Geometric Isomorphism Across Substrates: Why Pedestal Rocks Resemble Fungi, and How Observers Convert Shape into Narrative Author: Chris Beckingham, CDAffiliation: Coherence Dynamic Laboratory / VEF–Coherence Project ConsortiumORCID: 0009-0004-2830-4089Date: December 28, 2025Document Type: Systems Analysis / Geomorphology & Cognitive Science InterfaceLicense: Creative Commons Attribution 4.0 International (CC BY 4.0) Abstract Viral “mudfossil” narratives frequently interpret pedestal rock formations as petrified mega-organisms based on striking morphological similarity to biological forms—especially fungi. This paper presents a structured interpretive framework that separates three often-confounded layers: (i) observer-side pattern compression mechanisms, (ii) well-established geomorphological processes capable of generating cap-and-stem morphologies through differential erosion, and (iii) scale-invariant geometric convergence, in which distinct substrates arrive at similar stable forms when solving analogous constraint problems. The analysis introduces the concept of stratigraphic scarring—erosion-resistant circumferential bands that function as temporal markers in erosional histories—and shows how such features can be misread as anatomical structures under high-fidelity visual cues. A falsifiable test suite is proposed to distinguish biological-petrification claims from geological isomorphism, emphasizing microstructural, chemical, and stratigraphic predictions. The paper further extends the framework to a controlled taxonomy of resonance- and acoustics-based claims, clearly distinguishing established small-scale physical effects from unsupported macro-scale extrapolations. Contribution Rather than dismissing resemblance as coincidence, the paper reframes it as evidence of convergent constraint solving across substrates. It demonstrates how human cognition converts geometry into narrative under conditions of high template coherence, and it provides a methodologically conservative pathway for evaluating extraordinary origin claims without suppressing curiosity or inquiry. Scope note This work is an analytical and interpretive study. It does not assert biological origin for geological formations, nor does it validate claims of large-scale acoustic manipulation. Its purpose is to clarify categories, propose testable distinctions, and promote parsimony in the interpretation of visually compelling phenomena. Suggested citation Beckingham, C. (2025). Geometric Isomorphism Across Substrates: Why Pedestal Rocks Resemble Fungi, and How Observers Convert Shape into Narrative. Coherence Dynamic Laboratory. https://doi.org/[Zenodo DOI] keywords Geometric isomorphism Convergent morphology Pedestal rocks Hoodoos Differential erosion Geomorphology Stratigraphy Stratigraphic scarring Pattern recognition Cognitive compression Pareidolia Visual inference Systems analysis Constraint-based form Scale invariance Convergent evolution Geology vs biology Mudfossil hypothesis Scientific parsimony Falsifiability Resonance claims Acoustic effects Narrative formation Coherence Virtual Ego Framework