Institutional Placement Engine Edge Case Semantics & Specification (Core Engine)

This document formalizes the exact algorithmic decision boundaries, rounding rules, temporal interpretations, and dispute resolutions across all edge cases evaluated by the engine.

1. Academic & Backlog Rule Semantics

1.1 Backlog Clearing Temporal Horizon

Rule: When a drive requires "No active backlogs", the student's backlog status is evaluated as-of the drive date, NOT the current wall-clock date.
Cleared Month Prior: If a backlog was cleared on 2026-10-15 and the drive date is 2026-11-20, the backlog is status cleared $\rightarrow$ ELIGIBLE.
Cleared Day Before: If cleared on 2026-11-19 for a drive on 2026-11-20 $\rightarrow$ ELIGIBLE.
Cleared On Drive Day: If marked cleared on 2026-11-20 $\rightarrow$ ELIGIBLE (inclusive bounds).
Cleared Day After Drive: If cleared on 2026-11-21 $\rightarrow$ INELIGIBLE (was active on drive day).
History of Backlogs: If the company explicitly specifies "No history of backlogs" (historical_backlogs_max = 0), any cleared backlog in previous semesters renders the student INELIGIBLE, citing the historical clause.

1.2 Cut-Off Boundaries & Precision Arithmetic

Exact Cut-Off: A student with CGPA 7.000 against a minimum cut-off of 7.000 is ELIGIBLE ($\ge$).
Precision & Rounding: CGPA cut-offs are compared at standard floating-point precision ($10^{-6}$ epsilon). A CGPA of 6.995 is INELIGIBLE when cut-off is 7.0. Truncation vs half-up rounding is configurable via the rule parameter allow_rounding=false (default: strict non-rounding).
10th & 12th Percentages: A percentage cut-off of 60.0% with candidate having 59.99% is INELIGIBLE.

1.3 Lateral Entry & Missing Records

Lateral Entry: Students entering directly into Year 2 (Semester 3) via Polytechnic Diploma do not possess a 12th mark sheet. If a company rule specifies min_twelfth_percentage = 60.0%, the engine checks if diploma_percentage is present. If present and $\ge 60.0%$, the candidate passes with the reason noting diploma equivalence.
Missing Record: If neither 12th nor diploma is on file and the rule is hard, status is INELIGIBLE / NEEDS_REVIEW.

1.4 Gap Years Calculation

Calendar Days: A 1-year gap limit allows up to 365 days (or 366 in leap years) between educational stages.
Limit Horizon: A candidate with exactly 365 days gap is ELIGIBLE. A candidate with 366 days is INELIGIBLE unless an officer exemption is documented.

1.5 Branch Aliases & Degree Equivalence

Alias Equivalence: Canonical mapping normalizes variations:
- ["CSE", "Computer Science", "B.Tech - Computer Science & Engineering", "CS"] $\rightarrow$ Canonical CSE.
- ["IT", "Information Technology"] $\rightarrow$ Canonical IT.
- Allied CS $\rightarrow$ {CSE, IT, AI&DS, CCE, Software Engineering}.

2. Institutional Offer Policy Semantics

2.1 Dream Company Band Interpretation

Threshold Inclusivity:
- band_inclusive = true: An offer of exactly 10.0 LPA meets a dream threshold of 10.0 LPA $\rightarrow$ classified as DREAM.
- band_inclusive = false: An offer of 10.0 LPA is regular; only $> 10.0\text{ LPA}$ qualifies as dream.
Basis: Configurable between Total CTC (ctc) or Fixed Base Pay (fixed_pay). Default: ctc.

2.2 Offer Progression & Rejection

Strict One-Offer: Once a student holds an active countable offer, they are blocked from subsequent regular drives.
Dream Upgrade: A student holding a regular offer ($< 10\text{ LPA}$) is allowed to sit for a dream company drive ($\ge 10\text{ LPA}$).
Lateral Dream Moves: A student holding a dream offer of $15\text{ LPA}$ cannot sit for a $12\text{ LPA}$ drive (upward progression only).
Revoked Offers: A company revoking an offer frees the student, provided count_revoked_offers = false.
Declined Offers: Configurable toggle count_declined_offers: if true, turning down an on-campus offer counts against placement quota; if false, student remains unblocked.
Off-Campus Offers: Evaluated against toggle count_off_campus_offers (default: false, unverified external offers do not block students).

3. Conflict-Free Scheduling & Solver Bounds

3.1 Interval Invariants

No Overlapping Student Slots: A student cannot be scheduled in two interview panels or tests simultaneously: $$\forall s, \quad [start_{i}, end_{i}) \cap [start_{j}, end_{j}) = \emptyset$$
Transition Buffers: A mandatory 15-minute buffer is inserted when a student moves between physical buildings.
Lunch & Blackouts: All solver intervals respect college lunch hours (12:30 - 13:30) and pre-configured room blackout windows.