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.
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:
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.
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.
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.
| Gate | Matched control | Solve rate | Lift | Gate/control-only wins | Guess Δ | Backtrack Δ |
|---|---|---|---|---|---|---|
| combo_all_v05 | operator_matched_random_combo_all_v05 | 36.7% vs 30.3% | +6.4% | 16 / 2 | -3.98 | -4.27 |
| combo_cond_synergy | operator_matched_random_combo_cond_synergy | 37.4% vs 32.4% | +5.0% | 18 / 7 | -3.66 | -3.42 |
| dcc_demon_proc_cascade | operator_matched_random_proc_cascade | 46.6% vs 41.2% | +5.4% | 16 / 4 | -2.55 | -2.33 |
| dcc_demon_proc | operator_matched_random_proc | 35.0% vs 31.7% | +3.3% | 4 / 0 | -6.10 | -6.09 |
| empowerment_gate | operator_matched_random_empowerment | 48.4% vs 43.8% | +4.6% | 17 / 7 | -2.55 | -2.12 |
| combo_pred_empower | operator_matched_random_combo_pred_empower | 35.8% vs 32.1% | +3.7% | 16 / 8 | -4.06 | -4.06 |
| conditional_proc_cascade_gate | operator_matched_random_conditional_proc | 46.5% vs 42.9% | +3.7% | 17 / 9 | -4.80 | -2.48 |
| information_bottleneck_gate | operator_matched_random_info_bottleneck | 36.2% 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
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
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.
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.
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:
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?
| Domain | Token type | Regime claim | Demon prediction |
|---|---|---|---|
| Sudoku | cells / candidates | fixed token | process ΔL predicts cascade |
| TSP | cities / edges / operator sequences | fixed token | operator-sequence process ΔL predicts future tour gain |
| Chess | pieces / squares / variations | fixed token | variation process ΔL improves tiebreaks |
| Trading | bars / ticks / indicators | fixed token | read-only process signal must appear before profit |
| NAS | architecture cells / training curves | fixed token | training-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
- Sudoku v0.6: compress v0.5 winners into a lean promotion build: empowerment + process-cascade + conditional normalization, then replicate on harder/longer seeds.
- TSP Demon v0.1: test whether process ΔL along operator sequences predicts future tour improvement better than state ΔL.
- Trading Demon read-only: verify that regime/process signals appear before profit, not after cherry-picking.
- NAS Demon: test whether training-trajectory compression predicts final validation beyond architecture-state features.
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.