[MaxGhenis]

B2's floor builder, comparator and one-shot scorer, built to the B0.1 addendum as merged in #505 (docs/design/track_b_b0_1_addendum.md, sections 4-9 and 13). This is an invented-data build: no test sets the PSID directory, opens a PSID file, or reads a selection ledger or a B1 output, and nothing here has run on PSID data. B2 registers on issue #42 pinning this PR's merge commit, and only then runs, in the order section 9 sets.

What it builds

File	What it does
src/populace_dynamics/track_b/b2.py	The rules shared by the builder and the scorer. It holds the geometry, seeds and streams; root-parameterised household and design multiplicities; element 8's stratum rule; ν and t_star; the registered standard error; the bound, Monte Carlo and undefined-replicate rules; validity and the INVALID → FAIL → PASS → INCONCLUSIVE conjunction; the ladder inside the six level cells (d1342); tolerances and their plain-unit statements; exposure labels; report-only intervals; the candidate-3 disclosure, verbatim; and the thread guard.
scripts/track_b_b2_floor.py	The truth-only floor builder (section 9, steps 2-6). A read guard admits only b2_read_set_sha256's 80 files and checks each opened file's hash. It checks the domain and support counts against the frozen record, then computes household- and person-split floors (seeds 0-99), tolerances and se_up (4,000 household replicates on [20261002, b, 0]). It publishes the stratum census before and after the merges, the merges, L and ν. It applies section 5's eligibility first, exactly as written (every seed defined, at least 20 events, planning values present): a cell of the six that fails it is scored report-only. It stops at floor build with WEAK_POWER_OR_VACUITY, naming the cell and quantity, when ν is 0 or an eligible cell's σ, se_up or τ is zero or undefined. An uninformative tolerance stops B2; it never drops an eligible cell. Otherwise it runs the ladder over the eligible cells on the ruled binding evaluation, and writes one exclusive artifact (runs/track_b_b2_floor.json).
scripts/track_b_b2_compare_floor.py	The comparator. It requires the floor artifact to be committed, reads two fields of each boundary-2010 selection ledger, and prints exactly two booleans per ledger: whether the six M6-retained cells' person-split floor block and their seed 0-4 detail hash to the builder's values.
scripts/track_b_b2_score.py	The one-shot scorer. Before it fits anything it checks every input: a committed floor artifact that cleared the ladder, the same registration id, the expected commit on a clean worktree, unchanged shared code, addendum, planning record and counts record, all 16 cells' planning ratios, and the design summary recomputed against the floor artifact's. It fits candidate 3 at 2010 (seed 5200, NAWI realized through 2010) and projects draws 6200-6219. It bootstraps 4,000 design replicates on [20261002, b, 4], scores side A of gate seeds 0-4, and applies section 8. After every check that needs no PSID data (the floor, the planning record, the scoring inputs and NAWI), and before it reads any, it creates runs/track_b_b2_score.attempt.jsonl exclusively and appends each stage, synced to disk with its directory entry, so an interrupted run leaves its last stage on disk. It refuses to start if that log exists. Its output (runs/track_b_b2_score.json) is exclusive.

Element 8's stratum rule

• One-cluster strata merge, all at once, into the nearest stratum by code among those with two or more clusters before any merge. A tie goes to the lower code. If no stratum has two clusters, all merge into the lowest original code.
• Two-cluster strata follow arm D's rule: one cluster is drawn and copied twice.
• Strata of three or more clusters get exact Rao-Wu by integer copies. Each draws rng.multinomial(n_h − 1, 1/n_h) over its clusters, sorted by original (stratum, cluster), and each draw counts L·n_h/(n_h − 1). L is lcm(n_h − 1), and every stratum's copies are scaled by L. Strata are visited in ascending merged code. When every stratum has two clusters, L = 1 and the multiplicities are arm D's.
• ν is Σ(n_h − 1) over the merged strata.
• Copying. b2.copy_persons calls the planning script's pinned copy_persons unchanged while every count is below 1,000, so frames equal arm F's. Scale L can need more copies: merged strata of 2, 8, 12 and 14 clusters give L = 1,001. For those it runs the same construction with a wider power-of-ten identifier scale. Only the identifiers' encoding differs.

Threads

Every B2 process runs one BLAS, OpenMP and numexpr thread with OMP_WAIT_POLICY=PASSIVE, and the replicates run in up to four worker processes. That is within Max's 2026-10-11 cap of four threads on the shared host. b2.thread_settings refuses any other setting, and also requires POPULACE_FIT_N_JOBS from 1 to 4: unset, populace-fit's forests use every core, so protocol v2 pinned 4. Forest seeds are per tree, so the count does not change a fit. b2.require_workers refuses more than four workers. Both entry points call them first, before reading, checking or writing anything. A regression test drives each entry point with each thread variable set to 4 and requires that refusal.

The reason: on 2026-10-13, in B2's pinned environment, probes of candidate 3's projection loop with more than one OpenMP thread stalled in the participation gates' HistGradientBoostingClassifier.predict_proba. One sat at 0% CPU for more than ten minutes, and four more were stopped by 60- to 150-second timeouts, at 2 and 4 threads under PASSIVE and ACTIVE, on invented data. Correction, 2026-10-15: at the merge commit, in B2's registered runtime, the same probes completed at 2 and 4 threads, in 40-51 s against 16 s for one thread. A 4-thread probe in the earlier environment completed too, in 59 s. The stall is intermittent and its cause was not identified. One thread per process completed every time and was the fastest, so B2 keeps it. Field by field, the only thread-dependent part of a fitted gate is the thread count HistGradientBoosting records on its bin mapper (_BinMapper.n_threads). That counter is why the pickle-hash fit signatures differed between 1 and 4 threads, while the 20 projected draws were byte-identical. Candidate 3's frozen runner pins 8 threads and ACTIVE, but B2 projects through the selectors' _project, as protocol v2 did, so that guard does not apply.

Invariants (load-bearing logic)

• Merges: deterministic and independent of row order; clusters are conserved; every merged stratum has at least two clusters unless the whole design is one cluster (Hypothesis).
• Rao-Wu copies: in every replicate, stratum h's copies sum to L·n_h (Hypothesis). By exact enumeration, each cluster's mean copies is L, and the replicate total's variance divided by L² equals the stratified with-replacement estimator Σ_h n_h/(n_h − 1) Σ_i (y_hi − ȳ_h)², on mixed designs of two-, three- and four-cluster strata.
• ν and the census: ν equals clusters minus merged strata, and the published summary uses the merged strata (Hypothesis).
• Scale: a common copy scale leaves the six gated level cells unchanged (Hypothesis).
• Standard error and bound: se_c ≥ se_boot. The bound |g| + t* se ≤ tol is monotone in |g|, se and tol, and symmetric in g's sign.
• Outcome order: INVALID exactly when some cell is invalid. PASS implies every |g| ≤ tol, every bound within tolerance, the Monte Carlo rule, and four or more seeds passing. The outcome does not depend on cell order.
• Ladder: it partitions the cells, never drops a family's last cell, visits cells in descending tol/σ, and stops at the first power ≥ 0.90. It clears exactly when power ≥ 0.90 with four or more cells and not every tolerance capped.
• Determinism: two fresh processes with different hash seeds give an equal fitted state (a field-by-field digest of the whole fitted law), equal gate probability surfaces and byte-identical draws for all 20 seeds (tests/test_track_b_b2_threads.py).

Differential tests

• Against arm D: with every stratum at two clusters and root 20260930, the design multiplicities equal the planning script's design_multiplicities for replicates 0-99. The household multiplicities equal anchor_multiplicities likewise, and nothing in B2 reads BOOTSTRAP_ROOT_SEED.
• Against the planning script: design_summary, floor_eligible, cell values, the household floor, the fit, the context, the projections and the copied frames all match. With the same multiplicities, the scorer's gaps equal arm F's.
• Against the ruled-power module: t_star, ν and the ladder match. Over all 720 pruning orders the ladder ends where ladder_outcomes does.
• Against the selectors: the data-only domain, truth support and person-split floor match select_m6_qstar_train_only._boundary_context at boundary 2010, so the builder's hashes are comparable with the ledgers' floor fields.

Tests and tiers

• B2 tests: 212, all in the unit tier. test_track_b_b2_rules.py has 87, test_track_b_b2_pipeline.py 97, test_track_b_b2_design.py 19, test_track_b_b2_compare_floor.py 7 and test_track_b_b2_threads.py 2. All 212 pass with -n 4, both at the registered thread settings and with no thread variables set, as on CI. Without populace.fit, as on CI, the cross-process determinism test skips.
• B0.1 tests: addendum_power, addendum_record, counts, planning_values and ruled_power pass on this head: 243 tests. The other four B0.1 files rescan files on the Q6 exclusion list, so this build does not run them. This PR changes no file they test.
• Tier manifest: after merging master at 24da3c61, checked by pytest --collect-only -q -m <tier>: unit 7,547, artifact 4,080, integration_psid 1,384, reproduction_legacy 520, oracle_policyengine 308. Total 13,839, which is master plus this PR's 212 unit tests. The README table, which master had left at older figures, now matches. b2.py joins the birth-evidence seal's post-review exclusions, as the other Track B modules did.

Mutation checks

Each mutant changes one fragment of the code under test. The named tests then run and must fail, and the source is restored.

• At 61879ed6, 28 of 28 killed (Subfleet job 20261013-183728-b2-mutants):
  • Rao-Wu drawing n, copies of n, L as a maximum;
  • ν before the merges, ν as clusters;
  • singletons left separate, strata visited in reverse;
  • stream word 0, household root fixed;
  • normal z at finite ν, bound <, Monte Carlo tol/5, 5% undefined;
  • PASS before FAIL, ladder pruning a family's last cell, stopping at 0.85, a three-cell guard;
  • the floor's ν, σ and se_up stops skipped, merges unpublished, artifact overwrite;
  • the scorer's report-only and design preflights skipped, a non-cleared floor accepted, no registration, output overwrite, side A by person.
• At 7a1dd5fd, 2 more killed: σ > 0 restored to eligibility, and σ left out of the eligible-cell stop checks.
• At 485645d6, 3 more killed: the attempt log opened before the data-free checks, an unset POPULACE_FIT_N_JOBS accepted, and the scorer copying through the pinned helper.
• At 1d1ce716, 8 more killed:
  • three on the copier: no wide fallback, a fixed scale, a scale too small;
  • five on the rest: stop checks on all six cells, eight workers allowed, the floor builder skipping the worker bound, the scorer ignoring a prior attempt, stages not logged.
• At 03f82d3d, 2 more killed: the floor builder's guard moved after the registration check, and the scorer's guard removed.
• At 61879ed6, 15 more killed:
  • the build's 10: four merge and copy rules, six comparator outputs;
  • 5 on the thread guard and the state digest: the guard admitting 2 or 4 threads or dropping numexpr, the digest skipping nothing, ignoring array bytes, or reusing freed ids.
• At 6b89f658, the first build's 59 of 59 killed. M13 and P10 targeted the two-cluster guard, which the stratum rule has since replaced.

Mutant	File	Killed
M01: bound rule <= to <	src/populace_dynamics/track_b/b2.py	yes
M02: INVALID never fires	src/populace_dynamics/track_b/b2.py	yes
M03: three of five seeds suffice	src/populace_dynamics/track_b/b2.py	yes
M04: point gap outside tol is not FAIL	src/populace_dynamics/track_b/b2.py	yes
M05: Monte Carlo rule < to <=	src/populace_dynamics/track_b/b2.py	yes
M06: Monte Carlo divisor 10 to 5	src/populace_dynamics/track_b/b2.py	yes
M07: undefined share <= to <	src/populace_dynamics/track_b/b2.py	yes
M08: household undefined share ignored	src/populace_dynamics/track_b/b2.py	yes
M09: t* uses alpha/m	src/populace_dynamics/track_b/b2.py	yes
M10: t* ignores nu	src/populace_dynamics/track_b/b2.py	yes
M11: se_c drops a_c	src/populace_dynamics/track_b/b2.py	yes
M12: cross term never added	src/populace_dynamics/track_b/b2.py	yes
M13: guard admits 3+-cluster strata	src/populace_dynamics/track_b/b2.py	yes
M14: nu counts strata	src/populace_dynamics/track_b/b2.py	yes
M15: anchor multiplicities ignore root	src/populace_dynamics/track_b/b2.py	yes
M16: design stream word 4 to 3	src/populace_dynamics/track_b/b2.py	yes
M17: Rao-Wu copies once	src/populace_dynamics/track_b/b2.py	yes
M18: multinomial draws n-1	src/populace_dynamics/track_b/b2.py	yes
M19: ladder prunes a family's last cell	src/populace_dynamics/track_b/b2.py	yes
M20: ladder ascending order	src/populace_dynamics/track_b/b2.py	yes
M21: ladder stops above, not at, target	src/populace_dynamics/track_b/b2.py	yes
M22: four-cell guard > 4	src/populace_dynamics/track_b/b2.py	yes
M23: cap guard dropped	src/populace_dynamics/track_b/b2.py	yes
M24: tolerance uncapped	src/populace_dynamics/track_b/b2.py	yes
M25: tolerance k = 4	src/populace_dynamics/track_b/b2.py	yes
M26: plain-unit percentage	src/populace_dynamics/track_b/b2.py	yes
M27: exposure label keyed on level cells	src/populace_dynamics/track_b/b2.py	yes
M28: identical draws valid	src/populace_dynamics/track_b/b2.py	yes
M29: eligibility > 20 events	src/populace_dynamics/track_b/b2.py	yes
M30: se_up not inflated	src/populace_dynamics/track_b/b2.py	yes
M31: report interval at m=2	src/populace_dynamics/track_b/b2.py	yes
M32: canonical JSON with spaces	src/populace_dynamics/track_b/b2.py	yes
M33: six-cell detail keyed on level cells	src/populace_dynamics/track_b/b2.py	yes
M34: log-ratio zero value defined	src/populace_dynamics/track_b/b2.py	yes
M35: within < not <=	src/populace_dynamics/track_b/b2.py	yes
M36: PASS without its conditions	src/populace_dynamics/track_b/b2.py	yes
M37: household stream word 0 to 1	src/populace_dynamics/track_b/b2.py	yes
M38: root 20261002 to 20261001	src/populace_dynamics/track_b/b2.py	yes
M39: comparator reads the 2008 floor	scripts/track_b_b2_compare_floor.py	yes
M40: six-cell detail compared whole	scripts/track_b_b2_compare_floor.py	yes
P01: design replicates on protocol v2's root	scripts/track_b_b2_score.py	yes
P02: side A split by person	scripts/track_b_b2_score.py	yes
P03: critical value at m = 1	scripts/track_b_b2_score.py	yes
P04: report interval for gated cells	scripts/track_b_b2_score.py	yes
P05: domain check skipped	scripts/track_b_b2_score.py	yes
P06: floor outcome not checked	scripts/track_b_b2_score.py	yes
P07: shared code not checked	scripts/track_b_b2_score.py	yes
P08: existing output not refused	scripts/track_b_b2_score.py	yes
P09: household floor split by person	scripts/track_b_b2_floor.py	yes
P10: stratum guard skipped	scripts/track_b_b2_floor.py	yes
P11: ladder over all 16 cells	scripts/track_b_b2_floor.py	yes
P12: household replicate on protocol v2's root	scripts/track_b_b2_floor.py	yes
P13: se_up stop skipped	scripts/track_b_b2_floor.py	yes
P14: counts check skipped	scripts/track_b_b2_floor.py	yes
P15: ladder power without B2's tau	scripts/track_b_b2_floor.py	yes
P16: report-only reason for non-level cells	scripts/track_b_b2_floor.py	yes
P17: existing artifact not refused	scripts/track_b_b2_floor.py	yes
P18: registration id not compared	scripts/track_b_b2_score.py	yes
P19: non-ancestor floor accepted	scripts/track_b_b2_score.py	yes

Open points the registration settles

These were flagged by the builds. The registration on #42 states each before any run:

1. Ladder below four cells: section 5's literal steps keep pruning, and then the four-cell guard fails. The outcome is WEAK_POWER_OR_VACUITY under any reading.
2. More than 1% of a gated cell's household replicates undefined: the cell cannot pass (section 7), so B2 is capped at INCONCLUSIVE. The ladder does not price this.
3. A replicate that raises: it counts as undefined for every cell, and its exception class is recorded. A memory or operating-system error stops the run.
4. An undefined truth on a frame: it makes the cell invalid on that frame, as in M6.
5. The report-only interval: g ± t_ν⁻¹(0.975) se_c.
6. The registration id: the floor builder and the scorer take the same Candidate 2 design: latent-permanent conditioned chained QRF (research memo) #42 registration comment id.
7. Interruption: the scorer's attempt log records the last stage reached. The registration states the rule: a rerun needs a dated amendment, and is possible only if the log shows no stage at or after "full-support cells", the first stage that computes a candidate gap.
8. The two values of a_c: the ladder's power uses the ruled binding evaluation, whose registered variance is s²_gate − r² (section 11). The scorer registers a_c = e_B2 (section 7). Both are as written, so the power prices a larger registered variance than the scorer uses, which is conservative.
9. Output paths: runs/track_b_b2_floor.json and runs/track_b_b2_score.json.

Blindness

• No recursive or glob grep over the tree by the build lanes.
• No file on the Q6 exclusion list, no selection ledger, no ~/microcosm-launch-evidence/ file and no B1 output was opened.
• No PSID file was opened.
• The frozen counts record's support counts for 2012 and 2014 (rows present by cohort, rows PSID assigned or edited) were read. They are presence counts, published in the audit and passed by the addendum's blinded reviews; they hold no earnings value. No 2012 or 2014 earnings statistic and no 2008 or 2010 selector outcome was met.

axiom: n/a: evaluation-gate infrastructure, no policy encoding.

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Project	Deployment	Actions	Updated
social-security-model	Ready	Preview	Oct 14, 2026 6:26am UTC

[MaxGhenis]

Merged with a merge commit at the reviewed head (--match-head-commit 2ffcb933), as 22e3f82b.

Gates at merge

• gh pr checks 526 exited 0 on the latest run at 2ffcb933: all 11 checks passed, and deploy was skipped.
• mergeable was MERGEABLE and mergeStateStatus was CLEAN. The PR was not a draft, and no review requested changes.
• Master had not moved since the last merge into this branch (24da3c61).

Independent reviews

Each reviewer worked on a cleaned copy of the head, with the Q6 exclusion list removed, and read code only.

• GPT-6.1 Sol, round 1 (20261013-223342-b2-526-review-r1, at 0e292b0f): request changes.

  • High: the pinned copier refused 1,000 or more copies, so the stratum rule's scale L could make every replicate fail.
  • Medium: an ineligible cell stopped the whole gate.
  • Medium: --workers was unbounded.
  • Low: the README described the removed stratum stop.
  • All four were answered in 1d1ce716, which also added the attempt log and a pooled-replicate test.

• Opus 5.5, round 2 (in-session; Sol lanes were closed until 09:10Z): approved 1d1ce716. Its low findings were folded into 485645d6:

  • data-free checks before the attempt log;
  • test isolation from B2's committed run files;
  • an ordering test;
  • a scorer-level test at L = 1,001;
  • POPULACE_FIT_N_JOBS required to be 1 to 4;
  • a directory fsync.

  The same reviewer approved 485645d6, and 3e5e32de (comments only: the launch examples).

• GPT-6.1 Sol, round 2 (20261014-005111-b2-526-review-r2, at 1d1ce716): request changes. Medium: σ > 0 was an eligibility condition that section 5 does not list. Answered in 7a1dd5fd: eligibility is now section 5's exactly, and a zero or undefined σ on an eligible cell stops B2 at floor build.

• GPT-6.1 Sol, round 3 (20261014-020523-b2-526-review-r3, at 7a1dd5fd, covering every change since its round 2): approved. Its one low finding, README wording, was fixed in 2ffcb933, which the Opus reviewer confirmed as documentation only.

Verification

• 212 B2 tests pass, with and without thread variables set.
• 28 + 43 + 59 mutants were killed across the build rounds; each commit message lists its mutants.
• The cross-process determinism test passed in the gate environment at 3e5e32de. CI skips it, because populace.fit is not installed there.
• Tier manifest at merge: unit 7,547, artifact 4,080, integration_psid 1,384, reproduction_legacy 520, oracle_policyengine 308 (13,839), verified by collection.

Next

B2 registers on issue #42, pinning 22e3f82b. The registration states what the implementation adds to the addendum's text:

• the wide copy scale;
• section 5's exact eligibility and the eligible-cell stops;
• the attempt-log interruption rule;
• one thread per process, POPULACE_FIT_N_JOBS=4 and at most four workers.

The single-thread finding is in the PR body: candidate 3's projection hangs in the gates' HistGradientBoostingClassifier.predict_proba with more than one OpenMP thread, 5 of 5 times at 2 and 4 threads, under PASSIVE and ACTIVE, on invented data.

[MaxGhenis]

Correction to the thread finding in this PR's description and the audit comment above.

On 2026-10-13, probes of candidate 3's fit and projection on invented data with more than one OpenMP thread stalled in the gates' HistGradientBoostingClassifier.predict_proba. One sat at 0% CPU for more than ten minutes, and four more were stopped by 60- to 150-second timeouts.

On 2026-10-15, at the merge commit 22e3f82b in B2's registered runtime, the same probes completed:

• 1 thread: 16 s;
• 2 threads, PASSIVE: 40 s;
• 4 threads, PASSIVE: 51 s;
• 4 threads, ACTIVE: 19 s.

A 4-thread probe in the earlier environment also completed, in 59 s.

So the stall is intermittent, not "5 of 5", and its cause was not identified. B2 keeps one thread per process: it completed in every run, it was the fastest, and its cross-process determinism is tested. B2's registration on #42 gives this account and keeps the logs. b2.thread_settings' docstring still describes the stall as if it always occurs; the registration's account supersedes it.