Closing the Loop

scratch/g0c-ranker-v4-selection.json is a protein-identity and sequence-homology guard written by scripts/build_protein_guard.py: it excludes any corpus pool with a chain at ≥ 0.90 identity to an evaluation chain. Nothing consumed it. Exactly 3,097 of 15,204 cached pools sit outside it, as the review states.

My own check — zero exact PDB-code overlap between the g0c cache and the SPINDR test split — was not a substitute and I should not have offered it as reassurance. The guard is about homology, which no identifier comparison can see. --selection now applies it and the cache is rebuilt: 12,107 targets, 8,237 rankable.

Worse than the review put it. The pools carry fixed_repulsion as a per-pose array, and ranker_v2.py:456 scores learned + fixed_repulsion + intra_delta. So the archived exporter's fixed_repulsion: false shipped a residual as though it were the whole intermolecular term. That is the 48/225 in §0, and it is a defect in the export path, not a property of low-rank fields.

The offset now enters the pool softmax per pose — it varies within a pool, so it does not cancel — and the export flag is derived from whether the cache carries one, never set as a constant.

Correct, and my own measurement said so before the review arrived. Over 400 pools (1,957,167 pairs): 12 pairs in [1.0, 1.5) Å, 1,293 in [1.5, 2.0), 6,197 in [2.0, 2.5) — 0.001 %, 0.066 %, 0.317 %. Sparse, not absent. Meanwhile 73 % of all pairs sit beyond 4.5 Å.

The mechanism survives the correction — 12 pairs in two million is ridge shrinkage, not chemistry — but the sentence as written was wrong and is replaced by the numbers.

With F = −β⁻¹ log Z the loss is β(F_N − F_total) and the gradient carries the same β. The draft omitted it.

The substantive point is the one that matters: replacing a native point with a positive-measure set does not prevent divergence. Separable data still drives P(N) → 1 as the energy scale grows, because scaling θ sharpens the distribution without bound. β must be fixed, not fitted, and the parameters explicitly regularised or norm-constrained. This is now stated as a constraint on P1.3 rather than discovered during it.

The soft recursion is exact over a precisely smaller object than the draft claimed, and the difference is not cosmetic — P1 would otherwise train a different objective from the engine it is meant to improve. What is exact:

• the intermolecular term only, as a sum of unary node terms;
• over the retained discrete torsions — those below TorsionPlan::within_budget's cut are frozen at their input values and are not in the space at all;
• with cross-branch intramolecular pairs dropped or bounded, never summed exactly (§3.3);
• with no ring or conformer states in the outer sum.

Within that object it is exact, and that is worth having. Outside it, it is a surrogate, and the production engine returns a refined argmin rather than a Boltzmann draw — so the whole construction is a Boltzmann surrogate for what the engine does, which the draft should have said.

The sharpest of the seven. RMSD ≤ 1 Å is a global geometric constraint on the assembled pose; it does not decompose over the torsion tree, so the same recursion that gives the denominator exactly does not give Z_N at all. "Sums over a small restricted set" was hand-waving.

Repaired — and the repair turned out to be exact, not approximate. Built as src/near_native.rs. With native y_i, conformer x_i, u_i = R·x_i and m = mean(u_i − y_i), the cross term completes the square:

RMSD²(R,T) = mean |u_i + T - y_i|²
           = ( mean |u_i - y_i|² - |m|² )  +  |T + m|²
             \_______ floor(R) ________/     \___ ball ___/

So for each rotation the near-native set is exactly the ball |T + m| ≤ √(c² − floor(R)), centred on the translation that best superposes that rotation, and empty when floor(R) > c². Translation and rotation are the outer sums, so a per-rotation ball in translation is precisely the shape the factorisation carries: restrict the lattice sum, leave the torsion sum untouched, and the numerator costs the same recursion as the denominator. Membership is an O(1) squared-distance compare, not an O(atoms) RMSD evaluation.

Verified against direct RMSD at 8,000 translations × 3 rotations (worst reconstructed error 2×10⁻³); the native rotation's floor is 0 and its centre is the native translation; the floor is unbeatable over 4,096 probe translations; an out-of-reach rotation returns an empty ball rather than a tiny one.

Three limits, stated. For a rigid conformer this is the near-native set. With torsions free it is a superset — inclusion direction known and fixed, gap size a property of ligand flexibility that must be reported. And the RMSD is index-wise: a symmetry-corrected set is a union of balls, one per graph automorphism, still exactly representable but not computed here.

The support gate is built. measure_support counts what a given quadrature and lattice actually reach, so a training run publishes the fraction of targets it dropped rather than regularising an infinite loss in silence. That support falls monotonically as the quadrature coarsens is asserted, not assumed.

"Once per milestone" does permit cumulative tuning when five items all read the same 225 targets. Fixed where it was cheap: CV folds are now grouped by protein entry rather than by target (the corpus holds several pools per PDB code, and splitting them across train and test leaks a binding site into both), 3 fold draws replace 1, and both ridge grids were extended past the edges they had been peaking on.

Not fixed, and stated as an open debt: SPINDR train and val exist as raw structures (35,373 and 68 systems) but only test has prepared inputs, so there is no dev split to gate on without running the prep pipeline. Until there is, every arm in §0 and §3 is a touch of the evaluation split, and the honest accounting is that P0 spent four.

18 % of the receptor atoms the field was fitted on do not exist at inference. g0c's region_types is AUTODOCK_TYPES, in which HD falls through to OTHER — and receptor OTHER is 17.7 % of region atoms, every one of them a polar hydrogen (region_labels == -1, region_numbers == 0). parse.rs discards hydrogens, so the engine's receptor has none of them. The fit was also blind to donor status while the engine emits OA+ / N+ / NA+, sending exactly the polar atoms to the ? sentinel. Both fixed: hydrogens dropped, receptor classes taken from the donor-aware region_labels, ligand donor variants expanded on export.

The published PoseBusters warning is stale — the review is right and the first draft was wrong. scripts/evaluate_pure_equifield.py does call posebusters_top1; only CLAUDE.md's record of it is out of date.

Arm cp8c_ce: identical to cp8w_ce but with every channel flat-extended below 2.5 Å, from the first knot at or above it. This is not smoothing. The corpus places 0.001 % of its pairs below 1.5 Å and 0.4 % below 2.5 Å, so a flat extension is the only extrapolation the data licenses, and the engine's restored wall supplies the physics the fit cannot.

It targets the exact failure that survived P0.2: the 12 remaining minimum_distance_to_protein failures. Because the clamp acts on the expanded tensor it is not rank-preserving, so the arm ships a dense potential — which under a linear head is the same object at inference (§3.8), at 1,815 parameters instead of 296.

Every published low-rank number was computed on a corpus that has since changed in four ways: the homology guard removes 3,097 pools, the receptor vocabulary gained donor status and lost polar hydrogens, the loss gained a per-pose offset, and the folds are grouped by protein. The corrected sweep has now run — 8,237 rankable targets over 4,395 protein groups, 5-fold CV × 3 fold draws, both ridge grids extended past the edges each arm had been peaking on. Incumbent on this denominator: 6,178 / 8,237 = 75.0 %.

The margin survives at +0.8 points, down from +2.2. Across the three stages it reads +9.7 (158 targets) → +2.2 (9,766, unguarded, ungrouped) → +0.8 (8,237, guarded, grouped folds). And the peak flattened into a plateau: ranks 4, 8 and 16 sit within 0.1 points of one another, where §3.8 had reported a unimodal peak at 8. The shipped rank-8 export is inside the plateau and needs no refit — but rank 4 is the same number at half the parameters.

What the fit wins is ranking, not generating. 81.1 % against the engine's 75.0 % is +6.1 points on this denominator, and it does not transfer: docked, the same field reaches parity. That gap is the campaign's central open result.

torsion_field.rs already evaluates, elementwise over the whole translation window,

A_g(T) = C_g(T) + sum over children c of  combine over tau_c of  A_c(T)

with combine = min at zero temperature and combine = -kT log sum exp(-./kT) when with_temperature is set — which the archive already passes. The min-plus semiring becomes the log-sum-exp-plus semiring, and because a product of sums over disjoint sibling subtrees is the sum over the product space, A_root is the exact free energy of the entire discrete torsion space at every lattice point, at unchanged O(n·K) cost.

Now asserted rather than assumed, three ways: against brute-force enumeration of the whole product space at three temperatures; as a monotone limit rising onto the hard minimum as kT falls (the draft named resolve_coupled as the limit, which is wrong — it carries different intramolecular coupling; the limit is the hard torsion field); and pointwise against the field at every third lattice node.

Exactness domain: exactly the object named in C5, no larger.

What the draft claimed as the build, minus what already existed:

• The rotation/translation reducer. analyze_landscape sums Z over lattice and quadrature already, but nothing on a docking path calls it — landscape.rs is reachable only from features.rs. Wire it, and add the N-restricted partner from C6.
• Stored messages. descend_soft discards its per-child messages. Exact ancestral sampling needs them retained.
• The sampler. Inverse-CDF over the tabulated exp(−β·A_root) for (rotation, translation), then ancestral sampling down the tree. i.i.d. draws, no Markov chain, no burn-in, no contrastive-divergence bias — because the architecture enumerates its own state space.
• Gradients. ψ occupancies at the sampled poses, chained through the CP factors.

L(theta) = -log P(N) = beta * ( F_N(theta) - F_total(theta) )

grad L   = beta * ( <psi>_clamped-to-N  -  <psi>_model )

with N the factorable neighbourhood of C6, β fixed and the parameters norm-constrained per C4, and a published support fraction for targets whose N is empty at the training quadrature.

Why it is still worth doing after §0. The repaired field reaches parity by fixing an export defect; nothing about it was ever trained against poses it would itself generate. A ranking loss constrains the potential only on the support of a pool it did not produce — which is precisely why its short range was free to be wrong. Maximum likelihood constrains it where a generator's argmin actually goes. §0 is evidence the transfer is possible; it is not evidence the transfer is complete.

It is a Boltzmann surrogate. The production engine returns a refined argmin, not a draw from p_θ. Training the Boltzmann model is a tractable proxy for making that argmin right, and the gap between them is a stated assumption, not a claim.

The draft offered P(pose ∈ N) as an inference-time confidence. It cannot be: N is defined by the crystal pose, which is exactly what inference does not have. The review is right and the item is rewritten to the two quantities that are observable — Boltzmann mass in a neighbourhood of the predicted pose, calibrated against measured accuracy on a held-out split, and landscape entropy −Σp log p.

This also carries §3.9's own stated limit: its refutation used a translational measure within one orientation's field, while the model's p_k was over translation and rotation. The reducer removes that limit for free. Report it; do not resurrect the selection rule.

Vina's h-bond term is a function of surface distance alone. A hydrogen bond is not. On the receptor side the angle is free: the donor's X–H direction is fixed when the grid is filled, so the weight folds into the map and the search, the correlation and the torsion recursion are all untouched. Built as grid::HbondDirectionality, weighting the h-bond term by max(cos γ, 0)p, maximised over the donor's hydrogens because an –NH₂ donates along either bond.

The blocker was real and is removed. parse.rs derived is_donor from a bonded HD and then discarded the hydrogen — the direction was parsed and thrown away. parse::donor_hydrogen_directions now recovers it under the same bonding rule, so the two cannot disagree about which hydrogen belongs to which heavy atom.

Four properties are asserted rather than argued: the correction is written hbond_term · (w − 1) so off is arithmetically nothing, and the maps are bit-identical; hbond_term is exactly the h-bond addend of evaluate_pair, checked across both scoring functions, all sixteen donor/acceptor combinations and 900 distances; the weight is a continuous cosine power, 1 along the bond and 0 perpendicular and behind; and turning it on moves only maps for ligand types that can accept, and only ever upward — it can remove attraction, never add it.

Bit-identity when off is proven end-to-end: xt_off_ce returns exactly 109 / 139 / 146 / 219 on four different binaries, including the one with directionality compiled in.

Measured, and it is negative — for an arithmetic reason, not a physical one.

Paired at p = 2: top-1 −2 (+12 −14) p = 0.85, ceiling −6 (+9 −15) p = 0.31. Individually insignificant, but monotone in the exponent, and it is a real intervention — 220 of 225 top-1 poses change.

The cause is a missing normalisation, and it is analytic. The solid-angle mean of max(cos γ, 0)p is 1/(2(p+1)), so an unnormalised weight cuts the h-bond term to 1/6 of its strength at p = 2 and 1/10 at p = 4 — and Vina's weights.hbond was fitted against the isotropic term, so nothing restores it. Those arms measured a weakened hydrogen bond, not a directional one, and the monotone decline tracks the attenuation rather than the angular shape. That is my error in the experiment design, not a result about chemistry.

HbondDirectionality::normalise multiplies by 2(p+1) so the sphere average is 1 — asserted to within 2 % by a 200,000-point spiral quadrature at p = 1, 2, 4, 6 — letting the weight exceed 1 along the bond, which is the point: it moves h-bond strength from off-axis to on-axis at constant total. That is the fair test, and it fails much harder:

hdn2_ce against baseline: −34 (+12 −46), exact McNemar p = 8.2×10⁻⁶ — the only large, unambiguously significant effect in the whole campaign, and it is negative.

The thread closes, and the shape of the failure is informative. Weakening the h-bond loses real signal; concentrating it on-axis at constant total is catastrophic. Neither works because Vina's weights.hbond and the term's isotropic shape were co-fitted — changing the shape invalidates the magnitude — and because concentrating reward into a narrow cone creates sharp attractive wells that an exhaustive argmin walks straight into. That is §3.9.1's knife-edge-basin failure mode arriving from a new direction, on an engine that has no restart budget to protect it.

The machinery stays — bit-identical when off, fully tested — because a refit of the whole function is exactly what P1.3 does. What is refuted is the cheap way of using it: the angle must enter inside a refit, never as a multiplicative correction on top of one.

A silent no-op, found and now refused. hd2cp_ce — the field and the angular weight — returned bit-identical results to cp8w_ce on 225/225 targets. build_learned replaces every receptor map, so the correction to Vina's h-bond term is overwritten before it is ever read. That reads as "the feature does nothing" when it was never applied; the engine now refuses the combination rather than producing a misleading null. Directional h-bonds for a learned field must be inside the potential's own fit.

The training-free prior remains: median per-target near-native/decoy AUC 0.589 → 0.662, 84 win / 62 lose / 8 tie, sign test p = 0.082 — magnitude meaningful, consistency borderline.

One hard constraint, already measured: a hard angular cutoff never converges — 38.5 % error at l_max 8, which is Gibbs — so every angular factor must be C⁰ in the angle. A cosine power is the right family; a step function is not, even here where no expansion is involved. The ligand side is the expensive half: its angle depends on the pose, so it needs (l_max+1)² channels per polar class and correlate_channels, which is built and unwired.

Run, and it produced the most consequential finding of the session. Over 400 pools:

• Receptor OTHER is 17.7 % of region atoms and is entirely polar hydrogen — invisible to the engine's receptor. This is C8.
• No METAL class appears at all, on either side. Every metal coordination in the corpus is absent, so a field fitted here has nothing to say about metalloproteins and should not be claimed to.
• 24 of 77 populated pair-class cells carry fewer than 1,000 contacts, the halogen and sulfur cells worst: SA–NA has 6, BR–NA 7, SA–SA 20. Those are class labels attached to noise.
• Radial support is extreme: 73 % of all pairs sit beyond 4.5 Å while the three shortest knots hold 0.4 % between them.

Per-class contact counts are now emitted with every cache build, so a fit can no longer quietly claim coverage it does not have.

hydration.rs exists and is unwired. A buried polar atom with no partner should be penalised and is not; burial is a receptor-side quantity, so it deposits as a grid channel and costs the search nothing.

The MLP-over-pooled-channels arm topped out at exactly the linear number (92/158 = 58.2 %) on 158 targets. The negative is a statement about corpus size, and the corpus is now 8,237 guarded targets with corrected features. If the head wins, monotone_head.rs stops being a proved theorem and becomes load-bearing: its A* heuristic reuses the DP's own completion messages, was verified against brute force on 40 random trees, and expands 0.03 % of a 59,049-point product space at 10 nodes.

The monotonicity check is necessary, not sufficient — the review is right, and is_monotone_on documents itself as a sample test. A shipping head must be monotone by construction (non-negative pass-through weights), with is_monotone_on as a regression guard rather than as the guarantee. Cooperativity — the third h-bond worth more than the first — is the concave case, and is what the guarantee costs.

The refutation named its own cause: a driver cell bounds the drivers, while the closers move by whatever the implicit function theorem forces, and that amplification saturates the π cap until the half-width is under π/16 — leaving 2.8 Å of residual atom motion at π/8, over which an eroded Vina map is near its global minimum.

The repair acts on what the cell actually controls: bound the ring atoms' positions with a box per atom, so Σ min Φ over boxes is admissible and the amplification is gone by construction because atom motion is the box width. Feasibility is classical distance geometry — interval bounds from the boxes, intersected with rigid 1-2 and 1-3 distances, then Crippen–Havel triangle smoothing. Analytic loop closure (Coutsias–Seok) removes the measured 38.7 % cell-integrity defect outright.

Priority is honestly low. The covering-number wall stands regardless (~2×10⁷ conformers at dimension 9, on an underestimated exponent) and SPINDR carries few macrocycles — the refutation rests on 10 pairs across 5 targets.