Paper Citation Record · LEDGER

Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics

As of 21 August 2026, this Paper Citation Record lists 49 of 49 outbound references and 0 inbound Pith citation observations for arXiv:2601.19302.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2601.19302 v3

Coverage vector

measured 49 of 49 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-03T07:46:10.570732Z

measured 49 of 49 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

49 of 49 outbound references displayed

verified exact0
verified fuzzy0
unresolved47
parse uncertain0
malformed identifier2
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation c19e9e17-1965-4f51-bc33-341d64655b77 · outbound

This paper cites an unresolved cited work.

Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics Unresolved cited work

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-03T07:46:09.049512Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8c79b079-f5d9-4e60-ac84-3b1834f3b608 · outbound

This paper cites an unresolved cited work.

Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics Unresolved cited work

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-03T07:46:09.141662Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e4e72c04-cedb-42af-8ed4-b2dcd95dd646 · outbound

This paper cites an unresolved cited work.

Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics Unresolved cited work

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-03T07:46:09.205464Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 71521c50-cf3d-49ac-8e35-461a39f06bbe · outbound

This paper cites GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models.

Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-03T07:46:08.814889Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5d4383ee-5dfb-4f81-8d37-879ea8032e46 · outbound

This paper cites LLM-SR: Scientific Equation Discovery via Programming with Large Language Models.

Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics LLM-SR: Scientific Equation Discovery via Programming with Large Language Models

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-03T07:46:08.878538Z

Source-reported events for the cited work

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Observation e70bd923-5ffd-43f6-8ea9-2a48cc196516 · outbound

This paper cites SciBench: Evaluating College-Level Scientific Problem-Solving Abilities of Large Language Models.

Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics SciBench: Evaluating College-Level Scientific Problem-Solving Abilities of Large Language Models

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-03T07:46:08.919713Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9bbf999c-26dd-4536-8aa4-e8bcbc6b491f · outbound

This paper cites Formal Mathematical Reasoning: A New Frontier in AI.

Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics Formal Mathematical Reasoning: A New Frontier in AI

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-03T07:46:08.986721Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7775f59e-d9b4-45b1-8aed-edf91894d610 · outbound

This paper cites an unresolved cited work.

Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics Unresolved cited work

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-03T07:46:09.236888Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c5ad0309-a9d7-47d6-9f6c-1181d0bd399e · outbound

This paper cites So the final answer is {boxed_format}.

Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics So the final answer is {boxed_format}

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-03T07:46:09.299243Z

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Observation ab9e36a8-13a1-4efe-99a5-39f2c066c527 · outbound

This paper cites an unresolved cited work.

Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics Unresolved cited work

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-03T07:46:09.363919Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fe474382-1360-4d04-8827-c89441af2b0a · outbound

This paper cites an unresolved cited work.

Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics Unresolved cited work

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-03T07:46:09.449602Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation daa2393b-3d6d-466b-9f81-bb381a10086c · outbound

This paper cites F-1 User (Ours) {problem_statement} {answer_type_text} Please solve using an Equation-First approach:.

Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics F-1 User (Ours) {problem_statement} {answer_type_text} Please solve using an Equation-First approach:

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-03T07:46:09.478036Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7420cafa-c675-45c3-997a-8a449bfee85c · outbound

This paper cites an unresolved cited work.

Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics Unresolved cited work

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-03T07:46:09.538180Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1ca3ada5-426a-44f9-9d01-a6deaa38002c · outbound

This paper cites an unresolved cited work.

Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics Unresolved cited work

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-03T07:46:09.584240Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3ca91b18-245e-47f1-aa22-24a9e0f4cde4 · outbound

This paper cites - PoT: write Python code to implement the equations.

Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics - PoT: write Python code to implement the equations

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-03T07:46:09.648979Z

Source-reported events for the cited work

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Observation 60a71c83-0268-4bed-9b56-cdea49fd779f · outbound

This paper cites So the final answer is {boxed_format}.

Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics So the final answer is {boxed_format}

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-03T07:46:09.688179Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 55e7f000-eeec-4b52-b104-c85691771899 · outbound

This paper cites This mirrors expert problem-solving behavior and reduces ambigu- ity.

Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics This mirrors expert problem-solving behavior and reduces ambigu- ity

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-03T07:46:09.803430Z

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Observation c511bfd8-998b-4320-9d05-bbaddfe8c2e7 · outbound

This paper cites No explicit routing rules are imposed; the model freely rea- sons from equations to solution.

Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics No explicit routing rules are imposed; the model freely rea- sons from equations to solution

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-03T07:46:09.868005Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c93cca80-3f01-476d-80bf-c25f92c19aa0 · outbound

This paper cites B Token Efficiency Analysis This appendix provides detailed token efficiency analysis across models and benchmarks.

Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics B Token Efficiency Analysis This appendix provides detailed token efficiency analysis across models and benchmarks

Reference 22

Resolution: malformed identifier; no resolver link, observed 2026-08-03T07:46:09.931308Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a7fb6213-99ea-4c23-94b0-255fde0ade0c · outbound

This paper cites an unresolved cited work.

Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics Unresolved cited work

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-03T07:46:09.993364Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation eefa0d26-1e24-4ce8-85bd-3b1429aa51a4 · outbound

This paper cites Need to show: ∂X/∂x does not depend on x; ∂T /∂t does not depend ont.

Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics Need to show: ∂X/∂x does not depend on x; ∂T /∂t does not depend ont

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-03T07:46:10.050643Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 128dd1df-6112-425f-9e86-40c4509613ae · outbound

This paper cites Use this to relate X(x+a, t+b, v) to X(x, t, v)up to a constant.

Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics Use this to relate X(x+a, t+b, v) to X(x, t, v)up to a constant

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-03T07:46:10.102960Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 883f2671-3065-4c65-87c9-6328824d2aeb · outbound

This paper cites x: ∂X/∂x(x+a, t+ b, v) =∂X/∂x(x, t, v).

Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics x: ∂X/∂x(x+a, t+ b, v) =∂X/∂x(x, t, v)

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-03T07:46:10.166139Z

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Unavailable: canonical work link unavailable.

Observation 14fae993-897c-459a-ae44-ab74c960409e · outbound

This paper cites dX/dx =", dXdx) print(.

Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics dX/dx =", dXdx) print(

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-03T07:46:10.221802Z

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Unavailable: canonical work link unavailable.

Observation e58d3667-0279-459b-a1cd-af0721d97487 · outbound

This paper cites Numerically equivalent to showing ∂/∂x(∂X/∂x) = 0and∂/∂t(∂T /∂t) = 0.

Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics Numerically equivalent to showing ∂/∂x(∂X/∂x) = 0and∂/∂t(∂T /∂t) = 0

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-03T07:46:10.284356Z

Source-reported events for the cited work

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Observation 4def3d5a-fec4-4a0d-b093-9b30ce93377b · outbound

This paper cites T(x, t+ ∆, v)−T(x, t, v)depends only on ∆ and v (not onxort).

Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics T(x, t+ ∆, v)−T(x, t, v)depends only on ∆ and v (not onxort)

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-03T07:46:10.365040Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f04bef93-277c-4080-981b-cbf556050dbf · outbound

This paper cites Hence ∂X/∂x(x, t, v) = limh→0 f(h, v)/h=g(v) , independent ofx.

Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics Hence ∂X/∂x(x, t, v) = limh→0 f(h, v)/h=g(v) , independent ofx

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-03T07:46:10.435256Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 24678d8a-0332-42bd-bd7a-b231f2bd4d32 · outbound

This paper cites Correct Calculation, Wrong Format.

Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics Correct Calculation, Wrong Format

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-03T07:46:10.469409Z

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Observation 87e77871-d70d-443f-a733-fc81b3981242 · outbound

This paper cites an unresolved cited work.

Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics Unresolved cited work

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-03T07:46:10.493255Z

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Observation badd0360-f5af-43fa-92e8-aea970790301 · outbound

This paper cites an unresolved cited work.

Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics Unresolved cited work

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-03T07:46:10.497956Z

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Observation 9a835e32-a9f7-4dc5-b669-e1c8178f0af5 · outbound

This paper cites an unresolved cited work.

Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics Unresolved cited work

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-03T07:46:10.502395Z

Source-reported events for the cited work

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Observation 61d67ae6-2d44-42ab-855c-85bc62f8ff4e · outbound

This paper cites Correct Calculation, Wrong For- mat.

Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics Correct Calculation, Wrong For- mat

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-03T07:46:10.506776Z

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Observation ed697eff-2464-430c-bbd4-a698b720a9e6 · outbound

This paper cites an unresolved cited work.

Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics Unresolved cited work

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-03T07:46:10.511536Z

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Observation 46e96b16-200a-4721-b67f-c0a2e76a9efc · outbound

This paper cites an unresolved cited work.

Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics Unresolved cited work

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-03T07:46:10.515808Z

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Observation c5f20c82-ce34-404a-8d66-12d2fb242eba · outbound

This paper cites an unresolved cited work.

Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics Unresolved cited work

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-03T07:46:10.520036Z

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Observation 02a4dfda-77c2-4c96-8444-652125f2343c · outbound

This paper cites If F is a PRF , then for any fixed s, the distribution {f n k (s)}k←{0,1}n is computationally indistinguishable from uniform.

Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics If F is a PRF , then for any fixed s, the distribution {f n k (s)}k←{0,1}n is computationally indistinguishable from uniform

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-03T07:46:10.524297Z

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Observation 47ce29c6-c693-45bb-bf22-49154a8f8ba2 · outbound

This paper cites varying keys, fixed input.

Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics varying keys, fixed input

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-03T07:46:10.528658Z

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Observation 1b93e342-e9b3-42de-83de-7783934e0f87 · outbound

This paper cites an unresolved cited work.

Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics Unresolved cited work

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-03T07:46:10.534238Z

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Observation 487a5d1a-76b9-412e-9dc8-3424ac936989 · outbound

This paper cites an unresolved cited work.

Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics Unresolved cited work

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-03T07:46:10.538637Z

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Observation 7adc7329-0457-4a7b-93ac-a441e8e0a71c · outbound

This paper cites an unresolved cited work.

Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics Unresolved cited work

Reference 43

Resolution: unresolved; no resolver link, observed 2026-08-03T07:46:10.542893Z

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Observation 31eea6b6-8828-43ec-8b3e-50a6f1bd0932 · outbound

This paper cites an unresolved cited work.

Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics Unresolved cited work

Reference 44

Resolution: unresolved; no resolver link, observed 2026-08-03T07:46:10.548010Z

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Observation c2877dc3-73d4-4046-bd28-0bb329f1c011 · outbound

This paper cites an unresolved cited work.

Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics Unresolved cited work

Reference 45

Resolution: unresolved; no resolver link, observed 2026-08-03T07:46:10.552401Z

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Observation 114f1d87-d960-4006-b23c-df20e6469677 · outbound

This paper cites an unresolved cited work.

Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics Unresolved cited work

Reference 46

Resolution: unresolved; no resolver link, observed 2026-08-03T07:46:10.557107Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4fae2946-f889-4593-9583-0be7d5b77890 · outbound

This paper cites an unresolved cited work.

Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics Unresolved cited work

Reference 47

Resolution: unresolved; no resolver link, observed 2026-08-03T07:46:10.561823Z

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Unavailable: canonical work link unavailable.

Observation 73d39817-ac7b-454a-ab73-bf787364293b · outbound

This paper cites an unresolved cited work.

Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics Unresolved cited work

Reference 48

Resolution: unresolved; no resolver link, observed 2026-08-03T07:46:10.566532Z

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Unavailable: canonical work link unavailable.

Observation c8724dc4-aeef-4a09-99d7-e8aa8f283a36 · outbound

This paper cites an unresolved cited work.

Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics Unresolved cited work

Reference 49

Resolution: malformed identifier; no resolver link, observed 2026-08-03T07:46:10.570732Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4aed2986-1275-4cf7-8f69-2121a9fef0e1 · outbound

This paper cites Training Verifiers to Solve Math Word Problems.

Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics Training Verifiers to Solve Math Word Problems

Reference 2021

Resolution: unresolved; no resolver link, observed 2026-08-03T07:46:08.771900Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7110527b-f5c0-4411-81fa-639cd4bdab83 · outbound

This paper cites Large Language Models are Zero-Shot Reasoners.

Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics Large Language Models are Zero-Shot Reasoners

Reference 2024

Resolution: unresolved; no resolver link, observed 2026-08-03T07:46:08.788624Z

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Unavailable: canonical work link unavailable.

Observation 0ded48a7-d8ea-4e0d-b504-f230cf2c46fd · outbound

This paper cites In Proceedings of the 2025 Conference on Empirical Methods in Natural Language Processing, pages 35418–35442, Suzhou, China.

Formula-One Prompting: A Composable Equation-First Prefix for Applied Mathematics In Proceedings of the 2025 Conference on Empirical Methods in Natural Language Processing, pages 35418–35442, Suzhou, China

Reference 2025

Resolution: unresolved; no resolver link, observed 2026-08-03T07:46:08.798722Z

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Pith citing papers

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