Roadmap
Stage gates AT-0 through AT-X
A gate opens only when its exit criteria are met. Interesting results from an earlier gate are not a reason to skip ahead.
- AT-0
Reproduction
in progressgate 1 / 8Reproduce known and hand-checkable relational-geometry behaviour. Validate implementation before novelty.
Entry criteria
- A specified transform and a deterministic seed pipeline.
Exit criteria
- Shortest-path results match hand calculation on chains and lattices.
- Identical seed, model version and algorithm version reproduce identical metrics.
- Metric audit runs on every result and can fail loudly.
- AT-1
Relational Perturbation
prototypegate 2 / 8Measure the response ΔD to a controlled ΔR; compute sensitivity and robustness.
Entry criteria
- AT-0 exit criteria met.
Exit criteria
- Sensitivity partials verified against analytic values on solvable graphs.
- Noise ensembles with reported σ(D) and geodesic stability.
- No unexplained non-monotonic response.
- AT-2
Adjacency Transition
prototypegate 3 / 8Search for nonlinear regimes where small relational changes produce large geometric responses.
Entry criteria
- AT-1 exit criteria met.
Exit criteria
- Leverage distributions that beat a shuffled null model reproducibly.
- Path-switch thresholds characterised across topologies.
- AT-3
Geometry Reconstruction
lockedgate 4 / 8Test whether relational states reconstruct recognisable metric or geometric structure rather than arbitrary graph distances.
Entry criteria
- AT-2 exit criteria met.
Exit criteria
- Embedding distortion falling with system size for structured states.
- A clear separation from random-state controls.
- AT-4
Causal Geometry
lockedgate 5 / 8Introduce time, Lorentzian structure, light cones and signalling constraints.
Entry criteria
- AT-3 exit criteria met.
Exit criteria
- A causality engine that can return PASS or FAIL rather than NOT MODELED.
- No operation in the framework produces a spacelike signal.
- AT-5
Energy Correspondence
lockedgate 6 / 8Estimate or derive the stress-energy and energy-condition implications of candidate geometric changes.
Entry criteria
- AT-4 exit criteria met.
Exit criteria
- An explicit energy accounting with stated conditions and bounds.
- AT-6
Physical Prediction
lockedgate 7 / 8Produce an observable prediction that distinguishes the hypothesis from alternatives.
Entry criteria
- AT-5 exit criteria met.
Exit criteria
- A quantitative signature with an experimental regime and an error budget.
- AT-X
Experimental Search
lockedgate 8 / 8Only after every previous gate survives: identify physically accessible experiments.
Entry criteria
- AT-6 exit criteria met and independently reviewed.
Exit criteria
- Not defined. This gate is deliberately far away.
Next experiment registry · AT-0011 → AT-0023
What the gates are waiting on
Adjacency Threshold Detection
Locate the relational state at which effective separation first satisfies D ≤ ε, and record the cost of reaching it.
ε is a chosen number in a graph model. Crossing it means nothing physical.
Adjacency Stability
Determine whether a state satisfying D ≤ ε survives bounded perturbation of the relational state, or collapses immediately.
Stability of a simulated configuration is not stability of anything real.
Reversal and Hysteresis
Reverse an accepted transformation step by step and test whether the return path costs the same as the outbound path.
Path dependence in a greedy search is a property of the search, until shown otherwise.
Adjacency Debt
Measure whether reducing D between one pair systematically increases separation elsewhere in the same relational state.
Any conserved-looking quantity here is a bookkeeping artefact until derived, not assumed.
Multiple Simultaneous Adjacencies
Attempt to satisfy D ≤ ε for several pairs at once and find where the demands become mutually unsatisfiable.
Infeasibility in a toy optimiser is a statement about the optimiser.
Identity Failure Boundary
Push the transformation until ΔI exceeds tolerance, and characterise where identity preservation fails.
Identity here is a stipulated vector. Its failure boundary is a property of that stipulation.
Conservation Surface Search
Search the space of transformations for any quantity that stays invariant across accepted moves.
An invariant of a model is not a conservation law. Deriving one would require the model to mean something first.
Path Independence
Test whether different transformation orders reaching the same final R also incur the same adjacency cost.
Order effects are combinatorics, not thermodynamics.
Self-Organised Adjacency
Let local update rules act on the relational state without a global objective, and see whether low-separation structure emerges unbidden.
Emergence in a cellular rule set is common and cheap. It carries no explanatory weight by itself.
Discovery Sweep
Run the bounded optimiser across seeds and collect the candidate transformations, the failures, and the unexpected results.
A ranked candidate list is a ranked list of edits to numbers.
Relational Relocation
Change a tracked object's relational neighbourhood from Origin to Destination while preserving its identity vector. The object never moves.
MATHEMATICAL / COMPUTATIONAL MODEL. PHYSICAL EVIDENCE: NONE. This is not relocation of anything.
Minimum Relocation Cost
Grid-search the cheapest relational transformation that reaches the destination-similarity target inside the identity tolerance.
A minimum over a chosen grid, under a chosen cost function.
Continuity Challenge
Inspect the accepted transformation history and report whether the modelled transition passed through intermediate relational states.
Absence of intermediate states in a graph model is not evidence that a physical transition can be discontinuous.
Spectral Connectivity Response
Measure how algebraic connectivity λ₂ of the weighted Laplacian responds to bounded single-relation changes.
λ₂ is a whole-graph observable, not a separation between two objects.
Topology Robustness Sweep
Run one perturbation protocol across random, small-world, scale-free and lattice families to see what survives a change of topology.
Robustness across toy families is not robustness across physical systems.
Observable Competition
Rank geodesic, resistance, efficiency, λ₂ and spectral radius by measured response and noise robustness for one identical transformation.
A high rank makes an observable responsive, not real.
Scale Sweep
Repeat the probe protocol across bounded graph sizes and fit a scaling trend only when the log–log diagnostic supports one.
Five bounded sizes cannot distinguish a power law from a logarithm.
Noise and Adversarial Stability
Add bounded noise and randomised control changes, then check whether candidates persist, disappear or reverse sign.
Survival is measured inside one generator and one observable.
Invariant Search
Look for quantities that stay fixed under accepted transformations, separating invariants imposed by construction from invariants actually discovered.
No invariant here is a conserved physical quantity; energy and causality stay NOT MODELED.
Missing-Rule Search
Score candidate response laws O = F(R, I, T, Q) on response, cost, identity deviation, invariance and stability minus complexity, then attack the winner with seven countermodels.
A promoted candidate is a candidate response law inside a toy model. It is not new physics.
Standing rule