RTT Core: Coherence Budget

1. Purpose and role in RTT#

Goal:
Define the Coherence Budget as the RTT mechanism that governs:

• How much coherence a system has available for classical readout
• How coherence is partitioned across representational branches
• How drift and dimensional extension consume coherence
• How Validator Pulse spends coherence to produce classical information

Coherence Budget is the quantitative backbone of RTT’s readout logic.

2. Conceptual definition#

2.1 Informal definition#

The Coherence Budget is the finite resource that determines
which branch of a multi-branch state can become classical information.

It is not amplitude, probability, or energy.
It is the capacity for classical validation.

2.2 Core properties#

• Finite:
  Every representational manifold has a maximum coherence budget (C_{\max}).

• Partitioned:
  Coherence is distributed across branches (c_i).

• Consumptive:
  Validator Pulse consumes coherence; it cannot be reused.

• Drift-sensitive:
  Drift reduces coherence and may render branches ineligible.

• Regime-aware:
  Operator regimes may require minimum coherence thresholds.

3. Formal structure (RTT-level)#

3.1 Coherence distribution#

Let the representational manifold be:

[ \mathcal{M} = { b_i \mid i \in I } ]

Each branch (b_i) carries a coherence weight:

[ c_i \in [0, C_{\max}] ]

The total coherence budget satisfies:

[ \sum_{i \in I} c_i \leq C_{\max} ]

3.2 Eligibility condition#

A branch is eligible for classical readout if:

[ c_i \geq C_{\text{min}} ]

where (C_{\text{min}}) is the regime-dependent minimum coherence required for validation.

3.3 Consumption rule#

Validator Pulse consumes coherence:

[ V(b_k): c_k \rightarrow 0 ]

All other branches lose eligibility:

[ b_{j \neq k} \rightarrow \text{residue} ]

This enforces single-branch classical reality.

4. Relationship to drift and dimensional structure#

4.1 Drift reduces coherence#

Drift magnitude (\Delta_i) reduces coherence:

[ c_i' = c_i - f(\Delta_i) ]

where (f) is a drift-loss function determined by the regime.

Branches drifting outside the Dimensional Drift Envelope:

• Lose coherence rapidly
• Become ineligible for validation
• Collapse into non-informational residue after readout

4.2 Dimensional extension consumes coherence#

When a state is extended across a higher-dimensional manifold:

• Representation increases
• Coherence is spread thinner across branches
• Only one branch typically retains enough coherence for validation

This explains why “quantum cloning” experiments produce:

• Multiple representational copies
• Only one classical copy

5. Interaction with Validator Pulse#

Validator Pulse (see /docs/rtt/core/validator_pulse.md) is the mechanism that:

• Selects the branch with sufficient coherence
• Spends the coherence budget
• Produces classical information

Coherence Budget determines:

• Which branches can be chosen
• How many validation events are possible
• Whether an operator sequence is realizable

Validator Pulse determines:

• Which branch is chosen
• When coherence is consumed

Together they enforce RTT’s single-readout constraint.

6. Time structure: triadic time#

Coherence Budget lives in the coherence layer of triadic time:

1. State time:
   Evolution of (|\psi_i\rangle) across branches.

2. Coherence time:
   Evolution of coherence weights (c_i), including drift loss and redistribution.

3. Readout time:
   Validator Pulse consumes coherence and produces classical information.

Quadradic time would allow multiple independent coherence axes, but Coherence Budget is defined for single-axis coherence, making it inherently triadic.

7. Operator regime interactions#

7.1 Minimum coherence thresholds#

Operators may require:

• (c_i \geq C_{\text{min}})
• Drift below threshold
• Dimensional coordinates within envelope

Examples:

• Extension operators require coherence to remain above threshold during drift.
• Deferred validation operators require coherence stability over time.

7.2 Regime transitions#

Coherence loss can push a branch:

• Into eligibility
• Out of eligibility
• Across regime boundaries

This is how Coherence Budget enforces non-symmetric validation.

8. Example: alignment with quantum “cloning” experiments#

In /docs/rtt/core/alignment_quantum_cloning.md:

• The experiment creates two representational copies.
• Coherence Budget ensures only one copy retains enough coherence for readout.
• Validator Pulse consumes that coherence.
• The other copy collapses into residue.

Thus:

• Coherence Budget enables multi-branch representation.
• Validator Pulse enforces single-branch classical reality.

9. Paradox handling#

Coherence Budget resolves structural paradoxes such as:

• “Why can’t both copies be measured?”
  → Only one branch has sufficient coherence.

• “Why does the other copy disappear?”
  → It collapses into residue after validation.

• “Why isn’t this a violation of no-cloning?”
  → Coherence Budget prevents multiple classical readouts.

10. Canon integration and cross-links#

Primary cross-links:

• /docs/rtt/core/validator_pulse.md
• /docs/rtt/core/dimensional_drift_envelope.md
• /docs/rtt/core/time_triads.md
• /docs/rtt/core/alignment_quantum_cloning.md

Status:
This module defines the quantitative core of RTT’s readout logic.
Once coherence-indexing grammar is added, it can be promoted from draft to stable.