TECHNICAL, Route-ST2G v1: the DSSP screen's report path learns Tsai Theorem 2 and the SS/DSS ansatz check

Leg 383, construction class, floor-eligible. Repairs leg 359's flagged gap (a048de7) in leg 357's B7 screen (3f614d7), at the layer legs 362/370 left open.

1. The gate and its answer

Q. Does the upgraded screen classify (i) Tsai's own headline example as REACHED by Theorem 2 (the source's decay exponent matching this repo's measured one, per 359), and (ii) this programme's DSS object as NOT REACHED with the deciding clause recorded as the exact-SS ansatz hypothesis, with planted controls able to fail in both directions?

Answer: YES. All six pre-registered controls pass in their pre-registered directions; no control was widened, relaxed, or re-scoped after the numbers arrived.

The yes-branch consequence, in the gate's own words: the screen stops under-warning; every future candidate report carries the two new columns. CEILING: TIER 2: surviving a screen is not evidence for existence.

2. What was already built, and is not rebuilt here

The novelty pass (§1 of writeup/novelty/leg_383.md) found the dispatch thesis partially discharged after leg 359 wrote its flag:

None of that mathematics is re-derived and none of those functions are rewritten. Tsai 1998 is not re-fetched: leg 359 downloaded and hashed it (sha256 6d3182d5…) and leg 362 transcribed the load-bearing clauses verbatim into the module header. This leg quotes those banked clauses and adds no new citation.

3. The gap that was still open

Both extensions were landed as strictly opt-in parameters defaulting to None, deliberately, so that no existing call site's return-dict key set moved. The per-candidate report path was never rewired. On main at 104f5b3, solver/dssp_screen.py:

    decay = fitted_far_field_decay_exponent(field_fn)      # computed ...
    ...
    ledger = machine_read_ledger(l3, lam)                  # ... then dropped

screen_candidate() computed the decay exponent, discarded it, and never computed the ansatz classification at all. grep -rn "machine_read_ledger(" across the repository shows every caller using the two-argument form.

Re-measured, not recalled. The BEFORE column in the curated JSON is produced by calling machine_read_ledger(l3, lam) with exactly those two positional arguments, the literal pre-leg call, on the same measurements, in the same process. It is a measurement of the old behaviour, not a recollection of it.

Measured baseline: the planted Tsai-headline field returns fitted exponent -1.0000000000000002, L³ ladder converged=False with rel_change_last_step = 0.1305 against rel_tol = 1e-4 (genuine log-divergence), and the report path said NOT EXCLUDED.

4. The change

screen_candidate() now computes both columns unconditionally and returns them:

• theorem2_decay_to_zero ← decays_to_zero_at_infinity(decay)
• ss_ansatz ← classify_ss_ansatz(lam)

and passes both into machine_read_ledger(...), which routes to leg 362's three-way reading. machine_read_ledger()'s signature and defaults are untouched, so leg 357's two-argument shape and leg 370's opt-in Morrey key both still hold for direct callers (regression control R below). screen_candidate()'s ledger key set is likewise unmoved, {NRS_Tsai, Chae_Tsai, Pineau_Vicol, reportable}, which is what leg 357's own landed test asserts, and it still passes untouched. Morrey stays opt-in: it is a separate, far more expensive ball-average pass, and wiring it into every report was not this gate's question.

5. The six pre-registered controls

Fixed in writeup/novelty/leg_383.md at 1ca4ce5, before construction. Three must fire; three must stay silent: an instrument that can only fire is a tautology, and this repository has been burned by exactly that (leg 340).

Direction A, must fire

C3 is the discrimination control: the field also decays to zero, so T2 would have fired had T1 not been checked first. T1 and T2 are therefore distinguishable, not one flag wearing two names.

Direction B, must stay silent

C4 is the anti-tautology control: if the T2 column fired on a field that does not tend to zero, the column would be excluding everything and measuring nothing. C5 guards C2: if the ansatz clause fired on any static candidate, C2's NOT-REACHED verdict would be vacuous, the same classifier, on a λ>1 trajectory, goes the other way in the same process (DSS, satisfies=False). C6 checks that no clause is claimed on a field no theorem in the ledger reaches: "deciding_clause" not in row is asserted, not assumed.

Regression control R

machine_read_ledger(l3, lam) with its two original positional arguments still returns {NRS_Tsai, Chae_Tsai, Pineau_Vicol, reportable} with NRS_Tsai carrying exactly {excludes, verdict, reason}: leg 357's binary shape, byte-for-byte. Legs 357/362/370's banked JSON files are untouched.

Both-directions meta-check

Asserted as a property of the battery rather than claimed in prose: all four verdicts (EXCLUDED-BY-T1, EXCLUDED-BY-T2, NOT-REACHED-BY-ANSATZ, NOT EXCLUDED) are reachable through screen_candidate() on planted inputs, with ≥2 firing and ≥2 silent.

6. The gate's clauses, decided on magnitudes

Clause (i). Tsai 1998's headline example (eq 1.5) has exact decay exponent −1. The planted field fits to -1.0000000000000002, |diff| 2.22 × 10⁻¹⁶. This repository's own measured exponent on leg 351's Type-I Biot-Savart witness is -0.997134373688964, |diff| vs the source 2.87 × 10⁻³ (leg 359 banked -0.9971; re-measured here, agreeing to the banked precision). The source's exponent matches this repo's measured one at that magnitude, which is the sense in which leg 359 said the old screen would misclassify a genuinely self-similar candidate at this repository's own decay rate: it would have said NOT EXCLUDED, and it did, until this leg.

Clause (ii). The DSS object reads NOT-REACHED-BY-ANSATZ at measured λ = 2.691234472349262, and the recorded deciding_clause is checked programmatically to contain (1.2) and EXACT, i.e. Tsai 1998, eq (1.2), p.29–30: both Theorem 1 and Theorem 2 are stated "If u is of the form (1.2)₁", Leray's exact (continuous) backward self-similar ansatz. The object is discretely self-similar (a periodic-in-log-time orbit, not a fixed point of the rescaled flow) so it fails the hypothesis of both theorems regardless of decay or L^q status. The deciding clause is the ansatz, not a decay clause and not an L³ clause; that is asserted, not narrated.

7. Scope call: leg 382's certified enclosure, deliberately not wired in

solver/dssp_decay_enclosure.py (leg 382, 104f5b3) provides a certified, interval-arithmetic far-field decay enclosure, and its own capability row states it "does NOT replace dssp_screen's fitted column". It was read and deliberately left out, as the dispatch permits and requires to be said explicitly:

1. this gate asks whether the screen classifies correctly, not how rigorous the exponent it classifies on is;
2. swapping the estimator mid-leg would move the numbers underneath the very controls pre-registered to test the classification, confounding the comparison;
3. the fitted column stays in place, unchanged, as instructed.

Open clause left to a successor: a second, certified Theorem-2 column driven by the enclosure, recorded alongside the fitted one and never replacing it, the same alongside-not-instead discipline leg 382 adopted for its own column.

8. What this does not claim

Not a proof, not a construction, not evidence for existence. A candidate that survives this screen is only "not already excluded by a published theorem reachable on this repository's record". CLAY_OBLIGATIONS.md §6's two no-method obligations remain OPEN regardless of this gate's answer. No ban touched, no plan_of_record.py or DIRECTION.md edit, no L1 → L4 link moved. Clay odds unchanged, ~0.05%.