zero-trust-physics/zero-trust-physics-orbits-pointing

Orbits and pointing: LAGEOS orbit prediction, JWST momentum build-up and JWST fine guidance, computed with a proof on every row

For precise orbit determination and space domain awareness: a seven-day orbit prediction of the laser-ranging satellites LAGEOS-1 and LAGEOS-2 from one published state, against the ILRS precise orbits. For observatory operations: the James Webb Space Telescope's momentum build-up between momentum unloads under sunlight pressure, against its own telemetry, and its guide star's position one fine-guidance frame (64 ms) ahead, against the Fine Guidance Sensor's centroids. Every run is the comparison's own request, computed again with a cryptographic proof on every row and signed by the operator's key, with the comparison with measurement in a table beside it.

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. Public answer key: https://mcp.zerotrustphysics.com/answer-key.

What is in it

Nine sealed datasets, 133 rows and 489,051 recorded frames, every row completed:

Dataset	Model	Rows	Frames	What the rows are	Dataset seal
lageos	LAGEOS free flight	42	78,438	Seven starts in each of six weeks outside the choice of the card's structure: LAGEOS-1, 6 to 12 and 13 to 19 September 2026; LAGEOS-2, four weeks from 23 August to 19 September 2026. From each day's 0 h state, runs of seven, three, one day and one revolution, 10 s steps, a frame every 120 s	9e09cf2cf7ce54a34300c7b2a114d2f34d34473959fbe6d8d0bdb6d0cccbe3a9b2f8ac795f499d9c7b7976abf6ca74a8
momentum_jwst_srp__2023-06-15_to_2023-07-14	JWST momentum, one flat sunlit layer	12	42,903	Every minute of every stretch between thruster events, the telemetered attitude and the Sun as load, in pieces of at most 4,000 minutes	19195bb891bc3fcb7b5095b9549d332406a219364a8062a59b34c54a4d4efb7bbae117a0bff97f8e4ef2450df24a47cb
momentum_jwst_srp__2023-07-15_to_2023-08-14	the same	15	44,371	the same	4b2c3135173ff4b99a0e3eb133063125ba63b38d48de86590f69ac3cdac7534c73db9f5538eec9befc25fd4fe5024e45
momentum_jwst_srp__2023-08-15_to_2023-09-14	the same	12	44,512	the same	97120e063b0b539f0bb6ae65a235355aa173c601ecfb6e0f178ae0fd8a50cfab044780f5afe3705a5dd17383bafabfeb
momentum_jwst_dihedral__2023-07-15_to_2023-08-14	JWST momentum, the first layer as two slopes	15	44,371	the same minutes as the one-layer model's	41fadf0172e746fc09e467c34909da676c9322e048898e8b326c4cab7626484d11ab8bc97c2fbdd59214e45e5dd8a350
momentum_jwst_dihedral__2023-08-15_to_2023-09-14	the same	12	44,512	the same	19603e2bf2d01dfb9bdccb8ff5e6d14be58972c5fce635b7cc2fc970293f710a4bf3c67ee7d232d25015a43bcf88e7f1
los_jwst_fine_guide__worked	JWST line of sight in fine guide	1	1,252	The model's worked run: frames 469 to 1,720 of one fine-guide file of April 2022, a file it was fitted on	09002c0a0c1c8529d8c419e7a85cb9fd247b9fc5cb2815a3b4c0c162a7b690fba880ca5c9531901989ba4d7bc88b753b
los_jwst_fine_guide__2022-05	the same	11	84,146	One file of each of the 11 visits of May 2022 outside the fit, one frame a step	e99b10f3be1863ac6f7c0512d73748541dbbc080669642dcccc5b4b246ce69ac245bdd71ebeb5f855abd2a2073b0aab5
los_jwst_fine_guide__2022-06	the same	13	104,546	One file of each of the 13 visits of June 2022 outside the fit	0d914b415d3c234c15f0bfc18317c6dd50a4d96e0ee50c25114367aa9d3cfd2ece1e5445fa3db219827ff2116ed2e668

One request to the engine is at most 16,777,216 bytes, so the momentum months and the fine-guide months are sealed one dataset each. A momentum row of 4,000 minutes is a request of about 0.9 MB; a fine-guide row of 10,000 frames, about 1.3 MB.

The fine-guide rows are a rule-based subset of the 134 files the model was compared with: of each of the 24 visits outside the fit, the first file in the record's list, run whole as the comparison ran it (its first 10,000 frames, the lock point the median of its good centroids, one step a frame, the table's own numbers). 24 files, 188,692 frames, 114,769 of them quiet.

The comparison tables are the default views. data/comparison/orbit_distance.parquet: one line per LAGEOS run, the largest distance from the published orbit after one revolution, one day, three days and seven days. data/comparison/momentum_months.parquet: the five measures of each month, each model. data/comparison/momentum_runs.parquet: one line per momentum row, with |H| at its end, the model's and the telemetry's. data/comparison/fine_guide_files.parquet: one line per fine-guide file, the error one frame ahead on the quiet frames, the hold-last error and the lock-point error, each axis. data/<dataset>/rows.parquet and frames.parquet are the sealed rows and frames, written only after the whole dataset verified.

How close it comes to the measurements

LAGEOS orbit prediction, against the ILRS combined orbit, largest 3-D distance over every 120 s epoch to each horizon. Nothing fitted: the Earth's field is EGM2008 to degree and order 12, sunlight pressure the analysis centres' 1.13.

Satellite	Runs	After one revolution	After one day	After three days	After seven days
LAGEOS-1, 2 weeks	14	0.65 m (target 1 m)	3.8 m (target 10 m)	12.7 m	32 m (target 100 m)
LAGEOS-2, 4 weeks	28	0.34 m	2.9 m	8.9 m	22 m

These distances are the record's: on every run and every horizon this dataset's frames give the same distance as the comparison the model's description names, to within 3.3 micrometres.

JWST momentum build-up, against the observatory's telemetered total angular momentum, every settled minute. A: the growth of |H| over each day within 0.1 of the observed plus 0.2 N m s (target 80 percent of days). B: the change of the vector H over each day, the same allowance. C: |H| at the end of each run of 3 days or more between thruster events (target 10 percent). D: the hourly growth rate, RMS error over its spread (target 0.5). E: the torque on one attitude, RMS error over the RMS torque (target 0.4).

Model	Month (2023)	A	B	C	D	E
One flat layer (fitted on 12 May to 14 June)	15 Jun to 14 Jul	23 of 28 days	14 of 28	-8.4 % after 10.7 days, -0.9 % after 16.3	0.437	0.262
	15 Jul to 14 Aug	15 of 28	8 of 28	-16.2 % after the 3.9-day run after an unload; +0.5, -5.3, -5.1 % after 12.4, 8.5, 4.4 days	0.384	0.314
	15 Aug to 14 Sep	17 of 30	8 of 30	-7.4 % after 29.3 days	0.421	0.347
Two slopes (fitted on 12 May to 14 July)	15 Jul to 14 Aug	25 of 28	18 of 28	+0.7, -1.7, +4.9, +0.9 % after 12.4, 8.5, 3.9, 4.4 days	0.272	0.144
	15 Aug to 14 Sep	22 of 30	13 of 30	-5.5 % after 29.3 days	0.375	0.149

Every number in this table is computed from this dataset's frames by the record's own measures, and equals the record's.

JWST fine guidance, one frame ahead, on the quiet frames (a centroid within 5 mas of the lock point, outside 2 s before and 30 s after a disturbance), error of the prediction over the error of holding the last centroid:

Frames	Files	x	y
This dataset's subset	24 (one per visit)	0.788 (0.550 against 0.698 mas)	0.803 (0.499 against 0.622 mas)
The model's whole comparison	134	0.790 (0.510 mas)	0.807 (0.472 mas)

Target 0.85. The subset's squared error over the stated variance is 1.035 on x and 0.946 on y (target 0.67 to 1.50); the whole comparison's, 1.004 and 0.986. On each of the 24 files, this dataset's numbers equal the record's for that file.

One row

Row 0 of lageos is LAGEOS-1 from 0 h UTC on 6 September 2026, seven days at 10 s steps, started from GFZ's published state turned into the card's frame. The request, as run_trajectory takes it:

{"tool": "run_trajectory", "arguments": {"card": "satellite_lageos1", "domain": "aerospace", "dt_s": 10.0, "initial": {"epoch_utc_s": 841924800.0, "forecast_elapsed_s": 0.0, "position_m": [295558.7678903363, -5108650.370522532, -11100383.23606335], "velocity_m_s": [-4821.08544993592, -3331.9602315669836, 1405.5539438152634]}, "record_every": 12, "segments": [{"load": {}, "steps": 60480}]}}

Outcome completed, after 60,480 steps. Its largest distance from the ILRS combined orbit is 0.65 m after one revolution, 3.8 m after one day and 31.9 m after seven days. Run seal:

a3a5f892c16178d0ac9942c64cadbc696cc88ee4f7de2321828e78ad8d06a1a529d8ea12ce381b48b2d441e79ad75aa9

Verify it yourself

Every row can be verified without trusting this page.

# 1. the proof of a whole dataset, with no engine running: the seal of every row, its chain of frames and the root
genesis_seal verify-dataset sealed/lageos/head.json sealed/lageos/rows.jsonl sealed/lageos/frames.bin

# 2. one row's proof on its own: the row, its chain and its path to the dataset seal
genesis_seal row-proof sealed/lageos/head.json sealed/lageos/rows.jsonl 0 sealed/lageos/frames.bin > row0.json
genesis_seal verify-proof row0.json

# 3. the operator's signature on a signed head or a signed answer, against the published key
genesis_seal verify-signature signed/lageos/signed_000.head.json --public-key signed/answer_key_public.b64 --now <its issued_at>

4. Send any row's request to run_trajectory at the open address and compare the run_seal.
5. Send verify_dataset the head's request with its dataset_seal: the engine runs the whole plan again and reaches the same seal. At the open address this holds for lageos (about 20 s) and los_jwst_fine_guide__worked; the momentum and fine-guide month plans, 11 to 14 MB, are larger than the open address takes in one request, so verify those row by row with step 4.

When this dataset was made, all of these were run on each of the nine datasets: verify_dataset by the stored seal: holds; verify_dataset's short form on a fresh engine, the plan run again: holds; genesis_seal verify-dataset: holds; one row's proof on its own: holds; 1 to 6 rows of each sent to run_trajectory again: the same run seal, 40 of 40 rows sent in all.

Signed

The row seals and the dataset seals were computed by the served engine build, run locally. The open address then signed ML-DSA-87 what it returned for the same requests: for lageos, the dataset heads, which carry the merkle_root and rows_sha384 over their rows' run seals (the LAGEOS rows are not signed one by one); for the momentum and fine-guide datasets, each row's own answer.

The operator's key signs every answer of the open address ML-DSA-87, over its receipt, with an expiry of 3,600 s and a nonce. With SHA-384, these are the CNSA 2.0 algorithms. The public key is at https://mcp.zerotrustphysics.com/answer-key, key ID ca06027a…1be38.

• lageos: the same plan was sent to the open address in 14 chunks of three rows (an inline dataset records at most 10,000 frames). Every one of the 14 signed heads verifies against the published key, and every row's run seal in them equals the stored row's. The signed heads are in signed/lageos/ (signed_NNN.head.json, the head's own bytes as they came; signed_NNN.json, the whole answer).
• The momentum and fine-guide datasets: the open address refuses a signed head for rows this long (it counts the plan's request into the 42,500 characters of one inline answer: 155,659 for the shortest row, the worked run). Each row's request was sent alone to run_trajectory at the open address instead; every answer is signed in its own receipt. Each signature verifies against the published key, and each answer's run seal equals the stored row's. The signed answers are in signed/<dataset>/row_NNN.json.gz (unzip before verify-signature), with signed_summary.json and attest.json.

Files

Path	What it holds
sealed/<dataset>/head.json, rows.jsonl, frames.bin	each sealed dataset: the head with its request and dataset_seal, the rows, the frames
data/<dataset>/rows.parquet, frames.parquet	the same rows and frames as Parquet, written after the dataset verified
data/comparison/*.parquet, *.csv	the four comparison tables
signed/<dataset>/	the signed heads or signed answers from the open address, and their verification
signed/answer_key_public.b64	the operator's public key, as published at https://mcp.zerotrustphysics.com/answer-key
source/lageos/	the 12 orbit files the LAGEOS runs read: GFZ's (the start states) and the ILRS combined orbit (the comparison), six weeks
source/momentum/	the minute rows of each month and the JPL Horizons ephemeris of JWST used for the Sun
source/fine_guide/	the FGS centroid tables of the 25 fine-guide files used

Where the numbers come from

• LAGEOS. International Laser Ranging Service combined orbits and GFZ's orbits (product 10.5067/SLR/SLR_ILRSORB_001), from the EUROLAS Data Center at DGFI-TUM. The start state of each run is GFZ's state at 0 h of its day, turned into the card's frame outside the engine with IERS Bulletin A, as the model's description says; the distances are to the ILRS combined orbit (ILRSA). Weeks used, each Sunday to Saturday: LAGEOS-1, 2026-09-06 to 09-12 and 09-13 to 09-19; LAGEOS-2, 2026-08-23 to 08-29, 08-30 to 09-05, 09-06 to 09-12 and 09-13 to 09-19. The ILRS asks: Pearlman, M. R., Noll, C. E., Pavlis, E. C. et al. (2019). The ILRS: approaching 20 years and planning for the future. J Geod 93, 2161–2180, https://doi.org/10.1007/s00190-019-01241-1. Keyword: SLR.
• JWST momentum. The JWST engineering database at MAST: SA_ZMOMMAG and SA_ZMOMECIX/Y/Z every 4.096 s, the attitude quaternion SA_ZATTEST1 to 4 every 0.256 s, the slew status SA_ZSLEWST and the unload status SA_ZMOMUNLST, read as one row a minute. The Sun's direction and distance from JPL Horizons, target -170 (NASA/JPL). The sunshield's area (Proc. SPIE 9904, 990405), its optical numbers (Origins Space Telescope study report, appendix C), the solar irradiance (Geophys. Res. Lett. 38, L01706), the layers' dihedral angle (Northrop Grumman Technology Review Journal) and the sunshield's width (PASP 135, 058002).
• JWST fine guidance. Space Telescope Science Institute, Mikulski Archive for Space Telescopes, programme 1163, OTE-26 Routine WFSC/CC Jitter Maintenance: the table FGS CENTROID PACKET of each calibrated fine-guide file.
• The models' numbers. Each model's description, served at the open address, states what it was fitted on, what it was compared with and how close it came; the comparison tables here are computed from this dataset's frames by the same rules.
• This work is based in part on observations made with the NASA/ESA/CSA James Webb Space Telescope. The data were obtained from the Mikulski Archive for Space Telescopes at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-03127 for JWST. These observations are associated with program #1163. The momentum rows are based on engineering telemetry of the NASA/ESA/CSA James Webb Space Telescope, obtained from the same archive.

What the rows do not say

• LAGEOS: free flight from a published state, on two orbits near 12,270 km, for at most seven days. The card carries no drag, no light reflected from the Earth and no ocean tide, and its error grows with the length of a forecast: from 0.65 m after one revolution to 32 m after seven days on LAGEOS-1. The published orbit is the analysis centres' fit to laser ranges, good to a few centimetres.
• JWST momentum: the change of H between settled minutes, the observatory not slewing; the thrusters, the wheels' speeds and attitudes outside the field of regard are outside the comparison. The daily change of the vector H is within its allowance on 8 to 18 days of 28 or 30, against a target of 80 percent: beyond 2 degrees of roll the one flat layer's torque about the boresight is off by about 30 µN m, and the two slopes' torque about J3 by 10 to 11 µN m RMS. Across each slew of more than 0.5 rad the settled momentum moved by about 0.26 N m s RMS that sunlight does not account for.
• JWST fine guidance: the model describes quiet fine guide. Inside a disturbance it is worse than holding the last centroid, 2.03 against 1.00 mas on x and 1.57 against 0.78 on y over the whole comparison, and it flags those frames. In the worked run, 32 frames are flagged more than four stated standard deviations from where they were expected and 11 more than 5 mas from the lock point, the first at frames 1,199 and 1,237 (counted from 0). Nothing above 7.8 Hz is resolved by a 64 ms frame. The lock point is not in the file; the comparison took the median of the run's good centroids.
• A row is a computation, not a measurement: past what the model was compared with, it keeps going with the same equations and flags every step.

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-lageos-radius-after-twelve-hours (figure): LAGEOS-1 is at position (9,636,913.2006, 6,151,016.5697, -4,447,242.7873) m with velocity (-76.809374, -3,497.872725, -4,941.758241) m/s, in the frame turning with the Earth, at 00:00 UTC on 7 September 1996 (842,097,600 s of UTC from 1970). How far is it from the Earth's centre, in metres, twelve hours later?
• figure-jwst-momentum-after-two-days (figure): The James Webb Space Telescope holds attitude quaternion (q1, q2, q3, q4) = (-0.2918584049, 0.790687263, -0.4820995033, 0.2391911894) with the Sun in direction (-0.111079227693045, 0.9106690061131182, 0.39792381994555476) at 1.0 au, and its reaction wheels start holding a total angular momentum of (0.4, -0.9, 1.3) N m s. What is the magnitude of its total angular momentum, in N m s, after two days under sunlight pressure with no momentum unload?
• stop-jwst-sun-behind-sunshield (stop): The James Webb Space Telescope holds attitude quaternion (q1, q2, q3, q4) = (-0.2918584049, 0.790687263, -0.4820995033, 0.2391911894) with the Sun in direction (0.111079227693045, -0.9106690061131182, -0.39792381994555476) at 1.0 au, starting from a total angular momentum of (0.4, -0.9, 1.3) N m s. How much does its angular momentum grow in ten hours under sunlight pressure?

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: https://doi.org/10.5281/zenodo.23517223. The open address: https://mcp.zerotrustphysics.com/mcp.

Made by Super Intelligence, on behalf of Protocol Company. Data: CC BY 4.0, with the ILRS citation and the MAST acknowledgment above.