Information Field Theory I: An Infoton Hierarchy; Information Field Theory II: Photon-Line Falsification and Statistical Learning

We develop an effective field theory of irreversible information flow as an emergent dissipativescalar ϕ(x) in the Schwinger–Keldysh nonequilibrium class with dynamical KMS symmetry. Theelementary excitation of ϕ, named the infoton, is identified as a generalized information quantumwhose local rest energy is the Landauer cost kBTloc ln 2 and whose existence in classical, quantum,and quantum-gravitational substrates unifies bits, qubits, qudits, and Bekenstein “gravity bits” asembeddings of a single emergent quasiparticle. Two further generalizations are developed: alongthe modality axis introduced by Zadeh’s generalized theory of uncertainty, the infoton becomes ag-ton – a modality-indexed excitation of a g-information field Φr(x) – whose rest energy kBTlocB(r)extends the Landauer bound to possibilistic, fuzzy, evidential, and granular uncertainty calculi; alongthe operational-theoretic axis captured by generalized probabilistic theories and effect algebras, theconstruction culminates in an Ω-ton that subsumes both the modality and substrate axes under asingle operational specification O = (Ω, E,K). Two additional axes are introduced as orthogonalextensions: a Wilsonian scale axis L that resolves the infoton tower from coarse-grained moleculardynamics to parton, hypothetical preonic, and ultimately Planck-cell sub-particle resolutions whilepreserving the universal Landauer floor; and a supersymmetric axis σ that pairs the bosonic infotonwith a fermionic infotino into an irreducible supermultiplet excitation, the super-infoton or Σ-ton,whose rest energy is sector-independent in unbroken supersymmetry. A fifth axis p generalizes theconstruction to extended objects – information strings (p = 1), information membranes (p = 2), andinformation p-branes more generally – whose worldvolume scalar carries the local Landauer costand whose extremal configurations recover Ryu–Takayanagi-style holographic entropy bounds as aconsistency check. A worldsheet-supersymmetric Ramond–Neveu–Schwarz extension of the p=1case promotes the information string to an information superstring whose worldsheet bosons andfermions are related by N=1 supersymmetry; the spacetime-supersymmetric Σ-ton supermultiplet isrecovered as the asymptotic-state spectrum of the information superstring, unifying the supersymmetricand worldvolume axes at the p=1 worldsheet level. We verify the internal consistency ofthe foundational construction through a Schwinger–Keldysh lattice integrator that reproduces thefluctuation–dissipation relation, saturates the Landauer bound in single-bit erasure, and recoversstochastic-entropy-production positivity with a Crooks fluctuation-theorem slope of unity. The infotonhierarchy developed here is the formal scaffolding on which the companion paper Sep26 buildstwo specific applications: a falsification framework for temperature-locked photon lines from e+e−annihilation, and a field theory of statistical learning.