Editing Openai/69596681-3f7c-8006-b9fd-01d9d8191763 (section)

=== Assistant: Proceeding. ===
Proceeding. Below is METHODS BLOCK 17 — PIPELINE DAG, expanded to maximum algorithmic depth using machine-learning–style execution semantics (static scheduling, dependency resolution, short-circuiting, CI orchestration, determinism). This block defines how the entire system executes as a certified computation graph.

METHODS BLOCK 17 — PIPELINE DAG

OBJECTIVE
Define a static, acyclic execution graph that orders all blocks, enforces dependencies, guarantees determinism, and enables CI-style orchestration. This block specifies control flow, not scientific content. Any deviation in ordering or dependency handling ⇒ INVALID.

GRAPH DEFINITION
Define directed acyclic graph:

𝒢 = (𝒱, 𝒜)

Vertices 𝒱 correspond to METHODS BLOCKS 0–19.
Edges 𝒜 encode hard execution dependencies.
Graph is static, frozen, and hash-checked.

VERTEX SET
𝒱 = {
B0_HASH,
B1_AXIOMS,
B2_TYPES,
B3_MODEL,
B4_RESIDUALS,
B5_STRUCT,
B6_FEAS,
B7_IDENT,
B8_LIKELIHOOD,
B9_VALIDITY,
B10_EVIDENCE,
B11_INTEGRATOR,
B12_COLLAPSE,
B13_MC,
B14_PRECISION,
B15_ATTRIBUTION,
B16_CERTIFICATION,
B17_PIPELINE,
B18_ML_INTERPRETATION,
B19_AUDIT
}

EDGE SET (CANONICAL ORDER)
Edges u→v indicate u must complete successfully before v may execute.

B0_HASH → B1_AXIOMS
B1_AXIOMS → B2_TYPES
B2_TYPES → B3_MODEL
B3_MODEL → B9_VALIDITY
B9_VALIDITY → B4_RESIDUALS
B4_RESIDUALS → B5_STRUCT
B5_STRUCT → B6_FEAS
B6_FEAS → B7_IDENT
B7_IDENT → B8_LIKELIHOOD
B8_LIKELIHOOD → B11_INTEGRATOR
B11_INTEGRATOR → B10_EVIDENCE
B10_EVIDENCE → B12_COLLAPSE
B12_COLLAPSE → B13_MC
B13_MC → B14_PRECISION
B14_PRECISION → B15_ATTRIBUTION
B12_COLLAPSE → B16_CERTIFICATION
{ALL BLOCKS} → B19_AUDIT

No cycles permitted. No optional edges.

EXECUTION SEMANTICS
Execution is topologically ordered with deterministic scheduling.

Rules:
• Each block executes at most once per run
• Block outputs are immutable artifacts
• Downstream blocks may read but never modify upstream artifacts
• Any block receiving INVALID aborts downstream execution except attribution/audit paths

SHORT-CIRCUIT LOGIC
Certain blocks may short-circuit computation:

• If B9_VALIDITY fails ⇒ jump to B12_COLLAPSE, then B15_ATTRIBUTION, B19_AUDIT
• If B5_STRUCT fails ⇒ skip B6–B11 (except for attribution), go to B12
• If B6_FEAS collapses ⇒ skip B7–B11, go to B12
• If B12_COLLAPSE=1 ⇒ B16_CERTIFICATION skipped

Short-circuiting preserves DAG integrity; skipped blocks marked SKIPPED.

PARALLELISM RULES
By default, execution is sequential.
Parallel execution allowed only if:
• Blocks are independent (no shared artifacts)
• Execution order remains equivalent to topological order
• Floating-point operations are deterministic and ordered

Otherwise, parallelism forbidden.

ML analogy: static computation graph, not dynamic eager execution.

FAILURE PROPAGATION
If block B_i returns INVALID:
• All downstream blocks that depend on B_i are marked SKIPPED
• Verdict forced to COLLAPSE if applicable
• Attribution graph records B_i as first-fail if precedence allows

No retries. No fallback paths.

STATELESSNESS
The pipeline is purely functional at the run level:

Run(S, D, seed) → {Artifacts, Verdict}

No persistent state across runs except cached Verdicts under A3/A4 monotonicity.

CI/CD INTEGRATION
Pipeline is compatible with CI execution:

• Deterministic inputs
• Deterministic outputs
• Hash-based change detection
• Automatic INVALID on drift

A CI failure is defined as any change in artifacts without MethodHash change.

REPRODUCIBILITY CONTRACT
Two executions with identical:
• MethodHash
• DataHash
• CodeHash
• Seed

Must produce bitwise-identical artifacts and verdict.

FAILURE MODES
• Dynamic graph modification ⇒ INVALID
• Conditional edge creation ⇒ INVALID
• Executing blocks out of order ⇒ INVALID
• Re-executing a block ⇒ INVALID

ARTIFACT EMISSION
Emit immutable PipelineExecutionRecord:

⟨
ExecutionOrder,
BlockStatuses ∈ {PASS,FAIL,SKIPPED},
ShortCircuitEvents,
MethodHash,
Timestamp
⟩

Hashed and audit-logged.

ML INTERPRETATION
This block defines a certified evaluation pipeline:

• Static graph
• No training loops
• No data-dependent control flow
• Full reproducibility

Equivalent to running a formally verified inference program rather than an ML workflow.

END METHODS BLOCK 17.

If you confirm, the next block will be METHODS BLOCK 18 — ML INTERPRETATION, expanded into formal correspondence with machine learning concepts (classifiers, hypothesis classes, robustness, complexity control) without introducing new mechanics.

© Robert R. Frost
2026-01-03