GFRTU Prototype

Generative Fibered Relational Trace Universe

Iterate sheaf completion, fiber stabilization, and generative closure until the least nontrivial universe forms. Each loop enforces locality + gluing, the commuting diagram of \u03c3 (stabilizer) and \u0394 (drift), and the RTL-internal logic that witnesses the UG fixed point.

Stage Presheaf Sketch Depth 0% Tick 0

Orientation

Guided onboarding for the GFRTU

Use the briefing to learn how traces become presheaves, how locality/gluing are enforced, and how UG iterates climb toward the least fixed point. The tutorial walks through each primitive in a safe order.

Presheaf cadencePending

Record traces and sheafify them to unlock locality.

Stabilizer & driftPending

Commute \u03c3 and \u0394 until defect pressure is charted.

UG ladderPending

Iterate closure until the least nontrivial fixed point kicks in.

Field operationsPending

Launch expeditions to harvest proofs and drift signatures.

Research pulsesPending

Spend proofs to unlock RTL/stability boosts and automate closure.

Session assists

Audio, animation, and pacing toggles to suit your run.

comfort

Quickstart outlines the minimal winning loop: trace \u2192 sheaf completion \u2192 locality/gluing \u2192 stabilization \u2192 UG iterate.

Reset clears resources and onboarding but leaves the math overlay intact.

Deep plan

Massive clicker roadmap

A living playbook for scaling the GFRTU from a toy loop to a prestige-grade idle.

Roadmap v2
Economy overhaulLive

New currencies (insight, axioms, resonance) with multiplicative boosts and offline yield.

Upgrade latticeBuilding

Specialized upgrades, burst actions, and prestige shards to tune the fixed-point climb.

Narrative goalsStacked

Daily missions, accolades, and ascending universes to keep the clicker arc sticky.

Integrated documentation

Inline codex + math receipts

Cards below summarize the Acts, relationality.md, and README interpretations that power each move of the GFRTU loop.

docs/math references

Onboarding timeline

From trace to ascension

Track early, mid, and late beats; each step marks complete as you perform it and links to the math receipts.

0/6

Use this to pair the in-file testing harness with guided onboarding: run diagnostics after completing each cluster to ensure the lattice still behaves.

Relational coupling

How systems reinforce each other

A compact ledger that explains how onboarding, missions, achievements, and research lock together inside the GFRTU loop.

coherence links

Čech & Kan dynamics

Nerve coherence + Kan lift reactor

Drive an idle loop that only exists because the lattice is sheafified: tune a Čech cover, pulse the nerve, and project Kan lifts that convert homological balance into closure depth, hyperedges, and a new cohomology charge.

sheaf-only mechanic
Čech cover3

Select how many opens blanket the trace site; higher cover counts tighten H0 but tax overlap.

Overlap tension2.0

Overlap controls how much locality/gluing is demanded before the nerve stabilizes.

Twist (RTL weight)0.8

Twist adds RTL weight to differential maps; higher twist suppresses H1 leaks.

H0 (sections)0

Sheaf sections that survive all overlaps.

H1 (defect cycles)0

Obstructions from drift/defects escaping gluing.

H2 (hyperedge lifts)0

Hyperedge-scale echoes that power Kan lifts.

Cohomology coherence0
Kan lift budget0
Čech pulses0

Čech pulses consume locality + gluing to mint Čech charge, damp H1, and amplify H2 into hyperedges.

Kan lifts spend Čech charge to deepen closure and echo the trace site into ascension-ready hyperedges.

Trace site size: 0
Edges enforced by sheafification: 0
Drift amplitude: 0

Trace Field

Sheaves stitch recognitions

Primitive Operators

Manual moves that feed the three fixed points.

rtl actions

Generative Closure

Iterate until the least nontrivial fixed point stabilizes.

ug closure

Autonomy & Timing

Let the three commuting operators run on their own cadence.

Profile multiplier x1.0

Auto mode iterates: sheaf completion \u2192 stabilization \u2192 generative closure whenever resources permit, reflecting the commuting diagram of \u03c3 and \u0394 in the GFRTU.

Resource Ledger

per tick shown

Missions & Accolades

motivators

Closure Diagnostics

fixed-point witnesses
Sheaf coherence0%
Fiber stabilization0%
Generative closure depth0%
RTL commuting evidence0%

When generative depth hits 100%, the least nontrivial fixed point is reached and the universe jumps to the next stage, re-seeding resources with the new internal logic.

Upgrades & Engineering

Spend insight and axioms to wire stronger automation into the lattice.

incremental tuning

Upgrades persist across resets but not across ascensions. Insight is gained passively; axioms drop from stability and RTL actions.

Field Operations

Launch expeditions to harvest gluing proofs, defect spectra, and shard drift.

operations

Available

Active returns

Operations consume current sheaves, resonance, or defect pressure but return long-horizon boosts and proofs for research.

Research & Ritual

Push formal research using proofs, or perform rituals that temporarily warp multipliers.

focus
Research points0

Convert axioms + insight into formal proofs to unlock lattice research.

Ritual statusIdle

Spectral Timeline

chart.js + anime.js

Live charting of coherence, stability, and closure depth using Chart.js with anime.js pulses on surges.

Spectral energy0%

Lodash mean of coherence/stability/closure.

Drift pressure0

Tone.js pings when defects spike.

Cells & Higher Layers

local universes
Cells instantiated0
Stability locale opens0
Defect modes charted0
UG iterates0
CDS packages0
Closure mass0

Topos Ascension

Prestige at deep closure to earn profile shards and widen multipliers.

prestige
Profile shards0

Ascend to earn shards; each shard lifts global yield by 4%.

Ascensions0

A full reset that preserves shards, upgrades, and achievements.

Ascend when closure depth >= 100% to reset resources and push a harder ladder.

In-file diagnostics

Run embedded checks that simulate the GFRTU loop without leaving this file.

Diagnostics snapshot core behaviors: trace→sheaf pipelines, closure stage advances, and expedition + research wiring. Results are restored to your current save automatically.

Console

Math Overlay

GFRTU lawbook

Sheaf completion enforces locality + gluing: presheaf families must agree on overlaps and glue uniquely.

Fiber stabilization iterates \u03c3 and \u0394 until H* = { a : \u03c3(a)=a=\u0394(a) } assembles as a subsheaf.

Generative closure UG^n(\u2205) finds the least nontrivial fixed point supporting RTL arrows and stability locales.

Cells instantiate Sh(U,J|_U); CDS serializes each with RTL signature, laws, and defining expression.

Onboarding briefing

Hit the briefing to follow a staged tutorial: record traces, sheafify, enforce gluing/locality, stabilize fibers, then iterate UG.