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DOI 1.15 — Testing the converse: does a feature match guarantee SSIM=1.0?

View DOI 1.15 on Zenodo: https://doi.org/10.5281/zenodo.22013446

New DBBuilt on the current, join-free pipeline (build_notta_tta_comp_db.py), one independent database per model.

DOI 1.11's Pixel Identity Theorem proves SSIM=1.0 ⇒ pixel-identical ⇒ all eight comp_* features match. This report tests the converse, which isn't guaranteed by that proof: if the eight features match ground truth exactly, must SSIM still equal 1.0? Every query here is single-database — unlike DOI 1.13's cross-model comparisons, nothing needs to be ATTACHed — so all four models are covered by one script that simply changes the .open target between sections, captured in a single continuous recording instead of one video per model.

Part 1: does an 8/8 feature match mean SSIM=1.0? — verification_sql_final_4model.sql

WITH feature_match AS (
    SELECT
        (ssim_l_notta * ssim_c_notta * ssim_s_notta) AS ssim,
        (CASE WHEN comp_sharpness_gt = comp_sharpness_notta THEN 1 ELSE 0 END
       + CASE WHEN comp_edges_gt = comp_edges_notta THEN 1 ELSE 0 END
       + CASE WHEN comp_artifact_ringing_gt = comp_artifact_ringing_notta THEN 1 ELSE 0 END
       + CASE WHEN comp_artifact_block_gt = comp_artifact_block_notta THEN 1 ELSE 0 END
       + CASE WHEN comp_contrast_gt = comp_contrast_notta THEN 1 ELSE 0 END
       + CASE WHEN comp_texture_gt = comp_texture_notta THEN 1 ELSE 0 END
       + CASE WHEN comp_entropy_gt = comp_entropy_notta THEN 1 ELSE 0 END
       + CASE WHEN comp_noise_gt = comp_noise_notta THEN 1 ELSE 0 END) AS n_features_matched
    FROM blocks
),
all8 AS (
    SELECT ssim FROM feature_match WHERE n_features_matched = 8
)
SELECT 'n_matched_8' AS metric, CAST(COUNT(*) AS VARCHAR) AS value FROM all8
UNION ALL SELECT 'pct_ssim_eq_1', CAST(ROUND(100.0*SUM(CASE WHEN ssim=1.0 THEN 1 ELSE 0 END)/COUNT(*),4) AS VARCHAR) FROM all8
UNION ALL SELECT 'pct_ssim_lt_05', CAST(ROUND(100.0*SUM(CASE WHEN ssim<0.5 THEN 1 ELSE 0 END)/COUNT(*),4) AS VARCHAR) FROM all8;

-- Repeats identically for SwinIR, High-Fidelity, and Digital-Art,
-- each preceded by its own .open line.

Sums how many of the eight comp_* fields match ground truth exactly per block (n_features_matched), restricts to the perfect 8/8 group, and reports what fraction of that group actually hits SSIM=1.0 versus falls below 0.5. Answer: conditionally yes, not universally. SwinIR: 99.97% at SSIM=1.0, effectively confirming the converse for that model. The other three tell a different story — Standard 42.23%, Digital-Art 53.33%, and Upscayl High-Fidelity just 0.01%, with 63.05% of its feature-matched blocks actually below 0.5.

Part 2: tracing the mechanism — the C-pinning and S-near-1 checks

WITH feature_match AS (
    SELECT
        sigma_gt, ssim_l_notta, ssim_c_notta, ssim_s_notta,
        (ssim_l_notta * ssim_c_notta * ssim_s_notta) AS ssim,
        (CASE WHEN comp_sharpness_gt = comp_sharpness_notta THEN 1 ELSE 0 END
       + CASE WHEN comp_edges_gt = comp_edges_notta THEN 1 ELSE 0 END
       + CASE WHEN comp_artifact_ringing_gt = comp_artifact_ringing_notta THEN 1 ELSE 0 END
       + CASE WHEN comp_artifact_block_gt = comp_artifact_block_notta THEN 1 ELSE 0 END
       + CASE WHEN comp_contrast_gt = comp_contrast_notta THEN 1 ELSE 0 END
       + CASE WHEN comp_texture_gt = comp_texture_notta THEN 1 ELSE 0 END
       + CASE WHEN comp_entropy_gt = comp_entropy_notta THEN 1 ELSE 0 END
       + CASE WHEN comp_noise_gt = comp_noise_notta THEN 1 ELSE 0 END) AS n_features_matched
    FROM blocks
),
all8 AS (
    SELECT
        CASE WHEN sigma_gt = 0 THEN 'sigma_gt=0' ELSE 'sigma_gt>0' END AS sigma_group,
        ssim, ssim_l_notta, ssim_c_notta, ssim_s_notta
    FROM feature_match
    WHERE n_features_matched = 8
),
stats AS (
    SELECT
        sigma_group,
        COUNT(*) AS n,
        PERCENTILE_CONT(0.5) WITHIN GROUP (ORDER BY ssim) AS median_ssim,
        AVG(ssim_l_notta) AS avg_l, MIN(ssim_l_notta) AS min_l, MAX(ssim_l_notta) AS max_l,
        AVG(ssim_c_notta) AS avg_c, MIN(ssim_c_notta) AS min_c, MAX(ssim_c_notta) AS max_c,
        AVG(ssim_s_notta) AS avg_s, MIN(ssim_s_notta) AS min_s, MAX(ssim_s_notta) AS max_s
    FROM all8
    GROUP BY sigma_group
)
SELECT * FROM stats;

Splits the same 8/8-matched group into σ_gt=0 and σ_gt>0, then reports the min/avg/max of each SSIM factor (L, C, S) in both halves. Result, for every one of the four models: the contrast term C is exactly 1.0 — min, avg, and max all identical — in both groups. That's a new general theorem, not restricted to the σ_gt=0 masking regime already established in DOI 1.11: C=1 whenever σ_gt=σ_notta, for any shared value. The structure term S sits at exactly 1.0 in the σ_gt=0 group and extremely close to 1.0 (a narrow, model-dependent range) in the σ_gt>0 group. With C pinned and S nearly pinned, the luminance term L is the only factor still free to vary — and its spread is the entire content of Part 1's score divergence. The root cause is structural, not incidental: none of the eight comp_* features measures luminance at all, so matching all eight can constrain C and S but says nothing about L.