Honest ceiling. Serious candidate / diagnostic that recovers the threshold signs — NOT a validated unification. This result does not advance the gate: SG-7 stays OPEN / Diagnostic. What it adds is a value-free, target-blind tool and a falsifiable path — not a closure. No status was ever upgraded. Frozen branch
dcc66f1b2685/a5b1e6f9d951READ-ONLY. Updated 2026-06-25.
SG-7's standing problem (the 2026-06-24 downgrade): the 8-row heat-kernel threshold ledger that drives α₁=α₂=α₃ was fitted-to-target — the δ-triple magnitudes entered as constants tuned to hit unification, not derived from the frozen spectrum (deep check missed the printed rows by ~2×–18×). A fitted ledger is diagnostic-only.
This result delivers the remedy infrastructure, not the fix: a runnable AXIOM-CANONICAL-ROW-TRACE-COMPILER
that regenerates the threshold rows target-blind from a frozen mode table, and refuses any input that
smuggles in the answer. It has not been run on the real frozen spectrum. Therefore:
AXIOM-CANONICAL-ROW-TRACE-COMPILER is built, runnable, tested.AXIOM-CANONICAL-ROW-TRACE-COMPILER — for the frozen admissible SG-7 spectral domain there is a unique
target-blind row-label compiler ℓ: Ω_adm → {1,…,8, inert}, induced only by compact support, actor type,
gauge-charge insertion, orbifold/boundary status, chirality, bundle descent, Wilson/Hosotani data, and the frozen
admissibility predicate. With row projectors P_a = 𝟙_{ℓ⁻¹(a)}, the threshold rows are the finite parts
R_{a,i} = FP_{s=0} Tr_{H_KK}[P_a Q_i² μ^{2s} D_KK^{−s}], and the threshold vector δ_i = (1/2π) Σ_{a=1..8} R_{a,i}.
This axiom is value-free only if the row-label compiler and the finite-part scheme are frozen before any
comparison with the printed SG-7 ledger. That freeze-before-compare discipline is what the tool mechanically
enforces (§3). The eight rows: K6 gauge/ghost SU(3); K6 matter SU(3); S² gauge/ghost SU(2); S² matter SU(2);
S¹_Y hypercharge zero-packet; S¹_Y hypercharge heavy-packet; Higgs Wilson-line; orbifold/boundary fixed points
(+ an inert bin).
The runnable package (SG7_row_trace_compiler_runnable, published) was executed independently:
tests/test_compiler.py).delta column is
rejected with TargetLoadingError: Target-loaded columns are forbidden …: delta. The guard forbids any column
whose name contains delta, target, printed, expected, fit, fitted, ledger_value, row_value, answer,
observed_output — in both the mode table and projectors.json. So the compiler cannot be fed the
answer; it can only compile rows from frozen primitives (eigenvalues, degeneracies, charge insertions,
actor/factor/boundary/Wilson/admissibility labels).This is the precise anti-tuning to the known answer remedy for the "fitted-to-target" downgrade — as a mechanism, verified.
The gate stays OPEN because the load-bearing question is unanswered, not because a tool was missing:
Do not ask whether the rows sum. Ask where the rows come from. If they come from frozen primitives → the ledger is derived; if they enter as constants → SG-7 stays diagnostic-only.
To lift SG-7 from Reduced-to-Axiom (infrastructure) toward DERIVED-GIVEN-E, an owner must:
1. Produce real_frozen_modes.csv — the real frozen, target-blind projected KK mode table (the columns
the compiler requires), frozen before comparison to the published δ-triple. (PENDING — not produced here.)
2. Run the compiler and compare the regenerated rows to the printed ledger after the freeze.
- rows reproduce within a pre-declared tolerance from primitives → DERIVED-GIVEN-E;
- rows only match via a normalization reverse-engineered to hit the known δ → RELABEL_FAIL (relocation, not
closure);
- the real table cannot be produced target-blind → stays OPEN / SCHEME-ANCHORED.
Current baseline (honest): R1 (rows from primitives) BLOCKED; R2 (magnitudes) OPEN — the δ magnitudes remain fitted-to-target / not formula-derived. The single unfixed scheme-anchor is the per-factor KK ζ-normalization Z_X + overlap c_abi.
AXIOM-CANONICAL-ROW-TRACE-COMPILER — built, runnable, target-blind, verified as
infrastructure. This does not by itself derive the rows, prove the geometry unique, or derive the SM
inputs (separate anchors / scope boundaries).The §4 owner-artifact step was carried out, not deferred. A real frozen mode table real_frozen_modes.csv
(150 modes) was built target-blind — eigenvalues + degeneracies from the fixed K₆/S²/S¹_Y KK spectra,
gauge-charge insertions from the actual SM rep Dynkin indices, scheme freedoms set by canonical, declared,
un-tuned rules (Z_X = 1, μ = 1, cutoff (p,q) ≤ 12 inherited from the frozen K₆ table). The compiler ran clean
(anti-tuning to the known answer + schema passed). The result was then compared to the printed δ-triple post-hoc.
| δ₁ (U(1)_Y) | δ₂ (SU(2)_L) | δ₃ (SU(3)_c) | |
|---|---|---|---|
| Target-blind (this run) | −63.897 | +70.627 | +227172.5 |
| Printed (fitted) ledger | +4.8424 | −3.1112 | −1.7313 |
| Match? | ✗ sign+mag (13×) | ✗ sign+mag (23×) | ✗ sign+mag (1.3×10⁵) |
No match on any component — signs flip on all three, and δ₃ is off by five orders of magnitude. The δ₃ blow-up is structural, not a bug (independently confirmed): K₆ gauge-ghost and K₆ matter ride the identical KK tower, differing only by the fixed charge×coefficient ratio q₃·coef = (3·−1) vs (1.5·+1) = −2:1, which can never cancel — so the canonical insertion cannot produce the small printed δ₃.
Disposition: FINDING — blind ≠ printed. The blind primitives demonstrably do not generate the printed
δ-triple under the canonical scheme. This demonstrates (not merely asserts) the dossier's own R2/R3 concession:
the printed δ are injected / fitted reals; the invariant→row link is broken. The post-hoc falsifier fired
— and the printed values were an input to nothing. (Verified SAFE by an independent check + an
independent re-run of the column sums.)
Two honest caveats — this is a demonstration that the obvious reconstruction fails, NOT a clean falsification
of the geometry:
1. The log_mu finite-part is a self-admitted placeholder (finite_part.py: "runnable finite-part
placeholder … should replace or freeze before comparison") — not the actual ζ-regularized KK finite part.
The wild magnitudes (especially δ₃) are partly placeholder-scheme artifacts of the missing subtraction.
2. The frozen spectrum_K6.csv was not co-located in the run package, so its tower was internal-consistency-
checked but not byte-traced to source (a flagged UNKNOWN; it does not change the disposition — even granting
the towers, the triple fails on sign).
Net: SG-7 stays OPEN / Diagnostic — the gate does not move. What changed is the evidence grade: the
"fitted-to-target" status is now demonstrated by a target-blind run, not just conceded. A genuine
DERIVED-GIVEN-E attempt still requires the actual (non-placeholder) ζ-regularized KK finite-part co-packaged
with byte-anchored spectra, then a fresh blind run. No status was ever upgraded. (Artifacts published: real_frozen_modes.csv,
outputs/real_run.csv, the build_real_modes.py generator, and FINDING.md, inside the runnable package.)
The runnable package is published alongside this result so the verification is reproducible (a captured log is not a derivation). Serious candidate, NOT validated.