Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-07T10:20:57.028821Z
Paper Citation Record · LEDGER
Mirror Symmetry of Spencer-Hodge Decompositions in Constrained Geometric Systems
As of 9 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 3 inbound Pith citation observations for arXiv:2506.05816.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-07T05:40:43.305649Z
A source-named dated measurement, never combined with another source.
Source: pith, observed 2026-08-07T00:51:34.601485Z
Reference resolution
28 of 28 outbound references displayed
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External citation measurements
No source-named external measurement is stored.
Outbound references
Observation a68afc0f-f165-422f-9d78-0f536f682454 · outbound
This paper cites Sobolev Spaces , volume 140 of Pure and Applied Mathematics.
Mirror Symmetry of Spencer-Hodge Decompositions in Constrained Geometric Systems Sobolev Spaces , volume 140 of Pure and Applied Mathematics
Reference 1
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- raw_fallback, observed 2026-08-07T10:21:01.556331Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation c87a979b-6280-4791-9738-32fd34c24c6f · outbound
This paper cites Background independent quantum gravity: A status report.
Mirror Symmetry of Spencer-Hodge Decompositions in Constrained Geometric Systems Background independent quantum gravity: A status report
Reference 2
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation d5faaac1-6f2e-48e0-8df3-29777d00b8ff · outbound
This paper cites The index of elliptic operators on compact manifolds.
Mirror Symmetry of Spencer-Hodge Decompositions in Constrained Geometric Systems The index of elliptic operators on compact manifolds
Reference 3
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 4c7ba8c3-291c-485f-9c83-2bcfdc220873 · outbound
This paper cites Some Nonlinear Problems in Riemannian Geometry.
Mirror Symmetry of Spencer-Hodge Decompositions in Constrained Geometric Systems Some Nonlinear Problems in Riemannian Geometry
Reference 4
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Observation 53211cc5-9868-4d6c-b8c5-60c848f86b20 · outbound
This paper cites Exterior Differential Systems , volume 18 of Mathematical Sciences Research Institute Publications.
Mirror Symmetry of Spencer-Hodge Decompositions in Constrained Geometric Systems Exterior Differential Systems , volume 18 of Mathematical Sciences Research Institute Publications
Reference 5
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 1f8af91e-edf7-466f-a09b-270f095b776a · outbound
This paper cites Mirror symmetry for two-parameter models-i.
Mirror Symmetry of Spencer-Hodge Decompositions in Constrained Geometric Systems Mirror symmetry for two-parameter models-i
Reference 6
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Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 7ce60e24-d954-4e5d-99d3-378c40d08939 · outbound
This paper cites Noncommutative Geometry.
Mirror Symmetry of Spencer-Hodge Decompositions in Constrained Geometric Systems Noncommutative Geometry
Reference 7
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 29a4918b-32a8-4d3f-a26e-5379c64e0349 · outbound
This paper cites Lectures on Quantum Mechanics.
Mirror Symmetry of Spencer-Hodge Decompositions in Constrained Geometric Systems Lectures on Quantum Mechanics
Reference 8
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation b29c5f7e-db0c-4afd-9700-e61bfc05a924 · outbound
This paper cites Partial Differential Equations , volume 19 of Graduate Studies in Mathematics.
Mirror Symmetry of Spencer-Hodge Decompositions in Constrained Geometric Systems Partial Differential Equations , volume 19 of Graduate Studies in Mathematics
Reference 9
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Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 466ac10b-ecb4-46a5-892e-5731aff269aa · outbound
This paper cites Ghosts, ward identities and symmetries in yang-mills theory.
Mirror Symmetry of Spencer-Hodge Decompositions in Constrained Geometric Systems Ghosts, ward identities and symmetries in yang-mills theory
Reference 10
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 41be3b2e-e5ce-4033-9582-8ca64f155326 · outbound
This paper cites Mirror manifolds in higher dimension.
Mirror Symmetry of Spencer-Hodge Decompositions in Constrained Geometric Systems Mirror manifolds in higher dimension
Reference 11
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Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 2f980c89-ab1e-4e99-93e2-fa3a9b0dae8d · outbound
This paper cites Elliptic Partial Differential Equations of Second Order.
Mirror Symmetry of Spencer-Hodge Decompositions in Constrained Geometric Systems Elliptic Partial Differential Equations of Second Order
Reference 12
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation e80bca67-3835-4939-b5fc-135e763f1fd0 · outbound
This paper cites Mirror Symmetry , volume 1 of Clay Mathematics Monographs.
Mirror Symmetry of Spencer-Hodge Decompositions in Constrained Geometric Systems Mirror Symmetry , volume 1 of Clay Mathematics Monographs
Reference 13
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- raw_fallback, observed 2026-08-07T10:20:59.654436Z
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 85ffef9f-c2ad-4220-8e58-a02189b64811 · outbound
This paper cites The Analysis of Linear Partial Differential Operators I: Distribution Theory and Fourier Analysis.
Mirror Symmetry of Spencer-Hodge Decompositions in Constrained Geometric Systems The Analysis of Linear Partial Differential Operators I: Distribution Theory and Fourier Analysis
Reference 14
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Observation 0e7be32e-a01f-4f26-883d-8f835eb03dfe · outbound
This paper cites Quantization of Gauge Systems.
Mirror Symmetry of Spencer-Hodge Decompositions in Constrained Geometric Systems Quantization of Gauge Systems
Reference 15
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Observation 6763baec-abbe-49d4-8cb0-a49ce6355c30 · outbound
This paper cites Perturbation Theory for Linear Operators.
Mirror Symmetry of Spencer-Hodge Decompositions in Constrained Geometric Systems Perturbation Theory for Linear Operators
Reference 16
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- raw_fallback, observed 2026-08-07T10:20:58.860413Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation aadf13f3-fb88-46b7-91b6-9155b84072b9 · outbound
This paper cites Foundations of Differential Geometry , volume 1.
Mirror Symmetry of Spencer-Hodge Decompositions in Constrained Geometric Systems Foundations of Differential Geometry , volume 1
Reference 17
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- raw_fallback, observed 2026-08-07T10:20:58.634770Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 1ab8ade5-5866-4597-9bdf-82e25494a10f · outbound
This paper cites The large-n limit of superconformal field theories and supergravity.
Mirror Symmetry of Spencer-Hodge Decompositions in Constrained Geometric Systems The large-n limit of superconformal field theories and supergravity
Reference 18
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- raw_fallback, observed 2026-08-07T10:20:58.413727Z
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 938e3b02-4eff-45c6-a2de-5c8b44187c16 · outbound
This paper cites On the formal group laws of unoriented and complex cobordism theory.
Mirror Symmetry of Spencer-Hodge Decompositions in Constrained Geometric Systems On the formal group laws of unoriented and complex cobordism theory
Reference 19
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation b95ae0f1-2076-4096-8f7f-923f335aace8 · outbound
This paper cites Index Theory of Elliptic Boundary Problems.
Mirror Symmetry of Spencer-Hodge Decompositions in Constrained Geometric Systems Index Theory of Elliptic Boundary Problems
Reference 20
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation ac20642c-d0eb-47cc-b861-0ca64c08b0b9 · outbound
This paper cites Deformation of structures on manifolds defined by transitive, continuous pseudogroups.
Mirror Symmetry of Spencer-Hodge Decompositions in Constrained Geometric Systems Deformation of structures on manifolds defined by transitive, continuous pseudogroups
Reference 21
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- no resolver link, observed 2026-08-07T10:20:56.390274Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b8b04153-8c2c-4c70-89cd-208218a42d3c · outbound
This paper cites Partial Differential Equations I: Basic Theory , volume 115 of Applied Mathematical Sciences.
Mirror Symmetry of Spencer-Hodge Decompositions in Constrained Geometric Systems Partial Differential Equations I: Basic Theory , volume 115 of Applied Mathematical Sciences
Reference 22
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- raw_fallback, observed 2026-08-07T10:20:57.843199Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 2a4b3781-fffb-4bd2-b438-2ed9cb907d52 · outbound
This paper cites Interpolation Theory, Function Spaces, Differential Operators.
Mirror Symmetry of Spencer-Hodge Decompositions in Constrained Geometric Systems Interpolation Theory, Function Spaces, Differential Operators
Reference 23
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 917f1000-fbb1-4997-92db-1ec3d173402a · outbound
This paper cites Foundations of Differentiable Manifolds and Lie Groups , volume 94 of Graduate Texts in Mathematics.
Mirror Symmetry of Spencer-Hodge Decompositions in Constrained Geometric Systems Foundations of Differentiable Manifolds and Lie Groups , volume 94 of Graduate Texts in Mathematics
Reference 24
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation d3280a40-f8f4-47ea-ab94-76e578e39400 · outbound
This paper cites Quantum field theory and the jones polynomial.
Mirror Symmetry of Spencer-Hodge Decompositions in Constrained Geometric Systems Quantum field theory and the jones polynomial
Reference 25
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.
Observation 5fa7b89e-0867-4650-9669-5694b0d01c6f · outbound
This paper cites Constructing Two Metrics for Spencer Cohomology: Hodge Decomposition of Constrained Bundles.
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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Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation abffbb8e-73d5-4f77-973f-7e29de23109a · outbound
This paper cites Dynamical Geometric Theory of Principal Bundle Constrained Systems: Strong Transversality Conditions and Variational Framework for Gauge Field Coupling.
Mirror Symmetry of Spencer-Hodge Decompositions in Constrained Geometric Systems Dynamical Geometric Theory of Principal Bundle Constrained Systems: Strong Transversality Conditions and Variational Framework for Gauge Field Coupling
Reference 27
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Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 1610ce4c-3660-4efe-b0ae-a60ad5585116 · outbound
This paper cites Geometric Duality Between Constraints and Gauge Fields: Mirror Symmetry and Spencer Isomorphisms of Compatible Pairs on Principal Bundles.
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
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Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Pith citing papers
Observation 455d96d3-c3d0-49bf-81b0-1b0e8a1e8990 · inbound
Spencer Differential Degeneration Theory and Its Applications in Algebraic Geometry cites this paper.
Spencer Differential Degeneration Theory and Its Applications in Algebraic Geometry Mirror Symmetry of Spencer-Hodge Decompositions in Constrained Geometric Systems
Reference 24
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- no resolver link, observed 2026-08-07T05:40:43.305649Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 2ae9e6b8-1801-4b8c-a2f5-f791b653aa30 · 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 Mirror Symmetry of Spencer-Hodge Decompositions in Constrained Geometric Systems
Reference 26
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- no resolver link, observed 2026-08-07T04:12:57.880620Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation d42d3437-47a4-4260-a904-54ddb55b66b6 · 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 Mirror Symmetry of Spencer-Hodge Decompositions in Constrained Geometric Systems
Reference 29
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- local_arxiv, observed 2026-08-07T00:51:34.605284Z
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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.