docs: add hybrid PET workflow note

Author: gcomneno

docs/research/pet-hybrid-workflow.md

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+# PET hybrid workflow (end-to-end)
+
+## Goal
+
+Run the current hybrid PET pipeline from a difficult target integer to a forward executable candidate plan.
+
+This workflow does **not** recover the exact PET of the target in general.
+
+It does this instead:
+
+1. probe partial certified structure from the target
+2. translate the probe into bridge constraints
+3. synthesize and rank PET-compatible candidates
+4. materialize a forward constructive plan for a selected candidate
+5. execute that plan and verify the resulting candidate generator
+
+## Core tools
+
+- `tools/partial_signature_probe.py`
+- `tools/pet_hybrid_bridge.py`
+- `tools/pet_hybrid_synthesize.py`
+- `tools/pet_candidate_plan.py`
+- `tools/pet_constructive_plan.py`
+
+Auxiliary research tool:
+
+- `tools/find_probe_status_examples.py`
+
+## Minimal end-to-end sequence
+
+Example target:
+
+- `N = 212262408`
+
+### 1. Probe the target
+
+```bash
+python tools/partial_signature_probe.py 212262408 --schedule 10 --json > /tmp/pet-probe-212262408.json
+```
+
+This extracts:
+
+- certified known factors
+- residual classification
+- root lower bounds
+- exact root anatomy only if the probe closes it
+
+### 2. Build bridge constraints
+
+```bash
+python tools/pet_hybrid_bridge.py /tmp/pet-probe-212262408.json --json > /tmp/pet-bridge-212262408.json
+```
+
+This converts probe output into:
+
+- hard constraints
+- soft uncertainty
+- synthesis hints
+
+### 3. Synthesize and rank candidates
+
+```bash
+python tools/pet_hybrid_synthesize.py /tmp/pet-bridge-212262408.json --json > /tmp/pet-synth-212262408.json
+```
+
+This produces:
+
+- one or more candidate PET explanations
+- ranking
+- status-aware behavior where supported
+
+### 4. Build a forward plan for the selected candidate
+
+```bash
+python tools/pet_candidate_plan.py /tmp/pet-synth-212262408.json --rank 1 --json > /tmp/pet-candidate-plan-212262408.json
+```
+
+This produces:
+
+- root primes
+- root exponents
+- forward steps
+- `constructive_plan` payload
+
+### 5. Execute the constructive plan
+
+```bash
+jq '.constructive_plan' /tmp/pet-candidate-plan-212262408.json > /tmp/pet-exec-plan-212262408.json
+python tools/pet_constructive_plan.py /tmp/pet-exec-plan-212262408.json --json
+```
+
+This executes the plan and reports:
+
+- final integer
+- generator
+- final signature
+- local step history
+
+## What to check at the end
+
+The most important consistency checks are:
+
+- candidate planner output:
+  - `matches_candidate_root_generator = true`
+- constructive execution output:
+  - `already_minimal = true`
+  - `generator = final_n`
+
+When those hold, the ranked candidate has been successfully materialized as a valid forward constructive PET history.
+
+## Residual status interpretation
+
+Current practical reading:
+
+- `prime-power-by-sympy`
+  - often already yields `exact_root_anatomy = true`
+  - usually does not require dedicated synthesis logic
+
+- `perfect-power-composite-base`
+  - currently the best open structured residual for status-aware synthesis
+  - supported by a dedicated candidate/ranking behavior
+
+- `composite-non-prime-power`
+  - still open research territory
+  - currently handled by generic strategies
+
+## Non-claim
+
+This workflow is **not** a replacement for integer factorization.
+
+It is a constrained structural reconstruction workflow under explicit uncertainty.