Paper Citation Record · LEDGER

Tokenization Constraints in LLMs: A Study of Symbolic and Arithmetic Reasoning Limits

As of 8 August 2026, this Paper Citation Record lists 18 of 18 outbound references and 2 inbound Pith citation observations for arXiv:2505.14178.

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

pith.paper-citation-record.v1
2505.14178 v1

Coverage vector

measured 18 of 18 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T15:42:30.992566Z

measured 20 of 20 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-03T20:57:34.809865Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

18 of 18 outbound references displayed

verified exact0
verified fuzzy6
unresolved11
parse uncertain0
malformed identifier1
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 0fd2d769-f78b-402d-a542-c744e32ca5bd · outbound

This paper cites an unresolved cited work.

Tokenization Constraints in LLMs: A Study of Symbolic and Arithmetic Reasoning Limits Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-07T15:42:34.329097Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 4599ca91-fec4-476c-b833-bd6250bbdbec · outbound

This paper cites an unresolved cited work.

Tokenization Constraints in LLMs: A Study of Symbolic and Arithmetic Reasoning Limits Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-07T15:42:34.165446Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation d7c2356c-6246-422d-9a59-72be59ec06a5 · outbound

This paper cites a” , “b” , “b.

Tokenization Constraints in LLMs: A Study of Symbolic and Arithmetic Reasoning Limits a” , “b” , “b

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:42:33.999514Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation e6476d0a-d3e3-4db7-b452-da293604d5b7 · outbound

This paper cites an unresolved cited work.

Tokenization Constraints in LLMs: A Study of Symbolic and Arithmetic Reasoning Limits Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-07T15:42:31.993750Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation a97b606c-5bb6-464e-ae8f-f944cae39813 · outbound

This paper cites an unresolved cited work.

Tokenization Constraints in LLMs: A Study of Symbolic and Arithmetic Reasoning Limits Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-07T15:42:33.811086Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation ce5ba346-b7b0-41e6-905a-9bcdb6f63868 · outbound

This paper cites an unresolved cited work.

Tokenization Constraints in LLMs: A Study of Symbolic and Arithmetic Reasoning Limits Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-07T15:42:33.625547Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 8a916dfa-2d24-48f0-bae0-59bc5255c32a · outbound

This paper cites Return the reversed string in a dictionary format with the key ‘Result’.

Tokenization Constraints in LLMs: A Study of Symbolic and Arithmetic Reasoning Limits Return the reversed string in a dictionary format with the key ‘Result’

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:42:33.452087Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 1833ae76-c53a-452e-a637-4d8a72a5c3ff · outbound

This paper cites an unresolved cited work.

Tokenization Constraints in LLMs: A Study of Symbolic and Arithmetic Reasoning Limits Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-07T15:42:33.281578Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 4d1baf38-30b9-49b6-98e9-7f2aba231b08 · outbound

This paper cites • Display both the original string (showing characters remaining) and sorted list after each step.

Tokenization Constraints in LLMs: A Study of Symbolic and Arithmetic Reasoning Limits • Display both the original string (showing characters remaining) and sorted list after each step

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:42:33.096786Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation deb91901-2131-47df-a905-2d878955e327 · outbound

This paper cites [‘2’, ‘C’, ‘s’, ‘U’, ‘4’, ‘b’, ‘S’, ‘c’].

Tokenization Constraints in LLMs: A Study of Symbolic and Arithmetic Reasoning Limits [‘2’, ‘C’, ‘s’, ‘U’, ‘4’, ‘b’, ‘S’, ‘c’]

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:42:32.945155Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 0bdd95e1-3c24-487d-8c8c-181e45b8b636 · outbound

This paper cites an unresolved cited work.

Tokenization Constraints in LLMs: A Study of Symbolic and Arithmetic Reasoning Limits Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-07T15:42:32.770577Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation d6a46889-2e36-49e5-a28c-498b497d3253 · outbound

This paper cites an unresolved cited work.

Tokenization Constraints in LLMs: A Study of Symbolic and Arithmetic Reasoning Limits Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-07T15:42:32.346146Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 9951f03c-776a-4859-8a00-1eac9333f226 · outbound

This paper cites an unresolved cited work.

Tokenization Constraints in LLMs: A Study of Symbolic and Arithmetic Reasoning Limits Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-07T15:42:32.596771Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 0d5054d6-b0bc-49c2-a0d4-2b0d59c4bdd8 · outbound

This paper cites - Index 0: The element is ‘a’.

Tokenization Constraints in LLMs: A Study of Symbolic and Arithmetic Reasoning Limits - Index 0: The element is ‘a’

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:42:31.554965Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 68b6f79e-f1ea-4815-a292-33528bda2dc8 · outbound

This paper cites Result: 13 Correct Answer: 13 Table 22: Case Study 10 - Correct Prediction with GPT-4o mini (CoT prompt).

Tokenization Constraints in LLMs: A Study of Symbolic and Arithmetic Reasoning Limits Result: 13 Correct Answer: 13 Table 22: Case Study 10 - Correct Prediction with GPT-4o mini (CoT prompt)

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T15:42:31.228216Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 2ae0fda0-8c58-48b0-9b04-203c46098115 · outbound

This paper cites Neural Networks and the Chomsky Hierarchy.

Tokenization Constraints in LLMs: A Study of Symbolic and Arithmetic Reasoning Limits Neural Networks and the Chomsky Hierarchy

Reference 2022

Resolution: unresolved; no resolver link, observed 2026-08-07T15:42:28.200668Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6feea5cd-36db-42ea-a4f4-0d89669d7c94 · outbound

This paper cites RWKV: Reinventing RNNs for the Transformer Era.

Tokenization Constraints in LLMs: A Study of Symbolic and Arithmetic Reasoning Limits RWKV: Reinventing RNNs for the Transformer Era

Reference 2023

Resolution: unresolved; no resolver link, observed 2026-08-07T15:42:28.279603Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7028bbcc-3cde-44af-b79c-dc5efc31fd6f · outbound

This paper cites Transformers, parallel computation, and logarithmic depth.

Tokenization Constraints in LLMs: A Study of Symbolic and Arithmetic Reasoning Limits Transformers, parallel computation, and logarithmic depth

Reference 2024

Resolution: malformed identifier; no resolver link, observed 2026-08-07T15:42:28.502494Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 5a23bd02-de57-4bad-8d6a-0955155e1b6b · inbound

VisReason: A Large-Scale Dataset for Visual Chain-of-Thought Reasoning cites this paper.

VisReason: A Large-Scale Dataset for Visual Chain-of-Thought Reasoning Tokenization Constraints in LLMs: A Study of Symbolic and Arithmetic Reasoning Limits

Reference 66

Resolution: unresolved; no resolver link, observed 2026-08-03T20:57:34.809865Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 844f0711-4dbc-48fc-901b-c256293197f7 · inbound

The Effect of Scripts and Formats on LLM Numeracy cites this paper.

The Effect of Scripts and Formats on LLM Numeracy Tokenization Constraints in LLMs: A Study of Symbolic and Arithmetic Reasoning Limits

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-03T08:58:51.627099Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.