E3 ยท Publication Volume 25

Interval Intersection and Priority

overlay, dominance, splitting, merging and coding

Learning objectives

  • Explain the decision and evidence boundary for overlay, dominance, splitting, merging and coding.
  • Design and implement the relevant drillhole data or algorithm contract without hidden conventions.
  • Separate hard release gates from diagnostics, interpretation and authorised review.
  • Produce a deterministic interval-overlay result with a complete precedence trace from synthetic evidence.

The lesson is complete only when the learner can defend the data model, algorithm, tests and release decision. An attractive trajectory or clean interval table without source evidence and executable invariants remains unverified.

This is a general, institution-neutral tutorial with no relationship to any company or individual. All borehole identifiers, coordinates, depths, directions, intervals, values and review events in the lesson are synthetic and must not be used for an operational decision.

Decision context

Overlay must answer which source assertions apply to each atomic depth span and, only when required, which assertion controls a derived view. Priority is a domain rule, not a property of row order. The rule may depend on observation type, evidence state, effective time, scale, confidence or an explicit review decision. A dominant record does not erase lower-priority evidence.

Write the intended use, consequence of error, required evidence and release authority before selecting a transformation. The same source can be suitable for exploratory display and unsuitable for a released derivative. Fitness is evaluated against a versioned contract and use, not attached permanently to a file.

Core concept

Create an ordered set of all validated boundaries, split the depth axis into atomic half-open spans, identify active records for each span, and evaluate the versioned precedence rule. Emit one derived row per atomic span with active identities, selected value or conflict state and rule explanation. Merge adjacent derived rows only when their complete semantic payload and provenance are equivalent under a declared merge policy.

Keep received observations, accepted evidence views and derived results as distinct objects. This separation allows corrected evidence or a changed method to generate a new result without rewriting history. Every derived coordinate or interval therefore answers both a scientific question and a provenance question.

Algorithm and data model

Use three layers: immutable input collections, an atomic overlay relation and one or more purpose-specific resolved views. The overlay relation is lossless and can support different resolution policies. A categorical code carries a concept identity and scheme version, not only a label. If two active records have equal precedence but incompatible values, return a conflict rather than choosing lexicographically or by insertion order.

Define the transformation as a pure, testable operation wherever practical. Parsing, semantic validation, evidence selection, numeric calculation and release evaluation are separate stages. Each stage emits structured output and does not depend on interface state, filename order or an undocumented default.

Constraints and invariants

| Invariant | Executable or review test | | --- | --- | | Priority rules are versioned and independent of row order. | Reject or quarantine any record that violates this condition and record the exact affected identity. | | Atomic overlay preserves every active contributor. | Evaluate this condition before producing a derived trajectory or interval result. | | Equal-priority incompatibility produces a conflict. | Preserve received evidence and create a new version for every correction. | | Adjacent rows merge only under semantic and provenance equivalence. | Include the rule identifier, observed value and resolution state in audit output. |

An invariant must survive import, conversion, processing, export and rerun. A failed hard invariant produces no apparently valid substitute. Diagnostic checks remain visible with their threshold, scope and evidence, and require a reviewed rule before they can trigger correction.

Quantitative reasoning

For each atomic span J_k=[b_k,b_{k+1}), active set A_k=\{i:J_k\subseteq I_i\}. Resolution is a deterministic function R(A_k,p,v) of active records, purpose p and rule version v. Verify conservation by checking that the union of emitted spans equals the intended overlay extent and that each output lineage lists exactly the active contributors considered. Complexity is controlled by sorted endpoint events rather than testing every pair.

Every reported metric includes units, numerator and denominator where applicable, exclusions, comparison policy and evaluation version. Aggregate values are stratified when pooling could hide a local failure. A quantitative diagnostic supports a decision but cannot overrule missing identity, invalid geometry, unresolved conflict or broken lineage.

Evidence and uncertainty

Keep observation uncertainty, interpolation uncertainty, numeric approximation and metadata uncertainty separate. A smooth trajectory can be numerically precise while still poorly constrained between widely spaced stations. An exact interval overlay can still be unfit when a source depth datum is unknown. The assessed result states which uncertainty belongs to the phenomenon, the measurement, the algorithm and the interpretation.

Build an evidence packet containing immutable received records, semantic declarations, validation findings, algorithm inputs and outputs, test results, reviewer decisions and fingerprints. Contradictory evidence remains available. When a required dependency cannot be resolved, return an explicit unknown, conflict or blocked status rather than choosing the most convenient value.

Interfaces and storage

Interfaces transmit identities, units, coordinate and depth references, conventions, value states, versions and lineage beside numeric values. A trajectory exchange includes collar and datum context, accepted station identities, algorithm identity, numerical policy and output coordinates. An interval exchange includes support type, boundary convention and source links. Structured errors identify the record, field, observed value, expected condition and rule.

Store authoritative received evidence separately from reproducible derivatives and disposable views. Indexes, caches and visualisations may improve access but cannot become the only copy of angle conventions, accepted-station decisions or interval lineage. Export round trips verify that identifiers, precision, ordering and missing states survive encoding changes.

Governance and review

Assign responsibilities to roles rather than named organisations or people: evidence custodian, rule author, implementation maintainer, independent validator and release reviewer. A role may propose a correction but cannot erase source evidence. Rule and algorithm changes are reviewed, versioned and evaluated against fixed regression fixtures before they affect a release.

Exceptions are explicit decisions with scope, rationale, evidence, approving role, affected versions and review trigger. They never rewrite a failed rule and never propagate automatically. The host website has no ownership or scientific-authority role in this workflow; it only delivers the tutorial.

Integration checkpoint

a deterministic interval-overlay result with a complete precedence trace
a deterministic interval-overlay result with a complete precedence trace

Read the figure as a reasoning map from preserved evidence through explicit conventions, deterministic calculation, validation and release. Each arrow represents a declared relationship or transformation. Integrate a deterministic interval-overlay result with a complete precedence trace into the evolving synthetic drillhole package, rerun all earlier fixtures and record any changed assumption.

Synthetic worked example

A synthetic primary log assigns code L1 over [0,30); a reviewed correction assigns L2 over [12,18); an independent alteration observation spans [15,24). The resolved lithology view selects L2 only over [12,18), retains L1 elsewhere, and keeps alteration as a separate dimension. Atomic spans expose [12,15), [15,18) and [18,24) so provenance is exact. No source record is clipped or overwritten.

  1. Preserve the received records and state the intended decision without correction.
  2. Resolve identities, units, conventions and evidence eligibility; mark every unresolved item.
  3. Run the versioned algorithm and tests while retaining intermediate diagnostics.
  4. Issue accept, reject or quarantine and show how an independent reviewer can reproduce it.

Practice task

Implement the chapter artefact against a synthetic fixture containing one normal case, one boundary case, one invalid case and one unresolved-evidence case. Preserve the received fixture. Produce canonical input, validation findings, derivative output, processing manifest and a short release decision.

Acceptance criteria:

  • Every input identity, unit and convention required by the rule is explicit.
  • The implementation is deterministic under stable ordering and the declared numerical policy.
  • No correction overwrites received evidence or turns unknown into a guessed value.
  • All hard failures block the affected derivative and remain machine-readable.
  • A second implementation or reviewer can reproduce the result from the package alone.

Submit a deterministic interval-overlay result with a complete precedence trace, the golden and adversarial fixtures, exact findings and a limitations note. A screenshot is not sufficient evidence because it does not identify the input version, algorithm or rule configuration.

Common failure modes

  • Using the latest row as an undocumented winner.
  • Flattening independent observation dimensions into one code.
  • Merging adjacent labels while their provenance differs.
  • Dropping losing records from the output package.

These failures share a pattern: an implicit convenience is substituted for evidence. Diagnose the earliest boundary where the assumption entered, restore the source statement, make the convention or rule explicit, rerun every dependent derivative and supersede rather than overwrite the affected release.

Review questions

  1. What is an atomic interval span?
  2. Why is priority purpose-specific?
  3. When may adjacent resolved rows be merged?
  4. How should equal-priority conflicts be represented?

For every answer, identify the governing invariant, the evidence needed to evaluate it, the numerical or semantic policy involved and the correct behaviour when the condition fails.

Sources and further reading