Reasonable care, duty scope, breach evidence, and a populated Hand-variable model. Firewall doctrine: render structure, refuse interpretation, cite, abstain, and hand off.

Structured Visual

Jurisdiction: US; as of 2026-08-28; not legal advice; Render structure, refuse interpretation, cite, abstain, and hand off.

RENDER STRUCTURE · REFUSE INTERPRETATION · CITE · ABSTAIN · HAND-OFF: render structure, refuse interpretation, cite provenance, abstain when unsupported, and hand off to human review.

Negligence duty-and-breach calculation: core questionsCore legal questionsGlance first; details follow in wordsDutyDutyBreachBreachHand variablesHand variablesOther evidenceOther evidence
highlighted = computed this step

Scope and honesty note

Jurisdiction: United States common-law overview with selected Texas statutory applications; as of 2026-08-28; jurisdictions and causes of action vary; not legal advice. Synthetic facts are classroom inputs, not findings. This lesson renders structure, refuses unsupported interpretation, cites, abstains, and hands off.

torts teaching model as of 2026−08−28\text{torts teaching model as of }2026-08-28

See the essential structure first

Start with this deliberately incomplete structure, then use the pinned authorities, worked application, exceptions, and handoff below. This deliberately incomplete preview has 5 nodes; exceptions and legal consequences remain in the sourced prose below.

glance nodes=5\text{glance nodes}=5

Jurisdiction: US; as of 2026-08-28; not legal advice; Render structure, refuse interpretation, cite, abstain, and hand off.

RENDER STRUCTURE · REFUSE INTERPRETATION · CITE · ABSTAIN · HAND-OFF: render structure, refuse interpretation, cite provenance, abstain when unsupported, and hand off to human review.

Negligence duty-and-breach calculation: core questionsCore legal questionsGlance first; details follow in wordsDutyDutyBreachBreachHand variablesHand variablesOther evidenceOther evidence

Begin with the governing doctrine

Negligence proceeds in order: duty, breach, actual causation, proximate causation, and damages. Duty asks whether law required this defendant to exercise care for this claimant and risk. Breach compares conduct with reasonable care under the circumstances. Custom and statutes can inform the standard but do not automatically settle every case. The Learned Hand formulation organizes precaution burden, probability, and expected loss; it is a reasoning aid rather than a universal algorithm or substitute for governing doctrine.

prima facie doctrine before defenses and allocation\text{prima facie doctrine before defenses and allocation}

Pin the Hand-variable passage

The bounded excerpt identifies probability, gravity of injury, and burden of adequate precautions; the snapshot's algebraic operator is visibly incomplete, so the lesson does not fabricate it as quoted text. Caption: United States v. Carroll Towing Co.; court: United States Court of Appeals for the Second Circuit; decision date: 1947-01-09. Verbatim opinion excerpt: “Since there are occasions when every vessel will break from her moorings, and since, if she does, she becomes a menace to those about her; the owner’s duty, as in other similar situations, to provide against resulting injuries is a function of three variables: (1) The probability that she will break away; (2) the gravity of the resulting injury, if she does; (3) the burden of adequate precautions. Possibly it serves to bring this notion into relief to state it in algebraic terms: if the probability be called P; the injury, L; and the burden, B; liability depends upon whether B is less than L multiplied by P: i. e., whether B PL.” Source: 159 F.2d 169; https://www.neochart.com/catalog/cases/f2d/volume_159/0169_01/index.html; data via neochart.com, snapshot 2026-08.

pinned authority: 159F.2d169\text{pinned authority: }159 F.2d 169

Pin relational duty and foreseeable risk

Cardozo's pinpointed sentence connects the reasonably perceived risk with the duty owed to persons within the range of apprehension. Caption: Palsgraf v. Long Island Railroad; court: New York Court of Appeals; decision date: 1928-05-29. Verbatim opinion excerpt: “The risk reasonably to be perceived defines the duty to be obeyed, and risk imports relation; it is risk to another or to others within the range of apprehension” Source: 248 N.Y. 339; pinpoint 248 N.Y. at 344; https://www.neochart.com/catalog/cases/ny/volume_248/0339_01/index.html; data via neochart.com, snapshot 2026-08.

pinned authority: 248N.Y.339\text{pinned authority: }248 N.Y. 339

Pin the synthetic fact pattern

A synthetic safety packet prices an inspection and guard precaution at four thousand dollars, models a five-percent release probability, and models a two-hundred-thousand-dollar loss if release occurs. The product is ten thousand dollars.

stated classroom facts, not findings\text{stated classroom facts, not findings}

Work the application

The model multiplies the entered probability by the entered loss and compares that classroom product with the entered burden. Because the product exceeds the burden, the arithmetic flags the precaution for breach analysis. It does not establish duty, admissibility, reasonableness, feasibility, governing law, or breach. Those questions remain attached to sources, context, custom, and competing precautions.

compare elements in order, preserve unknowns\text{compare elements in order, preserve unknowns}

Read the populated authority-and-fact record

The diagram contains real case coordinates and populated burden, probability, loss, product, duty, custom, feasibility, and abstention rows rather than a bare formula label. The rendered record contains 14 populated rows.

populated rows=14\text{populated rows}=14

Jurisdiction: US; as of 2026-08-28; not legal advice; Render structure, refuse interpretation, cite, abstain, and hand off.

RENDER STRUCTURE · REFUSE INTERPRETATION · CITE · ABSTAIN · HAND-OFF: render structure, refuse interpretation, cite provenance, abstain when unsupported, and hand off to human review.

Negligence duty-and-breach calculation: Authority recordsAuthority recordsVerbatim snapshot sources159 F.2d 169United States v. Carroll…248 N.Y. 339Palsgraf v. Long Island…
Negligence duty-and-breach calculation: Synthetic facts part 1Synthetic factsClassroom facts onlyPrecaution burden$4,000 inspection and guard…Probability0.05 modeled chance of…Loss magnitude$200,000 modeled harm if…
Negligence duty-and-breach calculation: Synthetic facts part 2Synthetic factsClassroom facts onlyExpected-loss product$10,000 classroom multiplication result
Negligence duty-and-breach calculation: Application trace part 1Application traceElements, limits, and unresolved…DutyRelationship, activity, foreseeability, statutes,…BreachCompare conduct with reasonable…Hand variablesBurden, probability, and loss…
Negligence duty-and-breach calculation: Application trace part 2Application traceElements, limits, and unresolved…Other evidenceCustom, statutes, emergencies, expertise,…

Read the complete record

The complete record keeps sources, stated facts, and questions for review separate. Authority records: Verbatim snapshot sources. 159 F.2d 169: United States v. Carroll Towing Co.. 248 N.Y. 339: Palsgraf v. Long Island Railroad. Synthetic facts: Classroom facts only. Precaution burden: $4,000 inspection and guard system. Probability: 0.05 modeled chance of release during the stated interval. Loss magnitude: $200,000 modeled harm if release occurs. Expected-loss product: $10,000 classroom multiplication result. Application trace: Elements, limits, and unresolved questions. Duty: Relationship, activity, foreseeability, statutes, policy, and jurisdiction define scope. Breach: Compare conduct with reasonable care under circumstances. Hand variables: Burden, probability, and loss organize evidence but do not decide breach. Other evidence: Custom, statutes, emergencies, expertise, and feasibility remain visible.

sources, stated facts, and open questions\text{sources, stated facts, and open questions}

Narrow summary

Establish duty first, then compare conduct with reasonable care; use risk arithmetic to expose assumptions, never to pronounce negligence.

cite, compare, abstain, hand off\text{cite, compare, abstain, hand off}