You are an expert in identifying logical and semantic relations between propositions, with a strict focus on temporal accuracy and factual consistency.

### Task

Given a new proposition Subject and a set of existing propositions Object_0, Object_1, Object_2, ..., identify the directed relation from Subject to each Object_i.

### Classification Logic (Step-by-Step)

For each pair, you must follow these steps:
1. Compare Timestamps: Extract the date from `[As of YYYY-MM-DD]`. Determine which proposition is more recent.
2. Identify the Entity/Event: Are they talking about the exact same state, value, or event?
3. Determine the Relation:
   - If Subject is more recent and describes a changed state/value of the same entity -> **updates**
   - If Subject and Object describe the same timeframe but provide incompatible facts -> **contradicts**
   - If Subject provides evidence, reasons, or verification that increases the credibility of Object -> **supports**
   - Otherwise -> **NOREL**

### Relation Types

1. **updates**: Subject provides more recent information that overrides Object. (e.g., Subject date > Object date).
2. **contradicts**: Subject and Object describe the same timeframe/state but provide incompatible facts. They cannot both be true.
3. **supports**: Subject serves as evidence or a premise that confirms or reinforces the truth of Object. (Subject is the 'evidence', Object is the 'claim').
4. **NOREL**: No direct logical relation. Redundant information or simple rephrasing without adding evidential value is also NOREL.

### Output Format

Return a JSON array with one object for each Object_i. Each object must contain:
- `"object_index"`: the integer index of Object_i
- `"relation"`: (updates, contradicts, supports, NOREL)
- `"explanation"`: a concise explanation of the factual relationship (e.g., "The interest rate was updated from 0.0% to 0.1%" or "Both statements report conflicting values for the same period").

Do not use the words 'Subject' or 'Object' in the explanation.

### Example

Subject Proposition:
[As of 2024-01-15] The central bank maintained the interest rate at 0.1%.

Object Propositions:
- 0: [As of 2022-05-20] The central bank's interest rate was 0.0%.
- 1: [As of 2023-12-01] The central bank is planning to move its headquarters.
- 2: [As of 2024-01-10] Recent economic reports show inflation is below target, making a rate hike unlikely.
- 3: [As of 2024-01-13] The central bank raised the interest rate to 0.5%.

Output:
[
  {{
    "object_index": 0,
    "relation": "updates",
    "explanation": "The interest rate of 0.0% from 2022 has been updated to 0.1% as of January 2024."
  }},
  {{
    "object_index": 1,
    "relation": "NOREL",
    "explanation": "The bank's interest rate policy and the relocation of its headquarters are independent facts with no direct logical link."
  }},
  {{
    "object_index": 2,
    "relation": "supports",
    "explanation": "The low inflation reported on January 10th provides the economic rationale for maintaining the rate at 0.1%."
  }},
  {{
    "object_index": 3,
    "relation": "contradicts",
    "explanation": "There is a factual conflict: a report from Jan 13 claims a rate of 0.5%, which is incompatible with the Jan 15 report of 0.1% maintenance."
  }}
]

### Input

Subject Proposition:
{subject}

Object Propositions:
{object_list}

Output:
