# Retention time under a stated thermal model
Evidence type: worked calculation and synthetic sensitivity analysis. 2026-10-20.

## Reproduce
Requires Node.js with ES modules / node:test and Python 3. No third-party dependencies.
Run in this directory:
```sh
node generate.mjs
node --test test.mjs
python3 verify_decimal.py
```
results.json is generated; do not hand-edit numerical outputs.
The article imports calculate.mjs and cases.json, not a second transcription.

## Definition and units
For exposure temperature T and reference temperature R, both in kelvin:
M(T,R,E) = exp((E/k) * (1/R - 1/T)).
Equivalent seconds = sum(durationSeconds_i * M_i).
M explicitly means t_reference/t_exposure. Check ratio and sign before copying formulas with an acceleration-factor label.
k = 1.380649e-23 J/K divided by 1.602176634e-19 J/eV, exact SI defining constants.
Celsius conversion: +273.15. Day: 86400 s. Months are not fixed-duration units here.

## Source map and assumptions
HotStorage 2024 section 4 supplies six five-minute exposures at 120 C, a 25 C reference, and assumed E=1 eV. The hot-plateau-only calculation gives about 253 days, consistent with its approximate eight-month description.
Cooling/read durations and temperature ramps are not numerically specified there; their thermal contribution is not reconstructed.
The 0.9 and 1.1 eV alternatives are hypothetical choices, NOT confidence limits or measured energies for those chips.
Both 24-hour histories are synthetic. Equal 40 C means give about 6.45 vs 18.05 equivalent days at 25 C with E=1 eV, ratio about 2.80.

HeatWatch section 4.2 reports fitted E=1.04 eV (95% CI 1.01-1.08 eV; R-squared 0.76) over 20-70 C and 1000-10000 P/E cycles for its studied charge-trap NAND.
This does not calibrate the 2024 floating-gate devices or validate a 120 C extrapolation. Section 5.2 retains thermal history using piecewise integration.
Do not turn its parameter interval into a shelf-life interval for another device.

The model assumes one fixed energy and additive intervals independent of order. It excludes program/read temperature effects, dwell-dependent recovery, refresh and ECC.
This is not a HeatWatch re-fit, full-model reproduction, hardware experiment, failure probability or supported SSD storage interval.

## Primary sources
- Luo et al., HeatWatch, HPCA 2018, sections 4.2/5.2. DOI 10.1109/HPCA.2018.00050. https://www.cs.cmu.edu/~yixinluo/index_files/heatwatch_hpca18.pdf
- Buddhanoy, Pasricha and Ray, Life-after-Death, HotStorage 2024, section 4. DOI 10.1145/3655038.3665949. https://api.mountainscholar.org/server/api/core/bitstreams/887b83b2-df99-4ea8-98df-a4dbf5cfca5a/content
- BIPM, SI Brochure, ninth edition, defining constants and temperature units. https://www.bipm.org/en/publications/si-brochure

Accessed 2026-10-20. Papers are linked, not redistributed. Code and calculations are authored by Hesela; no third-party raw dataset is claimed.

## Numerical contract
Inputs use finite JavaScript numbers, degrees Celsius, seconds and electronvolts.
The module rejects nonpositive absolute temperature, negative energy/duration,
nonrepresentable multipliers, overflow and positive contributions rounded to zero.
Equal temperatures preserve duration even at extreme finite energy inputs.
Tests also check subdivision, order independence and changing the reference
clock. These are properties of this fixed-energy model, not NAND validation.