Paper Citation Record · LEDGER

Geometric Duality Between Constraints and Gauge Fields: Mirror Symmetry and Spencer Isomorphisms of Compatible Pairs on Principal Bundles

As of 12 August 2026, this Paper Citation Record lists 18 of 18 outbound references and 5 inbound Pith citation observations for arXiv:2506.00728.

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

pith.paper-citation-record.v1
2506.00728 v2

Coverage vector

measured 18 of 18 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T12:06:44.942468Z

measured 23 of 23 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+00:00

measured 5 of 5 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-07T12:07:42.812793Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-07T04:12:58.026843Z

Reference resolution

18 of 18 outbound references displayed

verified exact0
verified fuzzy9
unresolved9
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 44e1997e-b31b-4fea-a56a-33c7ce4849a9 · outbound

This paper cites Yeshiva University, Belfer Graduate School of Science, New York (1964).

Geometric Duality Between Constraints and Gauge Fields: Mirror Symmetry and Spencer Isomorphisms of Compatible Pairs on Principal Bundles Yeshiva University, Belfer Graduate School of Science, New York (1964)

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:06:47.636383Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation d37a216d-b18e-450b-8b61-7827e0b1428d · outbound

This paper cites an unresolved cited work.

Geometric Duality Between Constraints and Gauge Fields: Mirror Symmetry and Spencer Isomorphisms of Compatible Pairs on Principal Bundles Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:06:47.410746Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation d278f117-a50e-4ec1-b093-f1ee53b7ab78 · outbound

This paper cites Benjam- in/Cummings Publishing Company, Reading (1978).

Geometric Duality Between Constraints and Gauge Fields: Mirror Symmetry and Spencer Isomorphisms of Compatible Pairs on Principal Bundles Benjam- in/Cummings Publishing Company, Reading (1978)

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:06:47.277507Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 680ac7e3-89b6-4a16-afce-816269fe6727 · outbound

This paper cites Springer, New York (1989).

Geometric Duality Between Constraints and Gauge Fields: Mirror Symmetry and Spencer Isomorphisms of Compatible Pairs on Principal Bundles Springer, New York (1989)

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-07T12:06:43.800071Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a0caeea4-de50-4b86-ba58-5930366d6f33 · outbound

This paper cites an unresolved cited work.

Geometric Duality Between Constraints and Gauge Fields: Mirror Symmetry and Spencer Isomorphisms of Compatible Pairs on Principal Bundles Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:06:47.104466Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 421be545-d508-4cad-98e7-52ba0beaabac · outbound

This paper cites an unresolved cited work.

Geometric Duality Between Constraints and Gauge Fields: Mirror Symmetry and Spencer Isomorphisms of Compatible Pairs on Principal Bundles Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:06:46.911027Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation e3454c55-f16d-4892-a7b5-3186d94a892f · outbound

This paper cites Interscience Publishers, New York (1963).

Geometric Duality Between Constraints and Gauge Fields: Mirror Symmetry and Spencer Isomorphisms of Compatible Pairs on Principal Bundles Interscience Publishers, New York (1963)

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:06:46.717728Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 98d7de38-95a6-43b7-86f7-0fdb4c32e88d · outbound

This paper cites an unresolved cited work.

Geometric Duality Between Constraints and Gauge Fields: Mirror Symmetry and Spencer Isomorphisms of Compatible Pairs on Principal Bundles Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:06:46.543490Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 180b8dc9-a94d-4b2e-90f4-e936c52b18e9 · outbound

This paper cites an unresolved cited work.

Geometric Duality Between Constraints and Gauge Fields: Mirror Symmetry and Spencer Isomorphisms of Compatible Pairs on Principal Bundles Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:06:46.391556Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 3a94d0d0-0eb5-4386-9d3a-ca5f8d909dfe · outbound

This paper cites American Mathematical Society, Providence (1999).

Geometric Duality Between Constraints and Gauge Fields: Mirror Symmetry and Spencer Isomorphisms of Compatible Pairs on Principal Bundles American Mathematical Society, Providence (1999)

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:06:46.226078Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation c79e6118-faaa-4ef6-80df-93763d50bff3 · outbound

This paper cites Springer, New York (1991).

Geometric Duality Between Constraints and Gauge Fields: Mirror Symmetry and Spencer Isomorphisms of Compatible Pairs on Principal Bundles Springer, New York (1991)

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:06:46.059528Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation d2b424d6-dea8-47fd-a061-ec12683eb31d · outbound

This paper cites Hermann, Paris (1945).

Geometric Duality Between Constraints and Gauge Fields: Mirror Symmetry and Spencer Isomorphisms of Compatible Pairs on Principal Bundles Hermann, Paris (1945)

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:06:45.881096Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation eb22f02f-8a10-4ca6-9ed0-ea69b05d733a · outbound

This paper cites Cambridge University Press, Cambridge (1998).

Geometric Duality Between Constraints and Gauge Fields: Mirror Symmetry and Spencer Isomorphisms of Compatible Pairs on Principal Bundles Cambridge University Press, Cambridge (1998)

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:06:45.710313Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 2a93ca25-ab4e-4476-8d93-36e643a5aa0c · outbound

This paper cites an unresolved cited work.

Geometric Duality Between Constraints and Gauge Fields: Mirror Symmetry and Spencer Isomorphisms of Compatible Pairs on Principal Bundles Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:06:45.598997Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 24710e30-1cd6-4741-adef-d9fe09c54501 · outbound

This paper cites an unresolved cited work.

Geometric Duality Between Constraints and Gauge Fields: Mirror Symmetry and Spencer Isomorphisms of Compatible Pairs on Principal Bundles Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:06:45.454075Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 2eb6a87d-2023-470f-a396-19b8ae1d3c28 · outbound

This paper cites Springer, New York (1993).

Geometric Duality Between Constraints and Gauge Fields: Mirror Symmetry and Spencer Isomorphisms of Compatible Pairs on Principal Bundles Springer, New York (1993)

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:06:45.331519Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 7a014bf2-7fc8-4ca0-83ca-41290191c1be · outbound

This paper cites Springer, New York (2010).

Geometric Duality Between Constraints and Gauge Fields: Mirror Symmetry and Spencer Isomorphisms of Compatible Pairs on Principal Bundles Springer, New York (2010)

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:06:45.192665Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

Observation 41e2b58f-1574-4491-bdb8-5a9a7a309e5a · outbound

This paper cites Dynamical Geometric Theory of Principal Bundle Constrained Systems: Strong Transversality Conditions and Variational Framework for Gauge Field Coupling.

Geometric Duality Between Constraints and Gauge Fields: Mirror Symmetry and Spencer Isomorphisms of Compatible Pairs on Principal Bundles Dynamical Geometric Theory of Principal Bundle Constrained Systems: Strong Transversality Conditions and Variational Framework for Gauge Field Coupling

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-07T12:06:44.942468Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 36f05e03-a066-41cc-8acd-2dcf29062a96 · inbound

Constructing Two Metrics for Spencer Cohomology: Hodge Decomposition of Constrained Bundles cites this paper.

Constructing Two Metrics for Spencer Cohomology: Hodge Decomposition of Constrained Bundles Geometric Duality Between Constraints and Gauge Fields: Mirror Symmetry and Spencer Isomorphisms of Compatible Pairs on Principal Bundles

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-07T12:07:42.812793Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1610ce4c-3660-4efe-b0ae-a60ad5585116 · inbound

Mirror Symmetry of Spencer-Hodge Decompositions in Constrained Geometric Systems cites this paper.

Mirror Symmetry of Spencer-Hodge Decompositions in Constrained Geometric Systems Geometric Duality Between Constraints and Gauge Fields: Mirror Symmetry and Spencer Isomorphisms of Compatible Pairs on Principal Bundles

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-07T10:20:57.028821Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 718be92f-e621-4346-ba38-55616272d2c2 · inbound

Spencer-Riemann-Roch Theory: Mirror Symmetry of Hodge Decompositions and Characteristic Classes in Constrained Geometry cites this paper.

Spencer-Riemann-Roch Theory: Mirror Symmetry of Hodge Decompositions and Characteristic Classes in Constrained Geometry Geometric Duality Between Constraints and Gauge Fields: Mirror Symmetry and Spencer Isomorphisms of Compatible Pairs on Principal Bundles

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-07T10:20:48.552751Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3cf9e489-3f1a-4f17-a187-cb0c0aa29387 · inbound

Spencer Differential Degeneration Theory and Its Applications in Algebraic Geometry cites this paper.

Spencer Differential Degeneration Theory and Its Applications in Algebraic Geometry Geometric Duality Between Constraints and Gauge Fields: Mirror Symmetry and Spencer Isomorphisms of Compatible Pairs on Principal Bundles

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-07T05:40:43.297838Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3c00090f-a6c6-4969-b9b4-4b76b0555242 · inbound

Extension Research of Principal Bundle Constraint System Theory on Ricci-flat K\"ahler Manifolds cites this paper.

Extension Research of Principal Bundle Constraint System Theory on Ricci-flat K\"ahler Manifolds Geometric Duality Between Constraints and Gauge Fields: Mirror Symmetry and Spencer Isomorphisms of Compatible Pairs on Principal Bundles

Reference 24

Resolution: verified exact; local_arxiv, observed 2026-08-07T04:12:58.045090Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.