[Physics]: tunnelling 'settled' marks T as readable when it is far from the closed form

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@danielw-sudo がすでに取り組んでいます。

2026年11月7日 から。

  • #59 @danielw-sudo による — オープン

評価

難易度
5/5
見積もり時間
1週間以上
初心者へのやさしさ
25/100
issue の種類
バグ
明瞭さ
明確に書かれている
活発さ
停滞
技術スタック
react, typescript
領域
computer-graphics, testing

調査の方向性

Read closedForm.test.ts, USER_GUIDE.md, and docs/ARCHITECTURE.md, then inspect the simulation’s settled-state logic and the preset in RoadmapDeck.tsx. Reproduce the reported slider cases against the packet closed form and identify how initial packet overlap and the finite box or grid affect the readings. Done means agreeing on a physics fix, validating the listed cases, and re-measuring the guide’s -6.1 slope; an open linked PR already covers this issue.

索引モデルが issue の本文から書いたものです。

説明

physics-review

Found while closing #51 in PR #56 (Claude Opus 5.5, 2026-11-06). The card says settled: ready to read while T is far from the closed form, at slider values a learner can set, including the guide's own lab protocol and a shipped preset. USER_GUIDE.md and the lab protocol both tell learners to read T when the card says settled.

docs/ARCHITECTURE.md already recorded part of this as a limit, for settings with exact T above 1e-4. The overlap below, and its reach into the lab sweep, were not recorded.

Where a learner meets it
  • Guide lab sweep, E=3, V0=9, sigma=1.2: settled T is +2.4 % at d=1.2, +5.1 % at d=1.3, +10.9 % at d=1.4, +23.3 % at d=1.5, against the packet closed form.
  • The slope the guide states: ln T against d is given as -6.1. The closed form gives -6.21 over d = 0.5 to 1.5. The existing test holds -6.1 to 3 %, so it does not separate them.
  • Preset in RoadmapDeck.tsx, E=5, V0=12, d=2, sigma=0.9: settled T reads -15.3 % (0.000308 against 0.000364).
How it was measured

Grid of 1155 slider settings: E in {1, 2, 3, 5, 8, 10, 12}, V0 in {4, 8, 12, 16, 20}, d in {0.2, 0.6, 1, 1.5, 2.5}, sigma in {0.5, 0.9, 1.2, 1.4, 1.6, 1.8, 2}, skipping E = V0, at the app's 200 Hz step on 719 points. Each settled step was compared with the Gaussian-weighted rectangular-barrier sum, the same packet() that closedForm.test.ts uses.

512 settings settle. 132 of them read more than 3 % off while marked settled (82 high, 50 low; 35 by more than a factor of 2). An independent re-run reproduced 132 of 512 exactly.

Fault 1: T too high, up to about 2300 times

The packet starts at x = -5, so a wide packet already overlaps the barrier at t = 0. That tail is not tunnelling, but it comes out on the right and is counted in T.

Estimate: half the probability at or beyond the barrier's left edge, Q((5 - d/2) / sigma) / 2. For E=5, V0=20, d=1.5, sigma=1.4 that gives 6e-4; the engine reads 5.5e-4 against a closed form of 3.1e-7.

Reviewer's test, in a scratch copy: starting the packet far away (x = -25 in a +-80 box) removes the high reading in all 82 cases. That setting goes from 5.5e-4 to 3.16e-7, and the lab sweep at d=1.5 goes from +23 % to -0.13 %. Fourteen of the 82 then read 3 to 21 % low instead, so they are in fault 2 too.

E V0 d sigma closed form settled reading ratio (worst step)
5 20 2.5 0.9 1.5e-9 3.5e-6 2300
5 20 1.5 1.4 3.1e-7 5.5e-4 1760
3 20 1.5 1.2 7.4e-8 3.4e-5 460
5 16 1.5 1.4 4.1e-6 5.8e-4 140
3 12 1.5 1.2 1.6e-5 7.2e-5 3.7
Fault 2: T too low

Fifty settings read low. Most stay off to their last settled step, so waiting on the card does not cure it.

E V0 d sigma closed form first settled last settled
12 20 2.5 0.9 0.00197 0.00103 0.00121
8 20 2.5 0.5 0.00498 0.00365 0.00392
12 20 1.5 0.9 0.00201 0.00161 0.00178
12 16 1.5 1.2 0.0134 0.0111 0.0117

Cause not fully established. Reviewer's scratch measurements point to two parts, not re-run by me:

  • The box ends the run early: settled fires before the slow part of the packet has finished crossing. E=2, V0=16, d=0.2, sigma=0.5 goes from -8.3 % to -2.2 % in a +-80 box.
  • Grid size: E=12, V0=16, d=1.5 goes from -8.2 % to -4.4 % in the big box, then to -1.2 % at half the cell.
What a fix has to decide

Any fix changes physics output, so it needs a reviewer from another model family (Art. 1.4). Options, not yet chosen:

  • Keep the mark off when the estimated initial tail is not small against T. The numbers shown do not change, but the lab sweep's thin end would stop settling.
  • Start wide packets further left. initialX and barrierPosition were kept fixed by owner decision in #41, so this reopens that decision, and the box may have to grow.
  • For fault 2: a larger box, a finer grid (speed cost), or a stated accuracy limit in the guide.
  • Either way the guide's -6.1 needs re-measuring.

closedForm.test.ts records which cases it holds; its list avoids both faults on purpose, so it does not guard against them. Once fixed, the lab sweep's d=1.5 and the cases above should join its readable list.

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TypeScript
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マージ済み PR（30日）
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