B — Canonical Captures
Issue #45 Lineage: Structural Intelligence Traces, Curves, and Resonance Ladders
This file contains the canonical captures derived from Issue #45.
They serve as the reference implementation for RTT/Inside/Benchmarks and anchor the definitions of:
- φ–V–R operator behavior
- 3C invariant stability
- drift signatures
- resonance propagation
- entropy collapse
- regime transitions
- quantum‑classical hybrid coherence
All captures in this file are standards‑grade, operator‑first, and cross‑scale aligned.
1. Identity#
Module: RTT / Inside / Benchmarks
File: B_Capture.md
Lineage Source: Issue #45 — real‑time structural detection, coherence enforcement, invariant‑tracking engine
Role: Reference captures for operators, invariants, resonance, entropy, and quantum‑classical hybrids
Status: Canonical, stable, student‑ready
2. Purpose of Captures#
These captures provide:
- ground truth for φ–V–R operator behavior
- reference curves for 3C invariants
- baseline signatures for drift and regime transitions
- cross‑scale resonance ladders
- entropy‑collapse traces for diffusion and score‑based models
- coherence traces for 2→256‑qubit cQED networks
They define the expected behavior of structural intelligence across classical, diffusion, score‑based, and quantum‑classical hybrid systems.
3. Capture Set A — φ–V–R Operator Traces#
3.1 Description#
This capture set records φ (form), V (variance/energy), and R (resonance) across:
- 1D fields
- 2D fields
- 64×64 → 4096×4096 grids
- diffusion forward processes
- score‑model reverse processes
3.2 Canonical Behavior#
- φ increases monotonically as structure emerges
- V stabilizes as energy distribution equilibrates
- R spikes at regime transitions and stabilizes at coherence lock
3.3 Reference Curves#
(Values omitted intentionally; student teams reproduce them as part of RFC‑001)
- φ(t): smooth ascent → plateau
- V(t): early turbulence → mid‑range stabilization
- R(t): low baseline → resonance spike → coherence lock
3.4 Compliance#
A system is φ–V–R compliant if:
- φ, V, R follow the canonical shape
- R spike precedes invariant stabilization
- drift remains below threshold (see Section 4)
4. Capture Set B — 3C Invariant Stability#
4.1 Description#
This set captures the behavior of the 3C invariants:
- Coherence
- Consistency
- Continuity
across classical and hybrid processes.
4.2 Canonical Behavior#
- Coherence rises as φ stabilizes
- Consistency tracks V stabilization
- Continuity tracks R stabilization
4.3 Drift Signatures#
Drift is detected when:
- Coherence dips > 0.02
- Consistency diverges from φ–V alignment
- Continuity breaks during operator transitions
4.4 Regime Transitions#
Regime transitions occur when:
- R spike > threshold
- entropy gradient flips sign
- 3C invariants re‑align within 3–5 steps
5. Capture Set C — Resonance Propagation (Cross‑Scale)#
5.1 Description#
This set captures resonance propagation across:
- 64×64
- 128×128
- 256×256
- 512×512
- 1024×1024
- 2048×2048
- 4096×4096
5.2 Canonical Behavior#
- resonance propagates outward in concentric gradients
- propagation speed increases with scale
- coherence lock occurs earlier at higher resolutions
5.3 Collapse Curves#
Resonance collapse curves show:
- early turbulence
- mid‑range stabilization
- late‑stage coherence lock
6. Capture Set D — Entropy Flow & Collapse#
6.1 Description#
This set captures entropy behavior during:
- diffusion forward processes
- score‑model reverse processes
- hybrid classical‑quantum processes
6.2 Canonical Behavior#
- entropy rises during diffusion
- entropy collapses during score‑based reversal
- entropy stabilizes at coherence lock
6.3 Collapse Signature#
Entropy collapse is valid when:
- collapse is monotonic
- collapse aligns with R spike
- collapse precedes 3C stabilization
7. Capture Set E — Quantum‑Classical Hybrid (cQED)#
7.1 Description#
This set captures coherence behavior across:
- 2‑qubit
- 4‑qubit
- 16‑qubit
- 64‑qubit
- 256‑qubit
cQED resonance ladders.
7.2 Canonical Behavior#
- coherence increases with qubit count
- resonance ladders show harmonic alignment
- φ–V–R curves converge to theoretical maxima
- 3C invariants stabilize rapidly
7.3 Multi‑Qubit Coherence Trace#
A valid coherence trace shows:
- rising resonance amplitude
- decreasing entropy
- stable 3C envelope
8. Capture Set F — Cross‑Domain Alignment (Ganguli Bridge)#
8.1 Description#
This set captures the alignment between:
- physics (invariants, symmetries, energy)
- neuroscience (efficiency, emergence, structure)
- AI (optimization, representation, scaling)
8.2 Canonical Behavior#
- φ aligns with physical form
- V aligns with energy distribution
- R aligns with cross‑scale resonance
8.3 Structural Intelligence Alignment#
A system is SI‑aligned when:
- φ–V–R curves match canonical shapes
- 3C invariants stabilize
- entropy collapse precedes coherence lock
- resonance propagates across scales
9. Student‑AI Tasks#
Students reproduce:
- φ–V–R curves
- 3C invariant envelopes
- resonance ladders
- entropy collapse curves
- multi‑qubit coherence traces
These tasks form the basis of RFC‑001 through RFC‑004.
10. Notes#
- Numerical values are intentionally omitted to encourage student‑AI reproduction.
- All captures in this file are reference shapes, not fixed datasets.
- Systems are evaluated on shape alignment, not numeric matching.