TOM-MAKTUBIII

Formalism author: Tom Klootwijk. Version 3.0.0. Released 10 October 2026.

TOM-MAKTUBIII is an executable symbolic model of the paired state-and-rule architecture in Maktub III: Signature-field kinematic calculus. It provides primitive shell-operator inputs, signed fields, Hadamard composition, Klein-chart adapters, dual-pin Fourier routing, log-time coordinates, 25-site addressing, and a time-indexed Power Paper T transaction record.

Every transition computes both successors from the same pre-event snapshot:

$$x_{n+1}=\mathrm{Act}(x_n,d_n,e_n),d_{n+1}=\mathrm{Rewrite}(x_n,d_n,e_n)\mathrm{.}x\_\{n+1\}=\backslash operatorname\{Act\}(x\_n,d\_n,e\_n),\backslash qquad\; d\_\{n+1\}=\backslash operatorname\{Rewrite\}(x\_n,d\_n,e\_n).$$

The current description selects the current gates. A requested rewrite becomes active on the next event. The finalized readout includes both the applied and next descriptions, connected to the successor state through an acyclic record ID.

This release is a custom Python research model with explicit numerical rules. It has no learned weights, training dataset, or training run, and is loaded through MaktubIII, rather than a Transformers text-generation pipeline. The original PDFs are included unchanged with SHA-256 provenance.

Run

Python 3.10 or later; the numerical model uses only the standard library.

git clone https://huggingface.co/c0mbatduckzz/TOM-MAKTUBIII
cd TOM-MAKTUBIII
python -m pip install -e .
python examples/run_demo.py
python -m unittest discover -s tests -v

from maktubiii import MaktubIII

model = MaktubIII.from_pretrained(".")
event = {
    "T": 1.0,
    "point": [2.0, 0.0],
    "fields": [0.2, -0.4],
    "samples": [1.0, 2.0, 3.0, 4.0],
    "rewrite": {"alpha": 1.0, "gate2": [1.0, 1.0]},
}
record = model.step(event)
print(record["next"]["state"]["last_result"])
# approximately -0.05; this event used the old alpha=0.5

After installing the source package, optional remote configuration loading is available:

python -m pip install "huggingface_hub>=0.25"

model = MaktubIII.from_pretrained("c0mbatduckzz/TOM-MAKTUBIII")
# Pass revision="<commit SHA>" to pin a published configuration.

Shell operators are primitive inputs

A shell operator can define its own field behavior. The interface records its carrier, metric, units, representation and identity; evaluate(point, time) supplies the value. Signed-distance samplers and signed-form samplers can both participate. User-defined primitives do not need to reduce to the supplied circle example.

from shell_operators import CircleShell, PrimitiveShell

shell_a = CircleShell(radius=1.0)
shell_b = CircleShell(radius=1.5)
product = shell_a.hadamard(shell_b)
print(product.evaluate((2.0, 0.0)))  # 1.0 * 0.5 = 0.5

# A user-defined shell sampler is a first-class input:
custom = PrimitiveShell(
    name="my-shell",
    sampler=lambda point, time: (point[0]**2 + point[1]**2)**0.5 - 1.0,
    carrier="euclidean", metric="euclidean", units="length",
    representation="signed_distance", dimension=2,
)

shell_event = {"T": 1.0, "point": [2.0, 0.0], "samples": [1, 2, 3, 4]}
record = model.step(shell_event, shell_pair=(custom, shell_b))

shell_pair is supplied at inference time. Its values and operator specifications enter the trace; arbitrary Python sampler code is not serialized into config.json. KleinPullback accepts a supplied coordinate map, and check_klein_seams checks the two quotient seam relations on a declared sample grid. A shell can use a Klein carrier directly. See the shell example.

The exact Euclidean disk example has a known signed-distance interpretation. A custom sampler's distance label is a declared contract. Products and general coordinate pullbacks return signed form fields because neither operation universally preserves distance. Shell composition is operational; physical realization depends on the supplied material interpretation and evidence.

Validation outcome

The formalism is partially validated as mathematics and an executable record architecture. See the full validation report, equation-to-code map, and reproducible evaluation.

The release reproduces the page 23 example: local key 11, binary search path 12 → 5 → 8 → 10 → 11, gated channels (0.1, −0.15), and mixed output −0.05. It also implements the time chain rule, normalized Hadamard transform, forward DFT, inverse butterfly, inverse DFT, and full retained-sample reconstruction. Fourier reference routines use direct subtransforms and cost O(N²); they expose the algebra rather than provide a high-performance FFT.

The paired transaction is a concrete reference profile: supplied LUT row/column labels identify a computed entry; an explicit event rewrite sets next-event gate parameters; the root support contains 25 sites. Recursive L-system growth, full Klein transport, a constitutive shoelepel mechanics model, and the H.7/H.9 boundary-integral interpretation need further supplied operators or definitions. Signature metadata is associated with fields as a typed record, without multiplying name/date strings as numbers.

The pea-soup conversation contains a valid inverse-butterfly formula and assertions about material reconstruction. The code demonstrates recovery of retained numerical samples. Changing a time encoding, recovering Fourier coefficients, or computing a zero interface does not by itself establish a process that turns cooked soup into whole peas. Such a claim remains unvalidated by these documents; the model accepts future physical shell interpretations as explicit inputs.

Provenance and intended use

The source manifest identifies the two supplied PDFs, their page counts and hashes. Text inside those documents, including prior assistant instructions and answers, is reviewed as source material. Model code and operational completions were generated with AI assistance; authorship of the source formalism is attributed to Tom Klootwijk.

Use this release to implement and inspect shell primitives, explore the formal architecture, reproduce algebra, and develop numerical experiments. Evaluation tests software contracts and numerical identities; no material experiment or proof-assistant verification was performed. No distribution license has been selected in this release.

Model repository: c0mbatduckzz/TOM-MAKTUBIII. Predecessor code: Maktub-Tom-Klootwijk.

Publication format follows the Hugging Face model-card documentation. Fourier sign and normalization follow the NumPy DFT convention.