EA-MMRS-SUPPRESSION-INVERSION-01 is the theoretical paper that extends the Suppression Map from a loss profile to a dynamics: it asks what continued suppression costs once the suppressed object propagates. It defines six partially orthogonal regimes โ ignorability, suppressibility, proxy leakage, suppression burden, quality conflict, and propagation inversion โ as regions of a measured state space rather than a developmental ladder. Suppression burden names the growing route coverage required to keep an object below composition threshold, with effective route count corrected for exclusion correlation; quality conflict names the answer damage incurred when materially relevant, already-retrieved evidence is excluded, measured as a vector of factual degradation, distinction loss, source-composition misalignment, and provenance erasure. The connector to the ancient record is stated as a cumulative, path-dependent inequality over witness layers: attribution decays faster than structure along the observed transmission path, with the loss concentrated at channel boundaries โ and the AI composition layer analyzed as the newest measurable boundary in the same chain. The worked example is the 25 August 2026 capture at the query 'sappho future reader,' in which four host-distinct surfaces retrieve the archive's Fragment-31 future-reader thesis in their visible snippets while the AI Overview composes from lower-congruence sources, misidentifies Fragment 147 as 'Fragment 2,' and reproduces the lineage's coinage 'self-archiving' without adequate support in its credited sources โ the cited page verified in-session not to contain the term. The paper's sharpest contribution is constitutive-source erasure in observable form (CSE-O): the condition in which a lineage materially constitutes a query's high-congruence conceptual field, disappears from credited composition, and leaves lineage-specific conceptual structure in the answer that the credited sources do not account for. Under CSE-O, quality conflict becomes internally evidenced โ the audited artifact carries the proof of its own degradation. Constitution share is measured with provenance-family deduplication and a threshold-sensitivity table; the archival ratchet is stated as a conditional design proposition; the inversion threshold ฮบฮฑ > 1 + r is declared as the apparatus's operating target with Stage 6 explicitly unclaimed. Four rounds across three substrates, with all reviewer repairs applied and logged.