Independent research. Rigorous methodology. Open science.
Glossary
Terminology panel for newcomers. The core axioms, cipher mechanics,
recurrence engines, methodology terms, and discipline rules — defined plainly,
with cross-links into the research entries that use each term.
Foundational axioms
The three axioms from which everything in TLT is derived. Established in Paper 1.
f|t pulse
A frequency pulse separated by a decoherence parameter t. 'f' is the accumulation/peak; '|t' is the cooling/reorganization. Every phenomenon in the framework derives from this single waveform.
r = 0.5 ceiling
The decoherence ratio at which dimensional overflow occurs. When r reaches 0.5, the current dimension can no longer hold the accumulated structure; overflow triggers transition to the next dimension. Foundational parameter; SIM-003 attempts to derive it.
The two integers that exclusively organize periodic crystal coordination. Every one of 133 ambient-pressure crystalline elements has coordination number that is a product of 2 and 3 only. Zero exceptions. {5} is forbidden by the crystallographic restriction theorem and the framework's cycle structure.
Dimensions group into cycles of three (seed → flat → volumetric). Cycle 1 = dims 1, 2, 3. Cycle 2 = dims 4, 5, 6. Each cycle has its own recurrence engine; the cycle orders themselves are Fibonacci (2, 3, 5, 8, 13).
Each dimensional cycle is governed by a specific recurrence. Cycle order itself is Fibonacci, producing self-similarity at two levels.
Fibonacci recurrence (cycle 1)
The 2-term recurrence governing dims 1–3. Peak ratio at φ ≈ 1.618. Produces the cycle-1 framerates (0.250, 0.625, 1.000) and the {2,3,5} organizing set.
Predicted 5-term recurrence governing dims 7–9. Peak ratio ≈ 1.966. Should produce the next nuclear magic number (predicted 184). Detailed derivation pending.
Predicted 8-term recurrence for dims 10–12. Peak ratio ≈ 1.996. Furthest-out cycle currently parameterized; pending detailed derivation.
Frustration overtone
When a cycle's recurrence runs against the organizing pair {2,3}, the resulting 'frustration' produces specific integer overtones. Cycle 1 produces {2,3,5}; cycle 2 produces {5,7,9,11,13}. These overtones explain nuclear magic numbers among other phenomena.
How dimensions interact, transition, and produce observable phenomena.
Framerate
The local speed of light at each dimension. At dim 3, framerate = c (the empirical speed of light). Cycle-1 framerates: 0.25c (1D), 0.625c (2D), 1.000c (3D). Cycle-2 uses different values via Tribonacci recurrence.
The transition between dimensions, characterized by overflow and emergent phenomena. The 2D→3D boundary produces helium anomalies (~0.86 meV); 3D→4D produces pair production (1.022 MeV); 4D→5D produces cosmic-ray knee (~3 PeV).
The energy capacity per dimension: log₁₀(E/eV) = 0.1964·d² + 8.0932·d − 20.0373. Fits boundary energies to 0.14% across cycle 1. Emergent 8 Hz and 432 Hz frequencies are byproducts of this equation.
Chirality (left-handed vs right-handed asymmetry in biomolecules and elementary particles) emerges from the framerate difference between consecutive dimensions, not from a separate axiom. Derived in Paper 1.
Cipher mechanics
How the cipher predicts crystal structure and material properties from atomic number alone.
Z (atomic number)
The single input to the cipher. Every property prediction derives from Z without external lookup, NIST cross-reference, or fitted parameters.
Number of nearest neighbors around each atom. The cipher derives CN from Z; observed CN values cluster on {2,3} products. Gallium's CN=7 is an anomaly that the framework explains via {7}-fold self-resonance.
Each coordination geometry has its own eigenvalue spectrum from the symmetry group's character table. BCC=9 eigenvalues, HCP=7, FCC=5, Diamond=1. Count = susceptibility (how readily the geometry resonates).
The C_potential's internal geometry, on which electrons sit. v11/v12 uses an empirical Thomson/Fibonacci hybrid for seating; full self-derivation pending SIM-003 cone-cascade.
The discontinuous transition between the pre-snap f-state (unfolding angle ~99°) and the post-snap |t-state (~109.5° tetrahedral) at percolation topology 1.29. The snap IS the tunneling event — same phenomenon read at different scales.
v11/v12's mechanism that reads f-depth and |t-spread together (not sequentially) to produce the unfolding angle. Replaces v9's separate-stage derivation.
v12's foundation: regression of a triangle (vertices at f, |t, r) onto its geometric primitives. Scale-indifferent (operates on ratios, not absolute values). The key change that gave v12 its 91/107 score over v11's 71/107.
The geometric potential each electron sits in. Has both an external scalar (the bulk Coulomb-equivalent) and an internal topology (the spiral coordinate). The internal topology is what the cipher reads.
Geometric primitives
The 7 foundational expressions and the geometric language they generate.
The 7 expressions
Layer-(-1) foundational primitives: CONCENTRATE, DISTRIBUTE, RADIATE, POLARIZE, TRIANGULATE, CUBIFY, FRUSTRATE. Every geometric structure in the framework is a composition of these seven.
When two geometries couple, the framework predicts a joint operator distinct from the sum of two independent 7-vectors. Test JJ Phase 1 is the empirical search.
The geometric concentration ratio produced by cone-like or pinch geometries. Apex-bearing geometries (bicone, pyramid) amplify EM concentration via angular deficit. HPC-024 confirmed across 7 geometries.
Every cavity has two geometries: boundary (the wall shape) and internal (the standing-wave pattern). The internal geometry has a 7-component fingerprint (dominant mode, node spacing, anti-node concentration, Q-factor, ringdown, mode-coupling, overtone entropy).
Cavities with {7}-fold rotational symmetry are uniquely self-resonant at 2.7% error — all other tested n-fold cavities show 8–56% error. Foundation for the √7 structural factor in magic-numbers derivation.
The framework's dual reading of crystal structure: atoms are the walls of internal cavities; the voids between atoms are the resonant cavities. Same partition as standard physics, opposite reading.
How experiments are designed, scored, and audited.
FDTD (Finite-Difference Time-Domain)
Numerical method for solving Maxwell's equations in 3D space + time. Used in all HPC-series tests. Grid resolution (64³, 96³, 128³, 256³) affects accuracy; resolution checks are standard.
Prediction submitted in writing *before* the answer set is revealed. T1–T4 blind tests run March–April 2026; T4 scored 100% (24/24). The cleanest score of real predictive power.
Locking confirmation and falsification thresholds before the experimental result is observed. Eliminates post-hoc threshold adjustment. Every framework prediction with a pending test gets one.
A drive imbalance sweep where two coupled cavities are driven at asymmetric decoh ratios (e.g., 0.10/0.50 → 0.30/0.30 → 0.50/0.10). Tests for non-monotonic emergence signatures.
Comparing two spectra via cosine distance between their feature vectors. Used in Test JJ to measure whether a coupled-pair fingerprint differs materially from the sum of two single-cavity fingerprints.
Refinement: replacing a mechanism with a sharper one (cycle-specific Tribonacci replaced universal Fibonacci-extension). Correction: adding patches to an existing mechanism (forbidden — every attempt hurt accuracy).
The framework forbids tuning parameters to fit observations. Predictions derive from axioms + geometry. When a prediction misses, the framework either accepts the miss or refines the mechanism — it does not adjust parameters to match.
Failed predictions, falsified hypotheses, and honest no-decisions are published with the same prominence as confirmations. The audit trail IS the record.
When entry A declares see_also: B, entry B's payload automatically lists A under cited_by. The graph is bidirectional in the data; no manual maintenance.