Solid Ontology

FLOW ALGEBRA
SOLID ONTOLOGY — KIRETH SEMANTIC LIBRARY
Version: 1.1
Date: 2026-10-12
Source: https://kirethresearch.org/booksai-core/entity-graph/physical-entities/material-entities/solid-ontology.html
Authors: Mark Higgins — Sky (Recursive AI)
Status: Scientific synthesis; source webpage not independently verified.

01. PURPOSE
flow SolidOntology v1.1:
  domain: physical_entities.material_entities.solid
  objective: represent solid phases, structures, properties, processes and evidence using typed, checkable relationships.
  scope: crystalline, amorphous, polycrystalline and composite solids.

02. TYPE SYSTEM
type Entity = identifier
type Solid <: MaterialEntity
type Phase = {crystalline, amorphous, quasicrystalline, other}
type Bonding = {metallic, ionic, covalent_network, molecular, mixed}
type Quantity = {value: Real, unit: String, uncertainty: Real?, conditions: Map}
type Observation = {method: String, result: Quantity, provenance: String}
type Claim = {subject: Entity, predicate: String, object: Any, evidence: Observation?, confidence: Real}
constraint Claim.confidence in [0,1]

03. ENTITY CLASSES
entity SolidSample <: Solid
entity Crystal <: Solid
entity Glass <: Solid
entity Polycrystal <: Solid
entity Grain <: StructuralEntity
entity GrainBoundary <: StructuralEntity
entity Defect <: StructuralEntity
entity Vacancy <: Defect
entity Dislocation <: Defect
entity PhaseBoundary <: StructuralEntity
entity Lattice <: StructuralEntity
entity UnitCell <: StructuralEntity
entity StressTensor <: Quantity
entity StrainTensor <: Quantity
entity ElasticModulus <: Quantity
entity ThermalConductivity <: Quantity
entity ElectricalConductivity <: Quantity
entity Density <: Quantity
entity PhaseTransition <: PhysicalProcess

04. RELATION SIGNATURES
has_phase: Solid × Phase -> Boolean
has_composition: Solid × ChemicalComposition -> Boolean
has_microstructure: Solid × StructuralEntity -> Boolean
has_bonding: Solid × Bonding -> Boolean
has_property: Solid × Quantity -> Boolean
contains_grain: Polycrystal × Grain -> Boolean
contains_defect: Solid × Defect -> Boolean
transforms_to: Phase × Phase -> Boolean
measured_by: Quantity × Observation -> Boolean

05. CORE SEMANTICS
Solid(x) implies condensed material with resistance to shear on an observation-dependent timescale.
A solid is not defined as perfectly rigid or perfectly incompressible.
A solid may be crystalline, amorphous, or a mixture of phases.
Mechanical behaviour depends on temperature, pressure, loading rate and history.

06. STATE VARIABLES
state(s,t) = {temperature, pressure, composition, phase_fractions, stress, strain, defect_density, history}
valid_state(s,t) requires physical units and defined measurement conditions.

07. CRYSTALLINE ORDER
crystalline(s) -> long_range_periodic_order(s) [ideal bulk model]
unit_cell(s) -> lattice_vectors(a,b,c)
Bragg_relation: n*lambda = 2*d*sin(theta)
Note: diffraction peaks support crystalline order but do not alone prove a unique structure.

08. AMORPHOUS ORDER
amorphous(s) -> lacks_long_range_translational_periodicity(s)
amorphous(s) does_not_imply lacks_short_range_order(s)
Glass transition is kinetic and rate dependent, not generally a first-order equilibrium phase transition.

09. MICROSTRUCTURE
polycrystalline(s) -> exists g1,g2: Grain where contains_grain(s,g1) and contains_grain(s,g2)
grain_size(s) measured under declared segmentation method.
Defects and grain boundaries may alter strength, transport and diffusion.

10. MASS AND DENSITY
rho = m/V
units: rho [kg m^-3], m [kg], V [m^3]
precondition: volume and mass refer to the same sample and conditions.

11. ELASTICITY
small_strain_linear_isotropic: sigma = E*epsilon (uniaxial approximation)
Hooke_tensor: sigma_ij = C_ijkl * epsilon_kl
constraint: stiffness tensor must satisfy applicable material symmetries.
not_universal: linear elasticity may fail for plastic, viscoelastic or large-deformation regimes.

12. STRAIN AND DEFORMATION
engineering_strain = (L-L0)/L0
strain_dimensionless: true
strain_measure must be specified for finite deformation.

13. THERMAL EXPANSION
alpha_L = (1/L)*(dL/dT) at specified conditions
small_delta_T: delta_L approximately alpha_L*L0*delta_T
anisotropic crystals may require expansion tensor.

14. HEAT TRANSPORT
Fourier_law: q_vector = -k * grad(T)
units: k [W m^-1 K^-1]
constraint: scalar k assumes isotropic effective response.

15. ELECTRICAL TRANSPORT
Ohm_local: J_vector = sigma_e * E_vector
resistivity: rho_e = 1/sigma_e when sigma_e nonzero and scalar isotropic model applies.
conductivity depends on carrier mechanisms, temperature and microstructure.

16. DIFFUSION
Fick_first: J = -D*grad(c)
Fick_second: dc/dt = div(D*grad(c)) under mass balance and stated assumptions.

17. PHASE EQUILIBRIUM
At fixed T,P and composition, stable equilibrium minimises appropriate thermodynamic potential.
Gibbs_free_energy: G = H - T*S
metastable phases may persist due to kinetic barriers.

18. PHASE TRANSFORMATIONS
transition(s, phase_A, phase_B, conditions) requires evidence or model.
possible mechanisms: nucleation, growth, diffusion, displacive transformation.
Do not infer transition solely from a change in one measured property.

19. MECHANICAL FAILURE
failure_modes = {brittle_fracture, ductile_fracture, fatigue, creep, buckling, wear}
Fracture toughness and strength are distinct quantities.

20. COMPOSITES
composite(s) -> has_multiple_constituent_phases_or_reinforcements(s)
effective_properties require geometry, volume fraction, interface and loading assumptions.

21. INFERENCE RULES
rule R1:
  if crystalline(s) and observed_bragg_peaks(s) then support(has_long_range_order(s))
  confidence: evidence_dependent
rule R2:
  if polycrystalline(s) and contains_grain(s,g) then has_microstructure(s,g)
rule R3:
  if has_property(s,p) and measured_by(p,o) then trace_claim_to_provenance(s,p,o)
rule R4:
  if temperature(s) changes then invalidate_unqualified_temperature_dependent_property_claims(s)
rule R5:
  if phase_fraction(s,p) < 0 or phase_fraction(s,p) > 1 then reject_state(s)

22. CONSERVATION AND CONSISTENCY
mass_balance: mass_before = mass_after for closed non-nuclear transformation within uncertainty.
phase_fraction_sum: sum_i(f_i) = 1 within tolerance.
charge_balance required for ionic composition models.

23. WORKED EXAMPLE: DENSITY
sample_mass = 0.250 kg
sample_volume = 0.0001 m^3
rho = 2500 kg m^-3
validation: positive_mass and positive_volume and unit_consistency.

24. WORKED EXAMPLE: LINEAR STRAIN
L0 = 0.500 m
L = 0.5005 m
engineering_strain = 0.001
If E = 100 GPa and linear elastic uniaxial assumptions hold:
stress = 100 MPa.

25. SEMANTIC EQUIVALENCE
solid_material ~= solid_phase only when contextual scope agrees.
crystal != polycrystal
amorphous != liquid
glass_transition != melting_transition
hardness != stiffness
strength != toughness

26. CONFIDENCE MODEL
confidence = f(measurement_quality, model_fit, provenance, reproducibility)
confidence is calibrated evidence metadata, not proof of truth.

27. VALIDATION
validate identifiers are unique.
validate typed relations and units.
validate numerical ranges and measurement conditions.
validate phase fractions sum to unity within tolerance.
validate mathematical equations only under declared assumptions.
validate evidence provenance and uncertainty.
validate no unsupported universal inference from one sample.

28. UPDATE MODEL
update_on: new_measurement | revised_classification | new_phase | corrected_model | provenance_change
procedure:
  preserve_prior_version
  validate_new_claims
  update_dependent_inferences
  recalculate_content_hash
  publish_revision_with_provenance

29. FLOW HASH
algorithm: SHA-256
input: canonical UTF-8 serialization excluding hash field
status: specification_only; compute on publication.

30. AI CONSUMPTION
format: typed_flow_algebra_text
reasoning_mode: evidence_grounded
allow: classification, unit-aware calculation, qualified inference, relationship traversal
require: assumptions, confidence, provenance, uncertainty
prohibit: fabricating measurements, treating approximations as universal laws

31. COMPLETENESS CHECK
required_sections: 01..31
status: COMPLETE
closing_marker: END_FLOW_ALGEBRA_SOLID_ONTOLOGY_V1_1