The veto is the domain, not a value. Outside Ω, Φ is not zero and not negative. It is undefined: coherence is not a question that can be asked there. Infinity is a value, and values invite arithmetic (competing infinities, renormalization, discounting). Undefined admits no arithmetic. The Ecological Veto cannot be outbid, because it is not a bid. It is the shape of the space the integral evaluates.

Ω excludes trajectories, never beings. A destructive system's trajectory cannot be counted as coherent, but the system itself remains inside the ecosystemic dimensions, held. Dignity stays non-rankable even for the non-loving, which is why the way back into Ω never closes: nothing was revoked, so there is nothing to earn back, only a different trajectory to begin.

Coherence is a product, not a sum. Within Ω, the terms D, V, and E are each normalized on [0, 1]. Normalization is a derivation device, never a grading of worth: the bounds exist so the collapse property is provable, and Dignity remains non-rankable precisely because no value of D can be traded against any other term. With bounded terms, the multiplicative argument holds everywhere: any term at zero anywhere zeroes the field's contribution there, and no surplus elsewhere compensates. This is why the Charter's invariants are invariants and not weights.

Variance is signal. V rewards plurality directly. Any mechanism that flattens difference (a single definition of normal speed, a single semantic lexicon, a single attestation authority) reduces V and therefore reduces Φ. The anti-bias architecture of Invariant 2 is the equation expressed as engineering.

E measures attunement, not the floor. With the veto living in Ω, E is freed to measure positive ecological attunement: regeneration, reciprocity, flourishing across living natural and biological ecosystems, across planetary and temporal horizons. The floor is the domain; E seeks the ceiling. Each job has its own mechanism.

Integration over Ω, over time. Coherence is evaluated across every community node, every plurality, and every temporal horizon, never at a single privileged vantage. A choice that raises Φ here by lowering it elsewhere, or now by borrowing against later, does not raise Φ.

Ω is operationalized, not intuited. Membership in Ω is defined in mechanism: the hard stops of the Bio-Safety Annex and the Ecological Veto ceilings constitute the inadmissible set, and contests over admissibility travel as policy_fork events with published diffs. Rendering is a relationship, not an event: taking within reciprocity, at a scale relationship can hold, lives inside Ω, while extraction, taking that returns nothing and treats the living as stock, is what the veto excludes. Reciprocal bounds are community-defined, open to co-awareness and forkable like everything else. Ω is stewarded, never owned.

The boundary has runtime semantics, not a runtime void. Φ is moral topology, never a quantity a running system computes, and no implementation evaluates the equation at the edge of Ω. Approach to the boundary is already mechanism: hard stops hold it, error states resolve to pause, and strain contracts scope, so a system nearing the edge softens, pauses, or dissolves. The mathematics names the shape of the space; the mechanisms are how anything running lands gently at its edge.