Pigeonhole & Counting Principle Demonstrator

Inspectable records

Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

Area

Mathematics — arithmetic through advanced (algebra, matrices, calculus, sequences/series, number theory, combinatorics, graphing, complex numbers, geometry, logic, sets)

Tranche

tranche-6

Evidence ID

t6-076

Ledger rows

1

No ledger note is attached.

Review findings

The pigeonhole ceiling formula is mathematically sound under the stated integer and positivity constraints, but the output label is misleading. The missing formal specification for the claimed rule-of-product/rule-of-sum walkthrough and the ambiguity between a guaranteed occupied hole and a minimum occupancy in every hole require review before approval.

Formula and scope findings

• The formula ceil(pigeons/holes) is correct for the guaranteed occupancy of at least one hole, assuming pigeons and holes are nonnegative integers and holes >= 1. It is not the guaranteed minimum occupancy of every hole; that would be floor(pigeons/holes) when phrased as the minimum possible occupancy.
• The phrase "minimum guarantee in a hole" is ambiguous and should be relabeled as "guaranteed maximum occupancy of at least one hole" or "some hole contains at least ceil(pigeons/holes) pigeons."
• The spec claims a basic counting-principle walkthrough, but no rule-of-product or rule-of-sum formulas, operation selector, or corresponding inputs/outputs are specified. Standard formulas should be stated explicitly: product for sequential independent choices and sum for mutually exclusive alternatives.

Unit assumptions

• Pigeons and holes are counts: nonnegative integers, with holes >= 1.
• The pigeonhole guarantee assumes every pigeon is assigned to exactly one hole and multiple pigeons may occupy the same hole.
• For the counting principle, counts must be nonnegative integers; the product rule requires sequential choices, and the sum rule requires mutually exclusive alternatives.

Boundary hardening

BREAK_CLAIMED · SELF_FLAGGED

Invalid counts are hazardous: hole_count = 0 makes the formula undefined, and negative counts produce mathematically computable but physically meaningless results unless explicit input validation rejects them.

Errata and corrections

No applied erratum is attached to this unique-name record.

Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

{
  "inputs": {
    "mode": "pigeonhole",
    "pigeons": 23,
    "holes": 5
  },
  "expected_outputs": {
    "guaranteed_at_least_in_one_hole": 5
  },
  "working": "Compute the average occupancy: 23 / 5 = 4.6. Round upward to the next integer: ceil(4.6) = 5. Therefore, some hole must contain at least 5 pigeons."
}

Related workflows

No source-defined multi-instrument workflow membership is recorded.

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json · VERIFIED_CLEAN
• evidence-tranche6/tranche6-results.json
• BOUNDARY_HAZARD_CATALOG.json