Paper Citation Record · LEDGER

Constructing Two Metrics for Spencer Cohomology: Hodge Decomposition of Constrained Bundles

As of 11 August 2026, this Paper Citation Record lists 26 of 26 outbound references and 5 inbound Pith citation observations for arXiv:2506.00752.

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

pith.paper-citation-record.v1
2506.00752 v2

Coverage vector

measured 26 of 26 reference resolution

Typed states for the displayed outbound observations.

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

measured 31 of 31 standing notices

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

measured 5 of 5 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-07T10:20:56.827467Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-07T00:51:34.701220Z

Reference resolution

26 of 26 outbound references displayed

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External citation measurements

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Outbound references

Observation 64d08a36-ceee-4572-bad3-7209993b9e31 · outbound

This paper cites Foundations of Mechanics.

Constructing Two Metrics for Spencer Cohomology: Hodge Decomposition of Constrained Bundles Foundations of Mechanics

Reference 1

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Observation 648cfbb2-4f38-41dc-b78d-fa0fdb1d319b · outbound

This paper cites The index of elliptic operators: I.

Constructing Two Metrics for Spencer Cohomology: Hodge Decomposition of Constrained Bundles The index of elliptic operators: I

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:07:46.537961Z

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Observation f4635dcf-f92a-4969-9615-a99989ff2e95 · outbound

This paper cites Complex analytic connections in fibre bundles.

Constructing Two Metrics for Spencer Cohomology: Hodge Decomposition of Constrained Bundles Complex analytic connections in fibre bundles

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:07:46.370932Z

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This paper cites Exterior Differential Systems.

Constructing Two Metrics for Spencer Cohomology: Hodge Decomposition of Constrained Bundles Exterior Differential Systems

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:07:46.216215Z

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Observation 48f415c2-3912-4f14-98bd-5ab18b3f6bbb · outbound

This paper cites The atiyah-singer index theorem for families of dirac operators: two heat equation proofs.

Constructing Two Metrics for Spencer Cohomology: Hodge Decomposition of Constrained Bundles The atiyah-singer index theorem for families of dirac operators: two heat equation proofs

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:07:45.967365Z

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Observation 6cff316c-9766-48e7-9d91-b331afc99775 · outbound

This paper cites Les syst \`e mes diff \'e rentiels ext \'e rieurs et leurs applications g \'e om \'e triques.

Constructing Two Metrics for Spencer Cohomology: Hodge Decomposition of Constrained Bundles Les syst \`e mes diff \'e rentiels ext \'e rieurs et leurs applications g \'e om \'e triques

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:07:45.849509Z

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Observation fa660c8c-a24c-46e9-9f5c-982f92462790 · outbound

This paper cites Lower bounds on ricci curvature and the almost rigidity of warped products.

Constructing Two Metrics for Spencer Cohomology: Hodge Decomposition of Constrained Bundles Lower bounds on ricci curvature and the almost rigidity of warped products

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:07:45.665714Z

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Observation 02f6b27f-5ce4-4a39-8d22-51740d12f985 · outbound

This paper cites Complex Manifolds without Potential Theory.

Constructing Two Metrics for Spencer Cohomology: Hodge Decomposition of Constrained Bundles Complex Manifolds without Potential Theory

Reference 8

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Observation 7295f96a-3b07-4bf0-836f-d4da0a9a176a · outbound

This paper cites Anti self-dual yang-mills connections over complex algebraic surfaces and stable vector bundles.

Constructing Two Metrics for Spencer Cohomology: Hodge Decomposition of Constrained Bundles Anti self-dual yang-mills connections over complex algebraic surfaces and stable vector bundles

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:07:45.334304Z

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Observation 6f8e7301-de43-4982-af67-d370a0ad5a7c · outbound

This paper cites Vari \'e t \'e s diff \'e rentiables.

Constructing Two Metrics for Spencer Cohomology: Hodge Decomposition of Constrained Bundles Vari \'e t \'e s diff \'e rentiables

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:07:45.161433Z

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Observation 1d8f5ff0-0f20-4afb-b78f-89af19f7ff9b · outbound

This paper cites Principles of Algebraic Geometry.

Constructing Two Metrics for Spencer Cohomology: Hodge Decomposition of Constrained Bundles Principles of Algebraic Geometry

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:07:44.986712Z

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Observation 4f317392-0484-4eb0-8f62-27877b62a5ce · outbound

This paper cites Metric Structures for Riemannian and Non-Riemannian Spaces.

Constructing Two Metrics for Spencer Cohomology: Hodge Decomposition of Constrained Bundles Metric Structures for Riemannian and Non-Riemannian Spaces

Reference 12

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Observation 75023012-83d5-47bd-a6f6-0757a1b6ac17 · outbound

This paper cites Variations on a Theme by Kepler.

Constructing Two Metrics for Spencer Cohomology: Hodge Decomposition of Constrained Bundles Variations on a Theme by Kepler

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:07:44.746049Z

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Observation 775c3d8d-8ecd-423a-9e94-aabffbb4c899 · outbound

This paper cites The Theory and Applications of Harmonic Integrals.

Constructing Two Metrics for Spencer Cohomology: Hodge Decomposition of Constrained Bundles The Theory and Applications of Harmonic Integrals

Reference 14

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Observation 16836e7f-24a5-49cd-9411-1f1c3563396b · outbound

This paper cites Foundations of Differential Geometry, Volume I.

Constructing Two Metrics for Spencer Cohomology: Hodge Decomposition of Constrained Bundles Foundations of Differential Geometry, Volume I

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:07:44.480910Z

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Observation c5bc1dfa-5b85-4d43-bd38-4dcc146cf8ef · outbound

This paper cites Weighted Sobolev Spaces.

Constructing Two Metrics for Spencer Cohomology: Hodge Decomposition of Constrained Bundles Weighted Sobolev Spaces

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:07:44.363204Z

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Observation c8c513b1-0e39-463f-8bdf-b9a59aa504b7 · outbound

This paper cites Multiple Integrals in the Calculus of Variations.

Constructing Two Metrics for Spencer Cohomology: Hodge Decomposition of Constrained Bundles Multiple Integrals in the Calculus of Variations

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:07:44.205126Z

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Observation f29fadb5-c081-4e0e-894c-4e25c8e0aea5 · outbound

This paper cites Reduction of symplectic manifolds with symmetry.

Constructing Two Metrics for Spencer Cohomology: Hodge Decomposition of Constrained Bundles Reduction of symplectic manifolds with symmetry

Reference 18

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This paper cites Superconnections and the chern character.

Constructing Two Metrics for Spencer Cohomology: Hodge Decomposition of Constrained Bundles Superconnections and the chern character

Reference 19

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Observation aaba1239-ca00-4636-8d7d-337f76459e36 · outbound

This paper cites Faisceaux alg \'e briques coh \'e rents , volume 61.

Constructing Two Metrics for Spencer Cohomology: Hodge Decomposition of Constrained Bundles Faisceaux alg \'e briques coh \'e rents , volume 61

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:07:43.784795Z

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Observation 908e548a-655e-4af0-a851-7e62fe383167 · outbound

This paper cites Deformation of structures on manifolds defined by transitive, continuous pseudogroups , volume 76.

Constructing Two Metrics for Spencer Cohomology: Hodge Decomposition of Constrained Bundles Deformation of structures on manifolds defined by transitive, continuous pseudogroups , volume 76

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:07:43.620369Z

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Observation a4920ec0-062f-47dd-b0fa-9602285cdf09 · outbound

This paper cites Sp \'e cialisation de faisceaux et monodromie mod \'e r \'e e.

Constructing Two Metrics for Spencer Cohomology: Hodge Decomposition of Constrained Bundles Sp \'e cialisation de faisceaux et monodromie mod \'e r \'e e

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:07:43.453482Z

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Observation fc17f268-c912-4702-a0b4-4b5856ebb7d9 · outbound

This paper cites Topological quantum field theory.

Constructing Two Metrics for Spencer Cohomology: Hodge Decomposition of Constrained Bundles Topological quantum field theory

Reference 23

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Observation 17f1c92b-0f15-40be-b4e8-dd100a0a08fb · outbound

This paper cites Conservation of isotopic spin and isotopic gauge invariance.

Constructing Two Metrics for Spencer Cohomology: Hodge Decomposition of Constrained Bundles Conservation of isotopic spin and isotopic gauge invariance

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:07:43.186010Z

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Observation c230c275-36fc-47e6-8f09-8e127943b69f · outbound

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

Constructing Two Metrics for Spencer Cohomology: Hodge Decomposition of Constrained Bundles Dynamical Geometric Theory of Principal Bundle Constrained Systems: Strong Transversality Conditions and Variational Framework for Gauge Field Coupling

Reference 25

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

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

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

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Pith citing papers

Observation 5fa7b89e-0867-4650-9669-5694b0d01c6f · inbound

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

Mirror Symmetry of Spencer-Hodge Decompositions in Constrained Geometric Systems Constructing Two Metrics for Spencer Cohomology: Hodge Decomposition of Constrained Bundles

Reference 26

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Observation e8eb1648-f9fc-4f49-a9ea-bb529d01a430 · 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 Constructing Two Metrics for Spencer Cohomology: Hodge Decomposition of Constrained Bundles

Reference 18

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

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

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

Reference 20

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Observation 72dcb4cb-0012-416a-aa74-3791874f0286 · 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 Constructing Two Metrics for Spencer Cohomology: Hodge Decomposition of Constrained Bundles

Reference 22

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Observation 2895dd81-10e6-414d-bd8b-302a5a99087d · 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 Constructing Two Metrics for Spencer Cohomology: Hodge Decomposition of Constrained Bundles

Reference 25

Resolution: verified exact; local_arxiv, observed 2026-08-07T00:51:34.705270Z

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