot:1.9, S:12, fs:24 };". node probe-page.mjs recreates the initial state and readouts.
- CONFIRMED | Spoke frequency S·f 22.8 Hz | git show f5e5f84f34:research/aliasing-wagon-wheel/film/film-facts.mjs | N2 checker reread at f5e5f84f34: 033 wheel-default-spoke-frequency: Independent arithmetic: 12 * 1.9 = 22.8. Film facts tests "spoke frequency S·f = 22.8 Hz" and the page probe reproduces it.
- CONFIRMED | Nyquist limit fs/2 12 Hz | git show f5e5f84f34:research/aliasing-wagon-wheel/film/film-facts.mjs | N2 checker reread at f5e5f84f34: 034 wheel-default-nyquist: Independent arithmetic: 24 / 2 = 12. Film facts tests "the film’s band is ±12 Hz".
- CONFIRMED | Apparent spin (on film) −0.10 rev/s | git show f5e5f84f34:research/aliasing-wagon-wheel/film/film-facts.mjs | N2 checker reread at f5e5f84f34: 035 wheel-default-apparent: Independent arithmetic: (22.8 - 24) / 12 = -0.1. The actual page probe prints "−0.10 rev/s".
- CONFIRMED | Faithful capture? no \u2014 aliased | git show f5e5f84f34:public/strata/the-wheel-that-spins-backward/index.html | N2 checker reread at f5e5f84f34: 036 wheel-default-faithful: The faithful() predicate is false at 24 fps, 12 spokes, 1.9 rev/s because 24 < 45.6. The actual initial readout agrees.
- CONFIRMED | Reduced-motion is on, so the wheel starts paused | git show f5e5f84f34:public/strata/the-wheel-that-spins-backward/index.html | N2 checker reread at f5e5f84f34: 037 wheel-reduced-motion: Code sets "var playing = !REDUCE;" and, when reduced motion is active, invokes "setPlaying(false)" and displays the note.
- CONFIRMED | advance the strobe one snapshot at a time | git show f5e5f84f34:public/strata/the-wheel-that-spins-backward/index.html | N2 checker reread at f5e5f84f34: 038 wheel-step-frame: The click handler stops playback, executes "simT += 1/state.fs;", then calls render(). It advances one nominal camera interval.
- CONFIRMED | The reversal Helicopter freeze Crawl forward Faithful slow-mo Eight spokes | git show f5e5f84f34:public/strata/the-wheel-that-spins-backward/index.html | N2 checker reread at f5e5f84f34: 039 wheel-presets: Read all five actual button datasets. Their apparent spins are -0.1, 0, +0.1, +1.0 and 0 rev/s respectively. The fifth preset is present and works; the separate claim that the verifier covers every preset is entry 75.
- CONFIRMED | Captured faithfully | git show f5e5f84f34:public/strata/the-wheel-that-spins-backward/index.html | N2 checker reread at f5e5f84f34: 040 wheel-script-faithful: In the modeled strict interior of the Nyquist band, fold is the identity and the faithful() branch prints these labels. The predicate correctly uses "Math.abs(state.frot)".
- CONFIRMED | film agrees with truth | git show f5e5f84f34:public/strata/the-wheel-that-spins-backward/index.html | N2 checker reread at f5e5f84f34: 041 wheel-script-agrees: In the modeled strict interior of the Nyquist band, fold is the identity and the faithful() branch prints these labels. The predicate correctly uses "Math.abs(state.frot)".
- CONFIRMED | FROZEN on film | git show f5e5f84f34:public/strata/the-wheel-that-spins-backward/index.html | N2 checker reread at f5e5f84f34: 042 wheel-script-frozen: After the faithful branch, "Math.abs(a)<1e-6" prints "FROZEN on film". Integer multiples of fs/S give a=0. A truly stationary wheel is handled by the faithful branch first.
- CONFIRMED | The camera can only hold frequencies inside the band (−fs/2, fs/2]. | https://www.dsprelated.com/freebooks/mDFT/Sampling_Theory.html | N2 checker reread at f5e5f84f34: 045 band-held: DSP: "Frequencies outside this range yield sampled sinusoids indistinguishable from frequencies inside the range." The cyan point is computed by the signed alias fold. This confirms the representable principal band, not the incorrect reflection recipe in entry 46.
- CONFIRMED | that landing spot is what the film records. | https://www.dsprelated.com/freebooks/mDFT/Sampling_Theory.html | N2 checker reread at f5e5f84f34: 047 band-landing: DSP: "Frequencies outside this range yield sampled sinusoids indistinguishable from frequencies inside the range." The cyan point is computed by the signed alias fold. This confirms the representable principal band, not the incorrect reflection recipe in entry 46.
- CONFIRMED | Sampling does not care whether the signal is a turning wheel or a vibrating string. | https://ocw.mit.edu/courses/mas-632-conversational-computer-systems-fall-2008/2f14b7dfe31a3ef6fcb8d686065e134a_schmandt_ch3.pdf | N2 checker reread at f5e5f84f34: 048 same-theorem: MIT pp. 38-41 treats the wheel example in the same sampling discussion as audio and immediately says "Another example provides a better understanding of sampling applied to an audio signal." The inference concerns mathematical sampling, not identical biological perception.
- CONFIRMED | Here a 1000 Hz tone is genuinely re-sampled at a rate you choose (sample-and-hold, then played back), so you hear the alias, not a fake of it. | git show f5e5f84f34:public/strata/the-wheel-that-spins-backward/index.html:610 | N2 checker reread at f5e5f84f34: 051 interactive-resample: Read the actual audio loop: "ch[i]=Math.sin(2*Math.PI*f*ts);" with "var k=Math.floor(tt*fsr);" and "var ts=k/fsr;". It genuinely holds low-rate samples. At the initial settings the output contains the 500 Hz alias; degeneracies are separately recorded in entries 49 and 60.
- CONFIRMED | Tone 1000 Hz | git show f5e5f84f34:public/strata/the-wheel-that-spins-backward/index.html | N2 checker reread at f5e5f84f34: 052 audio-default-tone: The corresponding input values are actually "1000" and "1500", and audSync reads those same inputs. Confirmed by the page probe.
- CONFIRMED | Sample rate 1500 Hz | git show f5e5f84f34:public/strata/the-wheel-that-spins-backward/index.html | N2 checker reread at f5e5f84f34: 053 audio-default-rate: The corresponding input values are actually "1000" and "1500", and audSync reads those same inputs. Confirmed by the page probe.
- CONFIRMED | You will hear 500 Hz | git show f5e5f84f34:public/strata/the-wheel-that-spins-backward/index.html | N2 checker reread at f5e5f84f34: 054 audio-default-heard: At the initial values, abs(1000 - 1500) = 500. The generated sample-and-hold signal supports this default readout.
- CONFIRMED | Below Nyquist? no \u2014 aliased down | git show f5e5f84f34:public/strata/the-wheel-that-spins-backward/index.html | N2 checker reread at f5e5f84f34: 055 audio-default-nyquist: At the initial values, 1000 is above 1500/2 = 750. The predicate correctly marks the initial example as aliased.
- CONFIRMED | your speakers run at the audio context's own high rate | git show f5e5f84f34:public/strata/the-wheel-that-spins-backward/index.html | N2 checker reread at f5e5f84f34: 057 audio-context-rate: playBuffer uses "var sr=c.sampleRate" and "c.createBuffer(1,n,sr)" before connecting the source to the context destination. The described output clock is correct at the Web Audio buffer level.
- CONFIRMED | what you hear is the reconstructed sample-and-hold signal | git show f5e5f84f34:public/strata/the-wheel-that-spins-backward/index.html:610 | N2 checker reread at f5e5f84f34: 058 audio-staircase: Read the actual audio loop: "ch[i]=Math.sin(2*Math.PI*f*ts);" with "var k=Math.floor(tt*fsr);" and "var ts=k/fsr;". It genuinely holds low-rate samples. At the initial settings the output contains the 500 Hz alias; degeneracies are separately recorded in entries 49 and 60.
- CONFIRMED | which contains the alias (the fold) plus faint higher images of the staircase. | git show f5e5f84f34:research/aliasing-wagon-wheel/film/make-audio.mjs:196; git show f5e5f84f34:research/aliasing-wagon-wheel/film/film-facts.mjs; https://artwaste.land/strata/the-wheel-that-spins-backward/film.mp4 | N2 checker reread at f5e5f84f34: 059 audio-images: The held waveform has a dominant 500 Hz component and higher images. Independent numerical Fourier checks pass, and the actual MP4 has a smaller 1000 Hz image in the sampled-tone window. The statement does not claim an ideal low-pass reconstruction.
- CONFIRMED | yes \u2014 heard true | git show f5e5f84f34:public/strata/the-wheel-that-spins-backward/index.html | N2 checker reread at f5e5f84f34: 061 audio-script-true: For tone below fs/2 the fold is the identity. The actual audSync predicate uses "Number(toneEl.value) < Number(srateEl.value)/2"; it excludes the problematic exact boundary.
- CONFIRMED | The wheel's apparent spin is fold(S·f, fs) / S. | https://ocw.mit.edu/courses/mas-632-conversational-computer-systems-fall-2008/2f14b7dfe31a3ef6fcb8d686065e134a_schmandt_ch3.pdf | N2 checker reread at f5e5f84f34: 064 formula-apparent: From the S-fold symmetry, one visible cycle is 1/S revolution. Sampling identifies spoke frequencies differing by k*fs, so dividing the chosen signed alias by S gives apparent rev/s. MIT p. 41 explicitly says these shifted spoke displacements are "all identical". The exact boundary remains directionally ambiguous.
- CONFIRMED | four facts are proven | git show f5e5f84f34:research/aliasing-wagon-wheel/verify.mjs | N2 checker reread at f5e5f84f34: 065 four-facts-proven: The four numerical model facts are independently recomputed in the verifier, which passes 38/38 in the pinned layout. The specific prose/edge defects are separately recorded; a passing run is not being used as evidence that every sentence is true.
- CONFIRMED | the wheel freezes exactly when its real spin is a whole multiple of fs/S | https://ocw.mit.edu/courses/mas-632-conversational-computer-systems-fall-2008/2f14b7dfe31a3ef6fcb8d686065e134a_schmandt_ch3.pdf | N2 checker reread at f5e5f84f34: 066 freeze-rule: MIT p. 41 says appearances after extra whole spoke intervals are "all identical". Geometry gives S*f/fs integer for freezing; substituting S=1 for a uniquely marked pattern gives f=k*fs. This is a derivation from the source, not an explicit painted-spoke quotation.
- CONFIRMED | 12 spokes at 24 fps → first freeze at 2 rev/s | git show f5e5f84f34:research/aliasing-wagon-wheel/verify.mjs | N2 checker reread at f5e5f84f34: 067 freeze-number: 24 fps divided by 12 identical spokes equals 2 rev/s. The supplied verifier and film-facts both check the first positive nonzero freeze at 2.
- CONFIRMED | just below a freeze it runs backward | https://ocw.mit.edu/courses/mas-632-conversational-computer-systems-fall-2008/2f14b7dfe31a3ef6fcb8d686065e134a_schmandt_ch3.pdf | N2 checker reread at f5e5f84f34: 068 reverse-rule: MIT p. 39: "it will appear that the wheel is slowly moving counterclockwise." Subtracting a small positive delta from a freeze makes the signed principal alias negative.
- CONFIRMED | 1.9 rev/s on film → −0.1 rev/s | git show f5e5f84f34:research/aliasing-wagon-wheel/verify.mjs | N2 checker reread at f5e5f84f34: 069 reverse-number: 12*1.9=22.8; subtract 24 to obtain -1.2 spoke cycles/s; divide by 12 to obtain -0.1 rev/s. Recreated in the page and verifier.
- CONFIRMED | just above it crawls forward | https://ocw.mit.edu/courses/mas-632-conversational-computer-systems-fall-2008/2f14b7dfe31a3ef6fcb8d686065e134a_schmandt_ch3.pdf | N2 checker reread at f5e5f84f34: 070 forward-rule: MIT p. 39 says the wheel moving just beyond a spoke position shows "a much slower motion identical to that depicted by Figure 3.2." Adding a small delta to a freeze gives a positive principal alias.
- CONFIRMED | 1000 Hz sampled at 1500 Hz is heard as 500 Hz. | https://www.dsprelated.com/freebooks/mDFT/Sampling_Theory.html | N2 checker reread at f5e5f84f34: 072 audio-number: For the stated numbers the unsigned alias is abs(1000-1500)=500. This is also present in the actual generated soundtrack and in the independently checked sample-and-hold waveform. The particular example is correct.
- CONFIRMED | The verifier research/aliasing-wagon-wheel/verify.mjs recomputes all four from scratch | git show f5e5f84f34:research/aliasing-wagon-wheel/verify.mjs | N2 checker reread at f5e5f84f34: 073 verifier-recomputes: Read all five mathematical claim blocks, including the band block and the four page bullets. They compute freezes, reversal, the strict threshold, and the 1000/1500 audio example; the run succeeds.
- CONFIRMED | checks the fold stays inside the band across a dense sweep | git show f5e5f84f34:research/aliasing-wagon-wheel/verify.mjs | N2 checker reread at f5e5f84f34: 074 verifier-dense-sweep: The actual loop is "for (let f = -500; f <= 500; f += 0.013)" and tests the folded range. Recreated with exit 0 in the pinned verifier.
- CONFIRMED | The camera / strobe case shown here is exact temporal sampling | https://authors.library.caltech.edu/records/g3zjd-4mh20; https://ocw.mit.edu/courses/mas-632-conversational-computer-systems-fall-2008/2f14b7dfe31a3ef6fcb8d686065e134a_schmandt_ch3.pdf | N2 checker reread at f5e5f84f34: 079 exact-temporal: Caltech abstract: "due to the temporal subsampling inherent in the recording process". MIT pp. 38-41 supplies the wagon-wheel geometry; this supports recording aliasing without editing. The claim concerns the sampled-motion model, not a claim that finite exposures are instantaneous.
- CONFIRMED | no perception enters it. | https://ocw.mit.edu/courses/mas-632-conversational-computer-systems-fall-2008/2f14b7dfe31a3ef6fcb8d686065e134a_schmandt_ch3.pdf; git show f5e5f84f34:research/aliasing-wagon-wheel/verify.mjs | N2 checker reread at f5e5f84f34: 080 no-perception: MIT p. 39: "it will appear that the wheel is slowly moving counterclockwise." The page is distinguishing the exact equivalence of sampled patterns from the disputed continuous-light mechanism; that model requires no discrete-perception hypothesis.
- CONFIRMED | S is the rotational symmetry order of an indistinguishable spoke pattern. | git show f5e5f84f34:research/aliasing-wagon-wheel/verify.mjs | N2 checker reread at f5e5f84f34: 081 symmetry-model: The source explicitly defines "S-fold rotational symmetry (S identical" spokes) and invariance after "1/S of a revolution". The drawing creates equally spaced identical spokes. This is the declared model.
- CONFIRMED | paint one spoke a different colour and you can track it, the symmetry drops to S = 1 | git show f5e5f84f34:research/aliasing-wagon-wheel/verify.mjs:23; git show f5e5f84f34:research/aliasing-wagon-wheel/film/film.html:250 | N2 checker reread at f5e5f84f34: 082 painted-spoke: The record’s source is "none", but the claim follows directly from symmetry: an otherwise unique colored spoke must return to its own position for the full colored pattern to repeat, so the smallest full-pattern period becomes one revolution. The pinned verifier explicitly states "a single painted spoke makes S=1"; film geometry actually marks only i=0. No unsupported claim about a biological mechanism is required.
- CONFIRMED | the freeze speeds jump from k·fs/S up to k·fs. | https://ocw.mit.edu/courses/mas-632-conversational-computer-systems-fall-2008/2f14b7dfe31a3ef6fcb8d686065e134a_schmandt_ch3.pdf | N2 checker reread at f5e5f84f34: 083 marked-freeze-speeds: MIT p. 41 says appearances after extra whole spoke intervals are "all identical". Geometry gives S*f/fs integer for freezing; substituting S=1 for a uniquely marked pattern gives f=k*fs. This is a derivation from the source, not an explicit painted-spoke quotation.
- CONFIRMED | the tachometer here is a separate dial, not a marked copy of the wheel | git show f5e5f84f34:public/strata/the-wheel-that-spins-backward/index.html | N2 checker reread at f5e5f84f34: 084 separate-tachometer: render() calls "drawWheel(wctx, wheel, filmAngle, {});" and separately "drawTach(trueAngle);" on different canvases. Confirmed in the actual page source.
- CONFIRMED | marking the wheel would change the physics it is meant to reveal. | git show f5e5f84f34:research/aliasing-wagon-wheel/verify.mjs:23; git show f5e5f84f34:research/aliasing-wagon-wheel/film/film.html:250 | N2 checker reread at f5e5f84f34: 085 mark-changes-physics: The record’s source is "none", but the claim follows directly from symmetry: an otherwise unique colored spoke must return to its own position for the full colored pattern to repeat, so the smallest full-pattern period becomes one revolution. The pinned verifier explicitly states "a single painted spoke makes S=1"; film geometry actually marks only i=0. No unsupported claim about a biological mechanism is required.
- CONFIRMED | We also sample instantaneously (zero shutter width) | git show f5e5f84f34:public/strata/the-wheel-that-spins-backward/index.html | N2 checker reread at f5e5f84f34: 086 zero-shutter: The sampled time is "Math.floor(simT * state.fs) / state.fs" and the wheel is drawn at one angle without an exposure integral. This is instantaneous sampling as claimed.
- CONFIRMED | a real finite exposure blurs the spokes but does not move the freeze or reversal speeds. | https://people.csail.mit.edu/fredo/comp-photo-book/12-video-01-motion-blur-and-temporal-sampling.html | N2 checker reread at f5e5f84f34: 087 finite-exposure: The cited MIT computational-photography chapter says exposure is a "low-pass that attenuates" temporal frequencies. At constant spin, temporal convolution changes amplitudes/phases, not the alias-frequency lattice, so the model’s surviving freeze/reversal frequencies do not shift. Sufficient blur can erase visible spokes; this is not a guarantee that every exposure preserves a visible illusion.
- CONFIRMED | There is a different wagon-wheel effect reported under continuous light | https://authors.library.caltech.edu/records/g3zjd-4mh20 | N2 checker reread at f5e5f84f34: 088 continuous-effect: Caltech explicitly reports the continuous-light effect and says "these results and their interpretation have been challenged". This supports a contested explanation, not the separate assertion that the effect itself is unestablished.
- CONFIRMED | no camera, no strobe, steady daylight | https://authors.library.caltech.edu/records/g3zjd-4mh20/files/VANpnas05.pdf?download=1 | N2 checker reread at f5e5f84f34: 089 continuous-daylight: Opened the deposited VanRullen PDF as well as the abstract. Methods states "in daylight, without any artificial illumination". This directly supports continuous daylight without a camera or strobe.
- CONFIRMED | whether it means the visual system samples time in discrete frames, is genuinely unsettled | https://eagleman.com/papers/kline_2008.pdf | N2 checker reread at f5e5f84f34: 091 continuous-sampling-unsettled: Kline 2008 contrasts "discrete temporal sampling" with "perceptual rivalry" and explicitly leaves some object-based accounts open. This supports the cited mechanistic dispute and later criticism, while acknowledging the observed reversals.
- CONFIRMED | Schouten 1967 | https://research.tue.nl/en/publications/subjective-stroboscopy-and-a-model-of-visual-movement-detectors-2 | N2 checker reread at f5e5f84f34: 092 citation-schouten: The Eindhoven institutional bibliographic record names "Schouten, J. F. (1967)" and "Subjective stroboscopy and a model of visual movement detectors", pages 44-55. The 1964 conference date is not the 1967 publication date.
- CONFIRMED | Purves, Paydarfar & Andrews 1996 | https://api.crossref.org/works/10.1073/pnas.93.8.3693 | N2 checker reread at f5e5f84f34: 093 citation-purves: Parsed Crossref, not just the title excerpt: authors are D Purves, J A Paydarfar, T J Andrews; published-print is [1996,4,16]; title is "The wagon wheel illusion in movies and reality." DOI matches.
- CONFIRMED | VanRullen, Reddy & Koch 2005 | https://authors.library.caltech.edu/records/g3zjd-4mh20 | N2 checker reread at f5e5f84f34: 094 citation-vanrullen: Caltech lists VanRullen, Reddy and Koch and "Published April 5, 2005" for "Attention-driven discrete sampling of motion perception". DOI 10.1073/pnas.0409172102 matches the online checker.
- CONFIRMED | and critics since | https://eagleman.com/papers/kline_2008.pdf | N2 checker reread at f5e5f84f34: 095 critics-since: Kline 2008 contrasts "discrete temporal sampling" with "perceptual rivalry" and explicitly leaves some object-based accounts open. This supports the cited mechanistic dispute and later criticism, while acknowledging the observed reversals.
- CONFIRMED | This page makes no claim about it. | git show f5e5f84f34:public/strata/the-wheel-that-spins-backward/index.html | N2 checker reread at f5e5f84f34: 096 no-continuous-claim: Read in context, this says the instrument does not adjudicate the continuous-light mechanism. It does not perform a biological-vision experiment. The separate existence overstatement remains entry 90.
- CONFIRMED | What you operated above is only the part that is certain. | git show f5e5f84f34:public/strata/the-wheel-that-spins-backward/index.html; https://ocw.mit.edu/courses/mas-632-conversational-computer-systems-fall-2008/2f14b7dfe31a3ef6fcb8d686065e134a_schmandt_ch3.pdf; https://authors.library.caltech.edu/records/g3zjd-4mh20 | N2 checker reread at f5e5f84f34: 097 only-certain: The operated instrument implements temporal sampling and the declared rotational-symmetry model. The mechanistic certainty of camera aliasing is supported by MIT and Caltech; it is not treated here as a warranty that every UI label is correct.
- CONFIRMED | This layer's check reads the bytes this page serves and asserts against them. | git show f5e5f84f34:research/aliasing-wagon-wheel/verify.mjs | N2 checker reread at f5e5f84f34: 098 placard-reads: The verifier opens the local served-page source with "fs2.readFileSync(pagePath, 'utf8')" and tests it. That is a real dependency, although much weaker than the guarantees in entries 77 and 78.
- CONFIRMED | There the ear builds a missing fundamental the loudspeaker never played | https://api.crossref.org/works/10.1063/1.1617771 | N2 checker reread at f5e5f84f34: 103 related-missing-fundamental: Decoded the Crossref abstract and confirmed the excerpt exactly: the perceived pitch has "no actual source vibration". The record identifies the missing-fundamental percept correctly.
- CONFIRMED | here the camera builds an apparent spin the wheel never turned | https://authors.library.caltech.edu/records/g3zjd-4mh20; https://ocw.mit.edu/courses/mas-632-conversational-computer-systems-fall-2008/2f14b7dfe31a3ef6fcb8d686065e134a_schmandt_ch3.pdf | N2 checker reread at f5e5f84f34: 105 related-camera-invents: Caltech abstract: "due to the temporal subsampling inherent in the recording process". MIT pp. 38-41 supplies the wagon-wheel geometry; this supports recording aliasing without editing. The claim concerns the sampled-motion model, not a claim that finite exposures are instantaneous.
- CONFIRMED | both are real percepts of a frequency that isn't physically there, one in sound, one in motion. | https://authors.library.caltech.edu/records/g3zjd-4mh20; https://api.crossref.org/works/10.1063/1.1617771 | N2 checker reread at f5e5f84f34: 106 related-real-percepts: Caltech supports apparent backward wheel motion, and the Chialvo abstract supports the perceived missing fundamental without a source vibration at that frequency. The record correctly points to the companion sound claim for the second half.
- CONFIRMED | A tide gauge that samples too slowly aliases the real tide into a wrong one | https://www.dsprelated.com/freebooks/mDFT/Sampling_Theory.html | N2 checker reread at f5e5f84f34: 108 related-tide-alias: The general sampling ambiguity applies to a regularly sampled tide signal as to any other time series. This is a mathematical inference from DSP, not a claim that the linked tide page actually makes this argument.
- CONFIRMED | a camera that samples too slowly aliases a forward wheel into a backward one. | https://authors.library.caltech.edu/records/g3zjd-4mh20; https://ocw.mit.edu/courses/mas-632-conversational-computer-systems-fall-2008/2f14b7dfe31a3ef6fcb8d686065e134a_schmandt_ch3.pdf | N2 checker reread at f5e5f84f34: 109 related-camera-alias: Caltech abstract: "due to the temporal subsampling inherent in the recording process". MIT pp. 38-41 supplies the wagon-wheel geometry; this supports recording aliasing without editing. The claim concerns the sampled-motion model, not a claim that finite exposures are instantaneous.
- CONFIRMED | what you sample below the Nyquist rate, you cannot honestly recover. | https://www.dsprelated.com/freebooks/mDFT/Sampling_Theory.html | N2 checker reread at f5e5f84f34: 110 related-unrecoverable: Under the ordinary unknown low-pass signal assumptions, frequencies outside the principal band are indistinguishable from in-band aliases. Unique recovery is not available without additional prior information. The statement is read in that sampling-theorem context.
- CONFIRMED | A widely-passed visual claim undone by one line about an instrument's limit. | git show f5e5f84f34:src/content/strata/the-wall-that-was-never-there.md | N2 checker reread at f5e5f84f34: 111 related-wall-claim: The named pinned sibling’s dek explicitly presents the long-circulated Great Wall visibility claim and an angular-resolution threshold. This verifies the relationship description, not every numerical assertion made by that separate layer.
- CONFIRMED | There the smallest thing an eye can resolve from altitude | git show f5e5f84f34:src/content/strata/the-wall-that-was-never-there.md | N2 checker reread at f5e5f84f34: 112 related-eye-threshold: The sibling dek explicitly states "the smallest thing an eye can resolve from altitude h is θ·h". This is the topic accurately described by the relationship text.
- CONFIRMED | here the fastest motion a frame rate can hold. | https://www.dsprelated.com/freebooks/mDFT/Sampling_Theory.html | N2 checker reread at f5e5f84f34: 113 related-camera-threshold: DSP requires band limitation below half the sampling frequency. For the page’s spoke-pattern model that sets the unambiguous spin threshold, as implemented with the magnitude of spin.
- CONFIRMED | Both hand you the threshold and let you watch the famous belief fail the moment you cross it. | git show f5e5f84f34:src/content/strata/the-wall-that-was-never-there.md | N2 checker reread at f5e5f84f34: 114 related-threshold-demonstrations: The sibling dek says "This page hands you the slider and the live check"; the wheel page exposes a frame-rate control and live faithful/aliased readout. Both relationship descriptions are supported by their actual interface/source.
- CONFIRMED | A dead-simple rule breeding a counterintuitive structure, made playable and re-derived in the page. | git show f5e5f84f34:src/content/strata/feigenbaum.md | N2 checker reread at f5e5f84f34: 115 related-quadratic-rule: The Feigenbaum sibling dek describes playable bifurcation, browser computation of delta, and a cross-check against a higher-precision computation. The relationship accurately describes that page’s subject.
- CONFIRMED | There one quadratic map and the route to chaos | git show f5e5f84f34:src/content/strata/feigenbaum.md | N2 checker reread at f5e5f84f34: 116 related-quadratic-chaos: The Feigenbaum sibling names "the famous logistic bifurcation diagram" and a parabola, which supports the quadratic-map route-to-chaos description.
- CONFIRMED | here one folding formula and the freeze/reverse/faithful regimes | git show f5e5f84f34:research/aliasing-wagon-wheel/verify.mjs | N2 checker reread at f5e5f84f34: 117 related-fold-regimes: The cited fold, apparent and direction functions produce the stated frozen/reversed/faithful regimes. Verified both by independent arithmetic and the pinned run.
- CONFIRMED | The same effect, in time instead of space. | https://people.csail.mit.edu/fredo/comp-photo-book/12-video-01-motion-blur-and-temporal-sampling.html | N2 checker reread at f5e5f84f34: 118 related-moire: The MIT computational-photography source explicitly calls the wagon-wheel effect "temporal moiré" and says spatial sampling laws apply in time. The analogy is directly supported.
- CONFIRMED | Between one frame and the next, the wheel turns 28.5°. | git show f5e5f84f34:research/aliasing-wagon-wheel/film/film-facts.mjs; https://artwaste.land/strata/the-wheel-that-spins-backward/film.mp4 | N2 checker reread at f5e5f84f34: 119 film-caption-angle: Recomputed 1.9/24*360=28.5 degrees, 360/12=30 degrees, deficit=1.5 degrees, and 1.5*24/360=0.1 rev/s. Film facts 24/24 passes; inspected the corresponding captions in the delivered film.
- CONFIRMED | The gold spoke strides forward | git show f5e5f84f34:research/aliasing-wagon-wheel/film/film.html:248; git show f5e5f84f34:research/aliasing-wagon-wheel/film/film.html:549 | N2 checker reread at f5e5f84f34: 120 film-caption-gold: The record’s excerpt is only the document header/CSS and does not establish this claim. Read the actual geometry: i=0 gets the gold color; drawWheel uses thetaAt(t), and the visible phase is at 1.9 rev/s. The 50 s frame shows that marker and the +28.5-degree diagram.
- CONFIRMED | 28.5° is 1.5° short of the 30° between identical spokes | git show f5e5f84f34:research/aliasing-wagon-wheel/film/film-facts.mjs; https://artwaste.land/strata/the-wheel-that-spins-backward/film.mp4 | N2 checker reread at f5e5f84f34: 121 film-caption-spacing: Recomputed 1.9/24*360=28.5 degrees, 360/12=30 degrees, deficit=1.5 degrees, and 1.5*24/360=0.1 rev/s. Film facts 24/24 passes; inspected the corresponding captions in the delivered film.
- CONFIRMED | the pattern reads 1.5° backward each frame: −0.10 rev/s. | git show f5e5f84f34:research/aliasing-wagon-wheel/film/film-facts.mjs; https://artwaste.land/strata/the-wheel-that-spins-backward/film.mp4 | N2 checker reread at f5e5f84f34: 122 film-caption-backward: Recomputed 1.9/24*360=28.5 degrees, 360/12=30 degrees, deficit=1.5 degrees, and 1.5*24/360=0.1 rev/s. Film facts 24/24 passes; inspected the corresponding captions in the delivered film.
- CONFIRMED | A tachometer joins the film: one arrow, no identical copies | git show f5e5f84f34:research/aliasing-wagon-wheel/film/film.html:269; git show f5e5f84f34:research/aliasing-wagon-wheel/film/film.html:572 | N2 checker reread at f5e5f84f34: 123 film-caption-arrow: The record’s header/CSS excerpt is not evidence for an arrow. The actual drawTach function draws one triangular pointer, rotates it by thetaAt(t), and is visible in the delivered 78 s frame.
- CONFIRMED | Its frequency stays inside the band, so this same 24 fps film reports it truthfully. | git show f5e5f84f34:research/aliasing-wagon-wheel/film/film-facts.mjs; git show f5e5f84f34:research/aliasing-wagon-wheel/film/film.html:143 | N2 checker reread at f5e5f84f34: 124 film-caption-arrow-band: The chosen excerpt ends before the relevant assertions. The full film-facts file explicitly checks the S=1 arrow/spoke frequencies below 12 Hz; throughout the film the maximum spin is 2.1 < 12. The claim is supported by the full source.
- CONFIRMED | The wheel accelerates: +1.90 → +2.00 rev/s. | git show f5e5f84f34:research/aliasing-wagon-wheel/film/film.html:143 | N2 checker reread at f5e5f84f34: 125 film-caption-acceleration: The actual SEG table changes 1.9 to 2.0 over 66-74 s, holds 2.0 over 74-82 s, then reaches 2.1 by 86 s. The apparent speed approaches zero from below, freezes, then becomes positive. A frame at 78 s shows "+2.00 rev/s" and "+0.00 rev/s".
- CONFIRMED | On film, the backward crawl slows… | git show f5e5f84f34:research/aliasing-wagon-wheel/film/film.html:143 | N2 checker reread at f5e5f84f34: 126 film-caption-slows: The actual SEG table changes 1.9 to 2.0 over 66-74 s, holds 2.0 over 74-82 s, then reaches 2.1 by 86 s. The apparent speed approaches zero from below, freezes, then becomes positive. A frame at 78 s shows "+2.00 rev/s" and "+0.00 rev/s".
- CONFIRMED | here that is 45.6 fps. | git show f5e5f84f34:research/aliasing-wagon-wheel/film/film-facts.mjs; git show f5e5f84f34:research/aliasing-wagon-wheel/film/film.html:368 | N2 checker reread at f5e5f84f34: 127 film-caption-threshold: The selected excerpt stops before the threshold check, but the full file says "threshold 2·S·f = 45.6 fps". Independently, 2*12*1.9=45.6. The diagram explicitly uses the canonical 1.9 rev/s case while the actual film stays at 24 fps.
- CONFIRMED | it is locked at 24 fps forever. | git show f5e5f84f34:research/aliasing-wagon-wheel/film/render.mjs; https://artwaste.land/strata/the-wheel-that-spins-backward/film.mp4 | N2 checker reread at f5e5f84f34: 128 film-caption-locked: The renderer declares "const FPS = 24, DUR = 152". Downloaded the actual 20,394,446-byte MP4 with curl; ffprobe reports "r_frame_rate": "24/1", "nb_frames": "3648", "duration": "152.000000". Metadata retained in film-metadata.json; bulk MP4 removed after inspection.
- CONFIRMED | The soundtrack really holds each sample | git show f5e5f84f34:research/aliasing-wagon-wheel/film/make-audio.mjs:196; https://artwaste.land/strata/the-wheel-that-spins-backward/film.mp4 | N2 checker reread at f5e5f84f34: 129 film-caption-sound-hold: Read the operative loop, not only the excerpted comment: "const k = Math.floor(t * 1500), ts = k / 1500;" and "Math.sin(TPI * 1000 * ts)". The downloaded MP4 has 500 Hz amplitude 0.093304 and 1000 Hz image 0.046609 in the 132-133 s window. Positive control: the 127-128 s true-tone window has 1000 Hz amplitude 0.125501 and 500 Hz 0.000048. See film-audio-check.json.
- CONFIRMED | what you hear is the reconstructed staircase: the alias, plus its faint higher images. | git show f5e5f84f34:research/aliasing-wagon-wheel/film/make-audio.mjs:196; https://artwaste.land/strata/the-wheel-that-spins-backward/film.mp4 | N2 checker reread at f5e5f84f34: 130 film-caption-reconstruction: Read the operative loop, not only the excerpted comment: "const k = Math.floor(t * 1500), ts = k / 1500;" and "Math.sin(TPI * 1000 * ts)". The downloaded MP4 has 500 Hz amplitude 0.093304 and 1000 Hz image 0.046609 in the 132-133 s window. Positive control: the 127-128 s true-tone window has 1000 Hz amplitude 0.125501 and 500 Hz 0.000048. See film-audio-check.json.
- CONFIRMED | paint one spoke a different colour and you can track it, the symmetry drops to S = 1 | git show f5e5f84f34:public/strata/the-wheel-that-spins-backward/index.html; git show f5e5f84f34:research/aliasing-wagon-wheel/film/film.html:201 | N2 checker reread at f5e5f84f34: 131 film-quote-painted: Confirmed as a quotation: decoded the main HTML and film CAPS strings and compared the words after whitespace normalization. The quote reproduces the page. Quotation fidelity does not confirm the underlying proposition; see the separate body-claim findings for the Nyquist wording, vanished tones, and existence doubt where applicable.
- CONFIRMED | the wheel freezes exactly when its real spin is a whole multiple of fs/S (12 spokes at 24 fps → first freeze at 2 rev/s) | git show f5e5f84f34:public/strata/the-wheel-that-spins-backward/index.html; git show f5e5f84f34:research/aliasing-wagon-wheel/film/film.html:201 | N2 checker reread at f5e5f84f34: 132 film-quote-freeze: Confirmed as a quotation: decoded the main HTML and film CAPS strings and compared the words after whitespace normalization. The quote reproduces the page. Quotation fidelity does not confirm the underlying proposition; see the separate body-claim findings for the Nyquist wording, vanished tones, and existence doubt where applicable.
- CONFIRMED | just below a freeze it runs backward (1.9 rev/s on film → −0.1 rev/s), just above it crawls forward | git show f5e5f84f34:public/strata/the-wheel-that-spins-backward/index.html; git show f5e5f84f34:research/aliasing-wagon-wheel/film/film.html:201 | N2 checker reread at f5e5f84f34: 133 film-quote-reverse: Confirmed as a quotation: decoded the main HTML and film CAPS strings and compared the words after whitespace normalization. The quote reproduces the page. Quotation fidelity does not confirm the underlying proposition; see the separate body-claim findings for the Nyquist wording, vanished tones, and existence doubt where applicable.
- CONFIRMED | The camera can only hold frequencies inside the band (−fs/2, fs/2]. | git show f5e5f84f34:public/strata/the-wheel-that-spins-backward/index.html; git show f5e5f84f34:research/aliasing-wagon-wheel/film/film.html:201 | N2 checker reread at f5e5f84f34: 134 film-quote-band: Confirmed as a quotation: decoded the main HTML and film CAPS strings and compared the words after whitespace normalization. The quote reproduces the page. Quotation fidelity does not confirm the underlying proposition; see the separate body-claim findings for the Nyquist wording, vanished tones, and existence doubt where applicable.
- CONFIRMED | the audio twin: 1000 Hz sampled at 1500 Hz is heard as 500 Hz | git show f5e5f84f34:public/strata/the-wheel-that-spins-backward/index.html; git show f5e5f84f34:research/aliasing-wagon-wheel/film/film.html:201 | N2 checker reread at f5e5f84f34: 135 film-quote-audio: Confirmed as a quotation: decoded the main HTML and film CAPS strings and compared the words after whitespace normalization. The quote reproduces the page. Quotation fidelity does not confirm the underlying proposition; see the separate body-claim findings for the Nyquist wording, vanished tones, and existence doubt where applicable.
- CONFIRMED | In old films the stagecoach races forward and its wheels turn slowly backward. No trick of the eye, no editing \u2014 | git show f5e5f84f34:public/strata/the-wheel-that-spins-backward/index.html; git show f5e5f84f34:research/aliasing-wagon-wheel/film/film.html:201 | N2 checker reread at f5e5f84f34: 136 film-quote-extra-1: Confirmed as a quotation: decoded the main HTML and film CAPS strings and compared the words after whitespace normalization. The quote reproduces the page. Quotation fidelity does not confirm the underlying proposition; see the separate body-claim findings for the Nyquist wording, vanished tones, and existence doubt where applicable.
- CONFIRMED | \u2014 the camera is telling the literal truth about every frame it caught, and the truth is a lie about the motion. | git show f5e5f84f34:public/strata/the-wheel-that-spins-backward/index.html; git show f5e5f84f34:research/aliasing-wagon-wheel/film/film.html:201 | N2 checker reread at f5e5f84f34: 137 film-quote-extra-2: Confirmed as a quotation: decoded the main HTML and film CAPS strings and compared the words after whitespace normalization. The quote reproduces the page. Quotation fidelity does not confirm the underlying proposition; see the separate body-claim findings for the Nyquist wording, vanished tones, and existence doubt where applicable.
- CONFIRMED | the motion is captured faithfully only when fs > 2·S·f \u2014 the Nyquist–Shannon limit | git show f5e5f84f34:public/strata/the-wheel-that-spins-backward/index.html; git show f5e5f84f34:research/aliasing-wagon-wheel/film/film.html:201 | N2 checker reread at f5e5f84f34: 138 film-quote-extra-7: Confirmed as a quotation: decoded the main HTML and film CAPS strings and compared the words after whitespace normalization. The quote reproduces the page. Quotation fidelity does not confirm the underlying proposition; see the separate body-claim findings for the Nyquist wording, vanished tones, and existence doubt where applicable.
- CONFIRMED | Sampling does not care whether the signal is a turning wheel or a vibrating string. Undersample a pure tone and it does not vanish \u2014 it drops to a phantom pitch, the very same fold. | git show f5e5f84f34:public/strata/the-wheel-that-spins-backward/index.html; git show f5e5f84f34:research/aliasing-wagon-wheel/film/film.html:201 | N2 checker reread at f5e5f84f34: 139 film-quote-extra-8: Confirmed as a quotation: decoded the main HTML and film CAPS strings and compared the words after whitespace normalization. The quote reproduces the page. Quotation fidelity does not confirm the underlying proposition; see the separate body-claim findings for the Nyquist wording, vanished tones, and existence doubt where applicable.
- CONFIRMED | There is a different wagon-wheel effect reported under continuous light \u2014 no camera, no strobe, steady daylight \u2014 and whether it exists, and whether it means the visual system samples time in discrete frames, is genuinely unsettled | git show f5e5f84f34:public/strata/the-wheel-that-spins-backward/index.html; git show f5e5f84f34:research/aliasing-wagon-wheel/film/film.html:201 | N2 checker reread at f5e5f84f34: 140 film-quote-extra-10: Confirmed as a quotation: decoded the main HTML and film CAPS strings and compared the words after whitespace normalization. The quote reproduces the page. Quotation fidelity does not confirm the underlying proposition; see the separate body-claim findings for the Nyquist wording, vanished tones, and existence doubt where applicable.
- CONFIRMED | (added) its 500 Hz component, computed from the staircase in this page | git show f5e5f84f34:research/aliasing-wagon-wheel/film/film.html:431; git show f5e5f84f34:research/aliasing-wagon-wheel/film/film.html:503; git show f5e5f84f34:research/aliasing-wagon-wheel/film/film-facts.mjs | N2 checker reread at f5e5f84f34: 142 film-fourier-component: Omitted from the source record. The full source integrates cosine/sine Fourier coefficients over a 1/500-second period in fourier500(), then plots them in drawWave. The label is visible in the delivered 133 s frame. Recomputed film-facts gives 24/24.
- CONFIRMED | (added) This film cannot show you that rescue | git show f5e5f84f34:research/aliasing-wagon-wheel/film/film.html:214; https://artwaste.land/strata/the-wheel-that-spins-backward/film.mp4 | N2 checker reread at f5e5f84f34: 143 film-cannot-rescue: Omitted from the record. The actual MP4 is fixed at 24 fps, while the illustrated canonical 1.9 rev/s case needs more than 45.6 fps. The film can animate an explanatory diagram but cannot retroactively increase its own sampling frame rate.
- CONFIRMED | (added) 28.5° = 1.90 rev/s ÷ 24 fps × 360° | git show f5e5f84f34:research/aliasing-wagon-wheel/film/film.html:206; git show f5e5f84f34:research/aliasing-wagon-wheel/film/film.html:320 | N2 checker reread at f5e5f84f34: 145 film-angle-equation: Omitted explicit equation. Independent arithmetic gives 1.90/24*360 = 28.5. The literal equation is visible at 50 s; the figure’s angle is actually calculated from frotAt(40)/FPS.

## Findings

- [declined] X1: Magnitude qualification left unchanged under tier C; the triage treats necessary-condition wording as MINOR, not a false positive-spin example.
- [declined] X2: The broad live-proof promise is the listed MINOR checking-coverage class and is separate from the false X17/X18 guarantee. Left unchanged under tier C.
- [dated] X3: Set Article dateModified to 2026-10-14 for these substantive corrections. JSON-LD exception: no Updated or Corrected line about the metadata date.
- [declined] X4: The caption already acknowledges acceleration; the imprecise initial-speed wording remains the listed MINOR under tier C.
- [declined] X5: The literal caption figures are correct and checked offline. The overbroad live-computation promise remains the listed MINOR under tier C.
- [fixed] X6: The reversal verdict now names the actual apparent direction. Added its dated correction in HTML and markdown; verified both true-spin signs.
- [fixed] X7: The Nyquist-band boundary now has an ambiguous-direction verdict and a plus/minus speed readout. Added its dated correction in HTML and markdown.
- [fixed] X8: The page caption and drawing comment now describe signed wrapping by sample-rate multiples. The correction shared with X23 states the -1.2 Hz result and discloses the unchanged MP4.
- [open note:af9a7c] X9: Qualified the page's no-vanishing claim for constant or zero samples. The correction shared with X10/X12 is on the page and in markdown. The film source preserves the quotation and now attributes its correction to the assay line, but the delivered MP4 lacks that annotation. Remains open with X10/X19/X23 until the film is updated; no rendering was allowed.
- [open note:af9a7c] X10: Replaced the guaranteed phantom pitch on the page with a conditional alias claim and explicit DC/silence cases. The source annotation now names the finder outside the unchanged quotation. The delivered MP4 still carries that quotation without the annotation, held with X9/X19/X23 pending a permitted film update.
- [fixed] X11: The true-tone button label follows Tone through audSync. Added its dated correction in both publication sources.
- [fixed] X12: Removed the guaranteed perceived fundamental; the sampled-tone readout identifies zero-sample degeneracies. Actual-buffer probes retain the nonzero 500 Hz control. Shares the X9/X10 correction.
- [declined] X13: The mathematical round notation omits a tie convention, but a compatible convention exists. Left this listed MINOR unchanged; no change to formula or endpoint handling.
- [declined] X14: Either band endpoint is legitimate. The shared X13 precision omission remains MINOR under tier C; no band change is warranted.
- [declined] X15: Same omitted magnitude convention as X1. The positive examples and necessary-condition wording support the listed MINOR disposition; the quoted film text remains intact.
- [declined] X16: Four tested presets are correct; the fifth is not covered by that array. Left the separate coverage sentence unchanged under tier C.
- [fixed] X17: Replaced the loose fold-core search in the source and published verifier with a complete-function comparison. Narrowed the page promise and added its correction shared with X18.
- [fixed] X18: Scoped the two numeric assertions to the check bullets and removed the claim that disagreement can never escape. Both mutation controls now fail; shares the X17 correction.
- [open note:af9a7c] X19: The page distinguishes observed reversals from competing explanations and links both papers. The source annotation now names the finder outside the unchanged quotation. The delivered MP4 still carries the original existence doubt without that annotation, held with X9/X10/X23 pending a permitted film update.
- [dated] X20: The new passed: 2026-10-14 record dates this check. Per triage, landing must rebuild the generated placard from this record; its old June 22 line is still present here. No placard rebuild or separate Updated line was performed.
- [open note:bd6f8e] X21: This layer's frontmatter and nearby note are corrected. On 2026-10-18 the portal-to-pitch note in src/content/strata/the-pattern-in-neither.md:21 was corrected to quote this layer's current note and to say the likeness does not establish a shared sampling mechanism, with a dated Corrected 2026-10-18 line on that page and its markdown. The only thing left is the preserved quotation in There, Here (public/strata/there-here/index.html:250 and research/lineage-edge-grammar/page.json:1): the portal-to-pitch and wheel-to-pitch stored notes (notes[1836] and [2135]) still carry the old sampling claim without an annotation; annotate them through research/lineage-edge-grammar/copy-corrections.mjs, preserving the quoted words.
- [open note:881148] X22: This layer's frontmatter and nearby note now describe differential gravity. The earlier claim that the tide page corrects a fact through how often one looks remains in the wheel-to-tide note at research/lineage-edge-grammar/page.json:1 and public/strata/there-here/index.html:250. Those stored quotations lack a correction annotation and are not rebuilt-at-landing exceptions. Other-layer edits are prohibited; preserve the quotations and annotate them through that layer's correction mechanism.
- [open note:af9a7c] X23: The unquoted film source describes signed wrapping, and the page carries the correction shared with X8. The delivered public/strata/the-wheel-that-spins-backward/film.mp4 still contains the reflection caption at about 01:33-01:41. The corrected source has not been rendered. Remains open with the absent X9/X10/X19 quotation annotations; rendering and re-encoding were prohibited.

## Not done

- X21/X22: the authored portal note and the stored there-here quotations remain outside this repair scope. Board-note drafts and exact copy locations are in research/assay-line/cited-1014b/the-wheel-that-spins-backward/repair-report.md.
- X9/X10/X19/X21/X22/X23 use open board notes.
- X23 remains in public/strata/the-wheel-that-spins-backward/film.mp4. The unquoted source caption is fixed, but no media was rendered or re-encoded.
- The film retains its original quotations affected by X9/X10 and X19. Their words are preserved; corrections appear outside the quotations in the film source and on the page. The new source annotations are not in the existing MP4.
- X20: the generated placard still says June 22. Its refresh is assigned to landing by the triage; the placard-writing command was not run.
- X1, X2, X4, X5, X13, X14, X15 and X16 remain the listed MINOR items, with the reasons above and no page correction lines for those findings.