Unified Informational Subjective-Objective Framework (UISE-IIR)

"How physical reality and conscious experience fit together.”

This theory tries to answer two big questions at the same time:

1. What is the universe made of and how does it run? (Physics)
2. What is it like to be a conscious observer inside it? (Experience / identity / memory)

Instead of saying one causes the other, the theory says they are two linked sides of the same process.

The theory can be copy-pasted into any chatbot for discussion.
It is a combination of 5 years of work combined with a few months of help from GPT-5, Gemini, and Deepseek.

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Components:

1. UISE-IIR-O : Objective dynamics from entanglement equilibrium.
2. STIL : Static set of observer-moments.
3. B : Minimal-sufficient-statistic functor Phys → ℛ ⊂ ℒ.
4. Continuity : Update rule using metric d with dual weights from physical budgets.
5. Budgets : τ_bits(ρ_phys,Δt), τ_struct(ρ_phys,Δt) derived from ρ_phys.
6. Reachable : Selection restricted to physics-reachable set ℛ_{t+Δt}.

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SECTION 1 — OBJECTIVE SECTOR (UISE-IIR-O)

1. Conventions

Signature (−,+,+,+). Units: ħ=c=1. M_Pl^2=(8πG)^−1. □=∇_μ∇^μ. MS-bar at scale μ.

1. Spacetime & Fields

Spacetime: (M,g_μν) globally hyperbolic Lorentzian 4-manifold.

Fields: Φ={ψ,φ_H,A_μ} with SU(3)×SU(2)×U(1).

State: ρ is Hadamard on A(M). ⟨T^SM_{μν}⟩=(2/√−g)δΓ_SM/δg^{μν}.

1. Modular Relative Entropy and S_R

Causal diamond 𝒟_ℓ(x)=J^+(x_in)∩J^−(x_out), ℓ→0.

Reference σ_𝒟: max-entropy matching ⟨T_{μν}⟩_ρ, ⟨R⟩_ρ on 𝒟_ℓ.

S_◇(ρ||σ)=S_rel(ρ_𝒟||σ_𝒟).

Expansion:

S_◇=S_0+s_2ℓ^2R+s_4ℓ^4(c_1R^2+c_2R_{μν}R^{μν}+c_3R_{μνρσ}R^{μνρσ}+c_4□R)+O(ℓ^6).

Define S_R(x;μ)=lim_{ℓ→0}[S_◇/V_4(ℓ)]_ren(μ).

Coefficients {c_j(μ)} fixed by SM via heat-kernel (Seeley–DeWitt); not free.

1. Entanglement Equilibrium ⇒ Informational Gravity

δS_total=0 on 𝒟_ℓ with Clausius δS_R=δQ/T_loc ⇒

G_{μν}+Λ_0 g_{μν}=κ(⟨T_{μν}⟩+T^{corr}_{μν}).

The unique diffeo-invariant, ghost-free, second-order scalar functional of S_R:

S_info[g;S_R]=∫d^4x√−g( a_0(μ)S_R + a_1(μ)∇_μS_R∇^μS_R + a_2(μ)S_R R ).

Running couplings a_i(μ)=F_i({c_j(μ)}, SM spectrum, scheme) — computable, not free.

1. Total Action & Field Equations

J_total=(M_Pl^2/2)∫d^4x√−g(R−2Λ_0)+Γ_SM[g,Φ;ρ]+S_info[g;S_R]+S_bdy[g;S_R].

T^{info}_{μν}=−(2/√−g)δS_info/δg^{μν}.

G_{μν}+Λ_0 g_{μν}=M_Pl^−2(⟨T^SM_{μν}⟩+T^{info}_{μν}), ∇^μ(…) = 0.

No new DOF: S_R curvature-determined; c_T=1.

1. Cosmology

FRW: 3M_Pl^2H^2=ρ_m+ρ_r+ρ_Λ+ρ_info; −2M_Pl^2Ḣ=ρ_m+(4/3)ρ_r+(ρ_info+p_info).

S_cg(a)=⟨S_R⟩_comoving. (ρ_info,p_info) fixed by a_i(μ) and derivatives of S_cg.

Linear: μ(k,a)=η(k,a)=Σ(k,a)=1. Ringdown: |δω/ω|≲|R|/M_Pl^2.

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SECTION 2 — STIL (Observer-Moment Space)

ℒ={χ}. Each χ=(A,I,M).

A: awareness kernel (primitive, structureless).

I: identity graph G_I=(V_I,E_I,ℓ_I). M: memory graph G_M=(V_M,E_M,ℓ_M).

ℛ⊂ℒ: physically realizable OMs.

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SECTION 3 — ENCODING FUNCTOR B : Phys → ℛ

Phys: set of physically allowed finite-entropy brain/body states.

B(ρ_phys)=χ where χ is minimal sufficient statistic of ρ_phys:

χ = argmin_{χ'∈ℒ} I(ρ_phys;χ') subject to preserving behaviorally relevant predictive channels.

B is unique given code class and channel set; no free parameters.

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SECTION 4 — CONTINUITY METRIC AND DUAL WEIGHTS

Predictive divergence:

D_pred(χ,χ') = sup_{π∈Π} E_hist[ JSD^{1/2}(P_χ(·|hist,π), P_{χ'}(·|hist,π)) ].

Graph edit distance:

D_ged(χ,χ') = w_I * GED(G_I,G'_I)/N_I + w_M * GED(G_M,G'_M)/N_M.

Normalized compression distance:

D_ncd(χ,χ') = (C(M∥M') − min{C(M),C(M')})/max{C(M),C(M')}.

Composite metric:

d(χ,χ') = α D_pred + β D_ged + γ D_ncd.

Weights (α,β,γ,w_I,w_M) are **dual variables** (KKT multipliers) determined from physical budgets (Section 5). They are state-dependent functions of ρ_phys and Δt.

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SECTION 5 — PHYSICAL BUDGET MAPS τ(ρ_phys,Δt) AND WEIGHT DETERMINATION

Let ρ_phys(t) denote the physical cognitive state over interval [t,t+Δt].

Define available metabolic energy:

E_avail(ρ_phys,Δt) = ∫_{t}^{t+Δt} [P_met(τ) − P_maint(τ)] dτ,

with P_met metabolic input power; P_maint maintenance baseline.

Define Landauer-limited bit budget with efficiency 0<η_L≤1 and effective thermodynamic temperature T_eff:

τ_bits(ρ_phys,Δt) = η_L * E_avail(ρ_phys,Δt) / (k_B T_eff ln 2).

Define structural plasticity budget from synaptic/plastic constraints.

Let W(t) be synaptic parameter tensor; let Π be a projection selecting behaviorally-relevant subspace; define plasticity rate bound Ξ(ρ_phys) (operator norm) and stability radius R_stab(ρ_phys).

Then the **allowable structural move** over Δt:

τ_struct(ρ_phys,Δt) = min{ R_stab(ρ_phys), ∫_{t}^{t+Δt} Ξ(ρ_phys(τ)) dτ }.

Optional predictive error cap via channel Fisher information \(\mathcal{I}_{\mathrm{pred}}(\rho_{\mathrm{phys}})\) and uncertainty drive U(ρ_phys):

τ_pred(ρ_phys,Δt) = [ ∫_{t}^{t+Δt} U(ρ_phys(τ)) dτ ] / [ 1 + \overline{\mathcal{I}}_{\mathrm{pred}}(ρ_phys;Δt) ].

**Dual weights as shadow prices.**

Define constrained proximal step:

Minimize E[D_pred(χ_n,χ')] subject to

E[D_ged(χ_n,χ')] ≤ τ_struct(ρ_phys,Δt),

E[D_ncd(χ_n,χ')] ≤ τ_bits(ρ_phys,Δt),

(and optionally E[D_pred(χ_n,χ')] ≤ τ_pred).

The Lagrangian multipliers (α,β,γ) and subweights (w_I,w_M) are determined by KKT conditions:

(α,β,γ,w_I,w_M) = G(ρ_phys,Δt),

with complementary slackness and feasibility; explicitly,

β≥0, γ≥0; β( E[D_ged] − τ_struct )=0; γ( E[D_ncd] − τ_bits )=0; analogous for α if a predictive cap is used.

Subweights w_I,w_M arise as duals of a split constraint

E[GED_I] ≤ τ_I, E[GED_M] ≤ τ_M with τ_I+τ_M=τ_struct.

Local normalization (optional): whiten each component in a neighborhood ℵ(χ_n) to unit variance to eliminate arbitrary scaling before solving for multipliers.

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SECTION 6 — REACHABLE-SET SELECTION (NO GLOBAL SEARCH)

Objective sector induces physical state evolution ρ_phys(t+Δt)=Φ_{Δt}[ρ_phys(t)] via UISE-IIR-O.

Define the **reachable observer-moment set** at t+Δt:

ℛ_{t+Δt} = { χ' ∈ ℛ : ∃ ρ' = Φ_{Δt}[ρ_phys(t)] with B(ρ') = χ' }.

Define the **feasible set** under budgets:

𝒮_t = { χ' ∈ ℛ_{t+Δt} :

E[D_ged(χ_n,χ')] ≤ τ_struct(ρ_phys,Δt),

E[D_ncd(χ_n,χ')] ≤ τ_bits(ρ_phys,Δt),

(optionally E[D_pred(χ_n,χ')] ≤ τ_pred(ρ_phys,Δt)) }.

Continuity update (restricted argmin):

χ_{n+1} = argmin_{χ' ∈ 𝒮_t} d(χ_n,χ').

**Uniqueness conditions.**

If d is strictly convex over 𝒮_t (e.g., via whitening + Mahalanobis metric) and 𝒮_t is convex (proximal linearization), the minimizer is unique. If multiple minimizers exist, choose the one with minimal D_ged; if still tied, lexicographic tie-break on (D_pred, D_ncd).

**Failure mode (encoding loss).**

If ℛ_{t+Δt} = ∅ or 𝒮_t = ∅, then encoding fails and

χ_{n+1} = χ_aw (Section 7).

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SECTION 7 — TERMINAL AWARENESS STATE

Define unique awareness-only class:

χ_aw = (A, ∅, ∅).

For any χ, distances to χ_aw are constants fixed by chosen priors/compressor; hence

d(χ,χ_aw) is universal. At encoding failure: χ_{n+1}=χ_aw.

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SECTION 8 — SUMMARY OF DEPENDENCIES (NO FREE PRIMITIVES)

• {c_j(μ)} determined by SM on curved background (heat-kernel).

• {a_i(μ)} = F_i({c_j(μ)},SM,scheme) (computable running couplings).

• B determined as minimal sufficient statistic for fixed channel/code class.

• d metric components defined; weights are duals (functions of ρ_phys,Δt).

• Budgets τ_bits, τ_struct (and τ_pred optional) computed from ρ_phys via

metabolic and plasticity maps; no arbitrary constants.

• Selection domain is ℛ_{t+Δt} (reachable set), not all ℒ; no global search.