Triad-of-Triads With SRAG Enforcement Grammar: Swaps, Nulls, SoZ, And No-Backflow

Important Note: This manuscript is a direct follow-on to (i) Sign-First Closure for Apparent Chaos: A SRAG Bridge With Hall and Young as Canonical Cases and then to (ii) the theoretical foundation Theoretical SignNet Ruleset And Admissibility Grammar (SRAG) For Apparent Chaos: MAP0--SEB--MAP1 Under 4S3. If those two prior papers have not been read, they should be read first, because the present work assumes their fixed definitions (signed-net object, zeros governance, label-as-tag discipline, MAP0--SEB--MAP1 stage separation, and the Hall/Young swap-and-null falsifier posture) and only adds the executable certifier layer: Triad-of-Triads enforcement grammar with swaps, nulls, SoZ charging, and an explicit no-backflow law that forbids enforcement-to-recognition repair. Articel Key Words : Triad-of-Triads; SRAG; Sign-First Closure for Apparent Chaos; tokens-only interface; no-backflow law; Directive Handoff Protocol; redundancy squares; leave-one-out audit; swaps and nulls; Strong-to-Weak grading; Sum-of-Zeros (SoZ). Foundational — This extremely important manuscript, Triad-of-Triads With SRAG Enforcement Grammar: Swaps, Nulls, SoZ, And No-Backflow, turns SRAG from a recognition-side admissibility grammar into a certifier-grade gate engine by welding it to the Triad-of-Triads contract under fixed accounting. The concrete deliverable is the interface specification: SRAG is required to emit mandatory token rows (sign in {−1,0,+1}, zero policy, yield, swap_set_id, label_tag_set, translator_set, missingness tokens, refusal reasons), Triad-of-Triads is required to consume only those rows (no raw re-read) and output a tokens-only decision row (strong/weak/refuse with a fixed reason_token alphabet), and enforcement is required to consume only the decision row with an explicit no-backflow law enforced by Directive Handoff constraints. The paper is governance-first: it declares the falsifiers that make the bridge real (label-scramble invariance, swap invariance, sunrise–sunset asymmetry audit, SoZ starvation resistance, translator_set invariance under replay-only tightening, and hard refusal on post-view authority changes) and it pins tool attachment (STLF/Knob/SoZ/Strong-to-Weak) as declared translator steps that can only downgrade via visible dependence tokens rather than “improve” a claim by narrative repair. The net effect is a reusable mid-layer gate engine that can certify apparent-chaos signed-net objects across platforms while preventing the two failure modes that kill reproducibility: labels acting as acceptance authority and downstream success rewriting upstream recognition.