Paper Citation Record · LEDGER

Spencer Differential Degeneration Theory and Its Applications in Algebraic Geometry

As of 11 August 2026, this Paper Citation Record lists 25 of 25 outbound references and 2 inbound Pith citation observations for arXiv:2506.07410.

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

pith.paper-citation-record.v1
2506.07410 v2

Coverage vector

measured 25 of 25 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T05:40:43.310354Z

measured 27 of 27 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-11T06:34:44.6726+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-07T04:12:57.883488Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-07T00:51:34.587882Z

Reference resolution

25 of 25 outbound references displayed

verified exact0
verified fuzzy12
unresolved13
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 99222ae1-14f8-4883-9dff-9bcf14784e29 · outbound

This paper cites an unresolved cited work.

Spencer Differential Degeneration Theory and Its Applications in Algebraic Geometry Unresolved cited work

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-07T05:40:43.221502Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1f8db4a7-b9a7-409a-81ef-54c08c878e01 · outbound

This paper cites Atiyah and Isadore M.

Spencer Differential Degeneration Theory and Its Applications in Algebraic Geometry Atiyah and Isadore M

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-07T05:40:43.225575Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e9093735-c13c-4d4f-903c-d00e8dfdb2bd · outbound

This paper cites an unresolved cited work.

Spencer Differential Degeneration Theory and Its Applications in Algebraic Geometry Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:40:43.608161Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation d688f39a-468a-4ce7-b03e-4732515aa234 · outbound

This paper cites Géométrie des surfaces K3: modules et périodes , volume 126.

Spencer Differential Degeneration Theory and Its Applications in Algebraic Geometry Géométrie des surfaces K3: modules et périodes , volume 126

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:40:43.598540Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation e477c6e3-a454-43dd-88b1-3f9691c573fa · outbound

This paper cites Barth, Klaus Hulek, Chris A.

Spencer Differential Degeneration Theory and Its Applications in Algebraic Geometry Barth, Klaus Hulek, Chris A

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:40:43.588288Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 5964cd58-748e-4a70-9f9e-5eef1877b85d · outbound

This paper cites Le théorème de riemann-roch.

Spencer Differential Degeneration Theory and Its Applications in Algebraic Geometry Le théorème de riemann-roch

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:40:43.578761Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation fb925a8e-3769-4a4f-a328-26c2a6498bc7 · outbound

This paper cites Characteristic classes of hermitian manifolds.

Spencer Differential Degeneration Theory and Its Applications in Algebraic Geometry Characteristic classes of hermitian manifolds

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:40:43.569326Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation fbe4075c-d4be-4514-8858-edab51a92bad · outbound

This paper cites Sur l'analysis situs des variétés à n dimensions , volume 10.

Spencer Differential Degeneration Theory and Its Applications in Algebraic Geometry Sur l'analysis situs des variétés à n dimensions , volume 10

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:40:43.559369Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation d04e802f-5d65-4587-86fa-401be9660681 · outbound

This paper cites Variétés différentiables.

Spencer Differential Degeneration Theory and Its Applications in Algebraic Geometry Variétés différentiables

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:40:43.548515Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 134ed6d4-2813-494a-a249-b711b149e299 · outbound

This paper cites Principles of Algebraic Geometry.

Spencer Differential Degeneration Theory and Its Applications in Algebraic Geometry Principles of Algebraic Geometry

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:40:43.538742Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 914a8eb0-dddd-4324-b423-9eb8deea42ef · outbound

This paper cites Éléments de géométrie algébrique ii.

Spencer Differential Degeneration Theory and Its Applications in Algebraic Geometry Éléments de géométrie algébrique ii

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:40:43.527963Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 8adac75a-3ec8-49ee-87f4-932ddd921ee0 · outbound

This paper cites an unresolved cited work.

Spencer Differential Degeneration Theory and Its Applications in Algebraic Geometry Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:40:43.517939Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 42c13ad8-7672-4223-9842-ee8b983d3305 · outbound

This paper cites Foundations of Differential Geometry , volume 1.

Spencer Differential Degeneration Theory and Its Applications in Algebraic Geometry Foundations of Differential Geometry , volume 1

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:40:43.507078Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 8b669c12-2bdd-4ffc-b540-25cd8f238afb · outbound

This paper cites L'analysis situs et la géométrie algébrique.

Spencer Differential Degeneration Theory and Its Applications in Algebraic Geometry L'analysis situs et la géométrie algébrique

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:40:43.496445Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation cb46417e-a9e8-451e-a312-7941c6d6f209 · outbound

This paper cites an unresolved cited work.

Spencer Differential Degeneration Theory and Its Applications in Algebraic Geometry Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:40:43.486381Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 8cbdfd64-94d6-4d55-999b-a907d94e80c4 · outbound

This paper cites Theorie der Abel'schen Funktionen.

Spencer Differential Degeneration Theory and Its Applications in Algebraic Geometry Theorie der Abel'schen Funktionen

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:40:43.476254Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation aff22a11-20ad-4a80-bfb9-2a8cff51da62 · outbound

This paper cites Géométrie algébrique et géométrie analytique.

Spencer Differential Degeneration Theory and Its Applications in Algebraic Geometry Géométrie algébrique et géométrie analytique

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T05:40:43.465986Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation ef75a40a-b79a-4ab8-8fc6-43a810d01661 · outbound

This paper cites an unresolved cited work.

Spencer Differential Degeneration Theory and Its Applications in Algebraic Geometry Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-07T05:40:43.453124Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 5cab8847-a1d3-40bf-84fa-3c1fb3819649 · outbound

This paper cites an unresolved cited work.

Spencer Differential Degeneration Theory and Its Applications in Algebraic Geometry Unresolved cited work

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-07T05:40:43.286143Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3d1cf8c8-cb2e-4720-a69d-94ca11f93187 · outbound

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

Spencer Differential Degeneration Theory and Its Applications in Algebraic Geometry Constructing Two Metrics for Spencer Cohomology: Hodge Decomposition of Constrained Bundles

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-07T05:40:43.289682Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7a536ba5-d95e-421a-acb1-edede85ee38c · outbound

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

Spencer Differential Degeneration Theory and Its Applications in Algebraic Geometry Dynamical Geometric Theory of Principal Bundle Constrained Systems: Strong Transversality Conditions and Variational Framework for Gauge Field Coupling

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-07T05:40:43.294098Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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

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

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 4251e54c-d06f-4a08-9361-96667c80cdec · outbound

This paper cites Mirror symmetry in geometric constraints: Analytic and riemann-roch perspectives.

Spencer Differential Degeneration Theory and Its Applications in Algebraic Geometry Mirror symmetry in geometric constraints: Analytic and riemann-roch perspectives

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-07T05:40:43.301413Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 455d96d3-c3d0-49bf-81b0-1b0e8a1e8990 · outbound

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

Spencer Differential Degeneration Theory and Its Applications in Algebraic Geometry Mirror Symmetry of Spencer-Hodge Decompositions in Constrained Geometric Systems

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-07T05:40:43.305649Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 82408e61-bba7-46a1-9650-57e66aafd3bc · outbound

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

Spencer Differential Degeneration Theory and Its Applications in Algebraic Geometry Spencer-Riemann-Roch Theory: Mirror Symmetry of Hodge Decompositions and Characteristic Classes in Constrained Geometry

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-07T05:40:43.310354Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 0977d15a-55cb-42b4-8431-d82282e22d2b · 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 Spencer Differential Degeneration Theory and Its Applications in Algebraic Geometry

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-07T04:12:57.883488Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation eaef98b3-5299-4f59-868b-1821681fa827 · inbound

The Rigidity of Constraint: A Spencer-Hodge Theoretic Approach to the Hodge Conjecture cites this paper.

The Rigidity of Constraint: A Spencer-Hodge Theoretic Approach to the Hodge Conjecture Spencer Differential Degeneration Theory and Its Applications in Algebraic Geometry

Reference 30

Resolution: verified exact; local_arxiv, observed 2026-08-07T00:51:34.591495Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.