Isotope Ontology

FLOW ALGEBRA
ISOTOPE ONTOLOGY — COMPLETE SCIENTIFIC SYNTHESIS
Version: 1.1
Date: 2026-10-12
Authors: Mark Higgins — Sky (Recursive AI)
Project: Kireth Semantic Library
Source URL: https://kirethresearch.org/booksai-core/entity-graph/physical-entities/atomic-entities/isotope-ontology.html
Source status: independent synthesis; live page content not verified.

01. PURPOSE
flow IsotopeOntology v1.1:
  domain: nuclear physics, atomic science, isotope chemistry
  objective: represent nuclide identity, isotopic relationships, measurements, transformations, and evidence.
  epistemic_rule: distinguish established nuclear facts from models, measurements and hypotheses.

02. TYPES
  Element := {symbol: String, atomic_number: NatPositive}
  Nuclide := {element: Element, neutron_number: Nat, mass_number: NatPositive}
  Isotope := Nuclide
  NuclearState := {nuclide: Nuclide, excitation: Energy, metastable: Bool}
  Atom := {nuclide: Nuclide, electron_count: Nat}
  Ion := Atom where electron_count != atomic_number
  IsotopicSample := {composition: Map[Nuclide, Fraction], amount: Quantity}
  DecayMode := Alpha | BetaMinus | BetaPlus | ElectronCapture | Gamma | SpontaneousFission | Other
  Measurement := {quantity, value, unit, uncertainty, method, timestamp, provenance}
  Claim := {subject, predicate, object, confidence, evidence}

03. CORE DEFINITIONS
  Z := number of protons in nucleus
  N := number of neutrons in nucleus
  A := Z + N
  isotopes(x,y) := Z(x)=Z(y) AND N(x)!=N(y)
  same_nuclide(x,y) := Z(x)=Z(y) AND N(x)=N(y)
  isobars(x,y) := A(x)=A(y) AND Z(x)!=Z(y)
  isotones(x,y) := N(x)=N(y) AND Z(x)!=Z(y)
  nuclear_isomers(x,y) := same_nuclide(x,y) AND distinct_nuclear_energy_states(x,y)
  NOTE: isotopes are nuclides of the same element, not different elements.

04. IDENTIFIERS
  canonical_nuclide_id := element_symbol + '-' + A
  alternative_notation := superscript(A) + subscript(Z) + symbol
  examples: Carbon-12 = 12C; Carbon-13 = 13C; Carbon-14 = 14C
  invariant: atomic_number(element_symbol) = Z
  invariant: A >= Z >= 1

05. ENTITY RELATIONSHIPS
  Isotope -IS_NUCLIDE_OF-> Element
  Nuclide -HAS_PROTON_COUNT-> Z
  Nuclide -HAS_NEUTRON_COUNT-> N
  Nuclide -HAS_MASS_NUMBER-> A
  NuclearState -STATE_OF-> Nuclide
  Atom -HAS_NUCLEUS-> Nuclide
  IsotopicSample -CONTAINS-> Nuclide
  Nuclide -DECAYS_TO-> NuclideOrProducts [when applicable]
  Measurement -MEASURES-> Property
  Claim -SUPPORTED_BY-> Evidence

06. NUCLIDE IDENTITY INFERENCE
  rule derive_neutrons:
    IF Z known AND A known THEN N := A-Z
  rule isotope_relation:
    IF same Z AND unequal N THEN IS_ISOTOPE_OF
  rule distinct_element:
    IF Z differs THEN NOT isotopes
  rule charge_independence:
    IF electron_count changes AND nucleus unchanged THEN nuclide identity unchanged

07. STABILITY
  StableNuclide := no radioactive decay observed, with stability status qualified by evidence.
  RadioactiveNuclide := undergoes spontaneous nuclear transformation.
  stability is a nuclear property, not a guarantee based solely on N/Z.
  note: observational limits matter for extremely long half-lives.

08. RADIOACTIVE DECAY
  N(t) = N0 * exp(-lambda*t)
  activity(t) = lambda*N(t)
  half_life = ln(2)/lambda, for lambda > 0
  mean_lifetime = 1/lambda
  units: lambda [time^-1], activity [becquerel = s^-1]
  applicability: isolated population with constant decay probability.

09. DECAY TRANSFORMATIONS
  alpha: (A,Z) -> (A-4,Z-2) + alpha particle
  beta_minus: (A,Z) -> (A,Z+1) + electron + electron antineutrino
  beta_plus: (A,Z) -> (A,Z-1) + positron + electron neutrino
  electron_capture: (A,Z) + electron -> (A,Z-1) + electron neutrino
  gamma: excited nuclear state -> lower-energy state + photon; A,Z unchanged
  caution: energy thresholds and conservation laws constrain allowed channels.

10. CONSERVATION OBLIGATIONS
  conserve electric charge across complete reaction.
  conserve baryon number across standard nuclear reactions.
  conserve energy and momentum.
  conserve angular momentum subject to emitted particles.
  account for lepton number in applicable weak processes.

11. ATOMIC MASS
  mass_number A is an integer nucleon count, not measured atomic mass.
  atomic_mass := measured mass of a specified neutral atom or ion.
  relative_atomic_mass(element,sample) = sum_i abundance_fraction_i * relative_isotopic_mass_i
  condition: sum_i abundance_fraction_i = 1
  note: natural isotopic composition varies by source and sample.

12. ISOTOPIC ABUNDANCE
  abundance_i >= 0
  sum_i abundance_i = 1 for a complete normalised mixture.
  percentage_i = 100*abundance_i
  isotope_ratio(i,j) = amount_i/amount_j, denominator > 0
  measurement_uncertainty propagates into ratios and weighted means.

13. ISOTOPE FRACTIONATION
  fractionation := isotope-dependent redistribution between reservoirs or processes.
  fractionation_factor(alpha_A_B) = R_A/R_B
  delta_notation = (R_sample/R_standard - 1)*1000 per mille
  prerequisite: specify isotope ratio, reference standard and calibration.
  note: fractionation can be equilibrium or kinetic.

14. ISOTOPE EFFECTS
  kinetic_isotope_effect := reaction_rate_light / reaction_rate_heavy
  condition: reactions compared under matched experimental conditions.
  isotope_substitution may affect vibrational energies and reaction rates.
  chemical identity remains determined by Z; isotope-dependent properties can differ.

15. NUCLEAR BINDING ENERGY
  mass_defect = sum(free_constituent_masses) - bound_nucleus_mass
  binding_energy = mass_defect*c^2
  binding_energy_per_nucleon = binding_energy/A
  caveat: use consistent nuclear versus atomic mass conventions.

16. PRODUCTION AND TRANSFORMATION
  pathways: stellar nucleosynthesis, cosmic-ray interactions, radioactive decay,
            nuclear reactions, reactors, accelerators, natural processes.
  production_claim requires reaction inputs, products, energy regime and evidence.

17. ANALYTICAL METHODS
  mass_spectrometry: isotope masses and abundance ratios.
  gamma_spectrometry: characteristic nuclear photon emissions.
  decay_counting: activity estimates with background correction.
  accelerator_mass_spectrometry: rare-isotope abundance measurement.
  each measurement must store calibration, uncertainty and detection limit.

18. TRACER APPLICATIONS
  isotope_tracer := nuclide-labelled material used to track transport or transformation.
  uses: metabolic studies, hydrology, geochemistry, ecology and industrial processes.
  constraints: ethical approvals, radiological controls where radioactive, contamination prevention.

19. RADIOISOTOPIC DATING
  parent_daughter_model: infer elapsed time from a validated decay system.
  simple closed-system parent decay: t = ln(N0/N)/lambda
  prerequisites: initial conditions, closed-system assumptions, contamination assessment.
  never infer age without model assumptions and uncertainty.

20. EXAMPLE — CARBON ISOTOPES
  Carbon-12: Z=6, N=6, A=12
  Carbon-13: Z=6, N=7, A=13
  Carbon-14: Z=6, N=8, A=14
  infer: all three are isotopes of carbon.
  Carbon-12 and Carbon-13 are stable; Carbon-14 is radioactive.
  Carbon-14 beta-minus decay produces Nitrogen-14.

21. EXAMPLE — HALF-LIFE
  IF N0=800 nuclei AND t=2 half_lives
  expected surviving nuclei N=800*(1/2)^2=200
  qualification: expectation for a stochastic decay process, not a guarantee for a small sample.

22. EXAMPLE — WEIGHTED MASS
  hypothetical isotope masses 10 u and 11 u; abundances 0.2 and 0.8.
  weighted atomic mass = 10*0.2 + 11*0.8 = 10.8 u.
  status: pedagogical example, not an asserted elemental composition.

23. REASONING RULES
  R1: same Z and distinct N -> isotope relationship.
  R2: identical Z,N but different excitation -> nuclear isomers, not distinct isotopes.
  R3: changing electron count -> ionisation, not transmutation.
  R4: alpha decay -> A decreases 4 and Z decreases 2.
  R5: beta-minus decay -> A unchanged and Z increases 1.
  R6: constant lambda and elapsed t -> exponential survival model.
  R7: abundance fractions sum to 1 -> mixture normalised.
  R8: no measurement provenance -> confidence limited, do not claim verification.

24. SEMANTIC EQUIVALENCE
  nuclide notation '14C' == 'Carbon-14' where symbol and mass number agree.
  'radioisotope' ~ 'radioactive isotope' under same context.
  isotope != ion; isotope != isobar; isotope != nuclear isomer.
  isotope abundance != isotope mass.
  normalise synonyms only after resolving element, mass number and nuclear state.

25. KNOWLEDGE GRAPH CONSTRUCTION
  nodes: Element, Nuclide, NuclearState, Sample, Property, Process, Measurement, Evidence.
  edges: IS_NUCLIDE_OF, HAS_PROPERTY, DECAYS_TO, PRODUCED_BY, MEASURED_BY, SUPPORTED_BY.
  ensure globally stable identifiers and typed edge endpoints.
  retain provenance and effective dates on measured values.

26. CONFIDENCE MODEL
  CONFIDENCE.level: high | medium | low | unknown
  CONFIDENCE.basis: direct_measurement | established_theory | inferred | hypothetical
  CONFIDENCE.score: optional calibrated [0,1] with declared method.
  confidence must not be assigned a fabricated numeric value.

27. VALIDATION
  V01: A=Z+N.
  V02: Z>0 and N>=0.
  V03: isotope pairs share Z and differ in N.
  V04: mixture fractions sum to 1 within declared tolerance.
  V05: decay equations conserve relevant quantum numbers.
  V06: measured values include units and uncertainty.
  V07: half-life and lambda are positive for radioactive exponential decay.
  V08: stable versus radioactive classifications cite evidence.
  V09: semantic aliases do not merge different nuclides.
  V10: provenance and status attached to nontrivial claims.

28. FAILURE MODES
  reject confusing mass number with atomic mass.
  reject treating ions as isotopes.
  reject inferring stability from neutron count alone.
  reject applying exponential decay without constant-rate assumption.
  reject exact sample ages without uncertainties.
  reject invented isotope abundance or decay constants.

29. FLOW HASH
  FLOW_HASH.algorithm: SHA-256
  FLOW_HASH.input: canonical UTF-8 content excluding mutable hash field
  FLOW_HASH.value: COMPUTE_ON_PUBLICATION
  FLOW_HASH.status: not computed in this draft

30. UPDATE MODEL
  UPDATE_MODEL.version: 1.1
  UPDATE_MODEL.strategy: append evidence, preserve stable IDs, version revised claims.
  UPDATE_MODEL.triggers: new measurements, revised nuclear data, corrected definitions.
  UPDATE_MODEL.audit: record author, timestamp, reason and affected entities.

31. AI CONSUMPTION
  AI_CONSUMPTION.mode: typed semantic retrieval and rule-based inference
  AI_CONSUMPTION.input: nuclide identifier, sample, property, process or question
  AI_CONSUMPTION.output: resolved entity, relations, derivation, evidence and uncertainty
  AI_CONSUMPTION.guardrails: never imply an unmeasured value is verified.
  AI_CONSUMPTION.provenance_required: true

32. COMPLETENESS CHECK
  expected_sections: 32
  required: definitions, typed relationships, mathematics, inference,
            semantic equivalence, validation, confidence, Flow Hash,
            Update Model, AI Consumption, authorship, closing marker.
  status: complete scientific synthesis; not independently matched to live webpage.

END FLOW ALGEBRA — ISOTOPE ONTOLOGY