LMeta/LCDL MathGenesis Prompt Pack v1

What this pack does

It supports two deliberately separated programs:

1. Reference-library construction — ingest established mathematics and physics into typed, provenance-preserving objects.
2. Clean-room rediscovery — expose a learner only to minimal foundations and problem pressure, then stage, falsify, validate, and measure its inventions without leaking the modern reference library.

The pack is aligned with Forge Intelligence problem-class policies, typed artifact envelopes, LMeta units, FI-local LCDL contracts, maturity gates, concept/session dual-wikis, and the deterministic-to-bounded-model reasoning ladder.

Important deployment fact

The public handbook is a generated static site. The writable product source is the forge-intelligence repository. Use this pack to generate reviewed repository artifacts, then rebuild the separate forge-intelligence-website shell. Do not target generated HTML as the knowledge store.

Start here

1. Read SITE_ANALYSIS.md.
2. Read integration/GOVERNANCE.md and select a library partition in curriculum/seed_map.yaml.
3. Use prompts/00_system_library_governor.md as the system instruction for every task prompt.
4. Run 01_partition_and_ingestion_plan.md once per source collection, curriculum wave, or discovery archive.
5. Run the applicable builders (02–11).
6. Run the falsifier (12) and validation tribunal (13) in independent contexts.
7. Run ontology comparison (14), contamination audit (19 when clean-room), and promotion gate (15).
8. Run the repository assembler (16) to produce a write plan rather than uncontrolled writes.
9. Run the batch release auditor (20) before merge.
10. Run the isolated historian (21) only after a clean-room learner generation is frozen.

The most important rule

Do not populate the learner-visible library with concepts the learner is expected to rediscover. Build the complete modern library in reference, keep it inaccessible to learner agents, and expose only learner_seed plus curriculum during a clean-room experiment.

Output modes

Native MathGenesis mode — recommended

Use:

• schemas/math-knowledge-object.schema.json;
• schemas/library-batch.schema.json;
• a proposed knowledge/math/registry.yaml;
• object files under knowledge/math/objects/<partition>/.

Native mode distinguishes axioms, definitions, theorems, proofs, algorithms, constructions, problems, counterexamples, representations, quantities, experiments, physical models, curricula, and discovery lineage.

Compatibility mode

Use templates/compatibility_knowledge_module.yaml to wrap native objects in the existing generic knowledge-module shape. Use:

• jurisdiction: formal-universal for pure mathematics;
• jurisdiction: geometry/<axiomatic-context> for geometry when required;
• jurisdiction: physical-model/<regime> for physics.

Compatibility mode avoids an immediate migration, but native objects should remain canonical and be validated separately.

Prompt groups

Recommended first reference ingestion wave

A practical first merge is twelve modules:

• constructive logic and equality;
• natural-number arithmetic;
• divisibility and common-measure algorithms;
• ratios and proportions;
• Euclidean primitives and constructions;
• congruence and similarity;
• squared-side relations and elementary area;
• elementary algebra and equations;
• coordinate representation;
• sequences, limits, and accumulation foundations;
• measurement, units, and uncertainty;
• kinematics and elementary conservation models.

The broader staged backlog is in curriculum/reference_ingestion_backlog.yaml.

Recommended first clean-room experiment

Use only:

• learner seed: logic, equality, natural construction, finite sequences, comparison, point/line/circle/intersection, quantity/unit/time/position/observation/intervention;
• curriculum: common-measure, equal-grouping, ratio, construction, shadow, motion, accumulation, collision, and balance problem families;
• no modern aliases or reference retrieval.

Measure whether learner-created abstractions improve held-out solving, compress repeated reasoning, transfer between domains, and survive independent falsification.

Key files

• PROMPT_PACK.md — all prompts in one readable document.
• prompts/ — one system/task prompt per file.
• prompts.jsonl — batch-friendly records containing full system and user templates.
• prompt_catalog.yaml — compact prompt registry.
• schemas/ — native object, batch, planning, assurance, promotion, repository, training, and historian contracts.
• templates/ — policy, LMeta, envelope, catalog, registry, and wiki integration skeletons.
• curriculum/ — clean-room seed map, ancient-style problem families, and reference backlog.
• examples/ — schema-valid illustrative objects and batches.
• integration/ — target layout, runbook, governance, migration, and implementation backlog.
• lcdl_contracts/ — four proposal-quality FI-local governed task contracts.

Verification posture

The generating model never self-certifies. A generated object remains draft, source_grounded, or another bounded status unless the corresponding external receipt is supplied. Formal proof, symbolic verification, numerical convergence, dimensional consistency, held-out prediction, intervention evidence, and replication remain separate states.

Current implementation status

This artifact is a complete design and prompt pack, not a claim that its new task IDs are already registered in Forge Intelligence. The included contracts, policies, flows, schemas, fixtures, and integration plan are intended for repository review and implementation under the existing maturity and allowlist process.