organ-formula-foundry

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Organ Guide — Formula Foundry (typing core: catalog + coverage + composition type-algebra)

Module: _SYSTEM/Scripts/math/formula-foundry.mjs · Layer: Energy & Math · Invocation: both · CLI: catalog, coverage, compose, composable, sequences, synth, preflight

Purpose. Formula Foundry typing CORE A — the legal-move generator. Reads the typed formula-bank cards, classifies each card's input/output UNITS into a deterministic closed-set dimension, and decides whether one formula's output may legally feed another's input. Rejects dimensionally-incoherent compositions (bits→length, probability into an energy slot) — the silent-garbage hole the engine exists to close.

Exports

• classifyDimension(unitText)
  • in: a prose unit string (e.g. 'bits', 'joule', 'meters/second')
  • out: { dimension, witness } — closed-set dimension + the matched witness token (or null)
• dimensionsCompatible(a, b)
  • in: two dimension strings (from classifyDimension)
  • out: { compatible, confidence, reason }
• catalogFormulas(opts = {})
  • in: optional { bankDir }
  • out: { cards, count, banks, skipped } — unified read-view over the typed formula-banks; corrupt banks are listed in skipped
• async coverageReport()
  • in: none (reads banks + math-kernel exports)
  • out: { boundCount, kernelExportCount, unboundPrimitives, orphanCards, cardCount } — the kernel-fn↔bank-card binding worklist
• composeCheck(cardA, cardB)
  • in: two catalog card objects
  • out: { legal, compatibleSlots, reasons, from, to, outputDim } — whether A's output may legally feed B
• composableTargets(cardA, catalog = null)
  • in: one card + optional pre-loaded catalog
  • out: array of legal downstream targets { to, slots, outputDim }
• composeOperatorSequences(catalog = null, opts = {})
  • in: optional catalog + { min/max chain length, branching, domain filters }
  • out: { sequences, count, truncated, truncation, params } — enumerated legal operator chains
• synthesizeFormulaCandidates(opts = {})
  • in: optional catalog + synthesis constraints
  • out: { candidates, count, truncated } — research-status candidates
• draftFormulaBankCard(candidate)
  • in: a synthesized candidate
  • out: a research-status bank card (promotionStatus:'research', advisoryOnly:true, implementedBy:null)
• proofPreflightCandidate(card, opts = {})
  • in: a draft card + optional overrides
  • out: { inert, hasBinding, reason, promotionStatus, advisoryOnly, validationOk, validationErrors }

Security boundary

READ-ONLY over the formula-bank files; mints NO production cards. Synthesis output is INERT — promotionStatus:'research', advisoryOnly:true, no kernel binding — and cannot promote until someone binds a real kernel symbol AND a green worked example clears math-proof-gate (Core B). No protected-path access. Deterministic: no RNG, no clock, sorted iteration, closed-set classification.

When to use

Auditing math coverage (which kernel primitives are unbound / which cards are orphaned), checking whether two formulas can legally compose, enumerating legal operator chains, or prototyping new formula candidates by dimensional rules. The upstream typing gate before math-proof-gate validates.

Gotchas

• Dimension classification is keyword-based over a CLOSED set; short tokens (≤5 chars) require full word boundaries to avoid collisions with ordinary English (F-1 hardening).
• UNKNOWN dimensions are treated as compatible-by-default (cannot be disproven) — an UNKNOWN slot is not a rejection.
• Synthesized candidates are INERT and advisory; they NEVER auto-promote — binding + proof-gate is a separate manual step.
• Corrupt bank files are silently skipped; the only visibility of lost cards is the skipped field of catalogFormulas.
• Generator (synthesize) and scorer (bakeoff) are deliberately separate modules — this core does not grade its own candidates.

Session Notes

2026-06-13

• session: 40m | peak ctx: 0% | compacts: 0
• tools: Bash×824, Read×163, Edit×17, StructuredOutput×16, Write×8, TodoWrite×4, ToolSearch×2, ScheduleWakeup×2, Workflow×1, mcp×1, AskUserQuestion×1
• corrections: none
• errors: none