When the record cannot decide: a framework for functional inference in archaeology, with an application to moai transport

Technical Summary: A Framework for Functional Inference in Archaeology

Problem Statement
Archaeologists frequently infer that an artifact's morphology was engineered for a specific function based on evidence of mechanical feasibility and archaeological use. However, this reasoning often conflates three logically distinct claims: (1) mechanical feasibility (the form can perform the function), (2) archaeological use (the form was involved in the function), and (3) engineering origin (the form was produced specifically for that function). The paper identifies a "mechanical sufficiency gap": demonstrating that a feature is mechanically sufficient for a task does not prove it was designed for that task, as the same morphology could arise from stylistic convention, coincidental sufficiency, multi-purpose adaptation, or selection from a heterogeneous population. Current methods often lack a general protocol to distinguish admissible evidence from evidence that the record simply cannot decide.

Methodology: A Two-Layer Component-Diagnostic Framework
The authors propose a framework to decompose engineering-origin claims into causally distinct components and subject each to a rigorous, two-layer evaluation before any confirmatory test.

• Layer 1: Evidential Admissibility (Gate 0)
  Before testing a hypothesis, each component must pass a six-stage screen to determine if the available data can even address the claim. A component failing any stage is reported as "undecidable" with a specific reason, rather than as a disconfirmed hypothesis. The six stages are:

  1. Construct Validity: Does the measured variable capture the causal feature, or is it a proxy?
  2. Scale Validity: Does the contrast survive adjustment for size (allometry)?
  3. Observability: Is the feature recorded at the specific production stages being contrasted?
  4. Identifiability under Missingness: Given the mechanism of missing data, do complete-case frequencies estimate population frequencies? This uses worst-case partial-identification bounds (Manski, 1990) to determine if the ordering of stages is fixed or if unobserved cases could invert the result.
  5. Precision and Power: Is the sample size sufficient to distinguish competing states?
  6. Applicability: Does the engineering hypothesis actually entail the tested prediction for this component?

• Layer 2: Diagnostic Specificity
  Only components clearing Layer 1 proceed to Layer 2, which tests for functional specificity. This layer applies five conditional diagnostic expectations derived from the causal structure of engineering origin (e.g., task-scale calibration, feature distinctiveness, production-stage transitions, variance compression, and convergence with independent markers). A component is assigned a "diagnostically supportive" state (S7) only if it clears admissibility, shows a directional prediction, exceeds background morphological differentiation (functional specificity), and passes at least one applicable diagnostic test.

Application: The Walking-Moai Hypothesis
The framework is applied to the claim that the D-shaped, wide bases of Rapa Nui (Easter Island) moai statues were engineered for "walking" transport (rocking pendulum motion). The hypothesis is decomposed into four components:

• Component A (Wide Base): Tested via shoulder-to-base width ratios and direct base width measurements.
• Component B (D-shaped Outline): Tested via the plan-view outline of the base.
• Component C (Forward Lean): Tested via base angle measurements.
• Component D (Center of Mass): Tested via 3D modeling (not assessable via tabular survey data).

Key Results
The application yields a structured set of verdicts rather than a binary yes/no, demonstrating that different components occupy different evidential states:

1. Component A (Wide Base):

   • As a Ratio (S1 - Construct Invalid): The shoulder-to-base ratio shows a real, size-robust contrast (Welch t = 3.18, d = 0.55). However, decomposition reveals the contrast is driven entirely by narrower shoulders, not wider bases. Thus, the ratio is a construct-invalid proxy for a "wider base."
   • Direct Base Width (S8 - Directional Evidence Against): When base width is tested directly and size-adjusted, there is no evidence of a wider transport-stage base (coefficient −0.037, p = 0.33). The data provide directional evidence against substantial absolute widening.
   • Functional Specificity (S6): The residual proportional contrast (shoulder narrowing) does not exceed the population's background morphological differentiation when compared to negative controls (e.g., nose, forehead). It is real but non-diagnostic of transport-specific engineering.

2. Component B (D-shaped Outline):

   • State S4 (Non-identified under Missingness): The plan-view outline is observable in only ~2% of pre-transport (quarry) statues. Worst-case partial-identification bounds for D-shaped prevalence in quarry, road, and platform contexts overlap almost entirely. The data cannot determine the ordering of stages (e.g., whether D-shapes are more or less prevalent on roads than platforms).
   • Rescue Frontier: The framework calculates that resolving this non-identification would require observing nearly all currently unobserved road-stage bases (38 of 39) to change the state, highlighting a near-total observational gap rather than a small data deficiency.

3. Component C (Base Angle):

   • State S3/S1: Continuous degree measurements exist only for road statues (no comparison class). Categorical fields exist for road and platform statues but lack a codebook, rendering them construct-invalid.

4. Positive Control (Eye Sockets):

   • Applying the identical procedure to carved eye sockets (a feature observable across stages) yields disjoint bounds between quarry and platform contexts. This confirms the framework can return a decision when the record permits, proving that the non-identification of Component B is a property of the data/feature, not a flaw in the method.

Significance and Claims
The paper claims to provide a disciplined method for distinguishing intentional technical design from inherited production convention, selection, and record-formation processes. Its primary contributions are:

• Decomposition of Inference: It demonstrates that a single "engineering" claim is often a mixture of components with different evidential states (admissible, non-identified, or non-diagnostic). A single verdict collapses these distinctions.
• Distinction between Robustness and Specificity: The study shows that a statistical contrast can be real, reproducible, and size-robust (as seen in the shoulder-to-base ratio) yet fail to be diagnostic of engineering origin because it lacks functional specificity or is located in the wrong anatomical feature.
• Prospective Rescue Frontiers: The framework converts "the record cannot decide" into a quantified research design. By computing the minimum additional observation required to change a non-identified state (e.g., the 38-of-39 frontier for moai bases), it transforms missingness from a limitation into a specification of future fieldwork.
• Observational Equivalence: The paper identifies two types of impasses: decomposition non-identification (where multiple anatomical changes produce the same ratio) and record non-identification (where multiple population states produce the same observable record). The framework separates these, offering different remedies (measuring components directly vs. observing more cases).

The authors explicitly state that the framework does not refute the walking-moai hypothesis itself (which rests on experimental and ethnohistoric evidence outside the survey data) but delineates the limits of what the current survey morphometric record can adjudicate regarding the engineering origin of the statue bases. It serves as a general tool for functional inference in archaeology, applicable wherever morphology is used to infer design intent.