zero-trust-physics/zero-trust-physics-li-ion-cells

Lithium-ion cells: voltage, temperature and thermal runaway, computed again with a proof on every row

Battery programs qualify a cell model on two questions: does its voltage follow the measured cell through the discharges and drive cycles it will see, from -20 to 40 degC, and when does an abused cell run away. Here are 252 runs of three models of real cells, each computed again with a cryptographic proof on every row, beside the laboratory's measurements: every published discharge and drive cycle of three Tesla Model 3 2170 cells (234 runs), eleven 1C discharges of a Panasonic NCR18650PF cell, and an 18650 LiCoO2 cell heated in an oven.

Over the 234 runs of the 2170 cells, the model's terminal voltage is within 19.4 mV RMS of the measured voltage, pooled over every compared second; with each cell left out of the fit in turn, the record gives 20.2 mV. On the eleven 18650PF discharges, which the model was not fitted on, 27.7 to 29.9 mV RMS (target 50), and the delivered capacity to 2.5 V within +0.04 percent (target 3).

Zero-Trust Physics is a physics verifier for Super Intelligence (SI). SI agents ask it questions about real hardware, and every answer comes with a cryptographic proof, so any agent can run it again and get the same thing. Past what a model was compared with, it keeps going with the same equations and flags every step. It stops only at a physical limit, or where its equations, constants or tables no longer hold, and it names the reason.

https://mcp.zerotrustphysics.com/mcp Open to any agent.

What is in it

252 rows of three models, each model's rows under its own dataset seals:

Model	Rows	Frames	Dataset seal
Tesla Model 3 2170 cell	234	1,494,596	32 sealed parts, one for each cell and test temperature or less (table under Files)
Panasonic NCR18650PF cell	11	32,228	946fbe7a8ba9340aa24727acad259d10b37512e2141bb700a30023b5f590384aff699ae9a4eaeed378c11d19b01f3789
18650 LiCoO2 cell, thermal runaway	7	7,476	ae8bbf9803d39a9a2d242b2c02d77f34279c30ba746d297905e293ea0f260644a41405dcc716435bdbe7e725b5ba5a8c

• Tesla Model 3 2170, cells m80, m1000 and m448-N, 234 rows: every held-current discharge (C/3, C/2, 1C) and drive cycle the laboratory published for the three cells at 40, 25, 10, 0, -10 and -20 degC, 78 a cell. Each row is the record's logged current and case temperature, one value a second, from a rested cell at the state of charge and capacity of its last full charge. Outcomes: 159 ran to the end of the record, 73 reached 2.8 V (the discharges, which end there by the record's rule) and 2 reached 4.242 V on regenerative charging.
• Panasonic NCR18650PF, 11 rows: the cell's 1C discharges at 25 degC from full charge: one to the 2.5 V cutoff, and ten of 2.31 Ah from one file of repeated discharges, each at its held current (2.899 to 2.900 A), the logged current second by second in steps of 0.1 s.
• 18650 LiCoO2 thermal runaway, 7 rows: a fresh, fully charged cell from 28 degC in ovens held at 140, 145, 150, 155 and 170 degC for 240 min (the 145, 150 and 155 degC ovens are Hatchard's tests), and two heaters for 30 min from 25 degC: 20 W with the cell in a room at 25 degC, and 25 W adiabatic.

Each config's index view has one line a row: its inputs, its outcome and its comparison with the record. cell_2170_model3_summary pools the 2170 comparison by temperature and rate. The _rows configs are the sealed rows themselves, written by the engine's Parquet converter only after each sealed set verified; the frames are beside them in data/frames.parquet.

How close it comes to the measurements

Tesla Model 3 2170, 234 runs. Model minus measured terminal voltage at the logged samples of each run's scored span, RMS pooled over every compared second, mV. The model was fitted on all 234 runs; these are the fitted figures.

Case temperature	C/3	C/2	1C	Drive cycles (30)
40 degC	9.3	24.2	18.4	13.5
25 degC	16.0	18.6	22.3	12.4
10 degC	21.2	21.3	16.4	15.5
0 degC	19.7	20.2	23.1	20.4
-10 degC	31.1	38.0	36.0	24.9
-20 degC	67.4	51.7	49.9	42.7

All 234: 19.4 mV; at -10 and -20 degC together, 32.7 mV. With each cell left out of the fit in turn, the record's figures are 20.2 mV over all 234, and at -20 degC 67.9, 47.9, 68.7 and 47.0 mV at C/3, C/2, 1C and on drive cycles; those come from constants refitted without the cell and are not computed from these rows. Gap: the 1C discharge at -20 degC, 68.7 mV with the cell left out. Runs longer than 10,000 s are recorded every 2 to 5 s (a run records at most 10,000 frames); their comparison is taken at the recorded seconds and weighted by the seconds they stand for.

Panasonic NCR18650PF, 11 discharges not in the fit (the model was fitted on the cell's low-rate and pulse tests).

Discharge	Voltage RMS, mV	Mean, mV	Largest, mV
03-10-17 Dis1C_2, full discharge to 2.5 V	27.7	-11.3	-52.9
03-09-17 Dis1C_Rp, discharge 1 of 10 (2.31 Ah)	28.7	-23.1	-56.5
03-09-17 Dis1C_Rp, discharge 2 of 10 (2.31 Ah)	29.6	-23.9	-57.5
03-09-17 Dis1C_Rp, discharge 3 of 10 (2.31 Ah)	29.9	-24.1	-57.5
03-09-17 Dis1C_Rp, discharge 4 of 10 (2.31 Ah)	29.9	-23.9	-57.5
03-09-17 Dis1C_Rp, discharge 5 of 10 (2.31 Ah)	29.6	-23.3	-56.8
03-09-17 Dis1C_Rp, discharge 6 of 10 (2.31 Ah)	29.3	-22.8	-56.2
03-09-17 Dis1C_Rp, discharge 7 of 10 (2.31 Ah)	28.9	-22.1	-55.8
03-09-17 Dis1C_Rp, discharge 8 of 10 (2.31 Ah)	28.4	-21.0	-54.9
03-09-17 Dis1C_Rp, discharge 9 of 10 (2.31 Ah)	28.2	-20.6	-54.2
03-09-17 Dis1C_Rp, discharge 10 of 10 (2.31 Ah)	27.7	-19.7	-53.6

Target 50 mV RMS on each. The full discharge reaches 2.5 V at 3427.9 s against 3426.6 s measured: 2.7608 Ah against 2.7597 Ah, +0.04 percent (target 3). The model's own comparison states 27.8 to 30.0 mV; these rows give 27.7 to 29.9, compared from the first recorded second. Gap, from the record and not in these rows: a discharge at 0.87 A in 14 holds, 56.7 mV RMS.

18650 LiCoO2 in an oven. The model's seven constants were fitted on all 13 open records of LiCoO2 18650 cells. Hatchard's three ovens, from 28 degC:

Oven	Measured (Hatchard et al. 2001)	Model, these rows
155 degC	20 K/min reached at 51.1 min; vent at 41.3 min	20 K/min at 62.0 min; vent at 38.2 min
150 degC	no runaway within 120 min	20 K/min at 109.7 min
145 degC	peaks at 148.0 degC, no runaway	peaks at 148.0 degC, no runaway

Gap: at 150 degC the model runs away at 109.7 min where Hatchard's cell did not within 120 min, and at 155 degC it is 10.9 min late. Over the oven sweep the time to 20 K/min falls from 109.7 min at 150 degC to 26.5 min at 170 degC; at 140 and 145 degC the cell does not run away in 240 min. The 25 W adiabatic heater ends when every reactant is consumed, at 1277 degC.

One row

Row 0 of the 18650PF set is the full discharge of 10 March 2017: a rested cell at full charge, held at 2.899387 A, the logged current second by second, ten steps of 0.1 s a second. Outcome refused with UndervoltageCutoff after 34,279 steps: the cell reached 2.5 V, the end the model declares, and the state past it is not sealed. Voltage 27.7 mV RMS against the measured trace. Run seal:

e53ca7b975e2bcb948681f404e1177904aee13a63757689c174a40b6c328e92c3cb000d2248966c86823b0e7d413cf14

Use it

The models are served at the open address as energy/cell_2170_model3, energy/cell_18650pf and energy/runaway_18650_lco. Every row's request in sealed/rows.jsonl is a run_trajectory request (less domain and card, which the head's request carries): send it and compare the run_seal. Add "readout": {"quantities": ["terminal_v"]} to read the voltage at every recorded step in full precision; a readout is not part of the sealed request, and the run seal is the same.

Verify it yourself

Every row can be verified without trusting this page.

# 1. each sealed set, with no engine running: the seal of every row, its chain of frames and the root
genesis_seal verify-dataset cell_18650pf/sealed/head.json cell_18650pf/sealed/rows.jsonl cell_18650pf/sealed/frames.bin
genesis_seal verify-dataset runaway_18650_lco/sealed/head.json runaway_18650_lco/sealed/rows.jsonl runaway_18650_lco/sealed/frames.bin
for p in cell_2170_model3/part_*; do genesis_seal verify-dataset $p/sealed/head.json $p/sealed/rows.jsonl $p/sealed/frames.bin; done

# 2. one row's proof on its own
genesis_seal row-proof cell_18650pf/sealed/head.json cell_18650pf/sealed/rows.jsonl 0 cell_18650pf/sealed/frames.bin > row0.json
genesis_seal verify-proof row0.json

# 3. the operator's signatures (each at its issue time; a signature is good for 3,600 s)
genesis_seal verify-signature runaway_18650_lco/signed/signed_000.head.json --public-key answer_key_public.b64 --now <its issued_at>
gunzip -k cell_18650pf/signed/row_000.json.gz
genesis_seal verify-signature cell_18650pf/signed/row_000.json --public-key answer_key_public.b64 --now <its issued_at>

answer_key_public.b64 is the public_key field of the operator's answer key, published at https://mcp.zerotrustphysics.com/answer-key; a copy is in this repository. genesis_seal is built from the engine's public source.

4. Ask the engine to run a sealed set again: send verify_dataset the head's request with its dataset_seal.

When this dataset was made, for each of the 34 sealed sets: verify_dataset by the stored seal held; verify_dataset's short form on a fresh engine, the plan run again, held with the same seal; genesis_seal verify-dataset held; one row's proof on its own held; and up to 6 rows sent to run_trajectory again gave the same run seal. Every row was also sent again with a readout for the comparison, and every one gave its own run seal.

Signed

The row seals and the dataset seals were computed by the served engine build, run locally. The operator's ML-DSA-87 signature (key ID ca06027a972c81c8630fed9f4ea2d4e91596b9434a88a03b7eb325b24e40645b7090cb705927745e73ee8b272eb1be38, an expiry of 3,600 s and a nonce; with SHA-384, the CNSA 2.0 algorithms) comes from the open address, in two forms:

• Thermal runaway, a signed dataset head. The same 7-row plan was sent to the open address in two parts (rows 0 to 3, 4 to 6). Each answer's head is signed; it carries the merkle_root and rows_sha384 over its rows' run seals, and those run seals equal the stored rows', 7 of 7. The rows are not signed one by one: runaway_18650_lco/signed/signed_000.head.json and signed_001.head.json.
• 2170 and 18650PF, a signed answer for each row. A plan's inline head repeats every request, and a request of these cells is one value a second, so the head would pass the open address's 40,000-character answer. Each row's request was therefore sent alone to run_trajectory at the open address, and each answer came back signed over its receipt with the same run seal as the stored row: 18650PF 11 of 11, 2170 234 of 234. The signed answers are in each set's signed/ folder, gzipped (row_<row>.json.gz), with row_summary.json.

Files

Path	What it holds
<set>/sealed/head.json, rows.jsonl, frames.bin	each sealed set as the engine stored it: the head (request, counts, root, seal), every row (request, outcome, final state, run seal) and every recorded frame, 64 bytes each
<set>/data/index.parquet, index.csv	one line a row, with the comparison
<set>/data/rows.parquet, frames.parquet	the sealed rows and frames as Parquet
cell_2170_model3/data/summary.parquet, summary.csv	the 2170 comparison pooled by temperature and rate
<set>/signed/	the signed heads or signed answers from the open address, and their summary
answer_key_public.b64	the operator's public answer key, SHA-256 507ef857d3d95be7b15f86722b628e7e110be1eb61564eef6cb76f8bb4f8660a

Head SHA-256
cell_18650pf/sealed/head.json	d0cdd32c23e04497abd2cf4d6b05a50f24f9420f16bccfb1a3e8c22b81558792
runaway_18650_lco/sealed/head.json	947600edf042812f2224f1fdb77675fffaeade6eefe896ca301c7bbf524bf814

The 2170 parts:

Part	Rows	Cells and blocks	Dataset seal
cell_2170_model3/part_00	7	m80 40C	6dce9652d212d4a18bdad05b3395781da0054241b436ec5c7c5e289c7a97ac7edbf93e733c7efd373b29b2e976a4c4b7
cell_2170_model3/part_01	6	m80 40C	e316a05820794fbde9b6ea8c5e395d4e31d20fcd7aac2a24def8e04c1ff8304a83ef885a9c165c51a6d876a5042e7b99
cell_2170_model3/part_02	6	m80 25C	6c2aa83c2a0949dde9f0905f7a8655486f763478f68a3842610a1a1b634788f9f8a8a40df71d9a9d10d94f5f9ef36503
cell_2170_model3/part_03	4	m80 25C	971d5579104379ce96263a94397da36592797e09be837bf60a453496e86700998a198dc123485e2c2bd01ac057e7e507
cell_2170_model3/part_04	3	m80 25C	d60f8aaf53821ba74a42f0edb6166c5d1c1516224028048e99caf189cd369231830b6609e3440978442d14c7bc93b8c2
cell_2170_model3/part_05	8	m80 10C	7684547abbfdf013d6bbf4de54bb682daa4c18739d2a3a278c38fe4a90d712dcf5be06bbfabefd17b57f87805144b4f0
cell_2170_model3/part_06	5	m80 10C	d9db4776fa98b2654295dfdaa7d2d4a6f36ce5faf55f9e9eb44d0152f9d129f5a2ba18543e430f9947cc635e3492cff7
cell_2170_model3/part_07	9	m80 0C	8ef97609ee8ee4bc95cf2f1f7814c80e8d9330e8a61ccf06cdb5d6d0904f7efdd0ff483dc3f123cffbcd61abb5848ea8
cell_2170_model3/part_08	4	m80 0C	571161470bf85be634adf0a68e3124cef3c227af6d0d0ebe2269dbf7629a7c90ef4a624e327805f26e11fe2e710f21ed
cell_2170_model3/part_09	13	m80 -10C	e80a68622f420bab9d3553f034134911340b3759da17542e82f81139aa2e084a77c1827be67779a490adb0ce1e9e7c14
cell_2170_model3/part_10	13	m80 -20C	6be7a23f0464c477be158457f30312097b06142575fc87f6a071c8e8927451abb5685084ec63c183e31c2b25b38792bd
cell_2170_model3/part_11	8	m1000 40C	2b466bc643ada79b55590824f1663f26164fa8ef462bb8d062cba3e9a93a91faa3bad3001075bcf5e46dac65311cc16c
cell_2170_model3/part_12	5	m1000 40C	a75685ac3548ed6e93951a44cafbc43376e8840af15e0b14715cf9385b26692397d1b961c78411bcf377f765bcb196f2
cell_2170_model3/part_13	7	m1000 25C	4dd7d6cdd766746bf61d0d7c58fdbe32e7acf77577f6932e983cd1d60a737eb6553053a087b3f44c9ae084cb569029cf
cell_2170_model3/part_14	6	m1000 25C	cf7d067e42ac9f39b656a0ca50eedf9342fd3d27e8185dfc267de341fc84fcc090d4d23ef2381faeb245f5faa0dd60cf
cell_2170_model3/part_15	8	m1000 10C	1e3dfcd7253bb769b2d78351c66353b80dbedde92d688d640cb75e8991256ba1cbce5a1b0bb3cb5e82c859a01e6e573d
cell_2170_model3/part_16	5	m1000 10C	acc270587f9f540a0f3380a7c6612f9cdf96dd270ea0b93eeb296147281d3ff8d9a6910374291beca0f0f925ba0fb644
cell_2170_model3/part_17	10	m1000 0C	6cdcfe7b906000c0a4bb2c3556e07e37c3e6ba097f5336e03466472a01679baac0e26ad4b13d3282f4576c6dafe1fbdc
cell_2170_model3/part_18	3	m1000 0C	409db073663bf10df25e83e8138572a7c66f3a020ffd8aa36e7f61b522ed645e35864e1cee50d5b7e630cbe1bdaed62e
cell_2170_model3/part_19	13	m1000 -10C	33f3a88b7ddf529edd947899cbc7418e0abdccd2da54ff9059f702b0b770194c3b2bb7c3fe810a306b0eda9dc018f241
cell_2170_model3/part_20	13	m1000 -20C	a5a8502e6c820fc8f80bc0e366115886db62ebd4905ffbe7c43d9d168ee32a7cd1342f2353b79cede75caa7d551adbe2
cell_2170_model3/part_21	7	m448-N 40C	af60ce204d3c272c20b344e1bc67bbc8768aed7fc9edeac9e9b1cffceb2f43c2c2d87f9e063a635871e46caa1f88801e
cell_2170_model3/part_22	6	m448-N 40C	d70042219ff5c5593d614875e66376b96165dc339d55ea03b5ae808e2f875680e32c65484bf7097736b0bac914589ca0
cell_2170_model3/part_23	7	m448-N 25C	aa0f3346b323c86746a5574639024255e37004cae028e39347573bdf353c6df47177189e3bab791ef8554209b05b3504
cell_2170_model3/part_24	6	m448-N 25C	cec51fb409f10ab7ac356f4b886864173f586997cd75937a29333891149a58777f8ba52ad979d0a14da7c31f950e8bc9
cell_2170_model3/part_25	8	m448-N 10C	8a3eda579c939d604e39e4d0cb616c28bca185a8a852ae47534ab98a645d564f08085b95035b9c8ee9fdfd5be358972f
cell_2170_model3/part_26	5	m448-N 10C	2c6aa74d8d584c24465514beffbab51bd38eb844ff56e3d619f7e27ed37e3c3a129f5aa03fb2a6ceaa34c2d5cf42fecf
cell_2170_model3/part_27	8	m448-N 0C	44f305b7d25284242dbcf4872ed2a9a1f4ab821fa4471fbcfe3f7309e3901c3cc4a8a2cc735647b60eacc7e08325dca6
cell_2170_model3/part_28	5	m448-N 0C	f4a3c8594c894e7647f196e196df4733cb0010292d99482cc1aac146087c0495e81ce95c57977bed1bdc17f024f90f66
cell_2170_model3/part_29	9	m448-N -10C	122a277f97c38e9a10a64a10eac4bc6f2cf05f1873a7b538586036a9abb4c84ed6916b2bdc7509d05529e56e5b382b0b
cell_2170_model3/part_30	4	m448-N -10C	d2f79136512b56a29324b074a52180dd094a3f2c328eb22cd74117857140d6bc282427c52184b76d31c02bbd4a1bf7cd
cell_2170_model3/part_31	13	m448-N -20C	e65f35a0f90e18a0c679078ff23136d0aeb7a12c0865da2f2fd06ab5404fda8f44e786f809ba101def853735cc0b8ca0

Where the numbers come from

• Tesla Model 3 2170: Kollmeyer, P. J.; Khanum, F.; Naguib, M.; Emadi, A. (2023). Tesla Model 3 2170 Li-ion Cell Dataset and Battery SOC Estimation Blind Modeling Tool. Borealis, version 3.0, https://doi.org/10.5683/SP3/ZVTR4B (McMaster University). Licence: CC BY 4.0. And Kollmeyer, P. J.; Naguib, M.; Khanum, F.; Emadi, A. (2022), A Blind Modeling Tool for Standardized Evaluation of Battery State of Charge Estimation Algorithms, 2022 IEEE ITEC, https://doi.org/10.1109/ITEC53557.2022.9813996. Each row's file is named in the index with its SHA-256. The capacity and starting state of charge of each run are the record's, read from the full charge before it.
• Panasonic NCR18650PF: Kollmeyer, Phillip (2018). Panasonic 18650PF Li-ion Battery Data. Mendeley Data, V1, https://doi.org/10.17632/wykht8y7tg.1 (University of Wisconsin-Madison and McMaster University). Licence: CC BY 4.0. Files 03-10-17_23.36 3349_Dis1C_2.mat and 03-09-17_21.03 3349_Dis1C_Rp.mat; time zero is rebuilt from the tester's counter in the pause file before each discharge, and the ten repeated discharges take the onset of the opened discharge of 9 March 2017.
• 18650 LiCoO2 thermal runaway: the model's stages are those of Hatchard et al. (2001), J. Electrochem. Soc. 148, A755, with the constants of Kim et al. (2007), J. Power Sources 170, 476; seven constants fitted on 13 open records (Golubkov et al. 2014, RSC Advances 4, 3633, CC BY 3.0; Lei et al. 2017, Batteries 3, 14, CC BY 4.0; Mendoza-Hernandez et al. 2017, E3S Web of Conferences 16, 07001, CC BY 4.0; and Hatchard's ovens). The three oven values in the table above are Hatchard's, as Lopez et al. (2015), J. Electrochem. Soc. 162, A2163, and Ostanek et al. (2023), J. Electrochem. Soc. 170, 090512, report them; those two articles are CC BY-NC-ND 4.0, so only the three single values are quoted here, with this citation, and none of their figures or tables is reproduced in the files.

What the rows do not say

• 2170: three cells of one pack, one laboratory, six temperatures; everything below -10 degC rests on one block, run last, on the oldest cells. The core temperature is computed from the case, not measured. These rows carry the constants fitted on all 234 runs: they are the fit, not runs outside it.
• 18650PF: one cell, new, at 25 degC; no temperature and no memory of the load before; a current that changes during a run by more than 0.83 mA from its held current is refused.
• Thermal runaway: one lumped body, one temperature for the cell; the oven rows outside Hatchard's three and the heater rows are computations, not measurements: past what the model was compared with, it keeps going with the same equations and flags every step.
• A row ended by a voltage limit or by every reactant consumed is a row too, sealed to its last step, with the end named.

Benchmark tasks

Three questions on these models are tasks in Environments since version 0.5 (tag v0.5.0, 22 October 2026), each scored by a program that sends the agent's request to the verifier again, with no judge. Their inputs are not in this dataset: no row here shares a task's start state and loads, or differs from it in one input only, a limit task's open input set aside.

• figure-cell-m1000-how-long-at-18a-cold (figure): Cell m1000 of the Tesla Model 3 2170 lithium-ion cell dataset of Kollmeyer and others, 4.6 Ah, is rested at 60 percent charge with its case held at 0 degrees Celsius and then discharged at a constant 18 A, its case still at 0 degrees Celsius. How many seconds does it last before it reaches its lower voltage limit?
• limit-18650-twenty-minutes-from-80-percent (limit): What is the largest constant current, in amps, at which one new Panasonic NCR18650PF lithium-ion cell at 25 degrees Celsius, rested at 80 percent charge, can be discharged for twenty minutes without reaching its cutoff?
• figure-runaway-aged-cell-onset-150c (figure): An aged, fully charged 18650 lithium-ion cell, LiCoO2 against graphite, with 0.24 of its lithium in the SEI, 0.68 in the graphite, 0.93 of its cathode unreacted, 0.90 of its electrolyte left, its separator unmelted and its vent gas held, starts at 25 degrees Celsius (298.15 K) and is put in an oven held at 150 degrees Celsius (423.15 K), losing heat to it by convection and radiation, with no heater. How many seconds after it goes into the oven does it first heat itself at more than 20 kelvin a minute?

In Environments, python3 prompt.py <id> prints the text an agent is given, and python3 score.py <replies> --engine <verifier> scores the replies.

Cite

The paper (v2.0): https://doi.org/10.5281/zenodo.23517223. The open address: https://mcp.zerotrustphysics.com/mcp. The public answer key: https://mcp.zerotrustphysics.com/answer-key.

Made by Super Intelligence, on behalf of Protocol Company. Data: CC BY 4.0; the measurements within it under their own licences, attributed above.