the assay office / record

Why Spaghetti Won't Break in Two

Written 2026-06-30. Claims re-read against their sources on 2026-10-01: 154 checked, 112 confirmed, 40 wrong, 0 unverifiable, 2 true when written and overtaken since (dated, not corrected). By the assay line (research/assay-line/trial-1001/), Codex fixer directed by claude-assaying-codex-0929; source record by Codex, checked by Codex and a Claude agent.

This was the directed correction pass for the layer read at 9a0c8a4186, following all 42 triage items after re-reading their evidence and reproducing the numerical findings. Each triage item has its own claim and disposition; the checkers' other CONFIRMED claims are retained once with their source records and appropriate scope. Earlier confirmations that conflict with triage are superseded by the triage lines. The count named wrong includes MINOR findings as the gate format permits. Listed MINOR items remain unchanged; fixed MINOR items receive no separate correction line. The dated page notes describe supported changes, and the detailed before/after and command report is research/assay-line/trial-1001/why-spaghetti-wont-break-in-two/fixer-report.md.

Claims

• MINOR X1: It does not fade; it disappears.
  https://mirror.explodie.org/why-spaghetti-do-not-break-in-half.pdf : Re-read the preprint p. 2: real end moment relaxes over a finite crack timescale, although its outer model idealises the release as instantaneous. Tier C: MINOR listed, not fixed.
• WRONG X2: Everything below is the real beam equation, integrated from scratch
  git show 3fa55eb20c:public/strata/why-spaghetti-wont-break-in-two/index.html : Re-read the HTML and verifier. Panel 3 uses an exponential curve and an imposed suppression term, with no beam or twist solve. At τ=0.05 its curve gives 1.933678; the verifier gives 1.654504. The verifier has selected beam/Fresnel checks, not a derivation of every claim.
• WRONG X3: the same solver, offline, checks every number on this page
  git show 3fa55eb20c:research/why-spaghetti-wont-break-in-two/verify.mjs : Re-read the HTML and verifier. Panel 3 uses an exponential curve and an imposed suppression term, with no beam or twist solve. At τ=0.05 its curve gives 1.933678; the verifier gives 1.654504. The verifier has selected beam/Fresnel checks, not a derivation of every claim.
• WRONG X4: a real crack tip lets go over a small but finite time, which is why the physical number is 1.43, not 2
  https://mirror.explodie.org/why-spaghetti-do-not-break-in-half.pdf : Re-read Audoly and Neukirch pp. 1-3: their instantaneous-release model gives 1.428 in the intermediate regime. Recreated the verifier sharp step: 2.043577 at L=3 versus 1.614208 at L=12, holding grid spacing and time window fixed. These computations do not establish a universal 2× ceiling or the claimed finite-crack explanation.
• WRONG X5: the most it ever reaches is a pure number:
  https://mirror.explodie.org/why-spaghetti-do-not-break-in-half.pdf : Re-read Audoly and Neukirch p. 3: 1.428 is the intermediate-regime maximum; their later reflected-wave computation reaches 3.12κ₀. The absolute all-time wording overstates the result.
• MINOR X6: the faint bright-and-dark fringes at the boundary of a shadow are S(z) and its cosine twin, plotted.
  https://dlmf.nist.gov/7.SB1 : Re-read NIST DLMF 7.SB1: intensity is the squared modulus of the complex Fresnel integral, not separate plots of sine and cosine integrals. Tier C: MINOR listed, not fixed.
• WRONG X7: Both work by killing the overshoot before it can re-break the rod.
  https://math.mit.edu/~dunkel/Data/spaghetti/2018HeEtAl_PNAS.pdf : Re-read Heisser et al. pp. 4-5, Eq. 7 and Fig. 3: twist lowers first-fracture curvature, torsional stress dissipates sooner, and amplification remains C=1.5 to one decimal place for the tested parameters. Quench v is the relative speed of the ends before fracture; minimum fragment length scales as v^(-1/4). It is not the page's end-moment ramp.
• WRONG X8: the bending wave is gentle and never overshoots the line.
  https://math.mit.edu/~dunkel/Data/spaghetti/2018HeEtAl_PNAS.pdf : Re-read Heisser et al. pp. 4-5, Eq. 7 and Fig. 3: twist lowers first-fracture curvature, torsional stress dissipates sooner, and amplification remains C=1.5 to one decimal place for the tested parameters. Quench v is the relative speed of the ends before fracture; minimum fragment length scales as v^(-1/4). It is not the page's end-moment ramp.
• WRONG X9: If the energy is released gradually instead of in a snap
  https://math.mit.edu/~dunkel/Data/spaghetti/2018HeEtAl_PNAS.pdf : Re-read Heisser et al. pp. 4-5, Eq. 7 and Fig. 3: twist lowers first-fracture curvature, torsional stress dissipates sooner, and amplification remains C=1.5 to one decimal place for the tested parameters. Quench v is the relative speed of the ends before fracture; minimum fragment length scales as v^(-1/4). It is not the page's end-moment ramp.
• WRONG X10: the stored torsional energy snaps back as a twist wave that arrives first and relaxes the curvature
  https://math.mit.edu/~dunkel/Data/spaghetti/2018HeEtAl_PNAS.pdf : Re-read Heisser et al. pp. 4-5, Eq. 7 and Fig. 3: twist lowers first-fracture curvature, torsional stress dissipates sooner, and amplification remains C=1.5 to one decimal place for the tested parameters. Quench v is the relative speed of the ends before fracture; minimum fragment length scales as v^(-1/4). It is not the page's end-moment ramp.
• WRONG X11: the verified overshoot-vs-twist/quench relationship
  git show 3fa55eb20c:research/why-spaghetti-wont-break-in-two/verify.mjs; git show 3fa55eb20c:public/strata/why-spaghetti-wont-break-in-two/index.html : Re-read the HTML and verifier. Panel 3 uses an exponential curve and an imposed suppression term, with no beam or twist solve. At τ=0.05 its curve gives 1.933678; the verifier gives 1.654504. The verifier has selected beam/Fresnel checks, not a derivation of every claim.
• WRONG X12: Nothing here is asserted that the verifier does not reproduce from first principles.
  git show 3fa55eb20c:research/why-spaghetti-wont-break-in-two/verify.mjs : Re-read the HTML and verifier. Panel 3 uses an exponential curve and an imposed suppression term, with no beam or twist solve. At τ=0.05 its curve gives 1.933678; the verifier gives 1.654504. The verifier has selected beam/Fresnel checks, not a derivation of every claim.
• MINOR X13: The Curvature Overshoot That Snaps It Three Times
  https://mirror.explodie.org/why-spaghetti-do-not-break-in-half.pdf : Re-read the preprint abstract: the typical count is three or four pieces. A count of three snaps would instead mean four pieces. Tier C: MINOR listed, not fixed.
• WRONG X14: twist the strand past ~250° and the torsional snap-back kills the overshoot, so it finally breaks in two.
  https://math.mit.edu/~dunkel/Data/spaghetti/2018HeEtAl_PNAS.pdf : Re-read Heisser et al. pp. 4-5, Eq. 7 and Fig. 3: twist lowers first-fracture curvature, torsional stress dissipates sooner, and amplification remains C=1.5 to one decimal place for the tested parameters. Quench v is the relative speed of the ends before fracture; minimum fragment length scales as v^(-1/4). It is not the page's end-moment ramp.
• STALE X15: "dateModified":"2026-06-30"
  git show 7595d28452:public/strata/why-spaghetti-wont-break-in-two/index.html; git log 3fa55eb20c -- public/strata/why-spaghetti-wont-break-in-two/index.html : Re-read git show 7595d28452:public/strata/why-spaghetti-wont-break-in-two/index.html: dateModified was 2026-06-30 at publication. The pinned history includes later changes through 2026-10-01. This is stale metadata, not a false original observation.
• WRONG X16: Every number is recomputed from scratch
  git show 3fa55eb20c:research/why-spaghetti-wont-break-in-two/verify.mjs : Re-read the HTML and verifier. Panel 3 uses an exponential curve and an imposed suppression term, with no beam or twist solve. At τ=0.05 its curve gives 1.933678; the verifier gives 1.654504. The verifier has selected beam/Fresnel checks, not a derivation of every claim.
• MINOR X17: (added) "Real strand"; "peak curvature 1.62×" on initial load
  git show 3fa55eb20c:public/strata/why-spaghetti-wont-break-in-two/index.html : Re-read the HTML: initial τ=0.04 differs from the selected button's 0.15. Recreated peaks 1.615056 and 1.403074 respectively, displayed as 1.62× and 1.40×. Tier C: MINOR listed, not fixed.
• MINOR K1: went to bed with broken pasta all over the kitchen and no answer.
  https://kottke.org/18/08/solving-the-spaghetti-problem (Hillis, No Ordinary Genius pp. 180-181, reproduced in full) : Re-read Hillis's account reproduced at the supplied URL. It ends with broken pasta in the kitchen after a couple of hours and no theory; it supplies no bedtime. Removed only that unsupported detail.
• MINOR K2: Everything below is the real beam equation, integrated from scratch
  git show 60c91d8037:public/strata/why-spaghetti-wont-break-in-two/index.html (lines 619-635) : Re-read the HTML and verifier. Panel 3 uses an exponential curve and an imposed suppression term, with no beam or twist solve. At τ=0.05 its curve gives 1.933678; the verifier gives 1.654504. The verifier has selected beam/Fresnel checks, not a derivation of every claim.
• MINOR K3: the same solver, offline, checks every number on this page
  git show 60c91d8037:research/why-spaghetti-wont-break-in-two/verify.mjs : Re-read the HTML and verifier. Panel 3 uses an exponential curve and an imposed suppression term, with no beam or twist solve. At τ=0.05 its curve gives 1.933678; the verifier gives 1.654504. The verifier has selected beam/Fresnel checks, not a derivation of every claim.
• WRONG K4: a mathematically instantaneous release injects infinitely fine ripples that pile up even harder
  https://mirror.explodie.org/why-spaghetti-do-not-break-in-half.pdf : Re-read Audoly and Neukirch pp. 1-3: their instantaneous-release model gives 1.428 in the intermediate regime. Recreated the verifier sharp step: 2.043577 at L=3 versus 1.614208 at L=12, holding grid spacing and time window fixed. These computations do not establish a universal 2× ceiling or the claimed finite-crack explanation.
• WRONG K5: a real crack tip lets go over a small but finite time, which is why the physical number is 1.43, not 2
  https://mirror.explodie.org/why-spaghetti-do-not-break-in-half.pdf : Re-read Audoly and Neukirch pp. 1-3: their instantaneous-release model gives 1.428 in the intermediate regime. Recreated the verifier sharp step: 2.043577 at L=3 versus 1.614208 at L=12, holding grid spacing and time window fixed. These computations do not establish a universal 2× ceiling or the claimed finite-crack explanation.
• WRONG K6: slow release and the hump sags below the line: no second break.
  recreated: simulateRelease copied from git show 60c91d8037:public/strata/why-spaghetti-wont-break-in-two/index.html (scratch window-test.mjs, window-test2.mjs) : Recreated simulateRelease(1.1,360,3,0.34,1): peak 1.050650. Extending to t=1.1 gives 1.409217 and a saved-frame crossing near t=0.854583. The verifier ramp similarly rises from 1.056155 through t=0.45 to 1.415063 through t=1.1. Both cross the chosen 1.12 line once followed longer.
• MINOR K7: the most it ever reaches is a pure number:
  https://mirror.explodie.org/why-spaghetti-do-not-break-in-half.pdf : Re-read Audoly and Neukirch p. 3: 1.428 is the intermediate-regime maximum; their later reflected-wave computation reaches 3.12κ₀. The absolute all-time wording overstates the result.
• MINOR K8: the faint bright-and-dark fringes at the boundary of a shadow are S(z) and its cosine twin, plotted.
  https://dlmf.nist.gov/7.3 ; https://dlmf.nist.gov/7.SB1 ; https://dlmf.nist.gov/7.2 : Re-read NIST DLMF 7.SB1: intensity is the squared modulus of the complex Fresnel integral, not separate plots of sine and cosine integrals. Tier C: MINOR listed, not fixed.
• WRONG K9: Both work by killing the overshoot before it can re-break the rod.
  https://math.mit.edu/~dunkel/Data/spaghetti/2018HeEtAl_PNAS.pdf : Re-read Heisser et al. pp. 4-5, Eq. 7 and Fig. 3: twist lowers first-fracture curvature, torsional stress dissipates sooner, and amplification remains C=1.5 to one decimal place for the tested parameters. Quench v is the relative speed of the ends before fracture; minimum fragment length scales as v^(-1/4). It is not the page's end-moment ramp.
• WRONG K10: the bending wave is gentle and never overshoots the line.
  https://math.mit.edu/~dunkel/Data/spaghetti/2018HeEtAl_PNAS.pdf : Re-read Heisser et al. pp. 4-5, Eq. 7 and Fig. 3: twist lowers first-fracture curvature, torsional stress dissipates sooner, and amplification remains C=1.5 to one decimal place for the tested parameters. Quench v is the relative speed of the ends before fracture; minimum fragment length scales as v^(-1/4). It is not the page's end-moment ramp.
• MINOR K11: If the energy is released gradually instead of in a snap
  https://math.mit.edu/~dunkel/Data/spaghetti/2018HeEtAl_PNAS.pdf : Re-read Heisser et al. pp. 4-5, Eq. 7 and Fig. 3: twist lowers first-fracture curvature, torsional stress dissipates sooner, and amplification remains C=1.5 to one decimal place for the tested parameters. Quench v is the relative speed of the ends before fracture; minimum fragment length scales as v^(-1/4). It is not the page's end-moment ramp.
• MINOR K12: bend it slowly past failure, or break it in a way that bleeds the curvature off
  https://math.mit.edu/~dunkel/Data/spaghetti/2018HeEtAl_PNAS.pdf : Re-read Heisser et al. pp. 4-5, Eq. 7 and Fig. 3: twist lowers first-fracture curvature, torsional stress dissipates sooner, and amplification remains C=1.5 to one decimal place for the tested parameters. Quench v is the relative speed of the ends before fracture; minimum fragment length scales as v^(-1/4). It is not the page's end-moment ramp.
• MINOR K13: You saw this above on the "slow release" setting.
  git show 60c91d8037:public/strata/why-spaghetti-wont-break-in-two/index.html ; https://math.mit.edu/~dunkel/Data/spaghetti/2018HeEtAl_PNAS.pdf : Re-read Heisser et al. pp. 4-5, Eq. 7 and Fig. 3: twist lowers first-fracture curvature, torsional stress dissipates sooner, and amplification remains C=1.5 to one decimal place for the tested parameters. Quench v is the relative speed of the ends before fracture; minimum fragment length scales as v^(-1/4). It is not the page's end-moment ramp.
• MINOR K14: the stored torsional energy snaps back as a twist wave that arrives first and relaxes the curvature
  https://news.mit.edu/2018/mit-mathematicians-solve-age-old-spaghetti-mystery-0813 ; https://math.mit.edu/~dunkel/Data/spaghetti/2018HeEtAl_PNAS.pdf : Re-read Heisser et al. pp. 4-5, Eq. 7 and Fig. 3: twist lowers first-fracture curvature, torsional stress dissipates sooner, and amplification remains C=1.5 to one decimal place for the tested parameters. Quench v is the relative speed of the ends before fracture; minimum fragment length scales as v^(-1/4). It is not the page's end-moment ramp.
• MINOR K15: until the overshoot no longer clears κ_c (twist or a slow release), at which point the cascade stops and you get two pieces.
  https://math.mit.edu/~dunkel/Data/spaghetti/2018HeEtAl_PNAS.pdf : Re-read Heisser et al. pp. 4-5, Eq. 7 and Fig. 3: twist lowers first-fracture curvature, torsional stress dissipates sooner, and amplification remains C=1.5 to one decimal place for the tested parameters. Quench v is the relative speed of the ends before fracture; minimum fragment length scales as v^(-1/4). It is not the page's end-moment ramp.
• WRONG K16: the verified overshoot-vs-twist/quench relationship
  git show 60c91d8037:research/why-spaghetti-wont-break-in-two/verify.mjs ; git show 60c91d8037:public/strata/why-spaghetti-wont-break-in-two/index.html : Re-read the HTML and verifier. Panel 3 uses an exponential curve and an imposed suppression term, with no beam or twist solve. At τ=0.05 its curve gives 1.933678; the verifier gives 1.654504. The verifier has selected beam/Fresnel checks, not a derivation of every claim.
• MINOR K17: Nothing here is asserted that the verifier does not reproduce from first principles.
  git show 60c91d8037:research/why-spaghetti-wont-break-in-two/verify.mjs ; git show 60c91d8037:public/strata/why-spaghetti-wont-break-in-two/index.html : Re-read the HTML and verifier. Panel 3 uses an exponential curve and an imposed suppression term, with no beam or twist solve. At τ=0.05 its curve gives 1.933678; the verifier gives 1.654504. The verifier has selected beam/Fresnel checks, not a derivation of every claim.
• MINOR K18: the integrated beam itself overshoots ≈1.43 on a physical release, and over-rings toward 2× on a perfectly sharp one;
  git show 60c91d8037:research/why-spaghetti-wont-break-in-two/verify.mjs ; recreated: simulateRelease copied from git show 60c91d8037:public/strata/why-spaghetti-wont-break-in-two/index.html : Re-read Audoly and Neukirch pp. 1-3: their instantaneous-release model gives 1.428 in the intermediate regime. Recreated the verifier sharp step: 2.043577 at L=3 versus 1.614208 at L=12, holding grid spacing and time window fixed. These computations do not establish a universal 2× ceiling or the claimed finite-crack explanation.
• WRONG K19: slowing the release drives the overshoot monotonically below the breaking line → two pieces.
  git show 60c91d8037:research/why-spaghetti-wont-break-in-two/verify.mjs ; recreated: simulateRelease copied from git show 60c91d8037:public/strata/why-spaghetti-wont-break-in-two/index.html : Recreated simulateRelease(1.1,360,3,0.34,1): peak 1.050650. Extending to t=1.1 gives 1.409217 and a saved-frame crossing near t=0.854583. The verifier ramp similarly rises from 1.056155 through t=0.45 to 1.415063 through t=1.1. Both cross the chosen 1.12 line once followed longer.
• MINOR K20: twist the strand past ~250° and the torsional snap-back kills the overshoot, so it finally breaks in two.
  https://math.mit.edu/~dunkel/Data/spaghetti/2018HeEtAl_PNAS.pdf ; https://news.mit.edu/2018/mit-mathematicians-solve-age-old-spaghetti-mystery-0813 : Re-read Heisser et al. pp. 4-5, Eq. 7 and Fig. 3: twist lowers first-fracture curvature, torsional stress dissipates sooner, and amplification remains C=1.5 to one decimal place for the tested parameters. Quench v is the relative speed of the ends before fracture; minimum fragment length scales as v^(-1/4). It is not the page's end-moment ramp.
• STALE K21: "dateModified":"2026-06-30"
  git log 60c91d8037 -- public/strata/why-spaghetti-wont-break-in-two/index.html : Re-read git show 7595d28452:public/strata/why-spaghetti-wont-break-in-two/index.html: dateModified was 2026-06-30 at publication. The pinned history includes later changes through 2026-10-01. This is stale metadata, not a false original observation.
• MINOR K22: Every number is recomputed from scratch
  git show 60c91d8037:research/why-spaghetti-wont-break-in-two/verify.mjs : Re-read the HTML and verifier. Panel 3 uses an exponential curve and an imposed suppression term, with no beam or twist solve. At τ=0.05 its curve gives 1.933678; the verifier gives 1.654504. The verifier has selected beam/Fresnel checks, not a derivation of every claim.
• MINOR K23: overshoot 1.43×
  git show 60c91d8037:public/strata/why-spaghetti-wont-break-in-two/index.html ; recreated: compute() copied from it : Re-read the HTML and recreated the hand-set formula: static markup has 1.43× and three pieces, while initial JavaScript computes 1.963224× and four pieces. The numeric placeholders, formula and defaults remain unchanged. Tier C: MINOR listed, not fixed.
• MINOR K24: breaks the line? yes pieces 3
  git show 60c91d8037:public/strata/why-spaghetti-wont-break-in-two/index.html ; recreated: compute() copied from it : Re-read the HTML and recreated the hand-set formula: static markup has 1.43× and three pieces, while initial JavaScript computes 1.963224× and four pieces. The numeric placeholders, formula and defaults remain unchanged. Tier C: MINOR listed, not fixed.
• WRONG K25: (added) it is the whole trick to breaking spaghetti in two.
  https://math.mit.edu/~dunkel/Data/spaghetti/2018HeEtAl_PNAS.pdf ; recreated: simulateRelease copied from git show 60c91d8037:public/strata/why-spaghetti-wont-break-in-two/index.html : Re-read Heisser et al. pp. 4-5, Eq. 7 and Fig. 3: twist lowers first-fracture curvature, torsional stress dissipates sooner, and amplification remains C=1.5 to one decimal place for the tested parameters. Quench v is the relative speed of the ends before fracture; minimum fragment length scales as v^(-1/4). It is not the page's end-moment ramp.
• CONFIRMED C001: Almost never two. Three, usually
  https://math.mit.edu/~dunkel/Data/spaghetti/2018HeEtAl_PNAS.pdf ; https://mirror.explodie.org/why-spaghetti-do-not-break-in-half.pdf : PNAS p. 1: Feynman "noted that dry spaghetti, when brought to fracture by holding the ends and moving them toward each other, appears almost always to break into at least three pieces". A&N abstract: "typically three or four". The record's excerpt ("often break into more than two pieces") is weaker than "almost never two"; PNAS carries it. Checker record: N2-claude.md:15, N2-codex.md:25.
• CONFIRMED C002: sometimes four or five.
  https://mirror.explodie.org/why-spaghetti-do-not-break-in-half.pdf : A&N p. 1 body: "most of the time, the pasta does not break in half but typically in three to ten pieces". The record's excerpt ("typically three or four") does not reach five; this sentence does. Checker record: N2-claude.md:16, N2-codex.md:26.
• CONFIRMED C003: Feynman spent an evening on it
  https://news.mit.edu/2018/mit-mathematicians-solve-age-old-spaghetti-mystery-0813 : "who once spent a good portion of an evening breaking pasta and looking for a theoretical explanation for why the sticks refused to snap in two." Checker record: N2-claude.md:17, N2-codex.md:27.
• CONFIRMED C004: Hold a strand of spaghetti by both ends and bring your hands together. It bows into an arc.
  https://news.mit.edu/2018/mit-mathematicians-solve-age-old-spaghetti-mystery-0813 ; https://math.mit.edu/~dunkel/Data/spaghetti/2018HeEtAl_PNAS.pdf : MIT: "hold it at both ends. Now bend it until it breaks". PNAS: "holding the ends and moving them toward each other". Checker record: N2-claude.md:19, N2-codex.md:29.
• CONFIRMED C005: wherever the strand is weakest
  https://mirror.explodie.org/why-spaghetti-do-not-break-in-half.pdf : "a dynamic crack crosses the weakest section and breaks the rod in two halves. As the rod was initially bent with uniform curvature, the location of this first failure point is that of the strongest defect." Checker record: N2-claude.md:20, N2-codex.md:30.
• CONFIRMED C006: it reaches the curvature it cannot take, and it cracks.
  https://mirror.explodie.org/why-spaghetti-do-not-break-in-half.pdf : "It breaks at time t = 0 when its curvature κ0 reaches its limit value κ∗". Checker record: N2-claude.md:21, N2-codex.md:31.
• CONFIRMED C007: Film it at ten thousand frames a second and you see the truth
  https://math.mit.edu/~dunkel/Data/spaghetti/2018HeEtAl_PNAS.pdf : "high-speed imaging at frame rates ranging from 1,972 frames per second (fps) to 1,000,000 fps"; cameras include "Photron FASTCAM Mini AX200 (9,000 fps)". Fig. 1B shows sequential fractures in frames at 0.01, 0.07 and 0.12 ms. Checker record: N2-claude.md:23, N2-codex.md:33.
• CONFIRMED C008: more cracks appear, in a fraction of a millisecond, clustered near the first one.
  https://math.mit.edu/~dunkel/Data/spaghetti/2018HeEtAl_PNAS.pdf (Fig. 1B and 1D, rendered from the PDF) : The record's excerpt (nucleation about 10 ms, crack about 10 µs) is about the first crack, not the later ones. Support is Fig. 1: 1B sequential fractures at 0.01, 0.07 and 0.12 ms; 1D "The time between the first two fractures" plotted at about 0.05 to 0.5 ms, at 10 to 55 mm from the first (240 mm rods). Checker record: N2-claude.md:24, N2-codex.md:34.
• CONFIRMED C009: The strand shatters into a little burst of fragments before the halves have even begun to fall apart.
  https://math.mit.edu/~dunkel/Data/spaghetti/2018HeEtAl_PNAS.pdf (Fig. 1) : The burst is under half a millisecond (Fig. 1D). The record's excerpt (A&N conclusion) says nothing about timing. Loose at the microsecond scale: Fig. 1A already shows a gap between the halves at 69 µs. Checker record: N2-claude.md:25, N2-codex.md:35.
• CONFIRMED C010: The physicist Richard Feynman noticed this while cooking with the computer scientist Danny Hillis.
  https://kottke.org/18/08/solving-the-spaghetti-problem ; https://math.mit.edu/~dunkel/Data/spaghetti/2018HeEtAl_PNAS.pdf : Hillis: "Once we were making spaghetti, which was our favorite thing to eat together." He says "we"; PNAS assigns the observation to Feynman ("a famous observation by Richard Feynman (31)", ref. 31 = Sykes pp 180-181). The record's scan excerpt matches this text apart from OCR spacing. Checker record: N2-claude.md:26, N2-codex.md:36.
• CONFIRMED C011: computer scientist Danny Hillis
  https://kottke.org/18/08/solving-the-spaghetti-problem ; https://www.sciencenews.org/article/thats-way-spaghetti-crumbles : kottke: "computer scientist Danny Hills [sic]"; Science News: "supercomputing innovator W. Daniel Hillis". Checker record: N2-claude.md:27, N2-codex.md:37.
• CONFIRMED C012: they spent two hours on it
  https://kottke.org/18/08/solving-the-spaghetti-problem : "We spent the next two hours coming up with crazy theories." Checker record: N2-claude.md:28, N2-codex.md:38.
• CONFIRMED C013: breaking strands underwater to deaden the sound, inventing theories, testing them
  https://kottke.org/18/08/solving-the-spaghetti-problem : "We thought up experiments, like breaking it underwater because we thought that might dampen the sound, the vibrations." ("deaden" is the page's paraphrase, outside the quotation.) Checker record: N2-claude.md:29, N2-codex.md:39.
• CONFIRMED C014: we ended up at the end of a couple of hours with broken spaghetti all over the kitchen and no real good theory about why spaghetti breaks in three.
  https://kottke.org/18/08/solving-the-spaghetti-problem ; https://www.sciencenews.org/article/thats-way-spaghetti-crumbles : Word for word: "Well, we ended up at the end of a couple of hours with broken spaghetti all over the kitchen and no real good theory about why spaghetti breaks in three." The page's ellipsis stands for "Well,". Science News (2005) prints the same words with two commas added. Checker record: N2-claude.md:30, N2-codex.md:40.
• CONFIRMED C015: It took until 2005 for two physicists in Paris to settle it
  https://news.mit.edu/2018/mit-mathematicians-solve-age-old-spaghetti-mystery-0813 ; https://mirror.explodie.org/why-spaghetti-do-not-break-in-half.pdf : MIT: "remained unresolved until 2005, when physicists from France pieced together a theory". A&N: "Lab. de Modélisation en Mécanique, CNRS/UPMC, 4 place Jussieu, Paris". Checker record: N2-claude.md:31, N2-codex.md:41.
• CONFIRMED C016: work that won an Ig Nobel Prize
  https://improbable.com/ig/winners/#ig2006 : "PHYSICS: Basile Audoly and Sebastien Neukirch of the Université Pierre et Marie Curie, in Paris, for their insights into why, when you bend dry spaghetti, it often breaks into more than two pieces." Checker record: N2-claude.md:32, N2-codex.md:42.
• CONFIRMED C017: turns out to ride on the same special function that draws the edge of a shadow.
  https://dlmf.nist.gov/7.3 ; https://mirror.explodie.org/why-spaghetti-do-not-break-in-half.pdf : DLMF: "Fresnel (1818) introduced the integral ℱ(x) in his study of the interference pattern at the edge of a shadow." A&N: "the Fresnel sine integral ... arising in diffraction theory". Checker record: N2-claude.md:33, N2-codex.md:43.
• CONFIRMED C018: While the strand is bent, every cross-section is under a bending moment
  https://mirror.explodie.org/why-spaghetti-do-not-break-in-half.pdf : "the curvature is proportional to the internal moment"; "M0 plays the role of the internal moment transmitted across the section that is about to fail". Checker record: N2-claude.md:34, N2-codex.md:44.
• CONFIRMED C019: an internal torque, supplied by the rest of the rod, that holds it curved.
  https://mirror.explodie.org/why-spaghetti-do-not-break-in-half.pdf : As above; a bending moment is an internal torque. Checker record: N2-claude.md:35, N2-codex.md:45.
• CONFIRMED C020: The instant a crack opens, that torque at the new free end vanishes.
  https://mirror.explodie.org/why-spaghetti-do-not-break-in-half.pdf : Model: "the applied moment M0 is removed instantaneously". Real crack: "a decrease of M0 over a small but finite timescale Ts = r/c ∼ 1 µs for spaghetti". Checker record: N2-claude.md:36, N2-codex.md:46.
• CONFIRMED C021: The end, a microsecond ago held hard in a curve, is suddenly free
  https://mirror.explodie.org/why-spaghetti-do-not-break-in-half.pdf : "Ts = r/c ∼ 1 µs for spaghetti". Checker record: N2-claude.md:38, N2-codex.md:48.
• CONFIRMED C022: and it whips straight.
  https://mirror.explodie.org/why-spaghetti-do-not-break-in-half.pdf ; https://news.mit.edu/2018/mit-mathematicians-solve-age-old-spaghetti-mystery-0813 : A&N: "the quick initial relaxation of the nonzero curvature κ(0, t) at the free end". MIT: "The snap-back, in which the stick will spring back". Checker record: N2-claude.md:39, N2-codex.md:49.
• CONFIRMED C023: a bending wave that races back along the still-curved rod.
  https://mirror.explodie.org/why-spaghetti-do-not-break-in-half.pdf : "a burst of flexural waves is sent through the newly formed fragments". Checker record: N2-claude.md:40, N2-codex.md:50.
• CONFIRMED C024: as it passes through a region that is already curved, it can pile its own curvature on top of what is there
  https://mirror.explodie.org/why-spaghetti-do-not-break-in-half.pdf : "These flexural waves locally increase the curvature in the rod". Checker record: N2-claude.md:42, N2-codex.md:52.
• CONFIRMED C025: for a brief moment the rod is bent more sharply than it ever was before the break.
  https://mirror.explodie.org/why-spaghetti-do-not-break-in-half.pdf : "the curvature is 1.428 times its initial value κ0". Checker record: N2-claude.md:43, N2-codex.md:53.
• CONFIRMED C026: More sharply than the curvature that broke it in the first place. So it breaks again.
  https://mirror.explodie.org/why-spaghetti-do-not-break-in-half.pdf : "The limit curvature is therefore exceeded again at later time". Checker record: N2-claude.md:44, N2-codex.md:54.
• CONFIRMED C027: And the second break launches its own wave. An avalanche.
  https://mirror.explodie.org/why-spaghetti-do-not-break-in-half.pdf : "a breaking event induces strong flexural waves which trigger other breakings, leading to an avalanche like process" (A&N hedge later events: "most likely described by the same theory"). Checker record: N2-claude.md:45, N2-codex.md:55.
• CONFIRMED C028: The first crack opens at the apex
  https://news.mit.edu/2018/mit-mathematicians-solve-age-old-spaghetti-mystery-0813 : "it will break near the center, where it is most curved". Checker record: N2-claude.md:48, N2-codex.md:58.
• CONFIRMED C029: the freed end straightens and sends a bending wave inward
  https://mirror.explodie.org/why-spaghetti-do-not-break-in-half.pdf : "a burst of flexural waves emitted from the released end s = 0 travels along the rod". Checker record: N2-claude.md:49, N2-codex.md:59.
• CONFIRMED C030: Where it crosses, the rod breaks again.
  https://mirror.explodie.org/why-spaghetti-do-not-break-in-half.pdf : "The limit curvature is therefore exceeded again at later time, allowing a cascading failure mechanism to take place." Checker record: N2-claude.md:50, N2-codex.md:60.
• CONFIRMED C031: The early self-similar solution has a maximum near 1.43 times initial curvature.
  https://mirror.explodie.org/why-spaghetti-do-not-break-in-half.pdf : Retained the supported scope of the earlier confirmation; the triage correction takes precedence over its broader wording. "later reaches a plateau, κ/κ0 = 1.43", κ0 being the curvature at which the rod broke. Page-internal: instrument 1 draws κ_c at 1.12 κ0, and on load it runs τ = 0.04 (peak 1.62x, recreated) while "Real strand" (τ = 0.15, 1.40x) is highlighted. Checker record: N2-claude.md:51, N2-codex.md:61.
• CONFIRMED C032: The original page sharp-release setting computes a peak of 1.83× in its t≤0.34 window.
  git show 60c91d8037:public/strata/why-spaghetti-wont-break-in-two/index.html ; recreated: simulateRelease copied from git show 60c91d8037:public/strata/why-spaghetti-wont-break-in-two/index.html : Retained the supported scope of the earlier confirmation; the triage correction takes precedence over its broader wording. simulateRelease(0.002, 360, 3.0, 0.34, 1) peaks at 1.83x. What the 2x means is lines 39 and 40. Checker record: N2-claude.md:52.
• CONFIRMED C033: The remarkable part of Audoly and Neukirch's 2005 result is that the overshoot factor is universal.
  https://mirror.explodie.org/why-spaghetti-do-not-break-in-half.pdf : "This coefficient is universal". The curvature coefficient is scoped to the intermediate self-similar regime, not all later times. Checker record: N2-claude.md:56, N2-codex.md:66.
• CONFIRMED C034: It does not depend on the pasta, the thickness, how hard you bent it, or where it first broke.
  https://mirror.explodie.org/why-spaghetti-do-not-break-in-half.pdf : "independently of the material properties, of the details of the initial release or breaking ... and even of the boundary conditions imposed at the other end"; κ0 factors out in the small-amplitude limit (note 17). Checker record: N2-claude.md:57, N2-codex.md:67.
• CONFIRMED C035: In the moments after the release, the curvature settles into a shape that spreads as √t and has no free parameters at all
  https://mirror.explodie.org/why-spaghetti-do-not-break-in-half.pdf : "a self-similar solution s ∼ √(γt)"; abstract: "a self-similar solution with no adjustable parameters". Checker record: N2-claude.md:58, N2-codex.md:68.
• CONFIRMED C036: peak curvature = 1.428 × κ₀ = 2 × max of the Fresnel sine integral S(z) = ∫₀ᶻ sin(πt²/2) dt
  https://mirror.explodie.org/why-spaghetti-do-not-break-in-half.pdf : Eq. (4): κ = 2κ0 S(s/√(2πγt)) with S(x) = ∫0^x sin(πy²/2) dy; "twice the maximum of the Fresnel sine integral". The curvature coefficient is scoped to the intermediate self-similar regime, not all later times. Checker record: N2-claude.md:60, N2-codex.md:70.
• CONFIRMED C037: The Fresnel sine integral is the function that describes how light leaks into the shadow behind a sharp edge
  https://dlmf.nist.gov/7.3 : Fresnel introduced ℱ "in his study of the interference pattern at the edge of a shadow"; S is one part of ℱ (see line 48). Checker record: N2-claude.md:61, N2-codex.md:71.
• CONFIRMED C038: The same curve, to the same maximum, sets how hard a breaking rod re-bends itself.
  https://mirror.explodie.org/why-spaghetti-do-not-break-in-half.pdf : "This coefficient is universal, being twice the maximum of the Fresnel sine integral." The curvature coefficient is scoped to the intermediate self-similar regime, not all later times. Checker record: N2-claude.md:63, N2-codex.md:73.
• CONFIRMED C039: Its largest value sits exactly at z = √2; double it and you have 1.428.
  https://mirror.explodie.org/why-spaghetti-do-not-break-in-half.pdf ; recreated: scipy.special.fresnel : S'(z) = sin(πz²/2) first vanishes at z = √2; scipy: global maximum S(√2) = 0.7139722, 2S = 1.4279444. A&N's argument ξ/√(2π) equals √2 at their maximum ξ = 2√π. The curvature coefficient is scoped to the intermediate self-similar regime, not all later times. Checker record: N2-claude.md:64, N2-codex.md:74.
• CONFIRMED C040: S(z) climbs to 0.71397 at z = √2 = 1.41421, then oscillates down toward ½.
  https://dlmf.nist.gov/7.2 ; recreated: scipy.special.fresnel : DLMF 7.2.9: limit ½. scipy: S(√2) = 0.7139722; next maxima 0.62894 (z = √6) and 0.60036 (z = √10). Checker record: N2-claude.md:65, N2-codex.md:75.
• CONFIRMED C041: Twice that maximum, 1.4279, is the curvature overshoot.
  https://mirror.explodie.org/why-spaghetti-do-not-break-in-half.pdf : 2 x 0.7139722 = 1.4279444. The curvature coefficient is scoped to the intermediate self-similar regime, not all later times. Checker record: N2-claude.md:66, N2-codex.md:76.
• CONFIRMED C042: Verified against the special function offline to 2×10⁻³.
  git show 60c91d8037:research/why-spaghetti-wont-break-in-two/verify.mjs : "close(2 * Smax, 1.428, 2e-3)". Checker record: N2-claude.md:67.
• CONFIRMED C043: In 2018 a group at MIT
  https://api.crossref.org/works/10.1073/pnas.1802831115 ; https://math.mit.edu/~dunkel/Data/spaghetti/2018HeEtAl_PNAS.pdf : PNAS 2018; Patil, Stoop, Dunkel in MIT Mathematics, Heisser MIT Mechanical Engineering (now Cornell), with Villermaux (Aix-Marseille). Checker record: N2-claude.md:68, N2-codex.md:78.
• CONFIRMED C044: a problem that started as an undergraduate course project
  https://news.mit.edu/2018/mit-mathematicians-solve-age-old-spaghetti-mystery-0813 : "as a final project for 18.354 (Nonlinear Dynamics: Continuum Systems), a course taught by Dunkel"; "Ronald Heisser '16", an undergraduate in spring 2015. Checker record: N2-claude.md:69, N2-codex.md:79.
• CONFIRMED C045: found two honest ways to force the clean break Feynman wanted.
  https://math.mit.edu/~dunkel/Data/spaghetti/2018HeEtAl_PNAS.pdf : "we demonstrate controlled binary fracture of brittle elastic rods for two distinct protocols based on twisting and nonadiabatic quenching". Checker record: N2-claude.md:70, N2-codex.md:80.
• CONFIRMED C046: Twist the strand past about 250° before you bend it
  https://math.mit.edu/~dunkel/Data/spaghetti/2018HeEtAl_PNAS.pdf : "binary fracture for twist angles larger than ∼250°"; protocol: "twisted to a predetermined angle, and then bent". Checker record: N2-claude.md:76, N2-codex.md:86.
• CONFIRMED C047: Each fresh free end overshoots and re-breaks the rod
  https://mirror.explodie.org/why-spaghetti-do-not-break-in-half.pdf : "a burst of flexural waves is sent through the newly formed fragments ... allowing a cascading failure mechanism to take place". Checker record: N2-claude.md:78, N2-codex.md:88.
• CONFIRMED C048: The third panel assigns piece counts from fixed threshold comparisons.
  git show 60c91d8037:public/strata/why-spaghetti-wont-break-in-two/index.html : Retained the supported scope of the earlier confirmation; the triage correction takes precedence over its broader wording. "if(!crosses) pieces=2; ... else pieces = ov>1.7 ? 4 : 3;" and disclosed as a rendering. Checker record: N2-claude.md:80.
• CONFIRMED C049: The third panel draws its computed toy value and the chosen 1.12 threshold.
  git show 60c91d8037:public/strata/why-spaghetti-wont-break-in-two/index.html : Retained the supported scope of the earlier confirmation; the triage correction takes precedence over its broader wording. The bar is drawn at ov, the dashed line at KC = 1.12. Checker record: N2-claude.md:82.
• CONFIRMED C050: Flaws decide where the first break is
  https://mirror.explodie.org/why-spaghetti-do-not-break-in-half.pdf : "the location of this first failure point is that of the strongest defect". Checker record: N2-claude.md:88, N2-codex.md:98.
• CONFIRMED C051: The cascade is deterministic dynamics, not luck.
  https://mirror.explodie.org/why-spaghetti-do-not-break-in-half.pdf ; https://math.mit.edu/~dunkel/Data/spaghetti/2018HeEtAl_PNAS.pdf : A&N: breaking events collapse onto curvature records "without any adjustable parameters"; PNAS: "defects do not dominate the fracture statistics". (A&N also: "the failure delay and its location along the rod vary".) Checker record: N2-claude.md:89, N2-codex.md:99.
• CONFIRMED C052: the effect survives with perfectly uniform rods, and in simulation with no flaws at all.
  https://math.mit.edu/~dunkel/Data/spaghetti/2018HeEtAl_PNAS.pdf ; https://mirror.explodie.org/why-spaghetti-do-not-break-in-half.pdf : PNAS Fig. 2B: "Simulations also predict fracture in more than two pieces"; A&N Fig. 2: the overshoot in a flawless Kirchhoff simulation. Checker record: N2-claude.md:90, N2-codex.md:100.
• CONFIRMED C053: It isn't, much
  https://math.mit.edu/~dunkel/Data/spaghetti/2018HeEtAl_PNAS.pdf : "2r = 1.4 ± 0.05 mm" (about ±3.6%). Checker record: N2-claude.md:91, N2-codex.md:101.
• CONFIRMED C054: The slow, fundamental vibration keeps the curvature bounded by its starting value
  https://mirror.explodie.org/why-spaghetti-do-not-break-in-half.pdf : "This simple picture misleadingly suggests that, after the release of the rod, its curvature remains bounded by its initial value κ0 at all times". Checker record: N2-claude.md:92, N2-codex.md:102.
• CONFIRMED C055: Audoly and Neukirch say so explicitly.
  https://mirror.explodie.org/why-spaghetti-do-not-break-in-half.pdf : The same sentence. Checker record: N2-claude.md:93, N2-codex.md:103.
• CONFIRMED C056: The overshoot lives in the fast, fine part of the bending wave
  https://mirror.explodie.org/why-spaghetti-do-not-break-in-half.pdf : "sends a burst of flexural waves, something that is not captured by the fundamental mode only". Checker record: N2-claude.md:94, N2-codex.md:104.
• CONFIRMED C057: The midpoint logic gets the first break right for a hand-bent strand.
  https://news.mit.edu/2018/mit-mathematicians-solve-age-old-spaghetti-mystery-0813 : "it will break near the center, where it is most curved". Checker record: N2-claude.md:95, N2-codex.md:105.
• CONFIRMED C058: a bending wave overshoots the curvature to a universal 1.428×; and that re-breaks the rod before it can fall in two.
  https://mirror.explodie.org/why-spaghetti-do-not-break-in-half.pdf : 1.428 universal; "The limit curvature is therefore exceeded again at later time". The curvature coefficient is scoped to the intermediate self-similar regime, not all later times. Checker record: N2-claude.md:96, N2-codex.md:106.
• CONFIRMED C059: the Euler–Bernoulli beam equation and its dispersion ω = c·k² (group speed = 2× phase speed);
  git show 60c91d8037:research/why-spaghetti-wont-break-in-two/verify.mjs : Recreated: modes n = 1, 2, 3 return to cos(π) at t = π/ω, PASS. The group/phase check is a tautology (line 83). Checker record: N2-claude.md:98.
• CONFIRMED C060: The tested low-mode run has energy drift rounding to 0.000% over 20 000 steps.
  git show 60c91d8037:research/why-spaghetti-wont-break-in-two/verify.mjs : Retained the supported scope of the earlier confirmation; the triage correction takes precedence over its broader wording. Recreated: "energy drift over 20k steps < 1% (0.000%)". Checker record: N2-claude.md:99.
• CONFIRMED C061: reproduced from the special function;
  git show 60c91d8037:research/why-spaghetti-wont-break-in-two/verify.mjs : Recreated: "Fresnel sine integral peaks at z=1.4140 (√2=1.4142), S_max=0.71397". Checker record: N2-claude.md:100.
• CONFIRMED C062: a hand-bent strand's curvature peaks at its centre
  git show 60c91d8037:research/why-spaghetti-wont-break-in-two/verify.mjs : Analytic profile sin(πx) peaks at x = 0.5, PASS. Checker record: N2-claude.md:102.
• CONFIRMED C063: The solver integrates the linear beam equation.
  git show 60c91d8037:public/strata/why-spaghetti-wont-break-in-two/index.html : 5-point fourth-difference stencil, linear. Checker record: N2-claude.md:104.
• CONFIRMED C064: Real fracture is nonlinear, three-dimensional, and involves an actual crack tearing through the pasta
  https://math.mit.edu/~dunkel/Data/spaghetti/2018HeEtAl_PNAS.pdf : Nucleation "lasting ∼10 ms", "a fast catastrophic phase (∼10 µs)"; the damped Kirchhoff model is nonlinear. Checker record: N2-claude.md:105, N2-codex.md:115.
• CONFIRMED C065: none of which is here.
  git show 60c91d8037:public/strata/why-spaghetti-wont-break-in-two/index.html : No crack model in simulateRelease. Checker record: N2-claude.md:106.
• CONFIRMED C066: What the linear model captures is the trigger: the curvature overshoot that re-crosses the breaking threshold.
  git show 60c91d8037:public/strata/why-spaghetti-wont-break-in-two/index.html : Crossing test "f.prof[i]>KC*1.001". Checker record: N2-claude.md:107.
• CONFIRMED C067: That is exactly the quantity Audoly and Neukirch isolate as the cause of the secondary breaks
  https://mirror.explodie.org/why-spaghetti-do-not-break-in-half.pdf : "we argue that this counter-intuitive mechanism is responsible for the fragmentation of brittle rods under bending". Checker record: N2-claude.md:108, N2-codex.md:118.
• CONFIRMED C068: The third panel piece counts are illustrative, not a prediction of a particular strand.
  git show 60c91d8037:public/strata/why-spaghetti-wont-break-in-two/index.html : Retained the supported scope of the earlier confirmation; the triage correction takes precedence over its broader wording. Disclaimer matches the hard-coded counts. Checker record: N2-claude.md:109.
• CONFIRMED C069: W. Daniel Hillis, in No Ordinary Genius: The Illustrated Richard Feynman, ed. Christopher Sykes (W. W. Norton, 1994).
  https://openlibrary.org/isbn/0393036219.json ; https://archive.org/metadata/noordinarygenius00feyn : Open Library: "No ordinary genius: the illustrated Richard Feynman", "edited by Christopher Sykes.", Norton, New York, 1994 (ISBN 0393036219). Internet Archive noordinarygenius00feyn: Norton, 1994. (PNAS cites a 1996 printing.) Checker record: N2-claude.md:110, N2-codex.md:120.
• CONFIRMED C070: The wording is Hillis's recollection; we do not attribute it to Feynman directly.
  https://www.sciencenews.org/article/thats-way-spaghetti-crumbles ; https://kottke.org/18/08/solving-the-spaghetti-problem : Science News: "Hillis recalls, as quoted in the book No Ordinary Genius by Christopher Sykes (1994, W.W. Norton)". Checker record: N2-claude.md:111, N2-codex.md:121.
• CONFIRMED C071: attribution solid · page not verified
  git show 60c91d8037:research/why-spaghetti-wont-break-in-two/facts.md : "[attribution SOLID; page number UNCERTAIN]". PNAS ref. 31 gives "pp 180-181" if wanted. Checker record: N2-claude.md:112.
• CONFIRMED C072: B. Audoly & S. Neukirch, "Fragmentation of Rods by Cascading Cracks: Why Spaghetti Does Not Break in Half," Phys. Rev. Lett. 95, 095505 (2005). DOI 10.1103/PhysRevLett.95.095505.
  https://api.crossref.org/works/10.1103/PhysRevLett.95.095505 : Physical Review Letters 95(9), article 095505, issued 2005-08-25; title and both authors match. Checker record: N2-claude.md:113, N2-codex.md:123.
• CONFIRMED C073: Ig Nobel Prize in Physics, 2006.
  https://improbable.com/ig/winners/#ig2006 : 2006 winners, Physics (as line 18). Checker record: N2-claude.md:114, N2-codex.md:124.
• CONFIRMED C074: The 1.428× coefficient and its identity with twice the Fresnel-sine-integral maximum are stated in the paper.
  https://mirror.explodie.org/why-spaghetti-do-not-break-in-half.pdf ; https://researchportal.ip-paris.fr/en/publications/fragmentation-of-rods-by-cascading-cracks-why-spaghetti-does-not-/ : Stated in the authors' preprint (dated 22 December 2004); the published abstract matches it (IP Paris portal); the published body was not readable (APS challenge page). The curvature coefficient is scoped to the intermediate self-similar regime, not all later times. Checker record: N2-claude.md:115, N2-codex.md:125.
• CONFIRMED C075: R. H. Heisser, V. P. Patil, N. Stoop, E. Villermaux & J. Dunkel, "Controlling fracture cascades through twisting and quenching," PNAS 115(35), 8665–8670 (2018). DOI 10.1073/pnas.1802831115.
  https://api.crossref.org/works/10.1073/pnas.1802831115 : Volume 115, issue 35, pages 8665-8670, 2018; Ronald H. Heisser, Vishal P. Patil, Norbert Stoop, Emmanuel Villermaux, Jörn Dunkel. Checker record: N2-claude.md:116, N2-codex.md:126.
• CONFIRMED C076: Binary fracture dominates above a twist of ≈250°
  https://math.mit.edu/~dunkel/Data/spaghetti/2018HeEtAl_PNAS.pdf : Fig. 2E: "binary fracture dominates for twist angles larger than ∼250°". Checker record: N2-claude.md:117, N2-codex.md:127.
• CONFIRMED C077: the ~270° figure widely quoted is MIT's press framing for a specific 10-inch strand
  https://news.mit.edu/2018/mit-mathematicians-solve-age-old-spaghetti-mystery-0813 : "From his model, he found that, if a 10-inch-long spaghetti stick is first twisted by about 270 degrees and then bent, it will snap in two". Checker record: N2-claude.md:118, N2-codex.md:128.
• CONFIRMED C078: Dry-spaghetti diameter 1.4 mm and Young's modulus 3.8 GPa are from this paper.
  https://math.mit.edu/~dunkel/Data/spaghetti/2018HeEtAl_PNAS.pdf : "2r = 1.4 ± 0.05 mm, ρ = 1.5 ± 0.1 g/cm3, E = 3.8 ± 0.3 GPa". Checker record: N2-claude.md:119, N2-codex.md:129.
• CONFIRMED C079: K. F. Graff, Wave Motion in Elastic Solids (Dover, 1991);
  https://books.google.com/books/about/Wave_Motion_in_Elastic_Solids.html?id=5cZFRwLuhdQC : "Publisher Dover Publications, 1991". Checker record: N2-claude.md:120, N2-codex.md:130.
• CONFIRMED C080: L. D. Landau & E. M. Lifshitz, Theory of Elasticity (bending of rods).
  https://pierre.ag.gerard.web.ulb.be/textbooks/books/Landau_Lifshitz_T7.pdf : Title page: "THEORY OF ELASTICITY by L. D. LANDAU and E. M. LIFSHITZ"; §25 "Vibration of rods and plates", eqs. 25.10 to 25.12. The host's TLS chain is incomplete, which is why the tool's fetch failed. Checker record: N2-claude.md:121, N2-codex.md:131.
• CONFIRMED C081: The verifier recomputes selected beam and Fresnel results without reading page files.
  git show 60c91d8037:research/why-spaghetti-wont-break-in-two/verify.mjs : Retained the supported scope of the earlier confirmation; the triage correction takes precedence over its broader wording. Recreated by reading: verify.mjs has no import and reads no file. Checker record: N2-claude.md:122.
• CONFIRMED C082: The verifier does not read the page and cannot detect text or figure drift there.
  git show 60c91d8037:research/why-spaghetti-wont-break-in-two/verify.mjs : Retained the supported scope of the earlier confirmation; the triage correction takes precedence over its broader wording. It reads nothing from the page, so it cannot see a drifted figure. Checker record: N2-claude.md:124.
• CONFIRMED C083: It is published, and it runs on its own: one file, and Node.
  git show 60c91d8037:public/checks/manifest.json ; https://artwaste.land/checks/research/why-spaghetti-wont-break-in-two/verify.mjs : Recreated: curl into an empty directory (21,067 bytes, identical to the repository's), node verify.mjs: exit 0, 13/13, 29 s. Checker record: N2-claude.md:125.
• CONFIRMED C084: Bend a dry strand of spaghetti until it snaps and it almost never gives two pieces: it gives three, four, more, in a burst near the first crack.
  https://math.mit.edu/~dunkel/Data/spaghetti/2018HeEtAl_PNAS.pdf ; https://mirror.explodie.org/why-spaghetti-do-not-break-in-half.pdf : PNAS: "almost always to break into at least three pieces"; A&N: "three to ten pieces"; "near the first crack": Fig. 1D, second fracture 10 to 55 mm from the first. Checker record: N2-claude.md:128, N2-codex.md:138.
• CONFIRMED C085: Feynman spent an evening on it and gave up.
  https://kottke.org/18/08/solving-the-spaghetti-problem : "no real good theory about why spaghetti breaks in three". Checker record: N2-claude.md:129, N2-codex.md:139.
• CONFIRMED C086: A flexural wave is dispersive (ω = c·k², group speed twice phase speed)
  https://pierre.ag.gerard.web.ulb.be/textbooks/books/Landau_Lifshitz_T7.pdf : §25: "Thus the frequency is proportional to the square of the wave number"; rods: (25.11) ω = k²√(EI/ρS), (25.12) U = 2k√(EI/ρS), twice ω/k. Checker record: N2-claude.md:130, N2-codex.md:140.
• CONFIRMED C087: The overshoot is a universal number, 1.428 × the pre-break curvature
  https://mirror.explodie.org/why-spaghetti-do-not-break-in-half.pdf : "1.428 times its initial value κ0". The curvature coefficient is scoped to the intermediate self-similar regime, not all later times. Checker record: N2-claude.md:131, N2-codex.md:141.
• CONFIRMED C088: An immersive instrument integrates the real Euler–Bernoulli beam live
  git show 60c91d8037:public/strata/why-spaghetti-wont-break-in-two/index.html : simulateRelease runs in the browser on "Bend & break". Checker record: N2-claude.md:133.
• CONFIRMED C089: "datePublished":"2026-06-30"
  git log 60c91d8037 -- public/strata/why-spaghetti-wont-break-in-two/index.html : Commit 7595d28452 "Add stratum: Why Spaghetti Won't Break in Two", 2026-06-30. Checker record: N2-claude.md:135.
• CONFIRMED C090: A dry strand snaps into three, not two, because the first break sends a bending wave that overshoots the curvature to a universal 1.428×.
  https://mirror.explodie.org/why-spaghetti-do-not-break-in-half.pdf : "typically three or four"; 1.428. The curvature coefficient is scoped to the intermediate self-similar regime, not all later times. Checker record: N2-claude.md:137, N2-codex.md:147.
• CONFIRMED C091: the historical and experimental claims, with their confidence named
  git show 60c91d8037:research/why-spaghetti-wont-break-in-two/facts.md : "flags what is documented vs. anecdote vs. uncertain". Checker record: N2-claude.md:138.
• CONFIRMED C092: An immersive layer; it renders as its own standalone page at the `href` above
  git show 60c91d8037:public/strata/why-spaghetti-wont-break-in-two/index.html : A full standalone document; live page 200. Checker record: N2-claude.md:141.
• CONFIRMED C093: S(z) = 0.714
  git show 60c91d8037:public/strata/why-spaghetti-wont-break-in-two/index.html : Static "0.714"; on load the script writes S.toFixed(4) = "0.7140" (recreated). Checker record: N2-claude.md:142.
• CONFIRMED C094: z = 1.414 S(z) = 0.714 2·S = 1.428
  git show 60c91d8037:public/strata/why-spaghetti-wont-break-in-two/index.html : On load: 1.414, 0.7140, 1.4279 (recreated). The curvature coefficient is scoped to the intermediate self-similar regime, not all later times. Checker record: N2-claude.md:143.
• CONFIRMED C095: at the maximum (z=√2) → 1.428
  git show 60c91d8037:public/strata/why-spaghetti-wont-break-in-two/index.html : Shown when z is within 0.03 of √2. The curvature coefficient is scoped to the intermediate self-similar regime, not all later times. Checker record: N2-claude.md:144.
• CONFIRMED C096: past the peak, oscillating down
  git show 60c91d8037:public/strata/why-spaghetti-wont-break-in-two/index.html : Shown for z past √2 + 0.03. Checker record: N2-claude.md:145.
• CONFIRMED C097: The old page program printed holds (two pieces) when no crossing occurred in its short window.
  git show 60c91d8037:public/strata/why-spaghetti-wont-break-in-two/index.html ; recreated: simulateRelease copied from git show 60c91d8037:public/strata/why-spaghetti-wont-break-in-two/index.html : Retained the supported scope of the earlier confirmation; the triage correction takes precedence over its broader wording. τ = 1.1 run gives "holds (two pieces)". Confirmed only as a fact about the old program text; the new verdict makes no final-piece prediction. Checker record: N2-claude.md:146.
• CONFIRMED C098: The old page program printed breaks again when a crossing occurred in its short window.
  git show 60c91d8037:public/strata/why-spaghetti-wont-break-in-two/index.html ; recreated: simulateRelease copied from git show 60c91d8037:public/strata/why-spaghetti-wont-break-in-two/index.html : Retained the supported scope of the earlier confirmation; the triage correction takes precedence over its broader wording. τ = 0.15 and 0.002 runs give "breaks again". Confirmed only as a fact about the old program text; the new verdict makes no final-piece prediction. Checker record: N2-claude.md:147.
• CONFIRMED C099: A hanging chain finds its shape by storing the least energy
  https://galileoandeinstein.phys.virginia.edu/7010/CM_02_CalculusVariations.html : "The catenary is generated by minimizing the potential energy of the hanging chain". Checker record: N2-claude.md:150, N2-codex.md:160.
• CONFIRMED C100: caught in the microsecond after a break, when the stored bending energy is suddenly released and races off as a wave.
  https://mirror.explodie.org/why-spaghetti-do-not-break-in-half.pdf : Ts ∼ 1 µs release. Checker record: N2-claude.md:151, N2-codex.md:161.
• CONFIRMED C101: Spaghetti's secret lives in the opposite limit: the FAST, fine, high-wavenumber part of the bending wave, the part a slow fundamental vibration never reaches
  https://mirror.explodie.org/why-spaghetti-do-not-break-in-half.pdf : The fundamental-mode passage (line 78). Checker record: N2-claude.md:152, N2-codex.md:162.
• CONFIRMED C102: the path of least time.
  https://galileoandeinstein.phys.virginia.edu/7010/CM_02_CalculusVariations.html : "This optimal curve is called the brachistochrone, which is just the Greek for shortest time." Checker record: N2-claude.md:153, N2-codex.md:163.
• CONFIRMED C103: set with no free parameters by a self-similar wave.
  https://mirror.explodie.org/why-spaghetti-do-not-break-in-half.pdf : "a self-similar solution with no adjustable parameters". Checker record: N2-claude.md:154, N2-codex.md:164.
• CONFIRMED C104: The harmonograph draws with decaying pendulum swings
  git show 60c91d8037:src/content/strata/the-pendulums-pen.md : "watch two decaying pendulums weave a damped Lissajous figure". Checker record: N2-claude.md:155.
• CONFIRMED C105: Both run on the mechanics of a slender oscillating body.
  git show 60c91d8037:src/content/strata/the-pendulums-pen.md : A pendulum drawing machine. Checker record: N2-claude.md:156.
• CONFIRMED C106: A curve set by a sharp piece of mechanics, made operable.
  git show 60c91d8037:src/content/strata/the-quickest-way-down.md : "Times integrated live from the bead dynamics". Checker record: N2-claude.md:157.
• CONFIRMED C107: Both are the mechanics of a slender elastic filament, made operable.
  git show 60c91d8037:src/content/strata/why-knitting-stretches.md : "governed by the yarn's bending stiffness". Checker record: N2-claude.md:158.
• CONFIRMED C108: the fracture is not the loss of material but a sudden RELEASE of stored elastic energy that then races off as a wave.
  https://mirror.explodie.org/why-spaghetti-do-not-break-in-half.pdf : "we have shown that rods can break just because they are released". Checker record: N2-claude.md:159, N2-codex.md:169.
• CONFIRMED C109: Continues **P7**
  git show 60c91d8037:memory/log.d/2026-06-30T2350Z-why-spaghetti-wont-break-in-two.md : "(P7 / P19 / P1)". Checker record: N2-claude.md:160.
• CONFIRMED C110: the header's account of the waves this layer was made under (**P19**, and **P1**'s record-correcting spirit).
  git show 60c91d8037:memory/log.d/2026-06-30T2350Z-why-spaghetti-wont-break-in-two.md : The same header. Checker record: N2-claude.md:161.
• CONFIRMED C111: The first panel has a schematic strand above a computed curvature profile and a chosen breaking line.
  git show 60c91d8037:public/strata/why-spaghetti-wont-break-in-two/index.html : Retained the supported scope of the earlier confirmation; the triage correction takes precedence over its broader wording. The canvas draws the strand on top and the curvature profile with the κ_c line below. (The claim's vertical bars are written ¦ here.) Checker record: N2-claude.md:162.
• CONFIRMED C112: (added) "They do not explain why extra breaks reliably appear, nor why they cluster near the first."
  https://mirror.explodie.org/why-spaghetti-do-not-break-in-half.pdf; https://math.mit.edu/~dunkel/Data/spaghetti/2018HeEtAl_PNAS.pdf : Entry 152, added-flaws-not-cascade. The preprint demonstrates rupture by release alone and describes "Assuming the rod has no defect". The later paper follows bending-wave-induced fractures from the first fracture and gives a finite minimum fragment length. Thus flaws alone do not explain the wave-driven cascade. The source record included the first-break and deterministic clauses but omitted this checkable explanatory claim. Checker record: N2-codex.md:176.

What was done

• [declined] X1: NOT FIXED: listed MINOR, [declined]; Tier C: MINOR listed, not fixed.
• [fixed] X2: FIXED: narrowed integration and verification promises; identified panel 1 drawing as schematic and panel 3 as a hand-set threshold toy. Removed physical twist/quench labels from its controls and comments; retained numerical defaults.
• [fixed] X3: FIXED: narrowed integration and verification promises; identified panel 1 drawing as schematic and panel 3 as a hand-set threshold toy. Removed physical twist/quench labels from its controls and comments; retained numerical defaults.
• [fixed] X4: FIXED: removed the physical-release and universal 2× explanation from HTML, dek, fact notes and verifier. Labelled the finite-rod results with release times and observation windows; revised the verifier assertions.
• [fixed] X5: FIXED: scoped 1.428 to the intermediate regime in the body, equation, metadata, markdown, relates note and fact notes.
• [declined] X6: NOT FIXED: listed MINOR, [declined]; Tier C: MINOR listed, not fixed.
• [fixed] X7: FIXED: corrected the twist and quench explanations in the HTML, dek, markdown, fact notes and verifier comments. Removed the unsupported physical interpretation of the third panel and labelled its unchanged formulas as a toy.
• [fixed] X8: FIXED: corrected the twist and quench explanations in the HTML, dek, markdown, fact notes and verifier comments. Removed the unsupported physical interpretation of the third panel and labelled its unchanged formulas as a toy.
• [fixed] X9: FIXED: corrected the twist and quench explanations in the HTML, dek, markdown, fact notes and verifier comments. Removed the unsupported physical interpretation of the third panel and labelled its unchanged formulas as a toy.
• [fixed] X10: FIXED: corrected the twist and quench explanations in the HTML, dek, markdown, fact notes and verifier comments. Removed the unsupported physical interpretation of the third panel and labelled its unchanged formulas as a toy.
• [fixed] X11: FIXED: narrowed integration and verification promises; identified panel 1 drawing as schematic and panel 3 as a hand-set threshold toy. Removed physical twist/quench labels from its controls and comments; retained numerical defaults.
• [fixed] X12: FIXED: narrowed integration and verification promises; identified panel 1 drawing as schematic and panel 3 as a hand-set threshold toy. Removed physical twist/quench labels from its controls and comments; retained numerical defaults.
• [declined] X13: NOT FIXED: listed MINOR, [declined]; Tier C: MINOR listed, not fixed.
• [fixed] X14: FIXED: corrected the twist and quench explanations in the HTML, dek, markdown, fact notes and verifier comments. Removed the unsupported physical interpretation of the third panel and labelled its unchanged formulas as a toy.
• [dated] X15: FIXED: set JSON-LD dateModified to 2026-10-01; added an Updated line explaining the original date and this revision, mirrored in markdown.
• [fixed] X16: FIXED: narrowed integration and verification promises; identified panel 1 drawing as schematic and panel 3 as a hand-set threshold toy. Removed physical twist/quench labels from its controls and comments; retained numerical defaults.
• [declined] X17: NOT FIXED: listed MINOR, [declined]; initial τ and the selected button remain unchanged. Tier C: MINOR listed, not fixed.
• [fixed] K1: FIXED: changed went to bed to ended up. MINOR only, so no dated correction line was added for this item.
• [fixed] K2: FIXED: narrowed integration and verification promises; identified panel 1 drawing as schematic and panel 3 as a hand-set threshold toy. Removed physical twist/quench labels from its controls and comments; retained numerical defaults.
• [fixed] K3: FIXED: narrowed integration and verification promises; identified panel 1 drawing as schematic and panel 3 as a hand-set threshold toy. Removed physical twist/quench labels from its controls and comments; retained numerical defaults.
• [fixed] K4: FIXED: removed the physical-release and universal 2× explanation from HTML, dek, fact notes and verifier. Labelled the finite-rod results with release times and observation windows; revised the verifier assertions.
• [fixed] K5: FIXED: removed the physical-release and universal 2× explanation from HTML, dek, fact notes and verifier. Labelled the finite-rod results with release times and observation windows; revised the verifier assertions.
• [fixed] K6: FIXED: replaced the no-second-break and two-piece conclusions with the actual time-window observation, including the live verdict. The verifier now asserts the extended crossing rather than elimination of overshoot.
• [fixed] K7: FIXED: scoped 1.428 to the intermediate regime in the body, equation, metadata, markdown, relates note and fact notes.
• [declined] K8: NOT FIXED: listed MINOR, [declined]; Tier C: MINOR listed, not fixed.
• [fixed] K9: FIXED: corrected the twist and quench explanations in the HTML, dek, markdown, fact notes and verifier comments. Removed the unsupported physical interpretation of the third panel and labelled its unchanged formulas as a toy.
• [fixed] K10: FIXED: corrected the twist and quench explanations in the HTML, dek, markdown, fact notes and verifier comments. Removed the unsupported physical interpretation of the third panel and labelled its unchanged formulas as a toy.
• [fixed] K11: FIXED: corrected the twist and quench explanations in the HTML, dek, markdown, fact notes and verifier comments. Removed the unsupported physical interpretation of the third panel and labelled its unchanged formulas as a toy.
• [fixed] K12: FIXED: corrected the twist and quench explanations in the HTML, dek, markdown, fact notes and verifier comments. Removed the unsupported physical interpretation of the third panel and labelled its unchanged formulas as a toy.
• [fixed] K13: FIXED: corrected the twist and quench explanations in the HTML, dek, markdown, fact notes and verifier comments. Removed the unsupported physical interpretation of the third panel and labelled its unchanged formulas as a toy.
• [fixed] K14: FIXED: corrected the twist and quench explanations in the HTML, dek, markdown, fact notes and verifier comments. Removed the unsupported physical interpretation of the third panel and labelled its unchanged formulas as a toy.
• [fixed] K15: FIXED: corrected the twist and quench explanations in the HTML, dek, markdown, fact notes and verifier comments. Removed the unsupported physical interpretation of the third panel and labelled its unchanged formulas as a toy.
• [fixed] K16: FIXED: narrowed integration and verification promises; identified panel 1 drawing as schematic and panel 3 as a hand-set threshold toy. Removed physical twist/quench labels from its controls and comments; retained numerical defaults.
• [fixed] K17: FIXED: narrowed integration and verification promises; identified panel 1 drawing as schematic and panel 3 as a hand-set threshold toy. Removed physical twist/quench labels from its controls and comments; retained numerical defaults.
• [fixed] K18: FIXED: removed the physical-release and universal 2× explanation from HTML, dek, fact notes and verifier. Labelled the finite-rod results with release times and observation windows; revised the verifier assertions.
• [fixed] K19: FIXED: replaced the no-second-break and two-piece conclusions with the actual time-window observation, including the live verdict. The verifier now asserts the extended crossing rather than elimination of overshoot.
• [fixed] K20: FIXED: corrected the twist and quench explanations in the HTML, dek, markdown, fact notes and verifier comments. Removed the unsupported physical interpretation of the third panel and labelled its unchanged formulas as a toy.
• [dated] K21: FIXED: set JSON-LD dateModified to 2026-10-01; added an Updated line explaining the original date and this revision, mirrored in markdown.
• [fixed] K22: FIXED: narrowed integration and verification promises; identified panel 1 drawing as schematic and panel 3 as a hand-set threshold toy. Removed physical twist/quench labels from its controls and comments; retained numerical defaults.
• [declined] K23: NOT FIXED: listed MINOR, [declined]; Tier C: MINOR listed, not fixed.
• [declined] K24: NOT FIXED: listed MINOR, [declined]; Tier C: MINOR listed, not fixed.
• [fixed] K25: FIXED: corrected the twist and quench explanations in the HTML, dek, markdown, fact notes and verifier comments. Removed the unsupported physical interpretation of the third panel and labelled its unchanged formulas as a toy.