RQ2-P3: bridge-federated-pool mechanism instrument + synthetic tests + calibration gate
Build the funnelling-mechanism instrument for the RQ2-P3 follow-up: a new
`bridge-federated-pool` topology drawing each circuit's bridge from a finite
willing-bridge pool (size B) under Zipf willingness skew (alpha), so bridge
concentration genuinely varies as a manipulated IV. Defensive measurement only:
synthetic seeds, no engine, no traffic, no confirmatory record read.
- assembler.py: add `bridge-federated-pool` branch + zipf_weights/weighted_draw
helpers; existing lead `bridge-federated` branch left untouched and
bit-reproducible (fresh bridge per seed).
- battery.py: enumerate_rq2p3_cells() = B{2,4,8} x alpha{0,1,2} + anchor B=50,
alpha=0 (separate fn; frozen 6-cell lead lattice unmutated).
- analysis/rq2p3_calibration.py: DRY synthetic-only §7 calibration gate; no
confirmatory data read. confirm_load_rq2.py/confirm.py/stats.py unchanged.
- tests/test_sor_rq2p3_pool.py: 9 synthetic tests (helpers + pool reuse/variance
+ lead branch reproducibility).
Calibration gate RAN: items 3 (monotonicity) & 4 (entropy) PASS; items 1 & 2 do
NOT match their naive-funnel wording because the ratified posterior yields a MIX
(rho>0 across the whole sweep incl anchor rho=+0.838; B=1 -> H=2.54 bits HIGH) --
the note-unique-bridge-artifact.md prediction, surfaced early. HARD HOLD: no
confirmatory battery, no prereg freeze; NEEDS-OPERATOR banner raised for the §7
item-1/2 re-word decision. Lead prereg SHA f22331a72e... untouched; worktree-only.
Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>
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"""RQ2-P3 mechanism-instrument calibration gate (`rq2p3-mechanism-prereg.md` §7).
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DRY, SYNTHETIC-ONLY calibration of the new ``bridge-federated-pool`` topology: it
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assembles circuits from harness-generated per-circuit seeds (NOT a confirmatory data
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dir), then reports the four §7 gate items. **No confirmatory record is read** — this
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is the same blind-safe discipline as the lead-paper loaders; the confirmatory battery
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stays HARD-HELD until the prereg is frozen.
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Gate items (§7):
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1. Reproduce the lead degeneracy — ``B=50, alpha=0`` → ``c_i`` ≈ 1/C, near-constant,
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Spearman ρ inconclusive.
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2. Extreme ``B=1`` — all circuits share one bridge → ``c=1.0`` (a degenerate
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concentration extreme). NOTE: under the RATIFIED posterior a fully-shared bridge
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*maximizes* the observation-consistent anonymity set, so realized H comes out
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HIGH, not low — the mechanical "mix" the study exists to test. This is surfaced,
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not silently reconciled with the naive "low H" gloss.
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3. Monotonicity — mean top-3 concentration decreases in B and increases in alpha.
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4. Entropy calibration (inherited) — plug-in entropy of N equiprobable senders is
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exactly log2(N); Miller–Madow adds only the documented finite-N bias term.
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"""
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from __future__ import annotations
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import hashlib
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import json
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import math
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import statistics
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import sys
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from typing import Dict, List
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from cmd_chat.sor.analysis.confirm_load_rq2 import (
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bridge_concentration,
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per_circuit_entropy,
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top_k_bridge_concentration,
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)
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from cmd_chat.sor.analysis.stats import miller_madow_entropy_bits, spearman
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from cmd_chat.sor.assembler import assemble
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from cmd_chat.sor.battery import Cell, derive_seed, enumerate_rq2p3_cells
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R_DRY = 30 # runs/cell for the dry calibration (matches the prereg §6 R)
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C_DRY = 50 # circuits/run (matches C)
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def _run_circuit_seeds(cell_id: str, run_index: int, c: int = C_DRY) -> List[int]:
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"""Harness-side per-circuit seeds for the DRY pass (the confirmatory executor
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persists real per_circuit_seeds; this is calibration only). Deterministic from
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the frozen per-run seed rule so the calibration is reproducible."""
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run_seed = derive_seed(cell_id, run_index)
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return [int.from_bytes(hashlib.sha256(f"{run_seed}|circ|{j}".encode()).digest()[:8], "big")
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for j in range(c)]
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def _assemble_run(cell: Cell, run_index: int, c: int = C_DRY):
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return [assemble(cell, s) for s in _run_circuit_seeds(cell.cell_id, run_index, c)]
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def _pool_cell(b: int, alpha: float) -> Cell:
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return Cell("RQ2P3", f"RQ2P3/dry/B={b}/alpha={alpha}",
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{"bridge": "off", "topology": "bridge-federated-pool",
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"selector": "static", "pool_B": str(b), "pool_alpha": str(alpha)}, False)
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def cell_report(cell: Cell, r: int = R_DRY, c: int = C_DRY) -> Dict:
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"""Per-cell dry report: mean top-3 concentration over runs, pooled per-circuit
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(c_i, H_i) Spearman ρ, and the concentration spread."""
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per_run_top3: List[float] = []
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per_run_mean_h: List[float] = []
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conc_all: List[float] = []
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h_all: List[float] = []
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for ri in range(r):
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specs = _assemble_run(cell, ri, c)
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per_run_top3.append(top_k_bridge_concentration(specs, k=3))
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ent = per_circuit_entropy(specs)
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per_run_mean_h.append(statistics.fmean(ent))
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for ci, hi in zip(bridge_concentration(specs), ent):
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if ci is not None:
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conc_all.append(ci)
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h_all.append(hi)
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b = int(cell.factors["pool_B"])
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alpha = float(cell.factors["pool_alpha"])
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return {
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"B": b,
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"alpha": alpha,
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"mean_top3_concentration": statistics.fmean(per_run_top3),
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"concentration_stdev": statistics.pstdev(conc_all) if conc_all else 0.0,
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"mean_entropy_bits": statistics.fmean(per_run_mean_h),
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"spearman_rho_conc_vs_H": spearman(conc_all, h_all),
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"n_bridged_circuits": len(conc_all),
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}
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def calibration_gate(r: int = R_DRY, c: int = C_DRY) -> Dict:
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"""Run all four §7 gate items on the DRY pass and return a report dict."""
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sweep = [cr for cr in (cell_report(cell, r, c) for cell in enumerate_rq2p3_cells())]
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grid = {(cr["B"], cr["alpha"]): cr for cr in sweep}
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# Item 1 — anchor B=50, alpha=0 reproduces the lead degeneracy.
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anchor = grid[(50, 0.0)]
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item1_pass = anchor["concentration_stdev"] < 1e-3 and abs(anchor["spearman_rho_conc_vs_H"]) < 0.05
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# Item 2 — extreme B=1: all circuits share one bridge (degenerate concentration).
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ext = cell_report(_pool_cell(1, 0.0), r, c)
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lead_like = cell_report(_pool_cell(1_000_000, 0.0), r, c) # huge pool ≈ fresh bridge/circuit
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item2_conc_ok = abs(ext["mean_top3_concentration"] - 1.0) < 1e-9
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# The naive gate text says "low H"; the ratified posterior yields HIGH H. Surface it.
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item2_entropy_direction = "HIGH (mechanical mix)" if ext["mean_entropy_bits"] > lead_like["mean_entropy_bits"] else "low"
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item2_matches_naive_low_H = ext["mean_entropy_bits"] < lead_like["mean_entropy_bits"]
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# Item 3 — monotonicity: mean top-3 concentration decreasing in B, increasing in alpha.
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dec_in_B = all(
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grid[(2, a)]["mean_top3_concentration"] >= grid[(4, a)]["mean_top3_concentration"] >= grid[(8, a)]["mean_top3_concentration"]
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for a in (0.0, 1.0, 2.0)
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)
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inc_in_alpha = all(
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grid[(b, 0.0)]["mean_top3_concentration"] <= grid[(b, 1.0)]["mean_top3_concentration"] <= grid[(b, 2.0)]["mean_top3_concentration"]
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for b in (2, 4, 8)
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)
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item3_pass = dec_in_B and inc_in_alpha
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# Item 4 — entropy calibration (inherited): plug-in H of N equiprobable = log2(N) exactly.
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entropy_checks = []
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item4_pass = True
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for n in (2, 4, 8, 16, 50):
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mm = miller_madow_entropy_bits([1] * n)
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bias = (n - 1) / (2.0 * n * math.log(2.0))
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plugin = mm - bias
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ok = abs(plugin - math.log2(n)) < 1e-9
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item4_pass = item4_pass and ok
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entropy_checks.append({"N": n, "plugin_bits": plugin, "log2N": math.log2(n),
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"miller_madow_bits": mm, "plugin_equals_log2N": ok})
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return {
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"schema": "sor-rq2p3-calibration/1",
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"dry_only": True,
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"no_confirmatory_data_read": True,
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"R": r, "C": c,
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"sweep": sweep,
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"gate": {
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"item1_reproduce_lead_degeneracy": {
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"anchor_B50_alpha0": anchor,
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"pass": item1_pass,
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},
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"item2_extreme_B1": {
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"mean_top3_concentration": ext["mean_top3_concentration"],
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"mean_entropy_bits": ext["mean_entropy_bits"],
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"fresh_bridge_reference_mean_entropy_bits": lead_like["mean_entropy_bits"],
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"concentration_degenerate_c_eq_1": item2_conc_ok,
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"entropy_direction_vs_naive": item2_entropy_direction,
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"matches_naive_low_H_expectation": item2_matches_naive_low_H,
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"NEEDS_OPERATOR": not item2_matches_naive_low_H,
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"note": (
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"Concentration extreme is as specified (c=1.0). But the ratified "
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"posterior makes a fully-shared bridge MAXIMIZE the anonymity set, so "
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"realized H is HIGH, contradicting the §7 gate-item-2 'low H' gloss. "
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"This is exactly the mechanical 'mix' (ρ>0) the study exists to test "
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"(see note-unique-bridge-artifact.md), surfaced early at calibration. "
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"Not silently reconciled: flagged for the operator's freeze decision."
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),
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},
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"item3_monotonicity": {
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"decreasing_in_B": dec_in_B,
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"increasing_in_alpha": inc_in_alpha,
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"pass": item3_pass,
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},
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"item4_entropy_calibration": {
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"checks": entropy_checks,
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"pass": item4_pass,
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},
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},
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}
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if __name__ == "__main__":
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print(json.dumps(calibration_gate(), indent=2, sort_keys=True))
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sys.exit(0)
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