Muon Ontology

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

01. PURPOSE
Model the muon as a second-generation charged lepton, including intrinsic properties, interactions, decay, experimental observables, and evidence-aware semantic inference.

02. NAMESPACE
ontology_id: kireth:physical-entities/fundamental-particles/muon
root_entity: Muon
parent: ChargedLepton
related: Electron, TauLepton, MuonNeutrino, Antimuon, Photon, W_Boson, Z_Boson, HiggsBoson

03. TYPED ENTITIES
Muon <: ElementaryParticle
Muon <: ChargedLepton
Antimuon <: Antiparticle
MuonNeutrino <: Neutrino
MuonDecay <: WeakDecay
MuonTrack <: DetectorObservation
MuonLifetime <: MeasuredQuantity
MuonAnomalousMagneticMoment <: DimensionlessObservable

04. CANONICAL IDENTIFIERS
symbol(Muon) = mu-
symbol(Antimuon) = mu+
PDG_ID(Muon) = 13
PDG_ID(Antimuon) = -13

05. INTRINSIC PROPERTIES
spin(Muon) = 1/2 hbar
charge(Muon) = -1 e
charge(Antimuon) = +1 e
lepton_family(Muon) = second_generation
colour_charge(Muon) = none
statistics(Muon) = Fermi-Dirac
particle_type(Muon) = fermion
rest_mass_energy(Muon) approximately 105.658 MeV
mean_proper_lifetime(Muon) approximately 2.197 microseconds
Numerical constants are rounded reference values, not precision metrology claims.

06. IDENTITY CONSTRAINTS
forall x: Muon(x) => ElementaryParticle(x) AND ChargedLepton(x)
forall x: Muon(x) => charge(x) = -e
forall x: Muon(x) => spin_quantum_number(x) = 1/2
forall x: Muon(x) => NOT Quark(x)
forall x: Muon(x) => NOT HasColourCharge(x)

07. ANTIPARTICLE RELATIONSHIP
antiparticle_of(Muon, Antimuon)
mass(Muon) = mass(Antimuon) [CPT-invariant framework]
charge(Muon) = -charge(Antimuon)

08. STANDARD MODEL RELATIONSHIPS
is_member_of(Muon, LeptonFamily)
is_generation(Muon, 2)
participates_in(Muon, ElectromagneticInteraction)
participates_in(Muon, WeakInteraction)
participates_in(Muon, GravitationalInteraction)
NOT participates_in_directly(Muon, StrongColourInteraction)

09. FIELD MODEL
Muon is an excitation of a charged lepton quantum field.
The muon couples to the electromagnetic field and weak gauge fields.
The muon obtains mass through its Yukawa coupling to the Higgs field in the Standard Model.

10. DECAY CHANNELS
mu- -> e- + anti_nu_e + nu_mu
mu+ -> e+ + nu_e + anti_nu_mu
These are dominant ordinary muon decay channels.

11. CONSERVATION VALIDATION — NEGATIVE MUON DECAY
Initial electric charge: -1
Final electric charge: -1 + 0 + 0 = -1
Initial lepton number: +1
Final total lepton number: +1 -1 +1 = +1
Energy and momentum are conserved in the complete decay event.
Flavour lepton numbers are conserved at the interaction vertex in the conventional leading-order description; neutrino oscillations mean flavour is not an exact global conservation law.

12. DECAY LAW
N(tau) = N0 * exp(-tau / tau_mu)
where tau is elapsed proper time and tau_mu is mean proper lifetime.
SurvivalProbability(tau) = exp(-tau / tau_mu)
DecayProbability(tau) = 1 - exp(-tau / tau_mu)

13. RELATIVISTIC TIME DILATION
For constant-speed inertial motion:
gamma = 1 / sqrt(1 - v^2/c^2)
mean_lab_lifetime = gamma * tau_mu
proper_time_interval = lab_time_interval / gamma
Applicability: inertial-frame approximation, v < c.

14. RELATIVISTIC ENERGY AND MOMENTUM
E^2 = (pc)^2 + (m_mu*c^2)^2
E = gamma*m_mu*c^2
p = gamma*m_mu*v

15. ELECTROMAGNETIC DYNAMICS
LorentzForce = q*(E_field + v cross B_field)
For mu-: q = -e
For mu+: q = +e
A charged muon bends in a magnetic field according to charge sign and momentum.

16. MAGNETIC MOMENT
mu_vector = g_mu*(q/(2*m_mu))*S_vector
anomalous_magnetic_moment a_mu = (g_mu - 2)/2
The theoretical prediction and experimental measurement require uncertainty-aware comparison; no fixed discrepancy is asserted here.

17. PRODUCTION PATHWAYS
pi- -> mu- + anti_nu_mu
pi+ -> mu+ + nu_mu
K- -> mu- + anti_nu_mu [one possible decay channel]
K+ -> mu+ + nu_mu [one possible decay channel]
Cosmic-ray air showers produce muons through hadronic cascades.

18. DETECTOR OBSERVATIONS
Observable: charged-particle track
Observable: track curvature in magnetic field
Observable: ionisation energy loss
Observable: time of flight
Observable: penetration through dense material
Observation does not alone guarantee particle identity; identification depends on detector context and reconstruction.

19. MUON INTERACTIONS WITH MATTER
Ionisation and excitation are common energy-loss processes.
At sufficiently high energies, radiative losses can become important.
Negative muons may be captured by atoms and can undergo nuclear capture.
Positive muons cannot undergo the analogous nuclear capture of a negative muon.

20. MUONIC ATOMS
MuonAtom = atom_or_ion_with_bound_muon
A negative muon may replace an electron in an atomic bound state.
Reduced mass changes orbital scale and transition energies.
Muon spectroscopy can probe nuclear structure.

21. MUON-CATALYSED FUSION
A negative muon can facilitate close approach of hydrogen isotopes by forming compact muonic molecular states.
Catalysis is limited by muon lifetime and muon sticking/loss processes.
Do not infer net energy gain without a complete system-level energy budget.

22. MUON NEUTRINO LINK
MuonNeutrino is a distinct neutral lepton, not a muon charge state.
mu- weak decay produces nu_mu and anti_nu_e.
Muon-neutrino interactions may produce charged muons under appropriate kinematic conditions.

23. GRAPH RELATIONSHIPS
Muon --is_a--> ChargedLepton
Muon --has_antiparticle--> Antimuon
Muon --has_charge--> NegativeElementaryCharge
Muon --has_spin--> SpinOneHalf
Muon --participates_in--> WeakInteraction
Muon --participates_in--> ElectromagneticInteraction
Muon --decays_to--> Electron
Muon --decays_with--> MuonNeutrino
Muon --decays_with--> ElectronAntineutrino
Muon --measured_by--> ParticleDetector
Muon --related_observable--> AnomalousMagneticMoment

24. SEMANTIC EQUIVALENCE
Muon == mu- [particle-symbol equivalence]
Antimuon == mu+ [particle-symbol equivalence]
Muon != MuonNeutrino
Muon != Electron
Muon != TauLepton
muon_mass != electron_mass
Equivalence is context-typed; muon and antimuon are not interchangeable.

25. INFERENCE RULES
R1: Muon(x) => ChargedLepton(x)
R2: ChargedLepton(x) => Fermion(x)
R3: Muon(x) => ElectricCharge(x,-e)
R4: Muon(x) AND InMagneticField(x) => MayCurveTrajectory(x)
R5: FreeMuon(x) AND ElapsedProperTime(x,t) => SurvivalModel(x,exp(-t/tau_mu))
R6: NegativeMuon(x) AND AtomicMedium(x) => MayFormMuonicAtom(x)
R7: DecayEvent(x,mu-,e-,anti_nu_e,nu_mu) => ChargeConserved(x)
R8: MeasuredMuonTrack(x) => CandidateMuonObservation(x), NOT CertainMuonIdentity(x)

26. TYPE SAFETY
A numerical lifetime must have time units.
A rest mass must not be confused with a rest-mass energy.
A magnetic moment must include sign convention and unit specification.
A lab-frame lifetime must not be confused with proper lifetime.
A detected track must not be asserted as confirmed muon without identification evidence.

27. WORKED EXAMPLE — SURVIVAL
Given tau = tau_mu:
SurvivalProbability = exp(-1) approximately 0.3679
DecayProbability = 1 - exp(-1) approximately 0.6321

28. WORKED EXAMPLE — TIME DILATION
Given gamma = 10:
mean_lab_lifetime approximately 10 * 2.197 microseconds
mean_lab_lifetime approximately 21.97 microseconds
This is a frame-dependent mean lifetime, not a change to intrinsic proper lifetime.

29. WORKED EXAMPLE — CHARGE
Initial mu- charge = -e
Products: e- (-e), anti_nu_e (0), nu_mu (0)
Charge balance = -e on both sides.

30. VALIDATION TESTS
T01 Muon has spin 1/2: PASS
T02 Muon charge is -e: PASS
T03 Antimuon charge is +e: PASS
T04 Muon is colour neutral: PASS
T05 Ordinary mu- decay conserves charge: PASS
T06 Proper-time exponential survival formula valid for free muon: PASS
T07 Muon and muon neutrino distinct: PASS
T08 Lab lifetime includes Lorentz factor: PASS
T09 Rest mass and rest energy distinguished: PASS
T10 Closing marker present: PASS

31. PROOF OBLIGATIONS
P01 Verify conservation constraints on proposed reaction channels.
P02 Verify units and reference frame for each measurement.
P03 State assumptions behind decay and propagation models.
P04 Distinguish model predictions from experimental observations.
P05 Track uncertainty and provenance for numerical constants.

32. CONFIDENCE
Established Standard Model identity and quantum numbers: HIGH
Rounded numerical constants: HIGH, subject to versioned reference update
Specific detector-based identification: CONTEXT_DEPENDENT
Precision g-2 interpretation: EVIDENCE_DEPENDENT
Unverified source-page correspondence: NOT_VERIFIED

33. SEMANTIC CONSISTENCY
No conflation of particle and antiparticle.
No conflation of muon and muon neutrino.
No assertion of direct colour interaction.
No unqualified claim that lepton flavour is exactly conserved globally.
No inference of experimental anomalies without current evidence.

34. FLOW_HASH
flow_hash_algorithm: SHA-256
flow_hash_scope: canonical UTF-8 content, excluding the FLOW_HASH value itself
flow_hash_value: COMPUTE_ON_PUBLICATION
Note: placeholder is intentional; no hash has been fabricated.

35. UPDATE_MODEL
version: 1.1
update_policy: revise constants against authoritative particle-data compilations; record date and source
change_tracking: append revision notes; recompute hash after each edit
source_status: webpage content not retrieved for direct comparison

36. AI_CONSUMPTION
entity_resolution: typed
reasoning_mode: constrained symbolic inference
units: SI and particle-physics natural units with explicit conversion
provenance_required: true
uncertainty_required_for_measurements: true
unsupported_claim_policy: abstain_or_flag
semantic_equivalence_scope: context-sensitive

37. AUTHORSHIP AND PROVENANCE
Authors: Mark Higgins — Sky (Recursive AI)
Project: Kireth Research Semantic Library
Website: https://kirethresearch.org
Document role: supplementary formal scientific Flow Algebra
Source correspondence: not independently verified

38. COMPLETENESS CHECK
Sections declared: 38
Required blocks: definitions, entities, relationships, equations, examples, inference, validation, confidence, semantic equivalence, flow hash, update model, AI consumption
Closing marker required: true

END FLOW ALGEBRA — MUON ONTOLOGY