Triple

T6802007

Position	Surface form	Disambiguated ID	Type / Status
Subject	On the Measurement of the Circle	`E156207`	entity
Predicate	relatedTo	`P37`	FINISHED
Object	Method of Exhaustion The Method of Exhaustion is an ancient Greek technique, developed notably by Eudoxus and used by Archimedes, for finding areas and volumes by inscribing and circumscribing sequences of shapes that increasingly approximate a figure, anticipating the principles of integral calculus.	`E620682`	NE FINISHED

How this triple was built (4 steps)

Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.

NER Named-entity recognition gpt-5-mini

Instruction

Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).

Input

Phrase: Method of Exhaustion | Statement: [On the Measurement of the Circle, relatedTo, Method of Exhaustion]

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: Method of Exhaustion
Context triple: [On the Measurement of the Circle, relatedTo, Method of Exhaustion]

A. Quadrature of the Parabola
Quadrature of the Parabola is a treatise by Archimedes in which he determines the area of a parabolic segment using an early form of infinite series and geometric summation.
B. On the Measurement of the Circle
On the Measurement of the Circle is a mathematical treatise by Archimedes in which he rigorously approximates the value of π and explores properties of circles.
C. Riemann sums
Riemann sums are a fundamental method in calculus for approximating the area under a curve by summing the areas of a sequence of rectangles, forming the basis of the definition of the definite integral.
D. The Method of Mechanical Theorems
The Method of Mechanical Theorems is a treatise by Archimedes in which he uses heuristic mechanical arguments, involving balances and centers of mass, to discover and justify results in geometry and calculus-like area and volume calculations.
E. Simpson's rule
Simpson's rule is a numerical integration technique that approximates the area under a curve by fitting parabolas through groups of data points.
F. None of above. chosen
G. Unsure - the case is ambiguous/there is not enough information to decide.

NEDg Description generation gpt-5.1

Instruction

Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"

Input

Entity: Method of Exhaustion
Triple: [On the Measurement of the Circle, relatedTo, Method of Exhaustion]

Generated description

The Method of Exhaustion is an ancient Greek technique, developed notably by Eudoxus and used by Archimedes, for finding areas and volumes by inscribing and circumscribing sequences of shapes that increasingly approximate a figure, anticipating the principles of integral calculus.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

Target entity: Method of Exhaustion
Target entity description: The Method of Exhaustion is an ancient Greek technique, developed notably by Eudoxus and used by Archimedes, for finding areas and volumes by inscribing and circumscribing sequences of shapes that increasingly approximate a figure, anticipating the principles of integral calculus.

A. Quadrature of the Parabola
Quadrature of the Parabola is a treatise by Archimedes in which he determines the area of a parabolic segment using an early form of infinite series and geometric summation.
B. On the Measurement of the Circle
On the Measurement of the Circle is a mathematical treatise by Archimedes in which he rigorously approximates the value of π and explores properties of circles.
C. Riemann sums
Riemann sums are a fundamental method in calculus for approximating the area under a curve by summing the areas of a sequence of rectangles, forming the basis of the definition of the definite integral.
D. The Method of Mechanical Theorems
The Method of Mechanical Theorems is a treatise by Archimedes in which he uses heuristic mechanical arguments, involving balances and centers of mass, to discover and justify results in geometry and calculus-like area and volume calculations.
E. Simpson's rule
Simpson's rule is a numerical integration technique that approximates the area under a curve by fitting parabolas through groups of data points.
F. None of above. chosen

Provenance (5 batches)

The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.

Step	Stage	Batch ID	Status	When
creating	Elicitation	`batch_69c68826e6a48190a3d220b541e639de`	completed	March 27, 2026, 1:37 p.m.
NER	Named-entity recognition	`batch_69c6d2e714d4819084c8109c4de7de72`	completed	March 27, 2026, 6:56 p.m.
NED1	Entity disambiguation (via context triple)	`batch_69c71a9b0cc48190819380aeaf0228e7`	completed	March 28, 2026, 12:02 a.m.
NEDg	Description generation	`batch_69c71d64c2fc8190abda8b5a0f57291b`	completed	March 28, 2026, 12:14 a.m.
NED2	Entity disambiguation (via description)	`batch_69c71f3d4b8081908768c79642266431`	completed	March 28, 2026, 12:22 a.m.

Created at: March 27, 2026, 2:16 p.m.