Open Theorem And Observer-Conditioned Roadmap

Status snapshot: May 2026 proof-spine and observer-conditioned research route.

This page concentrates two routes that are otherwise spread across the preprint, Appendix A, Appendix C, Appendix H, the review protocol, and the public replication package.

The Open Theorem Roadmap is CCT's formal proof spine: bounded theorem targets, verifier repairs, proof obligations, counterexample searches, and method artifacts. Observer-conditioned physics is the long-horizon theory track, called Layer 3 in ontology-specific docs: calibration transport, observer/compiler structure, boundary/interface behavior, effective adjacency, OP0 specificity filters, and stability-depth questions.

OP labels are roadmap handles inside that spine. They name open theorem/problem lanes, while a theorem note, verifier, scaffold, schema, route surface, or review packet from that lane carries its own earned status. This lets a lane remain active while a bounded piece of it becomes inspectable and reviewable.

The observer-conditioned roadmap is the broader long-horizon theory route. Some observer-conditioned questions become OP lanes, while others first appear as calibration rows, ledgers, state/coherence objects, effective-adjacency capsules, mission-architecture templates, or Tau-X resource questions before they become theorem targets.

Both routes are active parts of the same staged program. They generate formal objects, simulations, ledgers, null routes, and review gates before any stronger interpretation is promoted.

Current Implemented Method Artifacts

Several theorem-roadmap and observer-conditioned targets have crossed into public-safe method artifacts:

Track Current public artifact What it establishes
BT3/BT5 command attribution Repaired verifier route separating controller command, actuator output, actuator noise, plant state, hidden channels, and joint capacity. Raw actuator-output influence no longer substitutes for controller-attributable influence in the synthetic route surface.
Scalar OP4/BT4 Declared-envelope verifier with square-root toy case plus gamma, log/sublinear, saturating, threshold, denominator, and hidden-resource diagnostics. Resource-envelope claims have a broader synthetic discriminator than the original toy case.
Vector OP4 Multi-resource simulator and scalarized route cases. Energy-only improvement must survive declared latency, memory, calibration, synchronization, reliability, alternate-channel, and Pareto/baseline routes.
BT6 Basin/path-measure verifier, finite-state discriminator, and finite-sample terminal/coarse KL interval diagnostics. Basin movement is routed through declared support, kernel/path ledgers, incumbent routes, denominator checks, and interval diagnostics.
OP2 Logged-dependence estimator, randomized holdout route surface, and finite-sample holdout-delta interval diagnostics. Observation-to-control claims are separated from observation quality, command-effect sublemma, hidden-channel, denominator, incumbent, and holdout-integrity gates.
BT7b Passive aperture/operator-norm verifier and proof-review stub. The theorem object is separated from legacy focusing-gain benchmarks, hidden gain, incident-power changes, resonant storage, near-field class changes, and denominator substitutions.
Scalar multiwell anti-uniqueness / OP0a Scalar theorem note, synthetic route companion, and post-specialist formal-review record. Hierarchy-like basin counts and local curvature matches become specificity-boundary objects: expressivity is visible, and selection requires stronger filters.
QFT-data specificity-filter scaffold / OP0b Public-safe Phi(C,[x_*]) -> QFTData schema, route examples, route-semantics checker, equivalence-audit fixtures, and QFT / representation scaffold-review clearance. Standard-Model-facing specificity is routed through source-object completeness, equivalence invariance, field-status discipline, null/incumbent closure, compression/holdout checks, and review gates.
Regime-local RFH metrology envelope / OP1 Algebraic envelope note, manifest examples, finite-window uncertainty sidecar, and specialist-review packet. Measurement-scaling claims are routed by declared resource class, estimator policy, back-action/disturbance envelope, hidden-resource handling, and finite-window uncertainty discipline.
Calibration holonomy Public-safe closed-loop retuning capsule. Calibration transport is expressed as loop rows with ordinary drift, hysteresis, estimator-offset, repeatability, and incumbent routes.
Effective adjacency and Tau-X ledgers Effective-neighborhood, effective-adjacency object-family, feedback-cycle timing, environmental-handle, and state/coherence payload artifacts. Space-and-motion intuition is translated into reachability, propagation, reconstruction, correction, timing, environmental, mission-architecture, and resource-ledger rows.

These are method-validation, branch-narrowing, proof-review, and Tau-X architecture / resource-ledger artifacts. Their job is to make assumptions, routes, and failure modes inspectable.

Active Formal Queue

The open queue remains live:

Item Current role Next burden
Scalar multiwell anti-uniqueness / OP0a Scalar theorem object for hierarchy expressivity and anti-uniqueness. Move from post-specialist scalar theorem-readiness into accepted scalar theorem text; keep high-dimensional R^m language behind relative Morse / handle-construction lemmas.
QFT-data specificity-filter scaffold / OP0b Public-safe scaffold for Phi(C,[x_*]) -> QFTData review. Build future non-synthetic target-data routes only after the equivalence relation, complexity denominator, anomaly/locality/unitarity/Lorentz/RG/topology payloads, and target-leakage policy are frozen.
OP1 Regime-local RFH theorem under physical constraints. Complete metrology/probability review for resource classes, back-action/noise envelopes, finite-window uncertainty bands, excluded regimes, and incumbent closure.
OP2 Observation-to-control bridge. Complete controls/statistics review, command-effect sublemma path, sensing/compute ledgers, and architecture-specific corollaries.
OP3 Forbidden designs and attribution limits. Strengthen command/capacity/hidden-channel theorem formulation beyond synthetic verifier repair.
OP4 Vector no-free-lunch resource accounting. Convert scalarized and Pareto route cases into a formal multi-resource theorem object.
BT6 Basin/path-measure extension. Move from population and diagnostic route objects toward formal finite-sample, continuous-time, diffusion, and capacity-selection corollaries.
BT7b Passive boundary/operator-norm theorem. Finish bounded-operator construction, target-functional boundedness, admissibility class, and small-signal remainder review.
Calibration transport Observer-conditioned effective-law bridge. Formal transport object, repeatability routes, perturbation controls, and calibration/metrology review.
Boundary grammar Passive/active/resonant/nonlinear/hidden-gain taxonomy. Build after BT7b so boundary claims inherit a theorem-ready norm and denominator policy.

Observer-Conditioned Physics Route

Observer-conditioned physics is the theory track that asks how finite observers, instruments, controllers, calibration regimes, and environments condition what becomes stable, legible, and steerable.

In first-touch docs, this is usually called observer-conditioned physics. In ontology-specific docs, it is called Layer 3. The difference is mainly audience and genre: the public review route uses operational language; the ontology route carries the deeper interpretation.

The current public route is:

  1. generate the formal candidate or discriminator;
  2. build a public-safe simulator, theorem stub, ledger, or route surface;
  3. run incumbent, null, denominator, support, and hidden-channel checks;
  4. seek specialist review for the formal or method object;
  5. promote the claim class that the artifact has earned.

This keeps the long-horizon theory active while assigning each artifact to the claim class it has earned.

Hardware And Bench Connection

The theorem and observer-conditioned tracks are not separate from hardware. They stage hardware exposure by specifying what a physical test is being asked to decide.

The path is:

  • formal targets define assumptions and denominators;
  • public verifiers and synthetic capsules make route behavior inspectable;
  • simulations identify operating regions and fragile assumptions;
  • preregistration locks controls, baselines, nulls, and decision labels;
  • benches test selected regimes against real instruments, materials, drift, noise, and replication;
  • results feed back into the theorem queue and observer-conditioned track.

Hardware therefore appears as the physical exposure layer of the roadmap, not as an afterthought.