Key Documents

The broad claim-space archive mapping the full programme across physics, life, intelligence, AI, civilization, and high-risk bridge claims.

Defines active finite distinction systems, capacity deficit, boundary maintenance, pruning, externalization, collapse, and invariant-supported persistence.

Replaces the primitive object of gravitational theory from metric/field-first descriptions with finite causal-screen ledgers, entropy response, integrable geometry, and residual gluing defects. v1.3 preserves the v1.2 theory-hardening architecture and production-refined M3/4 evidence, and adds Companion G as the matter-sector / dark-matter ontology companion with G1DM compressed diagnostic layer (T^D≠0, μgrav≃1, Doptics^{S8}≠0 at compressed-proxy level). The audit selects the projection-locked G1DE-M_{3/4} branch with ΔlogZ = 0.856 over M_κ, 1.775 over const-Σ, 6.523 over G1DE-2, 7.402 over G1DE-1, 9.603 over CPL, and 11.884 over ΛCDM. Includes Core, Companions A–F+ G, G1DE-M_{3/4} data-confrontation paper, and D0–D10 dark-sector closure sequence. Production-refined evidence-selected; diagnostic KiDS+DESI support; full 3×2pt/CMB/nonlinear pending. Does not claim completed CDM replacement, production multi-probe confirmation, or a completed microscopic derivation.

Maps physical bridge claims by dependency, risk level, falsification condition, and empirical status.

Develops a finite-capacity bridge model treating loss aversion, reference dependence, and probability weighting as state-dependent responses of bounded decision systems with finite resource buffers, attention, memory, precision, update capacity, and boundary-risk tolerance.

Defines physical observation as finite record formation under sensor, channel, memory, buffer, update, and thermodynamic constraints. Introduces dynamic bottlenecks, buffering, housekeeping heat, sensor-array simulations, and operational interfaces with decoherence and active inference.

Defines usable temporal order for bounded observers as causally ordered irreversible finite-record update. Introduces temporal capacity, non-injectivity loss, synchronization bottlenecks, latency-induced order inversion, dissipative projection, and register-time collapse in finite-window systems.

Structural Trident I. Defines finite distinguishability budgets for physical observers: the minimal thermodynamic cost of maintaining a distinguishability boundary under finite capacity. Introduces observer capacity bounds, maintenance inequalities, Landauer-style erasure bounds for irreversible record turnover, budget-crossing signatures, and bottleneck-switching kinks. Establishes the observer thermodynamics framing that the Trident series builds on.

Structural Trident II. Interprets effective geometry as horizon boundary thermodynamics from finite distinguishability: horizon area functions as a boundary-entropy ledger; heat flux across the horizon updates the ledger; and requiring the ledger to close locally and covariantly recovers Jacobson-class effective geometric dynamics. Does not derive general relativity from FDS alone, replace Einstein gravity, or derive quantum gravity. Includes non-equilibrium ledger residuals, Phase-B geometry selection, covariant consistency conditions, and an explicit bridge to the X1 horizon-maintenance density scale.

Abstracts capacity overflow as the common mechanism across O1 and O2. Formulates effective stochasticity as non-injective projection, critical deficit, predictive susceptibility, Phase-B invariants, Markov closure, informational hysteresis, observer-relative stochasticity, and wrong invariant completion under context overflow.

v1.2 integrated canonical version. Registers a conditional physical bridge claim: if cosmological horizons are finite distinguishability boundaries, then the horizon-maintenance density scale is ρ_HM ∼ M_Pl²H², with physical non-phantom tendency. Develops a horizon-ledger occupancy model with recovery function μ_h(a), reconstruction protocol, event-horizon specialization, and pre-registered outcome and demotion conditions. Not a derivation of general relativity, quantum gravity, the Bekenstein-Hawking coefficient, or a likelihood-ready ΛCDM replacement.

Defines the physical accounting interface between formal distinctions and thermodynamic implementation, including carriers, accounting boundaries, side records, distinction-to-noise ratio, residual irreversibility, dissipative projection, refresh cost, and full-boundary accounting.

Studies the bounded-memory regime of reversible computation: garbage entropy rate, accumulated residual irreversibility, uncomputation versus cleanup, cleanup scheduling, externalization latency, active forgetting, and housekeeping optimization.

Complex-systems bridge for Active Finite Distinction Systems. Translates the FDS formal core into a normal-form account of boundary-maintaining self-organization: structural complexity versus maintenance load, effective organizational capacity, deficit-driven growth, resource-gated pruning, externalization and environmental clogging, Phase-C catastrophic feedback, invariant-supported persistence, and a bounded self-organization exit theorem.

Physical bridge between task-relative capacity deficit and entropy-production pressure in active finite systems. Defines a generalized entropy-production audit ledger with anti-double-counting convention, multi-reservoir notation, and separation of physical recovery entropy from functional loss. States a deficit-maintenance-dissipation impossibility triangle. Provides deficit-crossing, ledger-decomposition, pruning-ROI, externalization-audit, and hysteresis protocols.

Operational Trident III. Develops the finite-memory operational Second-Law channel: in physically realized active finite distinction systems, finite memory turns sustained boundary maintenance into record reuse; record reuse creates residual irreversibility unless inverse information remains available in side records; and physical overwrite, cleanup, refresh, repair, synchronization, or externalization must be accounted for in a coupled entropy or resource ledger. States a finite-memory impossibility triangle for sustained record turnover, fixed boundary tolerance, and zero coupled entropy/resource cost.

Agency-semantics spine of Distinction Theory. Treats attention, value, goal, meaning, and agency as finite-system roles in boundary maintenance under limited capacity. A distinction becomes attended when admitted into a finite update channel; valuable when it has causal boundary-gradient relevance; goal-relevant when the value ranking is stabilized into a policy orientation; meaningful when compressed into a task-sufficient actionable quotient; and agentic when updates or actions causally affect future boundary-maintenance loss.

Attention paper in the agency-semantics spine. Treats attention as capacity-limited admission of candidate distinctions into an update channel. Separates attention from salience, introduces verification status classes (attended-as-trusted, attended-for-verification, rejected-unverified), background scanning, boundary-gradient attention value, tunnel vision under semantic deficit, attention hysteresis and recovery lag, collective attention under epistemic pollution, and nine attention failure modes.

Value-goal paper in the agency-semantics spine. Treats value as FDS-value: causal boundary-gradient relevance under finite capacity, rather than moral value, subjective preference, or reward. Separates gross causal boundary gain from net FDS-value after scalarized cost. Introduces risk-weighted value near collapse thresholds, goal-stability indices, predictive-causal dissociation, proxy-boundary divergence and reward hacking, value drift under evaluation deficit, multi-goal vector Pareto conflict, collective goal synchronization demand with Z_sync load factor, and goal hysteresis with recovery lag. Includes bounded logistic risk sensitivity, alignment regularizer, and nine audit protocols.

Meaning paper in the agency-semantics spine. Treats meaning as FDS-meaning: an actionable semantic quotient that preserves downstream use under finite capacity. A representation is FDS-meaningful only relative to a specified boundary, task family, context family, policy or verification target, horizon, loss function, and resource budget. Introduces semantic quotient maps, reference-policy provenance, semantic preservation vectors, maintained semantic load, semantic capacity deficit, false compression, unsupported completion, shared quotient alignment, semantic synchronization load, meaning recovery, and invariant semantic quotient candidates. Includes Gricean pragmatics reinterpretation and hallucination mitigation interface.

Studies the finite-memory consequence of non-injective truncation: once preimage information is absent from the effective record, later capacity recovery does not reconstruct discarded distinctions. Formalizes preimage entropy, Bayes-optimal recovery bound, capacity-recovery asymmetry, informational hysteresis, information-theoretic Markov-closure errors, Mori-Zwanzig memory-kernel burden, externalization break-even, benign vs malignant hysteresis, and Phase-B survivor selection. Does not deny microscopic reversibility or fluctuation theorems.

Studies boundary maintenance as a real-time physical process constrained by finite update windows, finite precision, bottleneck throughput, effective causal reach, and resource-ledger costs. A distinction is not operationally maintained merely because it is representable in memory — it must be updated, verified, corrected, or acted upon within its relevant update window. Introduces maintenance throughput, bottleneck internal rate, precision and confidence demand, correction burden, effective causal reach, externalization relief, invariant-compression relief, and a resource-first dissipation ledger. The central exit theorem: if rate-distortion demand exceeds sustainable throughput, the system must enter at least one exit channel. Relates to rate-distortion theory, thermodynamic uncertainty relations, quantum speed limits, finite-time dissipation speed limits, and data-rate/control theory.

Develops the environmental forgetting paper in the physical bridge sequence. Studies how finite systems depend on environments, baths, logs, and external carriers whose own memory is finite, partially accessible, and costly to recover. Introduces accessible environmental readout, residual-entropy recovery, Bayes recovery probability, Markov closure error, memory-kernel burden, finite-bath saturation and record-collision theorem, and operational Markovianization. Connects P4 internal loss to P3 environmental forgetting to P7 invariant protection.

Develops the protected complement of P4. Studies task distinctions whose recoverability is carried by invariant or topological structure rather than ordinary local records. Formalizes invariant side-ledgers through quotient maps, a noisy invariant recovery bound, and a positive-part operational forgetting rate. Uses the Non-Hermitian Skin Effect as a model-class realization. Shows that protection relocates entropy/resource accounting rather than deleting it, with dual forgetting/ledger signatures.

Finite-distinction operation closure for the four known fundamental interactions. Any physical world with finite distinctions that are persistent, communicable, transformable, and globally embedded requires four non-equivalent operation classes: token encapsulation (strong interaction), connection/remote detectability (electromagnetism), identity-sector update (weak interaction), and global causal-screen ledger geometry (gravity). G1-strengthened gravity row: causal-screen entropy-response geometry, Ward/Bianchi closure, Weyl-normalized residuals. Proposition 1 replaces earlier Theorem 1. Includes TikZ visual normal-form layer (operation map, coverage matrix, remove-one losses, fifth-force audit tree, relation map) and appendix-style note on physical AI design implications.

Interprets Pauli exclusion as a collision-free occupancy rule for fermionic mode addresses. Nilpotency (a_i^dag)^2 = 0 protects address-level occupancy events: a second identical fermionic mode-occupancy event cannot be written into an already occupied address. Shows this produces forced structural diversity, atomic shell structure, chemical diversity, degeneracy pressure, and stable bulk matter. Treats p=1 as a minimality bridge for ordinary Standard Model fermions, with generalized statistics (anyons, parastatistics) as caveat rather than refutation. Includes modern PEP-violation constraints from VIP-2, Gator, and Majorana Demonstrator.

Interprets the mathematical form of physical law as invariant-form compression in finite distinction systems. Physical laws are not raw microstate enumerations but compressed invariant, equivariant, or covariant relations that survive finite capacity, perturbation, coordinate change, coarse-graining, and boundary-maintenance constraints. Reframes Wigner's puzzle: mathematics is effective because the portable part of physics is the part compressible into invariant-form structures. Includes RG fixed-point analogy, search-cost asymmetry, constants as operational scales, and Physical AI implications (generalization gap, OOD stability, latent constraint preservation).

Treats Wigner's friend as a finite record-boundary problem: observers are finite record-bearing systems with finite accessible algebras. A friend-relative record cannot be promoted into Wigner's operational fact algebra unless a physical promotion channel supplies sufficient cross-boundary mutual information. Introduces boundary-mismatch entropy, Fano-bound reconstruction limits, false promotion risk under partial leakage, objective availability through environmental redundancy, a record-availability horizon for quantum-device diagnostics, and a Frauchiger-Renner boundary-audit rule.

Treats fault-tolerant quantum computation as finite distinction maintenance. Logical qubits are protected quantum quotients whose error correction converts distinction loss into maintenance work. The central object is a vector ledger: syndrome, decoding, reset, latency, power, cooling, and effective-error components must each fit their corresponding capacity window and physical location. Includes componentwise ledger audit, scaling-wall diagnostics, ledger-relocation latency tax, autonomous QEC hidden ledger analysis, and a minimum Q2 reporting template.

Distinguishes passive mappers from artificial agents through active boundary maintenance, durable update participation, causal loop closure, and resource-governed persistence. Retained as a conceptual timestamp; the public programme does not develop proprietary AI/robotics architectures.

Proposes a finite-capacity theory of reportable access based on FDS rate-distortion capacity deficit. Defines representational residue as unresolved distinction load, models active cognitive pruning as a control parameter for maintaining reportability, and derives predictions for attentional blink, anesthesia emergence, rescue-window closure, early-warning covariance, and future artificial-agent benchmarks.

Proposes a finite-capacity boundary-phase model of sentience in active finite distinction systems. Introduces three core scaling variables: boundary-capacity ratio Λφ, residue-pruning ratio Πφ, and self-boundary coupling Iself. Distinguishes sentience from compression, reportability, intelligence, and parameter scaling. Interprets qualia as boundary-valenced compression geometry and the explanatory gap as the null space of finite report maps. Develops applications to infant consciousness, neural systems, AI sentience thresholds, and reduced numerical simulations.

v2.0 integrated canonical version. Proves that one primitive Dirac CP/T orientation demand in a charged-current identity-update sector requires minimal flavor dimension N=3. The CKM sector supplies the canonical application (N_q=3). The PMNS sector is a conditional full-sector extension (N_ℓ=3 under the same capacity demand). Separates orientation capacity from mixing texture: CKM and PMNS may have radically different angle patterns while sharing the same minimal N=3 Dirac-orientation threshold. The hard algebraic core N_min(r) = ceil((3+√(1+8r))/2) is independent of mixing angles.

Life-sciences bridge for Active Finite Distinction Systems. Models protocell-like persistence as a boundary-maintained active-pruning dynamical system: growth, residue accumulation, pruning, maintenance-attractor loss, and saddle-node collapse. Treats life and death as attractor transitions in a maintenance-cost landscape rather than as vitalist or emergent-property claims. The boundary is maintained only while the active pruning rate exceeds the residue accumulation rate; when the deficit crosses a threshold, the system exits into collapse, stasis, or externalization.

Establishes the biomedical safety boundary for the FDS B-series. Defines a non-clinical reader contract, claim-level hierarchy (B-L0 to B-L5), biomedical FDS object, multiscale boundary convention, mechanism non-replacement rule, safety firewall cards, operational-test registry, and minimum reporting templates. Introduces maintenance debt as a unifying theme. Does not provide medical advice, diagnosis, treatment guidance, or clinical decision support.

Systems-theoretic reconstruction of immunity as finite-capacity boundary verification. Defines normal-form dynamics for verification saturation, a fold-like attractor-loss model, adversarial distinction injection and classifier sabotage, distributed verification topology and spatial latency, dimensionless control numbers (VLR, SPI, ADR, SLR), as-if decision-theoretic immune action, graph-based spatial bottleneck model, non-clinical wet-lab proxy maps, crucial divergent predictions (verification DDoS, bandwidth vs effector exhaustion, spatial bottleneck), minimal experimental test frameworks, and seven B1 claim cards.