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Assisted study of generated equations

The framework generates candidate equations (compute master equations, derived operators, community proposals). These are research hypotheses to study — not proven physics, not measurements, not discoveries. Two layers:

Layer 1 — the free hypothesis stamp (no LLM)​

Every generated equation is intrinsically labelled, in code, with no LLM call:

{
  "label": "hypothesis",
  "not_a_discovery": true,
  "statement": "Framework-generated research hypothesis for study — NOT proven physics, not a measurement, not a discovery. No result is asserted; verify independently.",
  "generated_by": "derived-operator:NPD01",
  "provenance": { "...": "..." },
  "zeqond": 2292807709
}

The framework states the honesty plainly itself — you never have to ask an LLM to be told a hypothesis is a hypothesis.

Layer 2 — the opt-in LLM study​

When you actually want deeper analysis, set run_llm: true. The study runs over the existing provider layer and returns a structured aid:

{
  "summary": "...", "resembles": "...",
  "dimensional_notes": "...", "testable_predictions": "..."
}

The prompt hard-frames the task as studying a hypothesis — the model must not claim the equation is true, established, or a discovery, and must flag what's uncertain. If the model doesn't return strict JSON, the raw text is surfaced and the structured body is null — never fabricated. Studies are persisted for review, and there is no code path from a study into the canonical registry.

Endpoints​

# Free stamp (no LLM):
curl -X POST https://zeqstate.com/api/equation-study -b "$COOKIE" \
  -H 'content-type: application/json' \
  -d '{"subject_kind":"wizard","equation":"E = hν"}'
# → { stamp: { label:"hypothesis", ... }, study: null }

# Opt-in LLM study (persisted):
curl -X POST https://zeqstate.com/api/equation-study -b "$COOKIE" \
  -H 'content-type: application/json' \
  -d '{"subject_kind":"derived-operator","subject_ref":"NPD01","run_llm":true}'

GET /api/equation-study and GET /:id browse persisted studies. Equations resolve inline or from derived_operators / community_operators.

Source: shared/api-core/src/lib/equationStudy.ts, routes/equationStudy.ts.