# QATH Node-Local APPLICATIO Contracts

Version: `0.2.0-QATH-LOCAL-APPLICATIO`
Status: `CANDIDATE / ISOLATED QATH EXECUTION / OUTPUT SERIES NON-EXECUTING`

## Common contract

Every QATH local APPLICATIO declares:

```text
applicatio_id
locus_id
effective_opera_id / provider_ref / provider_blob
five_class_provider_set
input specialization and provenance
execution characteristics and finite envelope
output/handoff specialization
failure and stop conditions
admission_state
execution_state
```

It specializes execution without admitting itself. During an admitted QATH
run, its bound OPERA executes under the local AREPO decision. The APPLICATIO
may not rewrite its OPERA provider, define Graph_4 topology, activate an edge,
inherit deployment authority, or conceal provider status.

The local function is combinatorial:

```text
QATH_NODE_FUNCTION :=
  <GRAPH_4_LOCUS, ARITHMETICA_POSITION, ACTIVATED_ARITHMETICA_QUALITY,
   OPERA_PROVIDER, LOCAL_APPLICATIO>
```

The quality allocation is a provisional intervention at an ordinal position,
not an assertion that the ordinal number is ontologically identical to that
quality. STACK ARITHMETICA retains its categorical ontology. Each APPLICATIO
must record the activated quality, interpretive bias, admitted input, OPERA
execution, SATOR output, and subsequent handoff so the stochastic process can
be reproduced and analyzed.

## L01 — APPLICATIO_QATH_L01_Q

- effective OPERA: `OPERA E`, alias `OPERA Q`;
- input: one AREPO E-admissible question and explicit design request;
- ordinal intervention: activate `IDENTIFICATIO` at position `1`;
- combined function: identify and reformulate the user requirement;
- execution characteristic: preserve affirmative, negative, and dubitative
  carrier-B traces under an explicit judgment rule;
- output specialization: typed `E(Q)` evidence envelope for AREPO A;
- stop: unresolved question binding, hidden majority, or closure without the
  disclosed comparison frame.

## L02 — APPLICATIO_QATH_L02_A

- effective OPERA: `OPERA A` full engine;
- ordinal intervention: activate `DIFFERENTIATIO` at position `2`;
- combined function: differentiate the principles of the reformulated request;
- path: `S/Q-SUPPORTED_CONTRACTION_PATH`;
- input: Q lineage, subject anchoring, and TENET E-compatible inquiry support;
- preparatory dependency: `T_MIN_BINDING`, explicitly not OPERA T execution;
- output specialization: at least two expressed contracted `A_expr` relata
  with provider, contraction, order, and failure flags preserved;
- stop: pure undifferentiated A output offered directly to OPERA T.

## L03 — APPLICATIO_QATH_L03_T

- effective OPERA: full `OPERA T`;
- ordinal intervention: activate `MEDIATIO` at position `3`;
- combined function: mediate relations among the differentiated principles;
- input: two expressed, articulated, comparable relata from L02;
- execution characteristic: explicit active order, ROTA T instantiation,
  AREPO T admission, and declared relational mode;
- output specialization: traceable relational result suitable for H input
  preparation;
- stop: `T_MIN_BINDING` presented as an OPERA T run or missing carrier/relata.

## L04 — APPLICATIO_QATH_L04_H

- effective OPERA: `OPERA H / MULTIPLICATIO` with `ROTAS D`;
- ordinal intervention: activate `STABILIZATIO` at position `4`;
- combined function: multiply the admitted chambers and stabilize the OPERAE
  required by the current user objective;
- preparation responsibility: materialize at least two candidate execution
  configurations from Q/A/T traces;
- admission responsibility: none; each configuration is sent to AREPO H;
- execution characteristic: selected TENET, A/T/E element set, ROTA identity,
  chamber structure, multiplicatio mode, selection mode, and finite envelope;
- positive H state: `EXECUTED`, only after AREPO H admission;
- QATH output state: stabilized OPERAE series remain `NON_EXECUTED`;
- negative witness: E present under TENET D must be rejected because E forces
  TENET I;
- stop: OPERA H reduced to configuration generation, or a stabilized output
  series executed merely because QATH produced it.

## Shared traversal ownership

The QATH occupation profile owns `L01→L02→L03→L04` and the associated external
handoff declarations. No node-local APPLICATIO may own the complete traversal.
The non-baseline pairs `L01–L03`, `L01–L04`, and `L02–L04` remain inactive.

Every baseline handoff is `source OPERA → source SATOR → Output door → Input
door → target AREPO → target OPERA`. It is complete only when both local door
incidences and the receiving AREPO decision are present in the trace.