# Operator-Driven Prime Discovery — Reproducibility Bundle (raw data)

**Companion to the paper *Operator-Driven Discovery of Prime Abstractions* and *The Operator
Compendium*** (Conceptual section of the Encyclopedia of Abstractions website). This bundle is the
raw material behind every quantitative claim in those papers: the per-application model outputs, the
per-operator result ledgers, the fixed-point/audit censuses, the candidate primes and hierarchy
edges the search surfaced, the retained negatives, and the exact prompts used to run each operator.

**Snapshot: 2026-07-04. Corpus frozen at 1,325 primes for the duration of the search.**

> **Provisional status.** The *raw data* here (crank outputs, censuses, candidate edges, templates)
> is final and complete. The only provisional numbers are the **acceptance counts** — how many
> candidate primes survive the owner's final human curation — which are not represented in this data
> at all (they live in the paper). A refreshed bundle will note final acceptance counts once curation
> completes. Nothing in the raw data changes with curation.

## How discovery worked, in one paragraph

Each of fourteen **operators** (dualization, generalization, temporalization, analogy completion, …)
is a transformation that takes a prime — or a tuple of primes — and proposes a candidate new prime.
Every application runs a five-stage funnel: a cheap model generates one candidate (the *crank*);
deterministic + cheap-model screens drop candidates that are aliases, restatements, or not-a-prime;
a stronger model adjudicates the survivors; a human curates the finalists. Most applications
*collapse* (return the input, or an existing prime); collapses are retained as signal. See
`method/OPERATOR_SEARCH_RUNBOOK.md` for the full pipeline and `method/OPERATOR_SEARCH_FINDINGS.md`
for the synthesis (including the **yield law** and the fixed-point saturation gradient).

## What is here, and which paper claim each file substantiates

- **`method/`**
  - `OPERATOR_SEARCH_FINDINGS.md` — the synthesis: yield law, saturation gradient, genus-convergence,
    limitations. The paper's Results and Discussion are distilled from this.
  - `OPERATOR_SEARCH_RUNBOOK.md` — the operational pipeline (all five stages, all fourteen operators).
  - `conceptual_foundation.md` — the closure argument + prior-art analysis (paper §2, §7).
  - `SATURATION.md` — the per-operator results table in prose (the completeness ledger).
  - `operators_summary.csv` — the same ledger, machine-readable: per operator, applications, model
    tier, fixed-point census, survivors, alias-confirmations, rejects, holds→stubs, cost.
    **This is the evidence for the yield law and the saturation gradient (paper §5.2–5.3).**

- **`crank_per_application/*.jsonl`** — one record per operator application: the input prime, the
  candidate the model proposed, its NEW/COLLAPSE verdict, and the nearest existing prime it named.
  **This is the "show your work" data**: from it a reader can independently recompute every NEW-rate,
  every fixed-point census, and every cross-input convergence count the paper reports. Files are named
  by operator/flavor (`sweep_1a`, `op02_sweep`, `op11_full`, `sweep_op05_framed`, …). Consolidated
  per-application records; the per-batch raw text logs are omitted as redundant.

- **`audit_censuses/*.jsonl`** — the fixed-point / "already-X" censuses per unary operator (temporal,
  spatial, modal, self-dual, threshold, perspective). **Substantiate the saturation gradient**
  (corpus is 59% already-temporal, 41% self-referential, 37% spatial, 22% modal — paper §5.3).

- **`manifests/*.yaml`** — per-operator adjudication manifests: the finds, the method notes, the
  frontier verdicts, and the run-by-run iteration record (including the failed template revisions).
  **Substantiate the finds (§5.4) and the method lessons (§6).**

- **`candidate_primes/*.md`** — the 128 candidate-prime stubs the search surfaced, each with
  frontmatter (proposer estimates), a Core Idea, and candid keep/cut notes. **The actual output of
  the search**, pending final curation. (Includes `interpolation.md`, the prime discovered by turning
  the method on itself — see paper §9.)

- **`candidate_dag_edges/`** — `dag_edge_worklist.yaml` (~295 candidate hierarchy edges harvested as a
  byproduct, flagged clean-new / already-typed / reverse-direction) + its adjudication runbook.
  **Substantiate the densification byproduct (§5.5).**

- **`retained_negatives/*.jsonl`** — the structurally-tempting-but-wrong candidates the pipeline
  correctly rejected. **The hard-negative set behind the discovery-as-training-data claim (§5.5, §7).**

- **`operator_templates/*.md`** — the frozen Stage-0 prompt for each operator (the crank prompt, the
  collapse test, the few-shot). **Method reproducibility**: rerun any operator from these.

## Reproducing a headline number (example)

*"Self-application returns a fixed point for 41% of primes."* Load `crank_per_application/op02_sweep.jsonl`,
count records whose candidate is a fixed point (verdict COLLAPSE with the input named as nearest, or an
empty candidate), divide by total applications. Cross-check against `audit_censuses/audit_self_duals.jsonl`.

## Caveats

- Cheap-model crank text is raw and occasionally malformed — that is the point (you see exactly what
  the pipeline saw). Downstream screens and the manifests record how each was adjudicated.
- Counts labelled "holds"/"accepts" in the manifests are the pipeline's *recommendation*, not accepted
  primes; the human curation gate is still open.
- This is a single-corpus, single-curator snapshot; the reproducible templates make it re-runnable.
