Caffeine Half-Life / Level Tracker

Inspectable records

Ledger state

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

Area

Biology, Medicine & Pharmacology (educational estimates only — every panel labeled not-medical-advice)

Tranche

tranche-6

Evidence ID

t6-069

Ledger rows

1

No ledger note is attached.

Review findings

The exponential half-life decay formula is standard for a simplified one-compartment, first-order elimination estimate, provided the adjustable half-life replaces the hard-coded 5 hr and all unit and dose-timing constraints are explicit. The four vectors use deterministic sampled plot points; no iterative solver is involved.

Formula and scope findings

• The displayed formula hard-codes a 5-hour half-life, while the inputs state that half-life is adjustable; it should be C(t)=Σ dose_i·(1/2)^((t−t_i)/H), where H is the supplied half-life.
• The model must define that only doses with t_i≤t contribute to the current level; otherwise future doses produce nonphysical pre-dose caffeine levels.
• “Level” is ambiguous: the formula computes estimated caffeine amount in the modeled compartment, in dose units such as mg, not concentration unless an additional volume parameter is supplied.
• The time-to-threshold algorithm must specify whether threshold crossing is evaluated only after the final logged dose or allows later scheduled doses, and whether “below” means strictly less than the threshold.

Unit assumptions

• dose_i is caffeine amount, assumed to be in milligrams; all doses must use the same amount unit.
• t, t_i, and H must use the same time unit. The examples below explicitly use hours or minutes.
• H must be positive and represents the elimination half-life in the same time unit as the timestamps.
• Doses are modeled as instantaneous absorption at t_i, with bioavailability equal to 1.
• The plotted quantity is estimated caffeine amount in the compartment, not blood concentration.

Boundary hardening

BREAK_CLAIMED · SELF_FLAGGED

A zero half-life produces an undefined division by zero, and evaluating the literal formula before an intake produces an extrapolated value outside the physical model domain. Inputs at or below the validity boundary should be rejected or explicitly flagged.

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": {
    "doses": [
      {
        "time_hr": 0,
        "dose_mg": 100
      }
    ],
    "half_life_hr": 5,
    "sample_times_hr": [
      0,
      5,
      10
    ],
    "threshold_mg": 10
  },
  "expected_outputs": {
    "sampled_points": [
      {
        "t_hr": 0,
        "y_mg": 100
      },
      {
        "t_hr": 5,
        "y_mg": 50
      },
      {
        "t_hr": 10,
        "y_mg": 25
      }
    ],
    "time_to_below_threshold_hr": 16.6096404744,
    "curve_features": {
      "finite_roots": [],
      "horizontal_asymptote_mg": 0,
      "dose_jump_at_hr": [
        0
      ]
    }
  },
  "working": "Use C(t)=100·2^(-(t−0)/5). At t=0: exponent=0, so C=100·2^0=100 mg. At t=5: exponent=−1, so C=100·(1/2)=50 mg. At t=10: exponent=−2, so C=100·(1/4)=25 mg. For the 10 mg crossing: 100·2^(−t/5)=10; 2^(−t/5)=0.1; −t/5=log2(0.1)=−3.32192809489; therefore t=5·3.32192809489=16.6096404744 hr. The curve remains positive for every finite t, so it has no finite root and approaches 0 mg."
}

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