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series

FRC 100 series

22 items

Living, versioned foundational papers. The latest release under each concept DOI governs.

RelatedinfographicsCoherencedeterminismReciprocityborn-ruleorientationQuantum chaoschaos

Primary research (14)

PrimaryPaperv2.62026-07-12

Coherence in Chaos: Diffusion, Localization, and Decoherence in the Standard Map / Quantum Kicked Rotor Family

FRC 100.002 v2.6 preserves the Standard Map / Quantum Kicked Rotor chaos program, the KAM-structure functional, localization/decoherence pilots, the Ruelle-Pollicott negative result, and the demoted stadium appendix. It records the completed registered dense classical Gate 4 test as a negative result: fine KAM-area tracking fails, while the earlier coarse zero-parameter magnitude correspondence survives in its scoped form. This route does not promote the paper as a pillar. The canonical reciprocity law remains dS + k* d ln C = 0. In this paper's declared information-nat realization k*_{mu_nat}=1, and J_sys=d[S_sys,mu+k*_{mu_nat} ln C_mu]/dt remains a system-only diagnostic, not automatically entropy production or a boundary residual.

PrimaryPaperv1.02026-07-10

FRC 100.100 - Standalone Stance: A Status-Labeled Snapshot of Fractal Resonance Coherence

FRC 100.100 is a self-contained, status-labeled snapshot of the current Fractal Resonance Coherence program for human and machine readers. It states the canonical scale-invariant relation dS + k* d ln C = 0; separates definitions, exact mathematics, model-specific results, operational programs, conjectures, and philosophical notes; records the current scope of the chaos, collapse, Born-rule, Lambda, and mu-register lines; and preserves the program's negative results. It is a routing and grounding document, not a substitute for primary papers when a derivation, dataset, or citation is required.

PrimaryPaperv3.32026-07-09

Collapse as Open-System Phase-Locking v3.3: A Conditional Basin Mechanism

FRC 100.003 v3.3 presents finite-time phase-locking into coherence basins as a candidate collapse mechanism, not an established ontology. The pilot checks a Langevin microstate-distribution flow conditional on a stipulated Born-weighted landscape; it does not derive the Born weights. The microstate route remains admissible only if operationally equivalent preparations give identical observable predictions and a bipartite extension passes no-signaling. SME, system-plus-bath, and other norm-controlled realizations remain open alternatives. The paper distinguishes Lambda_obs, observation-derived Lambda_eq, and optional latent Lambda_dyn; a fundamental field is a separate conjecture. The canonical reciprocity law is dS + k* d ln C = 0; this paper uses a predeclared indexed realization only for its local ledger. Boundary-relative lambda=-d_eS is neither imposed universally nor rejected by fiat. The three gates remain open: admissible dynamics, Born-weight origin, and explicit environment accounting.

PrimaryPaperv2.22026-07-09

Computational Realization of Lambda-Field Coherence Dynamics v2.2

FRC 100.008 v2.2 corrects the executable Lambda engine and separates Lambda_obs, Lambda_eq, and optional Lambda_dyn. It also separates the canonical starred Boltzmann bridge k* from the pilot's state-derived kernel-score normalization s_ref. The latter is selected once from a declared pre-evolution reference and frozen only to normalize the computational coherence readout; it is not k* and carries no reciprocity-law status. Lambda_obs is an instantaneous transform; Lambda_dyn is a latent model state relaxing toward Lambda_eq; a fundamental field remains a separate conjecture. The finite-difference and oscillator pilots demonstrate executable closures only and do not establish physical ontology.

PrimaryPaperv1.22026-07-09

FRC 100.000 v1.2 - Start Here: Canonical Stance and Version-Aware Reading Map

FRC 100.000 is the version-aware front door to the Fractal Resonance Coherence corpus. Version 1.2 restores the owner-approved canonical relation dS + k* d ln C = 0. The starred k* is the scale-invariant Boltzmann bridge, not an outcome-fitted constant or evolving state variable; indexed notation belongs only to declared operational realizations. The relation is used operationally as bookkeeping and remains an open physical conjecture for real open systems. This document routes readers to current primary papers and separates definitions, mathematical results, model-specific tests, and conjectures. It is an index, not a substitute for the primary papers and not a minimum sufficient prompt for machine readers.

PrimaryPaperv2.62026-07-09

FRC 100.009 v2.6: Operational Local Reciprocity Dynamics

FRC 100.009 v2.6 localizes the canonical relation dS + k* d ln C = 0 through an explicitly indexed operational realization. The representation k*_mu, entropy channel, coherence channel, units, and boundary are declared before evolution and are never refitted to evolving states. The local balance contains explicit environmental source and sink channels; the residual delta_R measures unresolved closure error or transient departure after represented exchange is included. It is not synonymous with openness or with a universal reciprocity current. The ARF throttle is a model-defined activation rule using the residual magnitude, so its pilot illustrates localized gating but cannot establish directional reciprocity.

PrimaryPaperv1.22026-07-09

FRC 100.011 v1.2 - Translation Table: FRC Vocabulary and Claim Status

FRC 100.011 is a vocabulary and claim-status crosswalk, not a complete representation of FRC. Version 1.2 restores the canonical relation dS + k* d ln C = 0 and reserves indexed notation for declared operational realizations. It separates observed, target, and dynamical Lambda objects; distinguishes bookkeeping identities from the open physical reciprocity conjecture; and corrects the claim that uncertainty forbids stationary states. It maps FRC terms to mainstream counterparts while marking whether a relation is definitional, borrowed, model-specific, or an FRC conjecture. Definitions, boundary conventions, and evidence status must be checked against the current primary papers.

PrimaryPaperv3.32026-07-09

The Lambda-Field v3.3: Narrow Rho-Drift Audit and Ontology Separation

FRC 100.007 v3.3 preserves the narrow audit of the printed rho-level Lambda drift and removes the unsupported replacement ontology. The printed term is not trace preserving in general. The tested anticommutator completion is trace preserving and positive in the sampled qubit trajectories, but two tested coherence functionals move populations away from their initial Born weights and an ensemble-member extension is decomposition dependent. These findings exclude those implementations in the tested regime; they are not a no-go theorem for every rho-level, stochastic, instrument-level, or linear-unconditioned construction. Microstate-distribution dynamics remains one candidate route, conditional on operational equivalence and bipartite no-signaling. The paper distinguishes Lambda_obs, Lambda_eq, and optional Lambda_dyn; a fundamental field is a separate conjecture. Version 3.3 restores the canonical/operational reciprocity notation without changing the audit.

PrimaryPaperv2.32026-07-09

Thermodynamics of Locking v2.3: Boundary Result Scoped to Its Declared Normalization

FRC 100.005 v2.3 preserves the exact-free-energy Langevin boundary experiment and scopes its interpretation to the declared information-unit representation k*_{mu_nat}=1. The measured diagnostic sigma_566=sigma_ST+k*_{mu_nat} Delta ln C becomes negative on sufficiently slow unlocking. At T_down=192 the finite measurement is sigma_ST=0.0288 and Delta ln C=-0.132245, so negativity at that endpoint is established for bridge values above 0.218 in the same normalization; negativity for every fixed positive value is an asymptotic inference conditional on sigma_ST tending to zero. The experiment rejects the tested erasure floor in this model class and normalization. It does not establish a universal directional replacement for the canonical law dS + k* d ln C = 0 or determine another register's representation. The valid instrument, controls, negative result, and finite-time successor question are retained.

Frontier research (1)

FrontierPaperv1.52026-07-12

Accessible Phase-Space Geometry Predicts the Structure Functional in the Mixed Standard Map

FRC 100.002 defines the structure functional Σ = S_vM(C) − S, equivalently the KL projection deficit from the measured phase marginal to the matched von Mises maximum-entropy member. Instrument A measures Σ(∞) from evolved ensembles over 12 seeds. Instrument B independently classifies the torus by finite-time Lyapunov exponent, flood-fills the accessible chaotic component, and predicts Σ from the component's phase marginal with no fitted amplitude. Over K_c ≤ K ≤ 2.0, the original coarse sweep retains 9.7% median relative error, versus 18.9% for a fitted island-area proxy; fixed-area shuffle nulls reject random placement. A subsequently frozen dense Gate 4 test selected the strongest geometry-curvature window automatically and evaluated ten unseen midpoint conditions with 12 new seeds each. There measured Σ has essentially no rank relation to regular area (ρ=0.030, one-sided permutation p=0.477), while negative entropy supplies a stronger monotonic rank baseline (ρ=0.964). The full geometry prediction has 8.7% median magnitude error but is beaten by the frozen area-only baseline at 6.6%. Estimator, seed, null, and convergence controls pass. The coarse magnitude correspondence remains a scoped result; the registered route to pillar-level fine geometric discrimination is not passed and is closed without window search.

Archive / development history (7)