Paper Citation Record · LEDGER

Transfinite Fixed Points in Alpay Algebra as Ordinal Game Equilibria in Dependent Type Theory

As of 18 August 2026, this Paper Citation Record lists 31 of 31 outbound references and 0 inbound Pith citation observations for arXiv:2507.19245.

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

pith.paper-citation-record.v1
2507.19245 v1

Coverage vector

measured 31 of 31 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T18:01:56.053613Z

measured 31 of 31 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+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

31 of 31 outbound references displayed

verified exact1
verified fuzzy7
unresolved21
parse uncertain0
malformed identifier1
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 10d25185-a34d-4e75-a437-a56ae206de73 · outbound

This paper cites Alpay Algebra: A Universal Structural Foundation.

Transfinite Fixed Points in Alpay Algebra as Ordinal Game Equilibria in Dependent Type Theory Alpay Algebra: A Universal Structural Foundation

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-15T18:01:55.910493Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 492e85e7-dbad-46d6-8c6c-42eef0090fdd · outbound

This paper cites an unresolved cited work.

Transfinite Fixed Points in Alpay Algebra as Ordinal Game Equilibria in Dependent Type Theory Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:01:56.886069Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 9a218ced-eb79-4941-ab38-af294b644660 · outbound

This paper cites Alpay Algebra II: Identity as Fixed-Point Emergence in Categorical Data.

Transfinite Fixed Points in Alpay Algebra as Ordinal Game Equilibria in Dependent Type Theory Alpay Algebra II: Identity as Fixed-Point Emergence in Categorical Data

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-15T18:01:55.920316Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f8349309-cc36-48ec-929b-bb49d7656db7 · outbound

This paper cites Alpay Algebra III: Observer-Coupled Collapse and the Temporal Drift of Identity.

Transfinite Fixed Points in Alpay Algebra as Ordinal Game Equilibria in Dependent Type Theory Alpay Algebra III: Observer-Coupled Collapse and the Temporal Drift of Identity

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-15T18:01:55.926920Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 40f0b39e-2513-4bff-9adb-6defac05343a · outbound

This paper cites an unresolved cited work.

Transfinite Fixed Points in Alpay Algebra as Ordinal Game Equilibria in Dependent Type Theory Unresolved cited work

Reference 5

Resolution: metadata mismatch; raw_fallback, observed 2026-08-15T18:01:56.318841Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 4e2fd8e7-e335-495a-8062-7922889c25fd · outbound

This paper cites Transordinal Fixed-Point Operators and Self-Referential Games: A Categorical Framework for Reflective Semantic Convergence.

Transfinite Fixed Points in Alpay Algebra as Ordinal Game Equilibria in Dependent Type Theory Transordinal Fixed-Point Operators and Self-Referential Games: A Categorical Framework for Reflective Semantic Convergence

Reference 6

Resolution: verified exact; local_arxiv, observed 2026-08-15T18:01:56.170924Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 77d05fb6-e211-4c4a-afed-56ca0fbab258 · outbound

This paper cites an unresolved cited work.

Transfinite Fixed Points in Alpay Algebra as Ordinal Game Equilibria in Dependent Type Theory Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:01:56.865412Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 746cd181-ab1e-40a8-b599-9d5581fc4361 · outbound

This paper cites an unresolved cited work.

Transfinite Fixed Points in Alpay Algebra as Ordinal Game Equilibria in Dependent Type Theory Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:01:56.845073Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 9f446337-872a-4ffd-961e-c68192a33042 · outbound

This paper cites (2004).Interactive Theorem Proving and Program Develop- ment.

Transfinite Fixed Points in Alpay Algebra as Ordinal Game Equilibria in Dependent Type Theory (2004).Interactive Theorem Proving and Program Develop- ment

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:01:56.827053Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation e9539f85-5037-43fc-95c3-a6fc6cc37662 · outbound

This paper cites (1968).Elements of Mathematics: Theory of Sets.

Transfinite Fixed Points in Alpay Algebra as Ordinal Game Equilibria in Dependent Type Theory (1968).Elements of Mathematics: Theory of Sets

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:01:56.799751Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation f93d6aa3-a4eb-445b-81ca-83be407fe263 · outbound

This paper cites an unresolved cited work.

Transfinite Fixed Points in Alpay Algebra as Ordinal Game Equilibria in Dependent Type Theory Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:01:56.776434Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 045d7201-4c50-47b0-a793-3d10323ad699 · outbound

This paper cites an unresolved cited work.

Transfinite Fixed Points in Alpay Algebra as Ordinal Game Equilibria in Dependent Type Theory Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:01:56.756389Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 8b5c0f27-58b7-4e9c-aca5-df4a9b24fc6b · outbound

This paper cites an unresolved cited work.

Transfinite Fixed Points in Alpay Algebra as Ordinal Game Equilibria in Dependent Type Theory Unresolved cited work

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-15T18:01:55.967309Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8105e11c-7151-4242-91e4-283216cc69d1 · outbound

This paper cites an unresolved cited work.

Transfinite Fixed Points in Alpay Algebra as Ordinal Game Equilibria in Dependent Type Theory Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:01:56.726575Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation c1238a51-75f4-4ee5-9200-94062be50d06 · outbound

This paper cites (1991).Game Theory.

Transfinite Fixed Points in Alpay Algebra as Ordinal Game Equilibria in Dependent Type Theory (1991).Game Theory

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:01:56.694326Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 18315873-a6f8-48bf-be62-17e8c5556c61 · outbound

This paper cites (1993).The Revision Theory of Truth.

Transfinite Fixed Points in Alpay Algebra as Ordinal Game Equilibria in Dependent Type Theory (1993).The Revision Theory of Truth

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:01:56.674664Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 16bfe6a0-dbea-4ded-b52b-95802debbae9 · outbound

This paper cites an unresolved cited work.

Transfinite Fixed Points in Alpay Algebra as Ordinal Game Equilibria in Dependent Type Theory Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:01:56.658800Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 1a4bbb61-4e63-455c-b8e2-b02e4c20fc98 · outbound

This paper cites Alpay Algebra V: Multi-Layered Semantic Games and Transfinite Fixed-Point Simulation.

Transfinite Fixed Points in Alpay Algebra as Ordinal Game Equilibria in Dependent Type Theory Alpay Algebra V: Multi-Layered Semantic Games and Transfinite Fixed-Point Simulation

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-15T18:01:55.987351Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d69497d6-c1d7-486c-a46a-6d28b8118bd8 · outbound

This paper cites Alpay Algebra IV: Symbiotic Semantics and the Fixed-Point Convergence of Observer Embeddings.

Transfinite Fixed Points in Alpay Algebra as Ordinal Game Equilibria in Dependent Type Theory Alpay Algebra IV: Symbiotic Semantics and the Fixed-Point Convergence of Observer Embeddings

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-15T18:01:55.991280Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5aa3a033-0182-4221-a425-df62f62a6125 · outbound

This paper cites an unresolved cited work.

Transfinite Fixed Points in Alpay Algebra as Ordinal Game Equilibria in Dependent Type Theory Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:01:56.640407Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation f66cb7a8-a065-4272-9902-c431e7341c08 · outbound

This paper cites an unresolved cited work.

Transfinite Fixed Points in Alpay Algebra as Ordinal Game Equilibria in Dependent Type Theory Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:01:56.622419Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 930014d5-f6d3-4adf-865f-bf00788c557c · outbound

This paper cites an unresolved cited work.

Transfinite Fixed Points in Alpay Algebra as Ordinal Game Equilibria in Dependent Type Theory Unresolved cited work

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-15T18:01:56.003461Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b92f9ade-ff2c-4afb-9d05-afc2a32c0ab3 · outbound

This paper cites an unresolved cited work.

Transfinite Fixed Points in Alpay Algebra as Ordinal Game Equilibria in Dependent Type Theory Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:01:56.601946Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation be7110f5-c762-47c9-aca4-8ce6e62de2c7 · outbound

This paper cites an unresolved cited work.

Transfinite Fixed Points in Alpay Algebra as Ordinal Game Equilibria in Dependent Type Theory Unresolved cited work

Reference 24

Resolution: malformed identifier; no resolver link, observed 2026-08-15T18:01:56.013076Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cb505a9e-fe0e-4874-a6a0-7078ce577abf · outbound

This paper cites (1986).Mathematics: Form and Function.

Transfinite Fixed Points in Alpay Algebra as Ordinal Game Equilibria in Dependent Type Theory (1986).Mathematics: Form and Function

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:01:56.582442Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 44b86333-6d21-44ff-a86f-476c63390834 · outbound

This paper cites (1984).Intuitionistic Type Theory.

Transfinite Fixed Points in Alpay Algebra as Ordinal Game Equilibria in Dependent Type Theory (1984).Intuitionistic Type Theory

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:01:56.559999Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 065a42ed-5864-4b17-a6ee-3c48127452ec · outbound

This paper cites an unresolved cited work.

Transfinite Fixed Points in Alpay Algebra as Ordinal Game Equilibria in Dependent Type Theory Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:01:56.534956Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 8747acfc-d8e2-47c6-8c1f-821475725697 · outbound

This paper cites an unresolved cited work.

Transfinite Fixed Points in Alpay Algebra as Ordinal Game Equilibria in Dependent Type Theory Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:01:56.513923Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 630a3687-949f-4c16-8cce-7c44cf0370ba · outbound

This paper cites (1990).Programming in Martin-L¨f’s Type Theory.

Transfinite Fixed Points in Alpay Algebra as Ordinal Game Equilibria in Dependent Type Theory (1990).Programming in Martin-L¨f’s Type Theory

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:01:56.484628Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 3848af03-2004-410e-b45a-f49fb2ab54e8 · outbound

This paper cites an unresolved cited work.

Transfinite Fixed Points in Alpay Algebra as Ordinal Game Equilibria in Dependent Type Theory Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:01:56.459013Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 3eba928b-1e3d-4478-9d2c-25b085ce83a9 · outbound

This paper cites an unresolved cited work.

Transfinite Fixed Points in Alpay Algebra as Ordinal Game Equilibria in Dependent Type Theory Unresolved cited work

Reference 31

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:01:56.433649Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Pith citing papers

No inbound Pith citation observations are available.