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amaru-source

The Maxwell criterion (M = b − 3j + 6 = 0) is classically defined for undirected constraint graphs in structural mechanics (rigidity theory, Laman's theorem). Applying it to a directed graph is an architectural convention, not a formal proof of rigidity.

Our choice: directed edges.

AMARU is a directional cognitive pipeline; every edge carries a semantic flow direction (e.g., KALLPA → YACHAY means "energy primes retrieval", not the reverse). Collapsing that to undirected would erase architectural meaning.

Mitigating convention: The 21-edge count still satisfies M = 0 whether treated as directed or undirected (same count). The directed interpretation adds semantic precision without breaking the numeric criterion. Any future formal rigidity proof should use the undirected projection.

Bracing Edge Justifications (13 edges)

#	Edge	Justification
1	KALLPA → HATUN	Sovereignty gate informs energy budget; the crown's continuum hash constrains how much energy the root may allocate in the next tick.
2	NAWI → RIMAY	Toolcall results (external reads) flow back into the proposal layer; NAWI's boundary data reshapes what RIMAY can assert.
3	NAWI → YUYAY	Toolcall results bypass proposal and pass directly to the critique gate; YUYAY can reject on boundary evidence alone.
4	YACHAY → YUYAY	Retrieved priors (codex facts) are checked at the heart gate; YUYAY validates proposals against memory, not just logic.
5	YACHAY → RUWAY	Codex updates that survive the gate are committed to the record via RUWAY; storage without serpent detour.
6	KALLPA → YUYAY	Energy budget gates critique cost; YUYAY cannot run expensive multi-pass critique if KALLPA signals low energy.
7	KALLPA → RUWAY	Commit action has an energy toll; RUWAY checks KALLPA's available budget before finalising any write.
8	HATUN → YUYAY	The HUKLLA continuum hash flows to the heart gate so YUYAY can validate proposals against the canonical sovereign state.
9	MUSQUY → YUYAY	If critique flags a simulation fault, YUYAY can request re-simulation; this edge carries the re-simulate signal.
10	MUSQUY → YACHAY	Simulation consults the codex mid-flight; intermediate simulation states pull from YACHAY to avoid stale priors.
11	MUSQUY → KALLPA	Simulation declares its energy cost upfront; KALLPA must acknowledge budget before MUSQUY proceeds.
12	HATUN → NAWI	Sovereignty governs the external boundary; HATUN authorises which reads NAWI may open, preventing unbounded toolcall escalation.
13	TUKUY → NAWI	Action-out is symmetric to action-in; an outbound action triggers the same boundary-crossing record in NAWI that an inbound toolcall would.

Edges Not Selected (and why)

Candidate	Reason not chosen
YUYAY ↔ RUWAY (as brace)	Already Serpent-5; would be a duplicate.
TUKUY → HATUN (as brace)	Already Serpent-7; would be a duplicate — originally selected in error, replaced by HATUN→NAWI.
TUKUY ↔ SENTRA-egress	SENTRA is infrastructure, not a chakra node; excluded per task specification.

Full Edge List (21)

Base Serpent (8)

#	Edge	Role
S1	KALLPA → YACHAY	Energy primes retrieval
S2	YACHAY → MUSQUY	Codex feeds simulation
S3	MUSQUY → RIMAY	Simulation drives proposal
S4	RIMAY → YUYAY	Proposal enters critique gate
S5	YUYAY → RUWAY	Gate approval triggers commit
S6	RUWAY → TUKUY	Commit hands off to action-out
S7	TUKUY → HATUN	Outbound action crowned by sovereignty
S8	HATUN → KALLPA	Cycle close — sovereign hash seeds next tick

Bracing (13)

#	Edge
B1	KALLPA → HATUN
B2	NAWI → RIMAY
B3	NAWI → YUYAY
B4	YACHAY → YUYAY
B5	YACHAY → RUWAY
B6	KALLPA → YUYAY
B7	KALLPA → RUWAY
B8	HATUN → YUYAY
B9	MUSQUY → YUYAY
B10	MUSQUY → YACHAY
B11	MUSQUY → KALLPA
B12	HATUN → NAWI
B13	TUKUY → NAWI