1)Resolution State Interface Concepts

A. What Resolution State Interface is, at the posture level

• Resolution State Interface (RSI)
  RSI is a solve-first posture: I declare a system boundary, declare its lattice (participants and couplings), choose the correct interface geometry, build the ledger, evaluate gates, apply closure rules, then report results as overlays.

• Universal relativity as posture, not a brand
  The “universal” claim is: the same solver skeleton is reused across domains, and I do not rewrite the grammar per domain.

• Core-12 as a minimal solver
  The Core-12 are not decorative. They are the minimal set I need to run the solver, keep the ledger explicit, and keep geometry confined.

B. System definition concepts

• Anchored identity
  An object treated as a ledger-bearing identity with a boundary interface. In RSI I use “anchored identity” as the primary term.

• System lattice picture
  A system is a set of anchored identities (nodes) and couplings (edges). The solver evaluates whether candidate edges exist, and whether they are stable under gates and closure.

• Membership vs perturbation
  RSI distinguishes “member” vs “perturber” by gate clearance and closure behavior, not by narrative labels.

• Boundary declaration
  A system has an explicit boundary. The boundary choice is part of the model. I do not smuggle it in later.

• Interface selection
  Geometry is a first-class input. I declare whether the relevant coupling is evaluated on a shell interface or a corridor interface.

C. Geometry doctrine and confinement

• Geometry confinement doctrine
  Distance and area scaling live inside the interface carrier \AP(⋅)\AP(\cdot)\AP(⋅). I do not put stray rrr or r2r^2r2 outside \AP(⋅)\AP(\cdot)\AP(⋅), except the strong-domain Eq. (11) exception.

• Shell interface
  Uses a full \AP(r)\AP(r)\AP(r) mapping, typically spherical: \AP(r)=4πr2\C\AP(r)=4\pi r^2 \C\AP(r)=4πr2\C.

• Corridor interface
  Uses an effective interface A ⁣P,eff(⋅)A_{\!P,\text{eff}}(\cdot)AP,eff​(⋅) representing restricted participation. I do not encode corridor geometry into \DE\DE\DE and I do not weaken \T\T\T with distance.

• Inverse-square families as interface growth
  Inverse-square behavior comes from shell interface growth in \AP(r)\AP(r)\AP(r), not from any distance decay in \T\T\T.

D. Ledger primitives and gates

• Ledger primitives (canonical roles)
  \T\T\T is energy per RSU layer (J).
  \DE\DE\DE is an integer recursion depth.
  \EF=\T \DE\EF=\T\,\DE\EF=\T\DE (J).
  \EA=\EF/\DE\EA=\EF/\DE\EA=\EF/\DE and at boundary \DE=1⇒\EA=\T\DE=1\Rightarrow \EA=\T\DE=1⇒\EA=\T.
  \SigE=\EF+\EA\SigE=\EF+\EA\SigE=\EF+\EA is explicit and non-negative.

• Existence gate \Sres\Sres\Sres
  Present-moment admission verdict: \Sres=\EA/\AP\Sres=\EA/\AP\Sres=\EA/\AP. This is “exists now.”

• Change gate \Dc\Dc\Dc
  The change permission ratio. This is “will transition.” It must not be conflated with \Sres\Sres\Sres.

• Stable band, threshold, collapse
  The stability classification is expressed with \Dc\Dc\Dc (stable band for \Dc<1\Dc<1\Dc<1, threshold at \Dc=1\Dc=1\Dc=1, collapse for \Dc>1\Dc>1\Dc>1).

E. Closure, engines, and multi-anchor accounting

• Closure loop
  When channel structure matters, the engine \K\K\K is computed and the solve closes through the regulated \Dc\Dc\Dc form.

• Engine channel sum
  \K=∑(\Kch \Thetaf \Dc)\K=\sum(\Kch\,\Thetaf\,\Dc)\K=∑(\Kch\Thetaf\Dc). Channels have openness rules and weights.

• Orientation factor \Thetaf\Thetaf\Thetaf
  Carries sign / handedness in engine and allocation contexts. It carries no geometry.

• Multi-anchor closure and allocation
  In multi-body environments I allocate through the explicit partner sum (Eq. (10)). I do not split \EF\EF\EF or \EA\EA\EA by hand.

• Ledger share readout
  A normalized share readout fif_ifi​ used for classification and membership verdicts.

F. Overlays and “verdict arrows”

• Overlays are reports, not primitives
  I solve scalars first (ledger + gates). Then I render directionality as overlay representations.

• Directionality indicators (verdict arrows)
  Vectors are overlay representations. Arrows are drawn after the solve.

• Gravity overlay (concept)
  The lattice readout when dominant coupling is the existence ratio on a shell interface.

• Electromagnetic overlay (concept)
  Shell dilution plus signed closure, with attraction/repulsion handled inside \Thetaf\Thetaf\Thetaf and sanctioned closure sums.

• Strong overlay (concept)
  Contact-scale corridor closure. Geometry exception is Eq. (11) with explicit R2\R^2R2 outside \AP(⋅)\AP(\cdot)\AP(⋅).

• Weak overlay (concept)
  Expressed through the change gate, engine, and allocation structure. In the intro posture, “weak” is not a separate primitive, it is a behavior regime.

G. Calibration discipline and evidence posture

• Constants as calibrated mappings
  Constants are calibrated mappings between RSI ledger primitives and legacy overlays, pinned once per regime and reused.

• Prediction/test cards
  A claim is stated as a compact card: interface declaration, ledger target, tolerance band, and kill-test stated up front.

• Kill-test discipline
  I include a kill-test column because decisive counterexamples matter more than accumulating discomfort.

• Macro Adjudication Benchmark + Unit Coherence Check
  A quick classification table for membership-like verdicts, with a unit discipline check baked in.

H. Horizons, scales, and long-view cosmology concepts

• Elios scale
  A finite lower bound scale in the recursion scheme. Associated symbols: rEliosr_{\text{Elios}}rElios​, \APmin\APmin\APmin, and the finite ratio \PiE\PiE\PiE.

• Tripp scale
  A contextual upper bound scale for recursion and system size in the intro posture. Associated symbols: rTrippr_{\text{Tripp}}rTripp​, \APmax\APmax\APmax.

• Contextual horizons (Tripp-scale horizons)
  Solver-defined contextual limits where further recursion does not materially change admission and allocation verdicts.

• Cosmology scaffold
  A cosmology posture built from the same primitives: boundaries, gate readouts, interface geometry discipline, and allocation.

• Time travel under RSI
  Treated as a conceptual module in the long-view section, grounded in how RSI treats horizons, admissibility, and causal structure. (This is a concept category you can decide to keep or gate behind “speculative.”)

2) Tier Systems

A. Claims ladder tiers (derived vs interpreted vs speculative)

This is the “what kind of claim is being made” ladder:

• Tier 1 (derived and audited)
  Derived directly from the solver grammar and audited against unit roles, gate roles, and invariants.

• Tier 2 (interpreted mapping)
  Interpretation of RSI readouts into legacy observables, via explicit mapping constants and a declared regime.

• Tier 3 (speculative extensions)
  Explicitly labeled extensions that are not yet validated. These stay flagged as speculative until they clear the evidence tiers.

B. Evidence standard tiers (Tier 0 through Tier 4)

This is the “how strong is the evidence posture” ladder:

• Tier 0: internal hygiene
  Unit and role consistency, gate separation, geometry confinement, ledger positivity, and multi-anchor accounting discipline.

• Tier 1: scaling reproduction without per-case tuning
  Reproduces robust scalings (inverse-square families) from gate + interface logic without micro-tuning.

• Tier 2: calibration pins that must be reused
  A single reference pin sets overlay scale, then that pin is reused across independent checks without retuning.

• Tier 3: cross-domain reuse
  The same ledger and gate grammar survives intact across domains (gravity, EM, strong, weak).

• Tier 4: explicit failure modes and kill tests
  Names the failure modes in advance (geometry outside \AP(⋅)\AP(\cdot)\AP(⋅), hidden primitives, gate role drift, etc).

3) Canonical Terminology and Definitions

A. Core ontology and structure

• Anchored identity
  An identity with a boundary that carries a ledger. It can be an atom, an apple, a planet, or a galaxy, depending on declared boundary and interface.

• Identity-node
  Use only in graph-mode when explicitly talking about nodes and edges as a graph representation.

• Anchor influence
  The influence region and coupling behavior attributed to an anchored identity in a declared lattice. Use this instead of “aura” except for a single brief analogy if you keep one.

• System lattice
  A candidate membership structure: identities (nodes) plus interfaces (edges), solved under gates and closure rules.

• Edge
  A coupling interface between identities. It can be a shell interface or corridor interface.

B. Interfaces and geometry

• Shell interface
  A coupling interface treated as a full shell geometry, typically spherical in the intro posture.

• Corridor interface
  A restricted coupling interface treated as an effective area A ⁣P,eff(⋅)A_{\!P,\text{eff}}(\cdot)AP,eff​(⋅), not as a distance-decay of \T\T\T.

• Geometry confinement rule
  All radius and area scaling is confined to \AP(⋅)\AP(\cdot)\AP(⋅). Only Eq. (11) may carry explicit R2\R^2R2 outside \AP(⋅)\AP(\cdot)\AP(⋅).

C. Ledger and gates

• Ledger carriers
  \EA\EA\EA, \EF\EF\EF, \SigE\SigE\SigE are ledger energies and must stay explicit and non-negative.

• Existence gate
  \Sres=\EA/\AP\Sres=\EA/\AP\Sres=\EA/\AP. “Exists now.” Present-moment admission verdict.

• Change gate
  \Dc=\EF/\EA\Dc=\EF/\EA\Dc=\EF/\EA. “Will change.” Stability and transition permission ratio.

• Stable band / threshold / collapse
  Classified using \Dc\Dc\Dc: stable if \Dc<1\Dc<1\Dc<1, threshold at \Dc=1\Dc=1\Dc=1, collapse if \Dc>1\Dc>1\Dc>1.

D. Overlays and reporting

• Overlay
  A reporting layer after the scalar solve (gravity, EM, strong, weak). Not a primitive.

• Directionality indicators (verdict arrows)
  Vector-like arrows that represent direction after the solver verdict.

E. Calibration language

• Calibrated constant
  A mapping pinned once per regime linking RSI primitives to a legacy overlay scale, then reused.

• Scaling-only check
  A check that tests scaling behavior only, without claiming amplitude accuracy.

• Audit-ready
  Enough declarations exist (boundary, interface, pins, units, failure modes) that another person can reproduce the solve.

F. Evidence standard language

• Macro Adjudication Benchmark
  The fast classification table mapping gate patterns and closure readouts to verdict categories.

• Unit Coherence Check
  A required unit-role check to prevent drift in what symbols mean.

4) Core Symbols

A. Ledger, gates, geometry

• \T\T\T: tension, energy per RSU layer (J).

• \DE\DE\DE: integer RSU layer count (dimensionless).

• \EF\EF\EF: field energy, \EF=\T \DE\EF=\T\,\DE\EF=\T\DE (J).

• \EA\EA\EA: anchor energy (J), with boundary identity \EA=\T\EA=\T\EA=\T when \DE=1\DE=1\DE=1.

• \SigE\SigE\SigE: explicit positive ledger sum, \SigE=\EF+\EA\SigE=\EF+\EA\SigE=\EF+\EA (J).

• \AP(⋅)\AP(\cdot)\AP(⋅): anchor plane mapping, the geometry carrier; all distance and area scaling stays here.

• \Sres\Sres\Sres: existence gate, \Sres=\EA/\AP\Sres=\EA/\AP\Sres=\EA/\AP (dimensionless).

• \Dc\Dc\Dc: change gate (collapse ratio), \Dc=\EF/\EA\Dc=\EF/\EA\Dc=\EF/\EA (dimensionless).

B. Engine and allocation

• \K\K\K: engine output (scalar).

• \Kch\Kch\Kch: channel constant used in the engine sum.

• \Thetaf\Thetaf\Thetaf: orientation factor used for sign / handedness in engine and allocation contexts.

• \BT\BT\BT: binding threshold term used in engine closure contexts.

• \Q\Q\Q: identity quotient / anchor contribution scalar used in multi-anchor closure.

• fif_ifi​: ledger share readout (normalized allocation share).

C. Overlay diagnostics

• Z\ZZ: RSI redshift diagnostic, Z=Δ\Sres/\Sres\Z=\Delta \Sres/\SresZ=Δ\Sres/\Sres.

• \Ssource\Ssource\Ssource: source-frame resolution state (used only when explicitly contrasting source vs observer).

D. Strong-only exception handles

• R\RR: separation handle used only in strong-domain Eq. (11) contexts.

• \NC\NC\NC: strong-domain output (confinement normalization) from Eq. (11).

E. Bounded recursion and horizon ladder symbols

• \PiE\PiE\PiE: finite RSU bound constant (used in RSU-bound discussion).

• rElios,\APminr_{\text{Elios}}, \APminrElios​,\APmin: lower bound radius and smallest stable anchor plane.

• rTripp,\APmaxr_{\text{Tripp}}, \APmaxrTripp​,\APmax: upper bound radius and largest anchor plane used in upper-bound discussions.

F. Existential logicism macro

• \EL: existential logicism (short form)

• \ELfull: existential logicism (full text form)