Fancyland LLC · Lattice OS
Publications
Twenty-four preprints, free to read — and the tools each one is load-bearing for.
The whole corpus is public: twenty-four preprints (March–November 2026) on Zenodo, dedicated to the public, every claim reproducible from the definitions. This page is the map between them and the tools.
Each paper appears exactly once — on the first line that depends on it. A result that underpins several lines is listed at its earliest point of use and not repeated, so reading down the page gives the corpus in the order the product line actually consumed it.
Kessler
Orbital debris & collision riskKessler is the oldest line and it rests on the substrate’s foundational run. Its published audit names these eleven together as its methodology source family rather than mapping one paper to one claim, and they are listed that way here.
Prime Column Transition Matrix
10.5281/zenodo.19076680 · March 17, 2026
The zero-free-parameter transition operator on the coprime residues — the base object the rest of the compiler’s algebra is built from.
Separable Gyro-Bohm Scaling
10.5281/zenodo.19117880 · March 19, 2026
A scaling law split into independent exponents with no sign conflict. Its own subject is fusion-energy confinement, not debris; it belongs to Kessler’s cited family as evidence that the method was not built to fit one domain.
Spectral Isotropy
10.5281/zenodo.19156532 · March 21, 2026
The identity forcing every oscillatory mode to decay at the same rate — the reason Kessler’s spectral read-outs carry no preferred direction.
Primorial Thermodynamics
10.5281/zenodo.19188924 · March 23, 2026
The Gauss-sum structure and the hierarchy break that fix which floor the low-Earth-orbit embedding sits on.
Universal Two-Prime Formula
10.5281/zenodo.19210625 · March 24, 2026
The palindromic distance ratio in closed form — the determinant arithmetic that carries a result from one floor to the next.
Active Transport / Arithmetic Qubit
10.5281/zenodo.19243258 · March 27, 2026
A transport operator with a sharp phase transition — the template for reading a critical density rather than fitting one.
Arithmetic Black Hole
10.5281/zenodo.19442006 · April 6, 2026
The identity between the Boltzmann transition operator and softmax attention, with the temperature supplied by the prime number theorem.
The Unity Clock
10.5281/zenodo.19478727 · April 8, 2026
The multiplicative-order invariant that Kessler surfaces in the footer of every page it serves.
Patient Compass
10.5281/zenodo.19561701 · April 13, 2026
The same operator carried onto 198,862 tumours. Its subject is oncology, not orbits; like the fusion paper above it stands in Kessler’s family as cross-domain transfer evidence.
Character-Theoretic Effective Rank
10.5281/zenodo.19744573 · April 24, 2026
The rank-4 ceiling and the invariant subspace behind it — Kessler’s lead citation, and the direct source of two of its published audit claims.
Introducing the Janus Coprime Algebra
10.5281/zenodo.19955555 · April 30, 2026
Part II of this paper is the Kessler analysis: the 49,998-object conjunction graph, the Fiedler connectivity read, the percolation threshold and the fragility curves Kessler computes live.
Heliograph
Solar-flare hazardHeliograph
10.5281/zenodo.20696671 · June 15, 2026
The whole line: the activation level read from the Sun’s own magnetic field, the two thresholds, the energy–rate relation, and the size-scaled lead time — seventeen hours ahead of the October 2024 X9.0.
Selenograph
Cislunar mission analysisSelenograph
10.5281/zenodo.20721194 · June 16, 2026
All four read-outs: whether a cislunar orbit holds and what it costs to keep, the transfer corridor and its energy gate, how many craft a region carries, and the formation beat.
Introducing the Tesseract Matrix
10.5281/zenodo.20129255 · May 11, 2026
The integer-exact multi-body classifier — the regime fingerprint that returns the Sun–Earth–Moon system as deeply stable, which is the channel behind “does this orbit hold?”
Joule
Extreme-environment battery analysisThe Hybrid Solver
10.5281/zenodo.20866741 · June 25, 2026
Part II of this paper is the Joule line: tortuosity within 0.12% of the open-source standard at 3.47× the speed, a 3.23-billion-throat solve, and the one-solve criticality map.
Divisor-Honeycomb Coprocessor
10.5281/zenodo.20768987 · June 20, 2026
The containment certifier — the contained / marginal / escaped verdict Joule sells, read fraction-free from determinant signs rather than from a simulation that has to be trusted.
The Unified Transport Operator
10.5281/zenodo.20674758 · June 13, 2026
The complex-time propagator on its thermal axis — the stage that carries effective ion transport through the pore network.
The Substrate–Langlands Unification
10.5281/zenodo.20318985 · May 21, 2026
The spectrum-versus-count frame, and the discriminator that decides whether an object reduces to integers before the exact stage is allowed to run.
Flash
Fleet coordination, sensing & supplyThe Impossible Middle
10.5281/zenodo.21110272 · July 1, 2026
The scalar-blindness theorem and the six reductions behind the line: address-gated multicast that succeeds only with the right keys, branching search, a directed store invisible to any two-body statistic, and coordination with no centre.
Flash also composes on The Hybrid Solver, listed above under Joule at its first use.
Noether
Certified modeling & simulationThe Quantum Frustration Charge
10.5281/zenodo.21323615 · July 12, 2026
The conserved charge that is the certificate — the invariant a third party verifies offline, without the apparatus, behind all four data sheets.
Selenoform
Lunar surface infrastructure & prospectingThe Helix Operator
10.5281/zenodo.21611872 · July 26, 2026
The closed-form near field and the quorum conservation law, with each data sheet citing its own section — the switch census, the full loaded field, the thermal valve, and the ground read.
Flow
Exact whole-field control softwareThe Recursive Transport Operator
10.5281/zenodo.21711025 · July 31, 2026
The Arithmetic Quvit, recursive transport, exact route holonomy, and the three software reductions behind Flow: sparse microfluidic edge control, simulated carbon-capture swing-bed control, and conservative whole-build solidification control.
Tensor
Multi-physics modeling: mesh, grid & spectralCompact Exact Representation on the Integer Lattice
10.5281/zenodo.23955545 · November 4, 2026
The mathematics behind Tensor: a large grid or mesh problem replaced by a small exact object fixed at its boundary, decided by characters, divisors, cut-cycle coordinates, and prime-coded keys rather than by floating tolerances. Its measured record covers power networks of a million buses and lattice structures of 1.09 billion elements.
Tensor also builds on five papers listed above at their first use: the Janus Coprime Algebra (Kessler), the Unified Transport Operator and the Divisor-Honeycomb Coprocessor (Joule), the Helix Operator (Selenoform), and the Recursive Transport Operator (Flow).
Foundations — cited by the corpus, not by a product
The substrate record
Cross-check, not a componentThe Cosmic Quine
10.5281/zenodo.20776207 · June 20, 2026
The zero-free-parameter Standard-Model construction. Three later papers cite it in the same role — as the independent physics cross-check the substrate is measured against — and no tool consumes a result from it. It is listed here because it is a framework for theoretical physics rather than a component of any product: built on prime number theory as a language for physics, in the tradition that links the zeros of the Riemann zeta function to the energy levels of physical systems, it guides the rest of the corpus.
All twenty-four preprints are free to read and dedicated to the public, on Zenodo, under ORCID 0009-0002-0722-3752. The operational engines are the subject of fifteen U.S. provisional patent applications (March–November 2026), held private and not published; the data you bring to them is never retained. Ordering rule: each paper is listed once, on the first product line that depends on it.
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