"""RQ2-P3 mechanism-instrument calibration gate (`rq2p3-mechanism-prereg.md` §7). DRY, SYNTHETIC-ONLY calibration of the new ``bridge-federated-pool`` topology: it assembles circuits from harness-generated per-circuit seeds (NOT a confirmatory data dir), then reports the four §7 gate items. **No confirmatory record is read** — this is the same blind-safe discipline as the lead-paper loaders; the confirmatory battery stays HARD-HELD until the prereg is frozen. Gate items (§7, re-worded 2026-07-21 pre-freeze — see ``docs/stage-05-rq2p3-gate-clarification.md``; the original items 1–2 encoded the naive-funnel prior and were mechanically wrong under the ratified posterior): 1. Reproduce the lead degeneracy ON THE FROZEN ``bridge-federated`` BRANCH (not the pool). The lead zero-variance degeneracy is a property of the injective fresh-bridge map: unique bridge per circuit seed → unique exit-signature → ``m_i=1`` → ``H_i≈0``, constant ``c_i=1/C``. A pool draws WITH REPLACEMENT, so it cannot (and must not) be asked to reproduce that; the regression teeth live on the untouched frozen branch. 2. ``B=1`` boundary — all circuits share the one bridge → ``c=1.0`` (concentration tooth kept). Under the RATIFIED posterior the anonymity set is then all circuits sharing the exit house, so realized H is at the HIGH end (maximal mix). The naive "low H" gloss is refuted by construction; expect high H. 3. Monotonicity — mean top-3 concentration decreases in B and increases in alpha. 4. Entropy calibration (inherited) — plug-in entropy of N equiprobable senders is exactly log2(N); Miller–Madow adds only the documented finite-N bias term. SCOPE NOTE: this gate validates the INSTRUMENT and MUST NOT pre-assert the sign of H-vs-concentration — that sign is the two-sided confirmatory question (H1/H2). The dry pass previews a mix (ρ 0→+0.838) as an EXPLORATORY finding; the two-sided pre-commitment in §2 is untouched. """ from __future__ import annotations import hashlib import json import math import statistics import sys from typing import Dict, List from cmd_chat.sor.analysis.confirm_load_rq2 import ( bridge_concentration, bridge_label, per_circuit_entropy, top_k_bridge_concentration, ) from cmd_chat.sor.analysis.stats import miller_madow_entropy_bits, spearman from cmd_chat.sor.assembler import assemble from cmd_chat.sor.battery import Cell, derive_seed, enumerate_rq2p3_cells R_DRY = 30 # runs/cell for the dry calibration (matches the prereg §6 R) C_DRY = 50 # circuits/run (matches C) def _run_circuit_seeds(cell_id: str, run_index: int, c: int = C_DRY) -> List[int]: """Harness-side per-circuit seeds for the DRY pass (the confirmatory executor persists real per_circuit_seeds; this is calibration only). Deterministic from the frozen per-run seed rule so the calibration is reproducible.""" run_seed = derive_seed(cell_id, run_index) return [int.from_bytes(hashlib.sha256(f"{run_seed}|circ|{j}".encode()).digest()[:8], "big") for j in range(c)] def _assemble_run(cell: Cell, run_index: int, c: int = C_DRY): return [assemble(cell, s) for s in _run_circuit_seeds(cell.cell_id, run_index, c)] def _pool_cell(b: int, alpha: float) -> Cell: return Cell("RQ2P3", f"RQ2P3/dry/B={b}/alpha={alpha}", {"bridge": "off", "topology": "bridge-federated-pool", "selector": "static", "pool_B": str(b), "pool_alpha": str(alpha)}, False) def _fed_cell() -> Cell: """The FROZEN lead ``bridge-federated`` branch (untouched, fresh bridge per circuit seed). Item-1 regression teeth live here, not on the pool.""" return Cell("RQ2", "RQ2/bridge=off/selector=static/topo=bridge-federated", {"bridge": "off", "topology": "bridge-federated", "selector": "static"}, False) def frozen_branch_regression(r: int = R_DRY, c: int = C_DRY) -> Dict: """Item 1: the untouched frozen ``bridge-federated`` branch must still show the lead degeneracy — unique bridge per circuit (unique exit-signature) → ``m_i=1`` → ``H_i≈0``, constant ``c_i=1/C``. Checked per-run (the confirmatory grouping unit).""" fed = _fed_cell() labels_all_distinct = True H_all_zero = True c_all_const = True mean_h: List[float] = [] for ri in range(r): specs = _assemble_run(fed, ri, c) labels = [bridge_label(s) for s in specs] labels_all_distinct &= (len(set(labels)) == len(labels)) ent = per_circuit_entropy(specs) mean_h.append(statistics.fmean(ent)) H_all_zero &= all(h < 1e-9 for h in ent) conc = [x for x in bridge_concentration(specs) if x is not None] c_all_const &= bool(conc) and all(abs(x - 1.0 / c) < 1e-9 for x in conc) return { "labels_all_distinct": labels_all_distinct, "H_all_zero": H_all_zero, "c_all_const_1_over_C": c_all_const, "mean_entropy_bits": statistics.fmean(mean_h), "pass": labels_all_distinct and H_all_zero and c_all_const, } def cell_report(cell: Cell, r: int = R_DRY, c: int = C_DRY) -> Dict: """Per-cell dry report: mean top-3 concentration over runs, pooled per-circuit (c_i, H_i) Spearman ρ, and the concentration spread.""" per_run_top3: List[float] = [] per_run_mean_h: List[float] = [] conc_all: List[float] = [] h_all: List[float] = [] for ri in range(r): specs = _assemble_run(cell, ri, c) per_run_top3.append(top_k_bridge_concentration(specs, k=3)) ent = per_circuit_entropy(specs) per_run_mean_h.append(statistics.fmean(ent)) for ci, hi in zip(bridge_concentration(specs), ent): if ci is not None: conc_all.append(ci) h_all.append(hi) b = int(cell.factors["pool_B"]) alpha = float(cell.factors["pool_alpha"]) return { "B": b, "alpha": alpha, "mean_top3_concentration": statistics.fmean(per_run_top3), "concentration_stdev": statistics.pstdev(conc_all) if conc_all else 0.0, "mean_entropy_bits": statistics.fmean(per_run_mean_h), "spearman_rho_conc_vs_H": spearman(conc_all, h_all), "n_bridged_circuits": len(conc_all), } def calibration_gate(r: int = R_DRY, c: int = C_DRY) -> Dict: """Run all four §7 gate items on the DRY pass and return a report dict.""" sweep = [cr for cr in (cell_report(cell, r, c) for cell in enumerate_rq2p3_cells())] grid = {(cr["B"], cr["alpha"]): cr for cr in sweep} # Item 1 — regression teeth on the FROZEN bridge-federated branch (not the pool): # unique bridge per circuit → unique signature → m_i=1 → H≈0, constant c_i=1/C. # The pool anchor B=50,alpha=0 is retained as an EXPLORATORY diagnostic only (it is a # mix, ρ>0 — it does NOT and must NOT reproduce the injective fresh-bridge degeneracy). fed_reg = frozen_branch_regression(r, c) anchor = grid[(50, 0.0)] # exploratory: pool at B=50 draws WITH replacement → mix item1_pass = fed_reg["pass"] # Item 2 — B=1 boundary: all circuits share one bridge → c=1.0 (concentration tooth), # and under the ratified posterior H is at the HIGH end (maximal mix). Reference = # the frozen fresh-bridge branch H (≈0). Passing means c=1.0 AND H high, by construction. ext = cell_report(_pool_cell(1, 0.0), r, c) fresh_ref_H = fed_reg["mean_entropy_bits"] item2_conc_ok = abs(ext["mean_top3_concentration"] - 1.0) < 1e-9 item2_high_H = ext["mean_entropy_bits"] > fresh_ref_H item2_pass = item2_conc_ok and item2_high_H # Item 3 — monotonicity: mean top-3 concentration decreasing in B, increasing in alpha. dec_in_B = all( grid[(2, a)]["mean_top3_concentration"] >= grid[(4, a)]["mean_top3_concentration"] >= grid[(8, a)]["mean_top3_concentration"] for a in (0.0, 1.0, 2.0) ) inc_in_alpha = all( grid[(b, 0.0)]["mean_top3_concentration"] <= grid[(b, 1.0)]["mean_top3_concentration"] <= grid[(b, 2.0)]["mean_top3_concentration"] for b in (2, 4, 8) ) item3_pass = dec_in_B and inc_in_alpha # Item 4 — entropy calibration (inherited): plug-in H of N equiprobable = log2(N) exactly. entropy_checks = [] item4_pass = True for n in (2, 4, 8, 16, 50): mm = miller_madow_entropy_bits([1] * n) bias = (n - 1) / (2.0 * n * math.log(2.0)) plugin = mm - bias ok = abs(plugin - math.log2(n)) < 1e-9 item4_pass = item4_pass and ok entropy_checks.append({"N": n, "plugin_bits": plugin, "log2N": math.log2(n), "miller_madow_bits": mm, "plugin_equals_log2N": ok}) return { "schema": "sor-rq2p3-calibration/1", "dry_only": True, "no_confirmatory_data_read": True, "R": r, "C": c, "sweep": sweep, "gate": { "item1_reproduce_lead_degeneracy": { "regressed_on": "frozen bridge-federated branch (untouched)", "frozen_branch": fed_reg, "exploratory_pool_anchor_B50_alpha0": anchor, "note": ( "Teeth are on the frozen fresh-bridge branch (unique signatures → m_i=1 " "→ H≈0, constant c=1/C). A pool draws WITH replacement so it cannot " "reproduce that; the B=50 pool anchor is an EXPLORATORY mix (ρ>0), not a " "regression target. Re-worded pre-freeze; see " "docs/stage-05-rq2p3-gate-clarification.md." ), "pass": item1_pass, }, "item2_B1_boundary": { "mean_top3_concentration": ext["mean_top3_concentration"], "mean_entropy_bits": ext["mean_entropy_bits"], "fresh_bridge_reference_mean_entropy_bits": fresh_ref_H, "concentration_c_eq_1": item2_conc_ok, "entropy_high_maximal_mix": item2_high_H, "note": ( "B=1 shares one bridge → c=1.0 (concentration tooth) AND, under the " "ratified posterior, the anonymity set is all circuits sharing the exit " "house → H at the HIGH end (maximal mix). The naive 'low H' gloss is " "refuted by construction; expect high H. Re-worded pre-freeze." ), "pass": item2_pass, }, "item3_monotonicity": { "decreasing_in_B": dec_in_B, "increasing_in_alpha": inc_in_alpha, "pass": item3_pass, }, "item4_entropy_calibration": { "checks": entropy_checks, "pass": item4_pass, }, "all_pass": bool(item1_pass and item2_pass and item3_pass and item4_pass), }, } if __name__ == "__main__": print(json.dumps(calibration_gate(), indent=2, sort_keys=True)) sys.exit(0)