Categorical Lens

Read this demo as local sections, restriction maps, gluing, obstructions, and Kan-style structured completion.

Collective intelligence: many agents have only local views, but global structure emerges through compatible local actions.

Objects
seed specs, gold contexts, generated foundry plans
Morphisms
model-generated translations from Scylla JSON to Homer/Athena/Prometheus sections
Sections
candidate local models proposed by the LLM
Gluing
claims or artifacts admitted when local sections agree on overlaps
Obstructions
qualified, review, or quarantine cells where gluing fails
Kan View
benchmarking whether the model can compute a useful foundry completion
Prometheus placeholders

TICKET Transformer

TICKET(foundry_automation_benchmark_run) - Topos Integration using Causal Kan Extension Transformers

Expression: TICKET(foundry_automation_benchmark_run) -> compose(evaluation_harness, assistant_spec, foundry_plan) -> glue(benchmark_admission)

FSQL: FROM prometheus_runs SLICE BY foundry("evaluation_harness") TICKET BY target_foundry

Admission policy: quarantine model-generated plans that miss Homer, Athena, Prometheus, gluing-audit, or Scylla-review sections

Homer Foundry Automation Benchmark

A model is asked to construct Homer, Athena, Prometheus, gluing-audit, and Scylla-review sections from a Scylla JSON spec.

3cases
5gates
15contexts
11overlaps

Model Prompt

Open the JSON-only model prompt.

Required Sections

homer_program, athena_sheaf_plan, prometheus_job_contract, prometheus_world_model_skeleton, gluing_audit_plan, scylla_review_surface

Seed Cases

CaseDomainContextsOverlapsDecision Surface
storefront_inventory_sheafstorefront_operations54inventory_and_staffing_maintenance
rps_equilibrium_sheafrps_demo53equilibrium_convergence
network_token_flow_sheafnetwork_economy_demo54token_flow_maintenance

Scoring Gates

GateChecksBlocks When
context_cover_gateCandidate plan includes domain-appropriate local contexts with stable context_id values.The model emits generic agents but no sheaf cover.
overlap_restriction_gateOverlaps name source contexts, shared evidence, compatibility predicates, and decision surfaces.The plan cannot say how local sections restrict to shared evidence.
prometheus_artifact_gateThe plan emits a Prometheus job contract and expected artifact bundle.The model only describes work in prose and omits executable artifact contracts.
gluing_audit_gateThe plan names promotion, obstruction, and next-observation behavior.All outputs are promoted without an obstruction surface.
scylla_review_gateThe plan includes a human-facing review surface with audit status and trust questions.The plan cannot explain what Scylla should show the user.

Recommended Experiment

deepseek_vs_kimi_foundry_autogen_001: admitted_sections_without_manual_repair