Paper Citation Record · LEDGER

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

As of 7 August 2026, this Paper Citation Record lists 21 of 21 outbound references and 3 inbound Pith citation observations for arXiv:2506.05915.

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

pith.paper-citation-record.v1
2506.05915 v2

Coverage vector

measured 21 of 21 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T10:20:48.559782Z

measured 24 of 24 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+00:00

measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-07T00:51:34.572507Z

Reference resolution

21 of 21 outbound references displayed

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External citation measurements

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Outbound references

Observation 61e2231a-0cf4-4da9-a94a-1029104fb755 · outbound

This paper cites an unresolved cited work.

Spencer-Riemann-Roch Theory: Mirror Symmetry of Hodge Decompositions and Characteristic Classes in Constrained Geometry Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-07T10:20:49.115719Z

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Observation d691c830-4d80-46cf-89b4-be86698476d1 · outbound

This paper cites A simple intrinsic proof of the gauss-bonnet formula for closed riemannian manifolds.

Spencer-Riemann-Roch Theory: Mirror Symmetry of Hodge Decompositions and Characteristic Classes in Constrained Geometry A simple intrinsic proof of the gauss-bonnet formula for closed riemannian manifolds

Reference 2

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Observation 78e678bb-c844-4c98-b0f8-fafcd2ee7f64 · outbound

This paper cites Intersection Theory , volume 2 of Ergebnisse der Mathematik und ihrer Grenzgebiete.

Spencer-Riemann-Roch Theory: Mirror Symmetry of Hodge Decompositions and Characteristic Classes in Constrained Geometry Intersection Theory , volume 2 of Ergebnisse der Mathematik und ihrer Grenzgebiete

Reference 3

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Observation 59d9a939-9acd-4fb5-98ec-eb740cbd74de · outbound

This paper cites Principles of Algebraic Geometry.

Spencer-Riemann-Roch Theory: Mirror Symmetry of Hodge Decompositions and Characteristic Classes in Constrained Geometry Principles of Algebraic Geometry

Reference 4

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Observation 237f94cc-b08e-44f1-bb50-d31c5e96d123 · outbound

This paper cites Integrability criteria for systems of nonlinear partial differential equations.

Spencer-Riemann-Roch Theory: Mirror Symmetry of Hodge Decompositions and Characteristic Classes in Constrained Geometry Integrability criteria for systems of nonlinear partial differential equations

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:20:49.027636Z

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Observation c2a448ec-e6dd-4522-a9ac-475286332832 · outbound

This paper cites Sur quelques points d'algèbre homologique.

Spencer-Riemann-Roch Theory: Mirror Symmetry of Hodge Decompositions and Characteristic Classes in Constrained Geometry Sur quelques points d'algèbre homologique

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:20:49.004798Z

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Observation 43b57bbe-7c0a-4cc9-8277-1c4f3a45ecc5 · outbound

This paper cites Topological Methods in Algebraic Geometry , volume 131 of Grundlehren der Mathematischen Wissenschaften.

Spencer-Riemann-Roch Theory: Mirror Symmetry of Hodge Decompositions and Characteristic Classes in Constrained Geometry Topological Methods in Algebraic Geometry , volume 131 of Grundlehren der Mathematischen Wissenschaften

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:20:48.982936Z

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Observation a58a8b7a-bd8b-4f80-872b-ece246f71129 · outbound

This paper cites Mirror Symmetry.

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

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:20:48.958658Z

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Observation f5b50445-0b20-4640-ade6-7f7a04b1be6a · outbound

This paper cites Humphreys.

Spencer-Riemann-Roch Theory: Mirror Symmetry of Hodge Decompositions and Characteristic Classes in Constrained Geometry Humphreys

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:20:48.940997Z

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Observation 8f33f7eb-8c9c-462c-81da-608fe50fb202 · outbound

This paper cites Macdonald.

Spencer-Riemann-Roch Theory: Mirror Symmetry of Hodge Decompositions and Characteristic Classes in Constrained Geometry Macdonald

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:20:48.918054Z

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Observation dc5918a7-939d-4dd3-b310-65baa67fefe2 · outbound

This paper cites Milnor and James D.

Spencer-Riemann-Roch Theory: Mirror Symmetry of Hodge Decompositions and Characteristic Classes in Constrained Geometry Milnor and James D

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:20:48.890802Z

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Observation 3ecc97d4-8ad9-40a7-a2e3-c74c5d1de37d · outbound

This paper cites Formal properties of over-determined systems of linear partial differential equations.

Spencer-Riemann-Roch Theory: Mirror Symmetry of Hodge Decompositions and Characteristic Classes in Constrained Geometry Formal properties of over-determined systems of linear partial differential equations

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:20:48.868079Z

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Observation c170fb17-3829-4089-a4e3-f69b16c7bdbd · outbound

This paper cites G \'e om \'e trie alg \'e brique et g \'e om \'e trie analytique.

Spencer-Riemann-Roch Theory: Mirror Symmetry of Hodge Decompositions and Characteristic Classes in Constrained Geometry G \'e om \'e trie alg \'e brique et g \'e om \'e trie analytique

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:20:48.839611Z

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Observation 3bf98670-10ad-40b8-abcd-346a9c7150d7 · outbound

This paper cites an unresolved cited work.

Spencer-Riemann-Roch Theory: Mirror Symmetry of Hodge Decompositions and Characteristic Classes in Constrained Geometry Unresolved cited work

Reference 14

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Observation 364b688a-a4d4-4a1f-8e7d-f6f1e385fb58 · outbound

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

Spencer-Riemann-Roch Theory: Mirror Symmetry of Hodge Decompositions and Characteristic Classes in Constrained Geometry Deformation of structures on manifolds defined by transitive, continuous pseudogroups

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:20:48.784441Z

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Observation 4779c039-183c-4a86-8de5-838a2ba7c75e · outbound

This paper cites The invariants of algebraic loci.

Spencer-Riemann-Roch Theory: Mirror Symmetry of Hodge Decompositions and Characteristic Classes in Constrained Geometry The invariants of algebraic loci

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:20:48.761339Z

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Observation bd1f3086-81c7-4440-aaf2-4525ace541ff · outbound

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Spencer-Riemann-Roch Theory: Mirror Symmetry of Hodge Decompositions and Characteristic Classes in Constrained Geometry Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-07T10:20:48.739384Z

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Observation e8eb1648-f9fc-4f49-a9ea-bb529d01a430 · outbound

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

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 e18042d6-670f-4127-826d-95c5434d1eeb · outbound

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

Spencer-Riemann-Roch Theory: Mirror Symmetry of Hodge Decompositions and Characteristic Classes in Constrained Geometry Dynamical Geometric Theory of Principal Bundle Constrained Systems: Strong Transversality Conditions and Variational Framework for Gauge Field Coupling

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-07T10:20:48.546906Z

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

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

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

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Observation 82820585-44f3-4292-ba30-7f9fa9926fc8 · outbound

This paper cites Mirror symmetry of spencer-hodge decompositions in constrained geometric systems.

Spencer-Riemann-Roch Theory: Mirror Symmetry of Hodge Decompositions and Characteristic Classes in Constrained Geometry Mirror symmetry of spencer-hodge decompositions in constrained geometric systems

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:20:48.709622Z

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Pith citing papers

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

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

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

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Observation 85ff7c31-76ad-4e53-b005-14accdec020d · 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-Riemann-Roch Theory: Mirror Symmetry of Hodge Decompositions and Characteristic Classes in Constrained Geometry

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-07T04:12:57.886576Z

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Observation cfa724c0-3fc1-4dfa-878f-6a43292b2bf8 · 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-Riemann-Roch Theory: Mirror Symmetry of Hodge Decompositions and Characteristic Classes in Constrained Geometry

Reference 31

Resolution: verified exact; local_arxiv, observed 2026-08-07T00:51:34.577948Z

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