KEY Index

The Key Emerges

A Constructive Inference Demo — From Survival to Structure

Opening Line (verbatim, on screen before anything runs)

"The system doesn't search for the key.
It survives in a space where only keys can exist."

Version

The Key Emerges — Headless Proof Kernel v1

The headless proof kernel is complete: 10 modules, ~2000 lines, seven verified outputs, no proxies, no synthetic unlocks, same kernel reused across levels, world enforced throughout.

Seven Required Outputs

#	Output	Status
1	Promoted structure from arm 1	✓
2	Promoted structure from arm 2	✓
3	Failed composition (world-enforced)	✓
4	Contrast branch failure (no survival pressure)	✓
5	Successful composition (actual evolved object)	✓
6	World state transition (locked → unlocked)	✓
7	Perturbation robustness (GIE held, accidental failed)	✓

Architectural Invariants

Same survival kernel at signal level and composition level — no modifications
No domain-specific logic inside the kernel
World constraint present from the first generation as hard veto
Admissibility exclusion tracked separately from non-survival
Contrast branch uses same world constraint — no special failure logic
Renderer is passive — observes state, never drives it
best_candidate_object returned directly from kernel — no re-evaluation hacks
All seven outputs trace to real computational events — no proxies, no synthetic unlocks

Module List

File	Role
`KEY_index.md`	This file
`core_types.py`	All shared data structures
`signal_model.py`	Latent curves C1, C2 and noisy exposure generation
`world_constraint.py`	Three-constraint lock — equations, not recognition
`transform_families.py`	Parameterized lens families, GA mutation/crossover
`invariance_metrics.py`	Fitness functions — dual pressure, arc-length remap, sinusoidal LSQ
`survival_kernel.py`	Reusable GA survival engine
`promotion.py`	Lifts survived candidates into independent structure objects
`composition.py`	Composition search — same kernel, new substrate
`contrast_branch.py`	Overfit failure + perturbation robustness test
`main.py`	Top-level orchestration — seven outputs

Coming next:

File	Role
`KEY_renderer_spec.md`	Renderer architecture — passive state projection
`KEY_visual_grammar.md`	Visual language for each stage
`KEY_stage_text.md`	On-screen text contract — sparse, truthful, sequenced

World Constraint (locked before curves were chosen)

Constraint A — Boundary/Admission: E_A = |mean(r) - R_lock| ≤ ε_A
- R_lock = 1.0, ε_A = 0.035
Constraint B — Groove Alignment: best-fit sinusoid residual + amplitude check
- A_lock = 0.12, ω_lock = 3, φ_lock = π/6, ε_B = 0.004, ε_amp = 0.03
Constraint C — Activation after 90° rotation: residual + trigger integral
- ε_C = 0.004, τ_trigger = 0.006

Signal Design (world-justified, not pre-chosen)

C1 — AffineDistortedCircle: a=1.12, b=0.88, tilt=17°
- Recoverable to R_lock=1.0 under radial normalization
C2 — WorldJustifiedRidge: A_raw=0.25, ω=3, φ=π/6, distortion=0.05
- Raw amplitude intentionally exceeds A_lock=0.12
- Surviving transform must recover periodicity AND normalize amplitude
- Distortion strength < 1/(2π·2.3) = 0.069 to preserve monotone x-axis

Collaborators

Christopher — empirical authority, direction, architectural integrity
Chat — formalization, substrate definitions, world constraint equations
Claude — implementation, pressure-testing, code

One-Line Proof

The accidental candidate passes the original world. It fails the perturbed world.

The GIE candidate passes both.

The difference is survival history, not luck.

Last updated: Headless Proof Kernel v1 complete.

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