Fancyland LLC · Lattice OS

Publications

Twenty-three preprints, free to read — and the instrument each one is load-bearing for.

The whole corpus is public: twenty-three preprints (March–July 2026) on Zenodo, dedicated to the public, every claim reproducible from the definitions. This page is the map between them and the instruments.

Each paper appears exactly once — on the first line that depends on it. A result that underpins several instruments 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 risk 11 papers

Kessler 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.

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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 the instrument computes live.

Heliograph Solar-flare hazard 1 paper
  1. Heliograph
    10.5281/zenodo.20696671 · June 15, 2026

    The whole instrument: 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.

    One paper, and that is not an omission — Heliograph’s reference list is classical solar physics throughout, with no substrate companions.

Selenograph Cislunar mission analysis 2 papers
  1. Selenograph
    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.

  2. 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 analysis 4 papers
  1. The 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.

  2. 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.

  3. 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.

  4. 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 & supply 1 paper
  1. The 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 & simulation 1 paper
  1. The 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 & prospecting 1 paper
  1. The 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 software 1 paper
  1. The 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.

Foundations — cited by the corpus, not by a product

The substrate record Cross-check, not a component 1 paper
  1. The 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 instrument consumes a result from it. It is listed here rather than assigned to a line, because placing it under one product would overstate what that product uses.