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U6: The derivation

Owner the computation, and never a person. Centre of gravity the pinned input. Smallest node one stored record with its inputs, its time and the version of the code that produced it. Level across. Status partial.

Nine stored deltas, each pinning the profile version, the mandate version, the pack version, the time and abp.delta/v1, recomputed by the gate on every build. What is missing is the series, the trigger and the crossing. No field on any node here is authored: a Trigger is received, a Crossing is computed, a Series is appended.

Node types

A node type is a required pattern of paths, not a label. The ones marked yes are walked on every build and the count is what matched; the rest are the vocabulary this universe needs and does not have.

Type	Formula	Exists today	Note
Excess	`[Excess] := a [GrantedCapability] with NO -authorised_by-> path to the [Mandate] in scope`	yes, 78 matched
UnboundedExcess	`[UnboundedExcess] := an [Excess] whose -bounded_by-> [Barrier] is not a [Control]`	yes, 61 matched
Shortfall	`[Shortfall] := a [Capability] that a [Mandate] -authorises-> and no [DeploymentShape] in scope -grants->`	yes, 2 matched
DeltaRecord	`a node -derived_from-> exactly one [GrantVersion] and exactly one [MandateVersion], -computed_by-> one [Computation], with an excess, an unbounded excess and a shortfall set; no field writable by a person`	not yet	Exists as a file under data/deltas/ and not yet as a node in the graph.
Computation	`a version of the code: abp.delta/v1 today`	not yet
Series	`the ordered set of [DeltaRecord]s for one shape and one mandate, each -supersedes-> the last`	not yet
Trigger	`an event that -causes_recompute-> of a [Series]: a credential change, a token claims change, an assurance level change, a device compliance change; a new observation in U3; a corrected mandate in U5; a new pack version in U1`	not yet
Crossing	`a [DeltaRecord] whose count -crosses-> a [Threshold] somebody set in advance; a record, never a verdict`	not yet

Verbs

Each is a verb with a distinct inverse, a stated domain and range, and the sentence it reads as. The ones marked live are in the edge vocabulary today; the rest are proposed here, or declared by the universe's owner elsewhere, and say so.

Edge	Reads as	Inverse	Reads as	Domain	Range	From	Status
`exceeds`	this granted capability exceeds this mandate	`exceeded_by`	this mandate is exceeded by these granted capabilities	`GrantedCapability`	`Mandate`	this site	live
`derived_from`	this record was derived from these pinned inputs	`derived_into`	these inputs were derived into this record	`DeltaRecord`	`GrantVersion or MandateVersion`	proposed here	proposed
`computed_by`	this record was computed by this version of the code	`computed`	this version of the code computed these records	`DeltaRecord`	`Computation`	proposed here	proposed
`causes_recompute`	this event caused this series to recompute	`recomputed_on`	this series was recomputed on this event	`Trigger`	`Series`	proposed here	proposed
`crosses`	this record crosses this threshold	`crossed_by`	this threshold is crossed by these records	`DeltaRecord`	`Threshold`	proposed here	proposed

What the map adds here

The gate's twelfth check, which recomputes every stored delta from its pinned inputs, extends to the series without a new idea: every record in a series recomputes, and a series with a gap in its supersedes chain fails the build. Lab 07's history folder, one entry per recompute, is the live instance of Series and it exists in riskmandate.ai's vault today.

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