docs: add PIST receipt-density backfill guide

6-Documentation/docs/lean/PIST_RECEIPT_DENSITY_BACKFILL_V1.md

@@ -0,0 +1,215 @@
+# PIST Receipt Density Backfill v1
+
+**Status:** CALIBRATED_ENGINEERING_DELTA  
+**Scope:** RRC equation corpus routing evidence backfill  
+**Script:** `4-Infrastructure/shim/pist_receipt_density_injector.py`
+
+---
+
+## Purpose
+
+This backfill converts existing RRC equation classification rows plus optional PIST spectral/classifier outputs into explicit `receipt_density` records.
+
+It is a routing-evidence population pass, not a promotion pass.
+
+```text
+receipt_density populated != theorem proved
+receipt_density populated != claim promoted
+receipt_density populated == route has structural/witness evidence for RRC use
+```
+
+---
+
+## Default inputs
+
+```text
+6-Documentation/docs/rrc_equation_classification.md
+shared-data/rrc_pist_exact_validation.json
+```
+
+The first file provides equation IDs, RRC shape hints, status, and declared axes.
+
+The second file provides optional PIST spectral/classifier outputs such as:
+
+```text
+proxy_pred
+exact_pred
+matrix_hash
+canonical_hash
+spectral_gap
+rank_estimate
+laplacian_zero_count
+```
+
+The injector explicitly filters Markdown table header/separator rows such as `Equation` and `---`, which older validation passes could accidentally treat as equations.
+
+---
+
+## Default output
+
+```text
+shared-data/rrc_receipt_density_backfill.json
+```
+
+Optional JSONL output for later DB/RDS import:
+
+```bash
+python3 4-Infrastructure/shim/pist_receipt_density_injector.py \
+  --jsonl-out shared-data/rrc_receipt_density_backfill.jsonl
+```
+
+---
+
+## Run command
+
+```bash
+python3 4-Infrastructure/shim/pist_receipt_density_injector.py
+```
+
+Strict mode, useful for CI:
+
+```bash
+python3 4-Infrastructure/shim/pist_receipt_density_injector.py --fail-on-missing-pist
+```
+
+Custom input/output:
+
+```bash
+python3 4-Infrastructure/shim/pist_receipt_density_injector.py \
+  --rrc-file 6-Documentation/docs/rrc_equation_classification.md \
+  --pist-report shared-data/rrc_pist_exact_validation.json \
+  --out shared-data/rrc_receipt_density_backfill.json
+```
+
+---
+
+## Record schema
+
+Each record has the form:
+
+```json
+{
+  "receipt_version": "pist-receipt-density-v1",
+  "equation_id": "bandwidth_adjusted_threshold",
+  "rrc_shape": "CognitiveLoadField",
+  "domain": "analysis",
+  "source_status": "CANDIDATE",
+  "receipt_density": 0.7125,
+  "confidence": 0.6842,
+  "density_components": {
+    "status_score": 0.45,
+    "axis_score": 1.0,
+    "spectral_quality": 0.73,
+    "shape_agreement": 0.82
+  },
+  "shape_prediction": {
+    "ground_truth_hint": "CognitiveLoadField",
+    "proxy_pred": "...",
+    "exact_pred": "...",
+    "matrix_hash": "...",
+    "canonical_hash": "...",
+    "spectral_gap": 0.42,
+    "rank_estimate": 8,
+    "laplacian_zero_count": 1
+  },
+  "top_axes": ["projection_declared", "negative_control_strength"],
+  "status": "CANDIDATE",
+  "promotion": "not_promoted",
+  "source": "pist_receipt_density_injector_v1",
+  "receipt_hash": "...",
+  "warnings": []
+}
+```
+
+---
+
+## Density calculation
+
+The density score is computed from four bounded components:
+
+```text
+status_score
+axis_score
+spectral_quality
+shape_agreement
+```
+
+Current weighting:
+
+```text
+receipt_density =
+  0.26 * status_score
++ 0.24 * axis_score
++ 0.26 * spectral_quality
++ 0.24 * shape_agreement
+```
+
+Confidence is slightly more classifier-weighted:
+
+```text
+confidence =
+  0.20 * status_score
++ 0.20 * axis_score
++ 0.28 * spectral_quality
++ 0.32 * shape_agreement
+```
+
+This is intentionally conservative. A missing PIST prediction can still produce a low-density record from declared RRC axes, but the record receives a `missing_pist_prediction` warning.
+
+---
+
+## Claim boundary
+
+The script writes every record as:
+
+```json
+"promotion": "not_promoted"
+```
+
+This is the central anti-drift boundary.
+
+The generated density says:
+
+```text
+This equation has routing evidence.
+```
+
+It does not say:
+
+```text
+This equation is true.
+This equation is proved.
+This equation is promoted to REVIEWED.
+```
+
+Promotion still requires external receipts, Lean/kernel verification where applicable, or human/adversarial review depending on the claim class.
+
+---
+
+## Next integration step
+
+Once the JSON output is inspected, the next safe step is an explicit DB writer guarded by a flag such as:
+
+```bash
+--write-rds
+```
+
+That writer should upsert only these fields:
+
+```text
+receipt_density
+receipt_density_source
+receipt_density_hash
+receipt_density_status
+receipt_density_warnings
+```
+
+and should not alter theorem truth, promotion state, or claim ladder status.
+
+---
+
+## Keeper phrase
+
+```text
+PIST stops being just a repair engine when its classifications become receipt density for the RRC corpus.
+```