Paper Citation Record · LEDGER

Why Pure Reasoning is Not Enough: Nature as the Source of Mathematical Innovation

As of 16 August 2026, this Paper Citation Record lists 34 of 34 outbound references and 0 inbound Pith citation observations for arXiv:2607.04505.

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

pith.paper-citation-record.v1
2607.04505 v1

Coverage vector

measured 34 of 34 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-11T18:26:00.157194Z

measured 34 of 34 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+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

34 of 34 outbound references displayed

verified exact0
verified fuzzy0
unresolved34
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 56d7d9f9-f9e9-4a58-a35f-9ff814360e33 · outbound

This paper cites le Rond d’Alembert.

Why Pure Reasoning is Not Enough: Nature as the Source of Mathematical Innovation le Rond d’Alembert

Reference 1

Resolution: unresolved; no resolver link, observed 2026-07-11T18:26:00.157194Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 999d2165-4f4c-4519-9b1e-756f060b9b97 · outbound

This paper cites Bernoulli.

Why Pure Reasoning is Not Enough: Nature as the Source of Mathematical Innovation Bernoulli

Reference 2

Resolution: unresolved; no resolver link, observed 2026-07-11T18:26:00.157194Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 28794e27-17d2-458d-a10c-59d32dc23f67 · outbound

This paper cites an unresolved cited work.

Why Pure Reasoning is Not Enough: Nature as the Source of Mathematical Innovation Unresolved cited work

Reference 3

Resolution: unresolved; no resolver link, observed 2026-07-11T18:26:00.157194Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 79178691-7359-4ef4-bb91-9bb8003a2236 · outbound

This paper cites Lagrange.

Why Pure Reasoning is Not Enough: Nature as the Source of Mathematical Innovation Lagrange

Reference 4

Resolution: unresolved; no resolver link, observed 2026-07-11T18:26:00.157194Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3ee6d003-8fc9-4cd5-94b9-c05d24f1a6af · outbound

This paper cites an unresolved cited work.

Why Pure Reasoning is Not Enough: Nature as the Source of Mathematical Innovation Unresolved cited work

Reference 5

Resolution: unresolved; no resolver link, observed 2026-07-11T18:26:00.157194Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b5ebd34e-7648-4315-9aa5-db8ac948b24d · outbound

This paper cites an unresolved cited work.

Why Pure Reasoning is Not Enough: Nature as the Source of Mathematical Innovation Unresolved cited work

Reference 6

Resolution: unresolved; no resolver link, observed 2026-07-11T18:26:00.157194Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a5e737d4-2d08-4431-8783-f4eb430d05f7 · outbound

This paper cites Kline.Mathematical Thought from Ancient to Modern Times.

Why Pure Reasoning is Not Enough: Nature as the Source of Mathematical Innovation Kline.Mathematical Thought from Ancient to Modern Times

Reference 7

Resolution: unresolved; no resolver link, observed 2026-07-11T18:26:00.157194Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation eb7bb50a-6acb-400c-9f73-a073f0b2db67 · outbound

This paper cites Dreams of a Final Theory.

Why Pure Reasoning is Not Enough: Nature as the Source of Mathematical Innovation Dreams of a Final Theory

Reference 8

Resolution: unresolved; no resolver link, observed 2026-07-11T18:26:00.157194Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1da83ba3-9048-44e4-bbb9-a3bce9462f09 · outbound

This paper cites Anthropic principle.

Why Pure Reasoning is Not Enough: Nature as the Source of Mathematical Innovation Anthropic principle

Reference 9

Resolution: unresolved; no resolver link, observed 2026-07-11T18:26:00.157194Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 13a6786f-87a0-4f29-8e6a-7e326be469a6 · outbound

This paper cites The Anthropic Landscape of String Theory.

Why Pure Reasoning is Not Enough: Nature as the Source of Mathematical Innovation The Anthropic Landscape of String Theory

Reference 10

Resolution: unresolved; no resolver link, observed 2026-07-11T18:26:00.157194Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5f6e9dd4-129e-417a-93b4-b805cdc8e21e · outbound

This paper cites Grassmann.Die lineale Ausdehnungslehre, ein neuer Zweig der Mathematik.

Why Pure Reasoning is Not Enough: Nature as the Source of Mathematical Innovation Grassmann.Die lineale Ausdehnungslehre, ein neuer Zweig der Mathematik

Reference 11

Resolution: unresolved; no resolver link, observed 2026-07-11T18:26:00.157194Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bd3f186b-7e82-46d3-b758-78c7b76e05aa · outbound

This paper cites an unresolved cited work.

Why Pure Reasoning is Not Enough: Nature as the Source of Mathematical Innovation Unresolved cited work

Reference 12

Resolution: unresolved; no resolver link, observed 2026-07-11T18:26:00.157194Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 43dede07-551b-4841-8bb7-248deac6259e · outbound

This paper cites Fourier.Théorie analytique de la chaleur.

Why Pure Reasoning is Not Enough: Nature as the Source of Mathematical Innovation Fourier.Théorie analytique de la chaleur

Reference 13

Resolution: unresolved; no resolver link, observed 2026-07-11T18:26:00.157194Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2cb5a1c8-25b0-4620-a03a-772e498167f0 · outbound

This paper cites an unresolved cited work.

Why Pure Reasoning is Not Enough: Nature as the Source of Mathematical Innovation Unresolved cited work

Reference 14

Resolution: unresolved; no resolver link, observed 2026-07-11T18:26:00.157194Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ca5e0529-0f44-4dab-a31a-7a4fdf4eb7b1 · outbound

This paper cites ÜberdieDarstellbarkeit einer Functiondurcheine trigonometrische Reihe.

Why Pure Reasoning is Not Enough: Nature as the Source of Mathematical Innovation ÜberdieDarstellbarkeit einer Functiondurcheine trigonometrische Reihe

Reference 15

Resolution: unresolved; no resolver link, observed 2026-07-11T18:26:00.157194Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 69cf5c7b-b350-4740-a760-948398587b28 · outbound

This paper cites ÜberdieAusdehnungeinesSatzesausderTheoriedertrigonometrischenReihen.

Why Pure Reasoning is Not Enough: Nature as the Source of Mathematical Innovation ÜberdieAusdehnungeinesSatzesausderTheoriedertrigonometrischenReihen

Reference 16

Resolution: unresolved; no resolver link, observed 2026-07-11T18:26:00.157194Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1a9f5002-e778-4cc3-bd2a-da936a9669d5 · outbound

This paper cites Lebesgue.

Why Pure Reasoning is Not Enough: Nature as the Source of Mathematical Innovation Lebesgue

Reference 17

Resolution: unresolved; no resolver link, observed 2026-07-11T18:26:00.157194Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d3eff885-0e18-413a-9130-cce2c0d575ba · outbound

This paper cites Schwartz.Théorie des distributions.

Why Pure Reasoning is Not Enough: Nature as the Source of Mathematical Innovation Schwartz.Théorie des distributions

Reference 18

Resolution: unresolved; no resolver link, observed 2026-07-11T18:26:00.157194Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fe45466c-1ead-4d42-ba7e-91f9e011a8f2 · outbound

This paper cites an unresolved cited work.

Why Pure Reasoning is Not Enough: Nature as the Source of Mathematical Innovation Unresolved cited work

Reference 19

Resolution: unresolved; no resolver link, observed 2026-07-11T18:26:00.157194Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a01e05db-9788-43f1-961c-42f7dd7c0f7a · outbound

This paper cites an unresolved cited work.

Why Pure Reasoning is Not Enough: Nature as the Source of Mathematical Innovation Unresolved cited work

Reference 20

Resolution: unresolved; no resolver link, observed 2026-07-11T18:26:00.157194Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a84b2525-93e3-4acc-8547-de02ba3c5aa4 · outbound

This paper cites an unresolved cited work.

Why Pure Reasoning is Not Enough: Nature as the Source of Mathematical Innovation Unresolved cited work

Reference 21

Resolution: unresolved; no resolver link, observed 2026-07-11T18:26:00.157194Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f1a85c72-6e81-4f63-b366-50cb4ad60bdf · outbound

This paper cites an unresolved cited work.

Why Pure Reasoning is Not Enough: Nature as the Source of Mathematical Innovation Unresolved cited work

Reference 22

Resolution: unresolved; no resolver link, observed 2026-07-11T18:26:00.157194Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2a0b8ad2-e74a-4009-8312-861e9c20b9e6 · outbound

This paper cites an unresolved cited work.

Why Pure Reasoning is Not Enough: Nature as the Source of Mathematical Innovation Unresolved cited work

Reference 23

Resolution: unresolved; no resolver link, observed 2026-07-11T18:26:00.157194Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8d764cbb-91b7-4cdb-9d19-d66f6d45750c · outbound

This paper cites an unresolved cited work.

Why Pure Reasoning is Not Enough: Nature as the Source of Mathematical Innovation Unresolved cited work

Reference 24

Resolution: unresolved; no resolver link, observed 2026-07-11T18:26:00.157194Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b24a34af-2b11-4d75-8ce7-85440050bae4 · outbound

This paper cites Complexity of the first-order theory of almost all finite struc- tures.

Why Pure Reasoning is Not Enough: Nature as the Source of Mathematical Innovation Complexity of the first-order theory of almost all finite struc- tures

Reference 25

Resolution: unresolved; no resolver link, observed 2026-07-11T18:26:00.157194Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 719210a0-007e-4d52-890e-cc01f25e4d4e · outbound

This paper cites an unresolved cited work.

Why Pure Reasoning is Not Enough: Nature as the Source of Mathematical Innovation Unresolved cited work

Reference 26

Resolution: unresolved; no resolver link, observed 2026-07-11T18:26:00.157194Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 99181281-f9e6-472f-a5ab-55e161ef65cb · outbound

This paper cites The Complexity of Theorem-Proving Procedures.

Why Pure Reasoning is Not Enough: Nature as the Source of Mathematical Innovation The Complexity of Theorem-Proving Procedures

Reference 27

Resolution: unresolved; no resolver link, observed 2026-07-11T18:26:00.157194Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fc3dc97b-5ed1-45ca-89e3-f7979bdbdd99 · outbound

This paper cites Kepler.Astronomia Nova.

Why Pure Reasoning is Not Enough: Nature as the Source of Mathematical Innovation Kepler.Astronomia Nova

Reference 28

Resolution: unresolved; no resolver link, observed 2026-07-11T18:26:00.157194Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f08508da-33fc-4c6f-b5da-b48217935185 · outbound

This paper cites Caspar.Kepler.

Why Pure Reasoning is Not Enough: Nature as the Source of Mathematical Innovation Caspar.Kepler

Reference 29

Resolution: unresolved; no resolver link, observed 2026-07-11T18:26:00.157194Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4780be03-0afc-4a10-9b0e-5251c5514b6c · outbound

This paper cites an unresolved cited work.

Why Pure Reasoning is Not Enough: Nature as the Source of Mathematical Innovation Unresolved cited work

Reference 30

Resolution: unresolved; no resolver link, observed 2026-07-11T18:26:00.157194Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fd0e08f7-d27e-451a-a81e-ba66da699916 · outbound

This paper cites Stephenson.Kepler’s Physical Astronomy.

Why Pure Reasoning is Not Enough: Nature as the Source of Mathematical Innovation Stephenson.Kepler’s Physical Astronomy

Reference 31

Resolution: unresolved; no resolver link, observed 2026-07-11T18:26:00.157194Z

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Unavailable: canonical work link unavailable.

Observation 63f33dec-dd97-47f0-85a4-09ca132d2287 · outbound

This paper cites Gilbert.De Magnete.

Why Pure Reasoning is Not Enough: Nature as the Source of Mathematical Innovation Gilbert.De Magnete

Reference 32

Resolution: unresolved; no resolver link, observed 2026-07-11T18:26:00.157194Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cf261ed1-5940-43b4-bd19-eecc6bb44813 · outbound

This paper cites Beltrami.

Why Pure Reasoning is Not Enough: Nature as the Source of Mathematical Innovation Beltrami

Reference 33

Resolution: unresolved; no resolver link, observed 2026-07-11T18:26:00.157194Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5bc96b56-6c0b-4add-bb3b-7ad2af4a9ea0 · outbound

This paper cites analytic.

Why Pure Reasoning is Not Enough: Nature as the Source of Mathematical Innovation analytic

Reference 34

Resolution: unresolved; no resolver link, observed 2026-07-11T18:26:00.157194Z

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Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.