BD × AI Lab · MDL×DCC
8Z Demon · feedback information engine

MDL×DCC Demon

A decision-quality layer for DCC: use MDL/LZ/process measurements, test which signals predict future progress, then let DCC gate cleaner, explore wider, or switch channels.

Sudoku v0.5 promotion candidatesDCC governorBekenstein/regime bridgenot a thermodynamic proof

Simple meaning

Demon is not a replacement for DCC. DCC remains the controller. Demon is the decision-quality layer that tells DCC which MDL/LZ/process signals deserve trust.

The first Sudoku evidence says the useful pattern is not merely “lower ΔL is better.” It is closer to:

differentiate → cascade → compress

That is a stronger form of the older compress → steer → compress loop: sometimes a good move temporarily increases local structure so that a later cascade can collapse many degrees of freedom.

Roles in the architecture

  • MDL/LZ measures structure, compression, and process change.
  • DCC chooses, gates, promotes, rejects, or widens search.
  • Demon audits which measured signal predicts later progress under fair controls.

The key upgrade

Plain MDL×DCC can ask: “does this look simpler now?”

Demon asks the sharper question: “did this kind of signal actually predict useful future gain against operator-matched random controls?”

Current Sudoku evidence

Interpretation: repeated feedback-information / engineering signal, not just a compression artifact. v0.5 now adds fair upgrade-bench evidence with promotion candidates.

Dv0.3h feedback-information verdict
process > candidate > stateuseful information ordering
positive ΔLpredicted later candidate gain
cleanerfewer guesses/backtracks in best gates

Key signal

The first strong result does not say “Demon solves Sudoku.” It says Demon can help DCC select cleaner trajectories by using process-side differentiation and cascade potential. The main useful channel so far is not static board-state compression, but trajectory/process information.

Sudoku DCC Upgrade Bench v0.5 — compare result

Verdict: promotion candidates found. The v0.5 compare pass loaded four analysis artifacts, aggregated 6,156 run-summary rows across 29 gates, and found 8 gates that beat their operator-matched controls strongly enough for promotion-candidate status.

8promotion candidates
6,156run-summary rows
29gates compared
matched controlsrequired for promotion

Most important result

The new upgrade bench supports the practical claim: Demon-style and related information gates can help DCC choose cleaner trajectories. The strongest direct solver gate by overall ranking was empowerment_gate; the strongest Demon-continuity gate was dcc_demon_proc_cascade. Both beat matched controls while using fewer guesses/backtracks.

GateMatched controlSolve rateLiftGate/control-only winsGuess ΔBacktrack Δ
combo_all_v05operator_matched_random_combo_all_v0536.7% vs 30.3%+6.4%16 / 2-3.98-4.27
combo_cond_synergyoperator_matched_random_combo_cond_synergy37.4% vs 32.4%+5.0%18 / 7-3.66-3.42
dcc_demon_proc_cascadeoperator_matched_random_proc_cascade46.6% vs 41.2%+5.4%16 / 4-2.55-2.33
dcc_demon_procoperator_matched_random_proc35.0% vs 31.7%+3.3%4 / 0-6.10-6.09
empowerment_gateoperator_matched_random_empowerment48.4% vs 43.8%+4.6%17 / 7-2.55-2.12
combo_pred_empoweroperator_matched_random_combo_pred_empower35.8% vs 32.1%+3.7%16 / 8-4.06-4.06
conditional_proc_cascade_gateoperator_matched_random_conditional_proc46.5% vs 42.9%+3.7%17 / 9-4.80-2.48
information_bottleneck_gateoperator_matched_random_info_bottleneck36.2% vs 32.6%+3.7%15 / 7-2.26-2.43

Interpretation: v0.5 does not prove a universal solver improvement yet, but it moves the branch from “interesting Demon signal” to a real DCC Upgrade Bench. The next promotion target is a lean v0.6 gate family built around empowerment + process-cascade + conditional normalization, then a transfer test in TSP.

Mass–information regime bridge

This section folds in the former separate Bekenstein bridge page. The companion theory frames the older i ≈ m·c⁴ intuition as an atomic-scale special case of a broader Bekenstein-style mass–information coordinate map.

The useful point is not that i = mc⁴ becomes a universal law. It does not. The useful point is that MDL×DCC’s empirical domains mostly use fixed-size informational tokens, and those domains may share the same information-regime geometry.

x = 1 · fixed-size tokens

Atoms, Sudoku cells, TSP cities, chess pieces, DNA bases, trading bars, ARC grid cells, crossword cells.

y ≈ 4 · atomic-scale bridge

The regime where the old i≈m·c⁴ intuition numerically matches Bekenstein-scale estimates.

R* ≈ 3.13 Å

The matching length scale where the Bekenstein-style bound lines up with the old two-step m → E → i intuition.

Core relation

R(m) = a · m^α I ≈ mˣ · cʸ x = 1 + α y = 1 + log_c[2πa / (ℏ ln 2)]

The (x,y) coordinate is a bookkeeping map derived from standard information bounds. It helps ask what kind of information regime a domain belongs to before trying to transfer MDL×DCC into it.

The two-step intuition

mass → energy → information E = m·c² old intuition: i ≈ E·c² ≈ m·c⁴ modern status: atomic-scale numerical regime, not universal law

That matters for MDL×DCC because the practical arenas are not arbitrary continua. They are usually made of bounded local units: candidates, moves, cells, cities, bases, bars, operators, or training-curve tokens.

Demon bridge

The original Maxwell-demon intuition was “sort rare useful fluctuations.” The computational version is narrower: measure trajectory information, test it against fair controls, and let DCC trust only signals that predict future gain.

Feedback does not mean magic. It means measurement → selection → consequence.

The Sudoku evidence says trajectory/process information is more useful than static state information. That matters because feedback information engines do not work from state alone; they work from measurement records across a trajectory.

Sudoku v0.3h/v0.5 signature: MI_pred(process ΔL → future gain) > MI_pred(candidate ΔL → future gain) >> MI_pred(state ΔL → future gain)

The current interpretation: DCC should not blindly chase immediate compression. In fixed-token search, progress may require temporary differentiation, followed by cascade, followed by compression.

Mechanism

The original Maxwell-demon intuition was “sort rare useful fluctuations.” The computational version is narrower and testable:

1. measure candidate/state/process change 2. compare active gate to operator-matched random control 3. ask whether the signal predicts future gain 4. let DCC trust only signals that survive the test

In Sudoku, process-side ΔL and cascade depth appear more useful than raw board-state compression. That is why v0.4/v0.5 add process-cascade gates, event-scout modes, and upgrade-bench comparisons.

Why transfer?

DomainToken typeRegime claimDemon prediction
Sudokucells / candidatesfixed tokenprocess ΔL predicts cascade
TSPcities / edges / operator sequencesfixed tokenoperator-sequence process ΔL predicts future tour gain
Chesspieces / squares / variationsfixed tokenvariation process ΔL improves tiebreaks
Tradingbars / ticks / indicatorsfixed tokenread-only process signal must appear before profit
NASarchitecture cells / training curvesfixed tokentraining-trajectory process compression predicts validation

Sudoku

Move ranking, logic-vs-guess switching, cascade-aware DCC decisions, fewer blind guesses/backtracks.

TSP

Operator promotion, MSTD/TEP/HyperDim budget allocation, DCC strictness, process-signal transfer tests.

Trading

First as read-only overfitting/regime diagnostic: did structure appear before profit or only after cherry-picking?

NAS / ARC

Test whether process-compression events predict final or downstream performance before giving them control power.

AMR

Use Demon as a non-actionable simulation governor: which abstract operator packages preserve future control?

Crossword

Use process-side signals and cascade/frozen-cell events to rank frontier choices and reduce dead-end fill paths.

Next tests

Claim boundary

8Z Demon does not claim physical thermodynamic proof, perpetual motion, or a literal Maxwell demon in Sudoku/TSP. It is a search-level feedback-information diagnostic inspired by stochastic thermodynamics.

The mass–information bridge does not make i = m·c⁴ a universal law. It treats that intuition as an atomic-scale numerical regime and uses standard Bekenstein/Landauer ideas as the formal anchor.

The current public claim is deliberately limited: Sudoku has produced early evidence that process-side information can help DCC choose cleaner trajectories. Cross-domain confirmation is pending.