69-constructions Skill

Self-play curricula via DuckLake time-travel with path-invariant verification

Trit: -1 (MINUS - consumer/verifier)

Origin

From Interverse transcript (Sep-Oct 2025):

"Executed my preceding ask of verification 69 times, which led to constructions of constructions... enumerate those 69 previous interactions relating to constructions as a verification step."

The 69 Curriculum

A year-long weekly schedule of condensed mathematics topics:

Week	Topic
Dec 5	Condensing and constructing morphisms
Jan 2	Role in robust AI systems
Jan 9	Modeling abstract mathematical objects
...	...
Sep 25	Representations of the world

Total: 69 weekly constructions covering condensed sets, derived categories, spectral sequences, ∞-categories, and cognitive modeling.

Path-Invariant Verification

UI creates task → DB stores task → UI reads task → DB confirms
                     ↓
              Path invariant:
         create;read = read;create = id

The system tests itself by verifying both directions:

• Forward: UI → DB → verification
• Backward: DB → UI → verification

DuckLake Time-Travel

-- Query historical state at construction #42
SELECT * FROM constructions
AS OF TIMESTAMP '2025-04-10'
WHERE construction_id = 42;

-- Diff between constructions
SELECT * FROM table_diff(
    'constructions',
    '2025-03-01',
    '2025-04-01'
);

Self-Play Structure

struct SelfPlayCurriculum
    constructions::Vector{Construction}  # 69 of them
    verifications::Matrix{Bool}          # 69×69 path checks
    time_travel_enabled::Bool
end

function verify_path_invariant(c::SelfPlayCurriculum, i::Int, j::Int)
    forward = apply(c.constructions[i], c.constructions[j])
    backward = apply(c.constructions[j], c.constructions[i])
    return forward == backward  # Commutativity check
end

Related Skills

• duckdb-timetravel (0): Temporal versioning layer
• self-validation-loop (-1): Prediction vs observation
• duck-time-travel (0): Time-travel queries
• condensed-analytic-stacks (+1): Scholze-Clausen bridge

Commands

# Run 69-construction verification
bb 69-constructions.bb --verify-all

# Time-travel query
duckdb -c "SELECT * FROM constructions AS OF '2025-06-01'"

---

Autopoietic Marginalia

The interaction IS the skill improving itself.

Every use of this skill is an opportunity for worlding:

• MEMORY (-1): Record what was learned
• REMEMBERING (0): Connect patterns to other skills
• WORLDING (+1): Evolve the skill based on use

Add Interaction Exemplars here as the skill is used.