Anatomy + Organs

The SZL anatomy is a set of composable organs. Each organ is named for a precise Quechua common noun (or, where honestly labelled, an acronym/coinage), has one function, one formula, and one Lean stub that states its proof obligation in lutar-lean or the PURIQ suite (formulas/PuriqLean.lean). Every organ exposes the puriq.{decide, act, reflect} interface defined in Doctrine v12.

The master action-selection operator that ties them together is

$$P(x,t) = \operatorname*{arg\,max}_{a \in \mathcal{A}} \Big[\; \Lambda(x)\cdot \mathrm{Yuyay}_{13}(a)\cdot e^{-\beta\,\mathrm{HUKLLA}(a)}\cdot \textstyle\prod_i \mathrm{Khipu}_i(a)\;\Big].$$

Each organ below is a specialisation of this operator. Every extra factor lies in $[0,1]$ and is non-negative, so it can only shrink the gated region — never bypass a gate.

#	Organ	Quechua / origin	Function
1	Amaru	amaru = serpent	Memory cortex / high-stakes reasoning
2	Yuyay	yuyay = thought/memory/wisdom	The 13-axis heart (admission gate)
3	Yawar	yawar = blood	Circulatory receipt ledger
4	Hukulla	HUKLLA acronym	Immune deadman / kill-switch
5	Kallpa	kallpa = strength/energy	Wires / propagation budget
6	Khipu	khipu = knotted-cord record	Receipt DAG / Merkle accumulator
7	Lambda	Λ math primitive	Spine aggregator
8	OTel-VSP	OpenTelemetry	Nervous / observability fiber
9	Kanchay	kanchay = light/radiance	Brand / public-claim surface
10	Hatun	hatun = great/large	Doctrine governance
11	Sumaq	sumaq = beautiful/fine	Designer / proof discharge
12	Killinchu-bridge	killinchu = kestrel	Embodied (physical-space) bridge

Glosses. All common-noun glosses follow Wiktionary and the standard Quechua lexica indexed at kaikki.org and Wiktionary puriy/puriq. HUKLLA is the SZL acronym (Hardened Unambiguous Kill-switch, Latch & Lineage Authority). No mystical terms are used anywhere.

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1 · Amaru — cortex

• Etymology: Quechua amaru = serpent.
• Function: memory cortex / high-stakes reasoning (a11oy.code PRIME tier). Action space $\mathcal{A}$ = candidate multi-step reasoning plans over recalled memory.
• Formula (SF-01): a KL drift penalty regularises plans toward a calibrated reference —

$$P_{\text{Amaru}}(x,t)=\operatorname*{arg\,max}_{a}\Big[\Lambda(x)\,\mathrm{Yuyay}_{13}(a)\,e^{-\beta\,\mathrm{HUKLLA}(a)}\,e^{-\gamma\,\mathrm{KL}(p_a\|p_{\text{ref}})}\,\textstyle\prod_i\mathrm{Khipu}_i(a)\Big].$$

The KL/Pinsker discipline is the v11 pinsker_kl_bound (Cover & Thomas §11.6).

• Lean stub: Lutar/DPI/DPIBound.lean (pinsker_kl_bound); PURIQ factor in formulas/PuriqLean.lean.

2 · Yuyay — heart

• Etymology: Quechua yuyay = thought / memory / wisdom.
• Function: the 13-axis heart (HEART tier). This is the admission gate — conjunctive AND, no compensation. Replay-hash anchor bacf5443…631fc5.
• Formula (SF-02): the gate is the indicator product over all 13 axes —

$$\mathrm{Yuyay}_{13}(a)=\prod_{j=1}^{13}\mathbf{1}\!\left[s_j(a)\ge \phi_j\right],\quad \phi_{1,2}=0.95,\ \phi_{3..9}=0.90,\ \phi_{10..13}:\text{T03/T04/T09/T10 cleared.}$$

Five axes operationalise the Situated Wise Reasoning Scale (Brienza et al. 2018, JPSP).

• Lean stub: the conjunctive gate; obligations in formulas/PuriqLean.lean. Kernel: 430 SLOC Python yuyay_v3.

3 · Yawar — blood

• Etymology: Quechua yawar = blood.
• Function: the circulatory receipt ledger (20 lines of Python; RUWAY is the only authorised writer). Action space = ledger-append actions, one per organ emission.
• Formula (SF-03): the chain-link indicator folds into the Khipu product —

$$C(a) = \mathbf{1}\big[\, \mathrm{sha256}(\text{prev}\,\|\,\text{packet}_a) = \text{root}_a \,\big].$$

Receipt rule: packet → json.dumps(sort_keys=True) → sha256 → hexdigest → append.

• Lean stub: chain-link obligation in formulas/PuriqLean.lean; receipt rule in Doctrine v11 §4.

4 · Hukulla — immune

• Etymology: HUKLLA acronym — Hardened Unambiguous Kill-switch, Latch & Lineage Authority (an SZL acronym, labelled honestly; not a Quechua word).
• Function: the immune deadman — 660 SLOC, 10 deterministic tripwires (T01–T10). T10 (STOP/undo/revert) is an absorbing halt.
• Formula (SF-04): the soft halt, with $\beta$ large so any fired tripwire dominates —

$$\mathrm{HUKLLA}(a)=\sum_{k=1}^{10}\mathbf{1}[T_k\text{ fires}],\qquad \text{utility} \propto e^{-\beta\,\mathrm{HUKLLA}(a)},\ \beta\gg 0.$$

Compound risk is bounded by Egyptian recursive doubling$\mathrm{HUKLLA}(a_1\ldots a_n)\le\sum 2^{k_i}$ (Rhind Mathematical Papyrus, British Museum EA10057).

• Lean stub: puriq_halting_safety in formulas/PuriqLean.lean; doubling in Lutar/Egyptian/AkhmimTable.lean.

5 · Kallpa — wires

• Etymology: Quechua kallpa = strength / energy.
• Function: the wires / propagation organ (FAST tier). Decides continue-vs-stop per step.
• Formula (SF-05): a Butler–Volmer halt budget — continue only while the marginal overpotential keeps current above the activation threshold —

$$i(\eta)=i_0\!\left(e^{\frac{\alpha_a F \eta}{RT}}-e^{-\frac{\alpha_c F \eta}{RT}}\right),\qquad \text{continue}\iff i(\eta)\ge i_{\text{act}}.$$

A principled stop condition, not an arbitrary step cap (Bard & Faulkner, Electrochemical Methods §3.3).

• Lean stub: budget factor B(a) in formulas/PuriqLean.lean.

6 · Khipu — DAG

• Etymology: Quechua khipu = knotted-cord record (the Inka accounting cords).
• Function: the receipt DAG / Merkle accumulator. Action space = DAG-edge insertions.
• Formula (SF-06): Merkle-root recomputation + the summation-cord invariant —

$$M(a)=\mathbf{1}\!\left[\text{root}'=H(\text{root}\,\|\,\text{leaf}_a)\right],\qquad \sum_{\text{root}}=\sum_{\text{pendants}}\Big(\sum_{\text{sub-pendants}}\Big).$$

Integrity by additive arithmetic, not collision-resistance alone (Urton, Signs of the Inka Khipu, UT Press 2003).

• Lean stub: Lutar/Khipu/SummationInvariant.lean; puriq_khipu_integrity in formulas/PuriqLean.lean.

7 · Lambda — spine

• Etymology: Λ — a math primitive (the aggregator backbone), not a word.
• Function: the spine aggregator — collapses a 13-vector to one trust scalar.
• Formula (SF-07): the canonical weighted geometric mean (definition D2) —

$$\Lambda(x)=\prod_{i=1}^{k} x_i^{\,w_i},\qquad \sum_i w_i=1,\ w_i>0,\ x_i\in[0,1].$$

Carries A1 IsMonotone, A2 IsHomogeneous (degree 1), A3 IsEgyptianExact, A4 IsBounded ($\Lambda(x)\le\max_i x_i$). Λ-uniqueness remains Conjecture 1, not a theorem.

• Lean stub: Lutar/Axioms.lean; puriq_lambda_monotone in formulas/PuriqLean.lean.

8 · OTel-VSP — nerves

• Etymology: OpenTelemetry + Verifiable Span Provenance (engineering term).
• Function: the nervous / observability fiber — the W3C traceparent spine.
• Formula (SF-08): the trace-continuity indicator —

$$O(a)=\mathbf{1}\big[\,\mathrm{traceparent}(\text{child}_a)\text{ extends }\mathrm{traceparent}(\text{parent})\,\big].$$

(W3C Trace Context).

• Honest label: traceparent_propagated is in-process only. Cross-mesh W3C propagation (Wire D) is in development — O(a) is honest within a single Space only.
• Lean stub: trace-continuity factor in formulas/PuriqLean.lean.

9 · Kanchay — brand

• Etymology: Quechua kanchay = light / radiance.
• Function: the brand / public-claim surface. Action space = public-claim emissions. (Kanchay is also the source of the brand color tokens used by this site.)
• Formula (SF-09): the claim-calibration indicator on the two sacred axes —

$$K(a)=\mathbf{1}\big[\,\mathrm{moralGrounding}(a)\ge 0.95\ \wedge\ \mathrm{measurabilityHonesty}(a)\ge 0.95\,\big].$$

Enforces the v11 banned-claims register (no "SLSA L3", no "zero sorry", no unscoped "fully verified").

• Lean stub: K(a) collapses to T01/T02 hard-fail tripwires; obligation in formulas/PuriqLean.lean.

10 · Hatun — doctrine

• Etymology: Quechua hatun = great / large.
• Function: doctrine governance. Action space = doctrine-amendment proposals.
• Formula (SF-10): the monotone-additivity guard —

$$D(a)=\mathbf{1}\big[\,a\text{ is additive}\ \wedge\ a\text{ edits no LOCKED number}\,\big].$$

This is what makes "v12 = v11 + PURIQ, no edits" structurally enforceable: any action that would change a LOCKED number yields $D(a)=0$.

• Lean stub: additivity guard in formulas/PuriqLean.lean; HR-3 / HR-7 in Doctrine v11.

11 · Sumaq — designer

• Etymology: Quechua sumaq = beautiful / fine.
• Function: the designer / proof-discharge organ (FRONTIER tier) — the aesthetic of an honest proof. Action space = proof-discharge / artifact-shaping actions.
• Formula (SF-11): the honest-proof indicator —

$$S(a)=\mathbf{1}\big[\,\text{every sorry in }a\text{ is tagged}\ \wedge\ \mathrm{proof\_status}(a)\in\{\text{PROVEN, SORRY, AXIOM, CONJECTURE}\}\,\big].$$

A hidden sorry sets $S(a)=0$ — Zero-Bandaid enforced inside the selection operator.

• Lean stub: status-tag obligation in formulas/PuriqLean.lean; canonical-formulas registry (v11 §12).

12 · Killinchu-bridge — embodied agent

• Etymology: Quechua killinchu = kestrel (a small Andean falcon).
• Function: the physical-space bridge — extends digital governance to embodied actuation (the killinchu flagship drone vertical). Action space = physical-actuation commands.
• Formula (SF-12): a geofence + dynamics-feasibility indicator —

$$G(a)=\mathbf{1}\big[\,\mathrm{pose}(a)\in\mathcal{S}_{\text{safe}}\ \wedge\ \|u(a)\|\le u_{\max}\,\big].$$

The geofence is the embodied analogue of the Bekenstein action-space bound (INV-4): a drone cannot enumerate an unbounded physical action space (LaValle, Planning Algorithms, ch. 13–15).

• Lean stub: feasibility factor G(a) in formulas/PuriqLean.lean.

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Invariant-preservation summary

Every organ factor lies in $[0,1]$ and is non-negative, so multiplying the master utility by it can only shrink the gated region — never bypass a gate. The four master invariants (INV-1…INV-4) therefore hold for every organ by construction.

Organ	Extra factor	Range	Invariant it anchors
Amaru	$e^{-\gamma\mathrm{KL}}$	$(0,1]$	preserves INV-1…4
Yuyay	identity (the gate)	$\{0\}\cup(0,1]$	algebraic root of INV-1
Yawar	$C(a)$ chain-link	$\{0,1\}$	folds into Khipu → INV-3
Hukulla	$e^{-\beta H}$, $\beta\gg0$	$(0,1]$	INV-1 puriq_halting_safety
Kallpa	$B(a)$ BV budget	$\{0,1\}$	preserves INV-1…4
Khipu	Merkle / sum indicator	$\{0,1\}$	INV-3 puriq_khipu_integrity
Lambda	$\Lambda(x)$ itself	$[0,1]$	INV-2 puriq_lambda_monotone
OTel-VSP	$O(a)$ trace-continuity	$\{0,1\}$	preserves INV-1…4
Kanchay	$K(a)$ sacred-axis	$\{0,1\}$	INV-1 (T01/T02)
Hatun	$D(a)$ additivity	$\{0,1\}$	locks v11 numbers
Sumaq	$S(a)$ honest-proof	$\{0,1\}$	Zero-Bandaid
Killinchu	$G(a)$ geofence	$\{0,1\}$	INV-4 (bounded $\mathcal{A}$)

Full derivations and citations: PURIQ Doctrine and the sub-formula suite. Lean obligations live in formulas/PuriqLean.lean (all sorry-tagged, none hidden).