docs(sor): follow-up plan — RQ2-P3 mechanism prereg + RQ3 run-brief + unique-bridge artifact note
RQ2-P3 mechanism study (NEW prereg, approved-path/params-locked, not yet frozen):
pool-based willing-bridge instrument, concentration swept as a manipulated IV
(B∈{2,4,8}×α∈{0,1,2}), two-sided/direction-agnostic, run-level cluster bootstrap.
RQ3 companion run-brief (execution-freeze for the already-frozen RQ3): agent=qwen2.5:3b
local Ollama, churn kill_prob=30/steps=20, baselines + Holm-7 completion pinned.
note-unique-bridge-artifact.md: on-record analysis that the lead RQ2-P1 shrink is plausibly
a fresh-bridge-per-circuit artifact (unique exit-signature -> singleton set -> H~0), and that
realistic bridge reuse (a mix) may raise anonymity -> the mechanism study may qualify the lead
RQ2 headline. No edit to the frozen prereg or committed lead paper.
Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>
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# Pre-registration (DRAFT) — RQ2-P3 funnelling-mechanism study
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> **STATUS: APPROVED-PATH, PARAMS LOCKED — NOT YET FROZEN.** Design + parameters
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> operator-approved 2026-07-21 (grid B∈{2,4,8}×α∈{0,1,2}; run-level cluster bootstrap;
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> two-sided/direction-agnostic). Remaining step before any confirmatory cell: **human freeze
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> checkpoint** — record the SHA-256 of the final text in §10 and the operator freeze sign-off.
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> Build + synthetic tests + the §7 calibration gate MAY proceed now; the confirmatory battery
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> MUST wait for the freeze.
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> This is a **new study with its own slug** (`sor-consent-rq2p3`). It **does not modify**
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> the frozen lead prereg (`sor-consent-prereg.md`, SHA
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> `f22331a72e0d0ccf38b787e63acabbe9d666456ec76076787a6d545c3193425b`), whose RQ2-P3
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> result stands as reported ("inconclusive — not testable as-instrumented").
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## 0. Why this study exists
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The lead paper found federation **shrinks** the per-circuit anonymity set (RQ2-P1,
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ΔH = −0.96 bits, Holm-significant) but could **not** test the *mechanism* (RQ2-P3): the
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bridge-federated instrument assigns a **fresh willing bridge per circuit seed**
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(`assembler.py:131`, `_bridge_label(seed)`), so every circuit routes through a distinct
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bridge, top-3 concentration is constant (`c_i = 1/C`), the covariate has **zero variance**,
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and Spearman ρ is undefined (`stats.spearman` returns 0.0 by construction). The lead paper
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reported this honestly as an as-instrumented degeneracy, not a null of a well-posed test.
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**The mechanical insight this study exists to test (see `note-unique-bridge-artifact.md`).**
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The adversary's observation is `exit_signature = (exit_house, bridge_label)`, and the
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per-circuit anonymity set `m_i` = the distinct entry nodes among circuits sharing that
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signature (`confirm_load_rq2.py`). A **fresh bridge per circuit ⇒ every signature is unique
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⇒ group size 1 ⇒ m_i = 1 ⇒ H ≈ 0.** That — not funnelling — is why bridge-federated produced
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H ≈ 0 and drove the lead ΔH negative. Introduce a **finite shared pool** and many circuits
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share a bridge ⇒ shared signature ⇒ larger set ⇒ **higher H**. Under this posterior a bridge
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is a **mix**: more concentration plausibly *raises* anonymity, the opposite of the naive
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funnel story. So this study is, honestly, **a test of whether the lead paper's "shrink" is a
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unique-bridge artifact** — and it may *qualify or correct* the lead RQ2-P1 headline.
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This study re-instruments the willing-bridge layer with a **finite pool + skewed
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willingness** so concentration genuinely varies, and — the key upgrade — treats
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concentration as a **manipulated independent variable** (a dose-response design) rather than
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a passive covariate. The direction is left **two-sided**: the naive prediction is funnel
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(ρ < 0); the mechanical prediction under the ratified posterior is mix (ρ > 0). We pre-commit
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to reporting whichever the data shows, including a correction to the lead result if warranted.
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The analysis code (`bridge_concentration`, `rq2_p3_funnel`) is already correct; only the
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*instrument* and this *prereg* are new.
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## 1. Blinding & integrity posture (read first)
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- **This study is NOT blind to the RQ2-P1 shrink direction** (the lead paper is published).
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Mitigations that keep it honest: (a) the funnelling hypothesis was **pre-stated as a live
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mechanism** in the lead paper's introduction, not invented post-hoc; (b) the confirmatory
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targets below are **two-sided**; (c) concentration is a *manipulated* IV, so the test is a
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designed dose-response, not a re-slice of the lead data.
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- **The lead RQ2-P1 result is NOT re-litigated here.** Any ΔH this pool instrument produces
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is labeled **EXPLORATORY / replication**, never a re-run of the frozen RQ2-P1.
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- **No detector retuning.** The entropy estimator, posterior construction, and Spearman path
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are inherited **unchanged** from the frozen lead pipeline; only bridge assignment changes.
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## 2. Research question & hypotheses
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**RQ2-P3′.** Within the consent-gated bridge-federated topology, does willing-bridge
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**concentration** causally reduce the per-circuit anonymity set (funnelling)?
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- **H1 (within-cell association, two-sided).** Spearman ρ between per-circuit top-3 willing-
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bridge concentration `c_i` and per-circuit entropy `H_i`. **Funnel** iff BCa 95% CI < 0;
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**mix** iff CI > 0; **inconclusive** iff CI spans 0. Direction is *not* presumed.
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- **H2 (dose-response, two-sided).** OLS slope β of H on realized top-3 concentration, over
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**per-run mean points** (9 cells × 30 runs = 270 clustered points), cell-level BCa CI.
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**Funnel** iff slope CI < 0; **mix** iff slope CI > 0.
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- **H3 (joint, direction-agnostic).** Mechanism **RESOLVED** iff H1 and H2 agree in sign and
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both exclude 0; the *sign* is the finding (funnel vs mix). **Unresolved** if either spans 0.
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## 3. Instrument change (the only new code)
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Replace the per-seed fresh bridge with a **willing-bridge pool** of size `B` and a fixed
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skewed willingness weight vector, under a **new topology factor** so lead-paper cells stay
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bit-reproducible:
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```
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# new assembler branch: topology == "bridge-federated-pool"
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weights = zipf_weights(B, alpha) # fixed from the CELL seed; stable per run
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idx = weighted_draw(sha256(f"sor-bridge-pool|{circuit_seed}"), weights)
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bridge = f"bridge#{idx:02d}" # B distinct labels, REUSED across circuits
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```
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- Weights derive from the **cell** seed (not the circuit seed) so the willingness profile is
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fixed within a run and circuits genuinely share bridges → concentration varies.
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- Everything else (hop structure, houses, exit-signature grouping, posterior, Miller–Madow H,
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BCa) is **identical to the frozen lead pipeline**.
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- Touchpoints: `assembler.py` (new branch + pool helper), `battery.enumerate_cells()` (sweep).
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`confirm_load_rq2.py`, `confirm.py`, `stats.py` are **unchanged**.
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## 4. Design matrix (concentration as IV)
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Bridge-federated-pool, selector `static`, matched-N, bridge willingness the only manipulation:
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- **Pool size** `B ∈ {2, 4, 8}` — 3 levels.
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- **Willingness skew** `alpha ∈ {0 (uniform), 1.0 (moderate Zipf), 2.0 (heavy Zipf)}` — 3 levels.
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- Full 3×3 = 9 concentration cells (each realizes a distinct mean top-3 concentration).
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Run order randomized within cell; deterministic from an ordering seed distinct from data seeds.
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## 5. Dependent variables
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- **Per-circuit H_i** — Miller–Madow entropy of the uniform posterior over the observation-
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consistent anonymity set (inherited **verbatim** from the frozen lead pipeline).
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- **Per-circuit top-3 concentration c_i** — `confirm_load_rq2.bridge_concentration` (unchanged).
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## 6. Sampling, seeds, stopping rule
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- **R = 30** seeded runs/cell, **C = 50** circuits/run (matched to the lead study).
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- Base seed **S0 = 20260719**; per-cell seed = `SHA256(S0 ‖ cell_id ‖ run_index)` (matched).
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- **Fixed stopping rule:** all 9 cells × R run to completion. No optional stopping, no interim
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looks. An uninformative cell is reported **inconclusive**, never extended.
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## 7. Instrument-validation gate (boolean; blocks the confirmatory run)
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All must pass **before** any confirmatory cell:
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1. **Reproduce the lead degeneracy.** `B = 50, alpha = 0` → `c_i ≈ 1/50` constant, ρ undefined
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— a regression check that this instrument reproduces the published RQ2-P3 result.
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2. **Extremes.** `B = 1` → all circuits share one bridge → `c = 1.0`, minimal set, low H.
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3. **Monotonicity.** Realized mean top-3 concentration is **monotone decreasing in B** and
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**increasing in alpha**, across the sweep, on a dry (non-confirmatory) calibration pass.
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4. **Entropy calibration unchanged.** H = log₂N on equiprobable synthetic senders (inherited).
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If any gate item fails → STOP, do not report; surface as NEEDS-OPERATOR.
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## 8. Analysis plan
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- Effect size + BCa 95% CI for every test; p never reported alone; 10,000 resamples; α = 0.05.
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- **H1:** `confirm.rq2_p3_funnel(c, H)` per cell + pooled, but resampled with a **run-level
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cluster bootstrap** (resample whole runs, not individual circuits). Rationale: circuits
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sharing a bridge have identical `c_i` and correlated `H_i`, so per-circuit resampling
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pseudo-replicates and falsely narrows the CI (the same defect noted for lead RQ1-P1). The
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run is the independent unit.
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- **H2:** OLS slope of per-run mean-H on per-run mean top-3 concentration (270 clustered
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points); BCa CI resampling **over runs within cells** (cluster bootstrap).
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- **Multiplicity:** Holm–Bonferroni over **this study's own family** {H1-pooled, H2-slope}
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(the lead study's family-of-7 is closed and not reopened).
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- **Confirmatory vs exploratory:** the 9-cell sweep is confirmatory; any per-cell ρ contrast or
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ΔH replication is labeled EXPLORATORY.
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- **Data exclusion (pre-data):** quarantine only on integrity failure (SHA/pcap mismatch,
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non-reproducing seed). No performance-based exclusions.
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## 9. Rails (immutable, inherited)
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Prereg frozen after approval — never edited (deviations only in a stage-05-style log; no
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HARKing; nulls are results). Containment: isolated docker only, self-generated fixture traffic,
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lab-only. Budget $0. Worktree only on `feat/sor-consent-relay`. Raw data immutable + SHA-256.
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## 10. Freeze block (to complete at approval)
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```
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FROZEN: <date>
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PREREG SHA-256: <hash of final text>
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APPROVED BY: <operator>
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POOL/ SKEW LEVELS LOCKED: B∈{2,4,8}, alpha∈{0,1.0,2.0}
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```
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