Paper Citation Record · LEDGER

SPDM: Geometry-Modulated State Space Modeling with Manifold Constraints for Time Series Forecasting

As of 13 August 2026, this Paper Citation Record lists 34 of 34 outbound references and 1 inbound Pith citation observation for arXiv:2606.09917.

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

pith.paper-citation-record.v1
2606.09917 v1

Coverage vector

measured 34 of 34 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-06-27T20:01:38.433950Z

measured 35 of 35 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-02T08:17:30.688149Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

34 of 34 outbound references displayed

verified exact7
verified fuzzy0
unresolved24
parse uncertain0
malformed identifier0
metadata mismatch3

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 0fdbc102-8ce0-4a90-83ba-b1bb2d448434 · outbound

This paper cites Geometric meansinanovelvectorspacestructureonsymmetricpositive-definite matrices.

SPDM: Geometry-Modulated State Space Modeling with Manifold Constraints for Time Series Forecasting Geometric meansinanovelvectorspacestructureonsymmetricpositive-definite matrices

Reference 1

Resolution: unresolved; no resolver link, observed 2026-06-27T20:01:38.433950Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9cb868d1-845e-4ec6-a7c1-834e3d93e8b1 · outbound

This paper cites Riemannian geometry and matrix geometric means.

SPDM: Geometry-Modulated State Space Modeling with Manifold Constraints for Time Series Forecasting Riemannian geometry and matrix geometric means

Reference 2

Resolution: unresolved; no resolver link, observed 2026-06-27T20:01:38.433950Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 222c1edd-0704-41b5-9a9d-c6830dd7a211 · outbound

This paper cites Geo-mamba: Geometry- informed state-space learning of functional brain organization.

SPDM: Geometry-Modulated State Space Modeling with Manifold Constraints for Time Series Forecasting Geo-mamba: Geometry- informed state-space learning of functional brain organization

Reference 3

Resolution: verified exact; doi, observed 2026-06-27T20:11:13.718890Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation c814980d-3900-4b7a-89ef-6cfe6e1e581d · outbound

This paper cites Long-term Forecasting with TiDE: Time-series Dense Encoder.

SPDM: Geometry-Modulated State Space Modeling with Manifold Constraints for Time Series Forecasting Long-term Forecasting with TiDE: Time-series Dense Encoder

Reference 4

Resolution: metadata mismatch; arxiv_id, observed 2026-07-02T20:57:23.412505Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation cac85e32-aff3-4a04-859f-bbc9c766b7ae · outbound

This paper cites Robustmanifoldbroad learningsystemforlarge-scalenoisychaotictimeseriesprediction:A perturbation perspective.

SPDM: Geometry-Modulated State Space Modeling with Manifold Constraints for Time Series Forecasting Robustmanifoldbroad learningsystemforlarge-scalenoisychaotictimeseriesprediction:A perturbation perspective

Reference 5

Resolution: unresolved; no resolver link, observed 2026-06-27T20:01:38.433950Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 05998175-33b5-4b1b-a3c6-ce0ee607fd2c · outbound

This paper cites an unresolved cited work.

SPDM: Geometry-Modulated State Space Modeling with Manifold Constraints for Time Series Forecasting Unresolved cited work

Reference 6

Resolution: unresolved; no resolver link, observed 2026-06-27T20:01:38.433950Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0ac2cc00-89ed-4d35-b775-0fe138ec7371 · outbound

This paper cites Mamba: Linear-Time Sequence Modeling with Selective State Spaces.

SPDM: Geometry-Modulated State Space Modeling with Manifold Constraints for Time Series Forecasting Mamba: Linear-Time Sequence Modeling with Selective State Spaces

Reference 7

Resolution: verified exact; local_arxiv, observed 2026-07-02T20:57:23.418247Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T20:38:14.544227+00:00.

Observation 6ff557a0-6313-4c8c-b36d-2347888b6b8a · outbound

This paper cites Dygraphformer: Transformer combining dynamic spatio-temporal graph network for multivariate time series forecasting.

SPDM: Geometry-Modulated State Space Modeling with Manifold Constraints for Time Series Forecasting Dygraphformer: Transformer combining dynamic spatio-temporal graph network for multivariate time series forecasting

Reference 8

Resolution: unresolved; no resolver link, observed 2026-06-27T20:01:38.433950Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 36a7d100-f9c3-4e83-b8da-c071de0c1c00 · outbound

This paper cites Long time series of ocean wave predictionbasedonpatchtstmodel.

SPDM: Geometry-Modulated State Space Modeling with Manifold Constraints for Time Series Forecasting Long time series of ocean wave predictionbasedonpatchtstmodel

Reference 9

Resolution: unresolved; no resolver link, observed 2026-06-27T20:01:38.433950Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 74b8d64a-cf75-4a59-8249-acb612bb0521 · outbound

This paper cites A riemannian network for SPD matrixlearning,in:ProceedingsoftheAAAIConferenceonArtificial Intelligence, pp.

SPDM: Geometry-Modulated State Space Modeling with Manifold Constraints for Time Series Forecasting A riemannian network for SPD matrixlearning,in:ProceedingsoftheAAAIConferenceonArtificial Intelligence, pp

Reference 10

Resolution: unresolved; no resolver link, observed 2026-06-27T20:01:38.433950Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bc4446f4-918c-491e-aeaa-a096b437c116 · outbound

This paper cites Riemannian curvature of deep neural networks.

SPDM: Geometry-Modulated State Space Modeling with Manifold Constraints for Time Series Forecasting Riemannian curvature of deep neural networks

Reference 11

Resolution: unresolved; no resolver link, observed 2026-06-27T20:01:38.433950Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 75a2a0e3-4006-4585-9293-adf1138cccfc · outbound

This paper cites Time series forecasting via direct per-step probability distribution modeling URL:https://arxiv.org/abs/2511.

SPDM: Geometry-Modulated State Space Modeling with Manifold Constraints for Time Series Forecasting Time series forecasting via direct per-step probability distribution modeling URL:https://arxiv.org/abs/2511

Reference 12

Resolution: verified exact; arxiv_id, observed 2026-07-02T20:57:23.415283Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation a63ab9c8-171c-411a-a52d-302058575e63 · outbound

This paper cites Dfimformer: Dynamic frequency-enhanced itransformer for multiscale time series forecast- ing.

SPDM: Geometry-Modulated State Space Modeling with Manifold Constraints for Time Series Forecasting Dfimformer: Dynamic frequency-enhanced itransformer for multiscale time series forecast- ing

Reference 13

Resolution: unresolved; no resolver link, observed 2026-06-27T20:01:38.433950Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4cd4d5a6-b7ae-478d-8551-5a8f1da45b92 · outbound

This paper cites IEEE/CAA Journal of Automatica Sinica 10, 1882–1892.

SPDM: Geometry-Modulated State Space Modeling with Manifold Constraints for Time Series Forecasting IEEE/CAA Journal of Automatica Sinica 10, 1882–1892

Reference 14

Resolution: unresolved; no resolver link, observed 2026-06-27T20:01:38.433950Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4568a5a6-e89f-4a3b-a2f6-5272a9cf5a34 · outbound

This paper cites Bi-Mamba+: Bidirectional Mamba for Time Series Forecasting.

SPDM: Geometry-Modulated State Space Modeling with Manifold Constraints for Time Series Forecasting Bi-Mamba+: Bidirectional Mamba for Time Series Forecasting

Reference 15

Resolution: verified exact; arxiv_id, observed 2026-07-02T20:57:23.403784Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 52d7445e-03ea-48a8-8f79-e93aa133ea4d · outbound

This paper cites an unresolved cited work.

SPDM: Geometry-Modulated State Space Modeling with Manifold Constraints for Time Series Forecasting Unresolved cited work

Reference 16

Resolution: unresolved; no resolver link, observed 2026-06-27T20:01:38.433950Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c8c7b523-1f24-4dba-b463-332a245f7d1a · outbound

This paper cites iTransformer: Inverted Transformers Are Effective for Time Series Forecasting.

SPDM: Geometry-Modulated State Space Modeling with Manifold Constraints for Time Series Forecasting iTransformer: Inverted Transformers Are Effective for Time Series Forecasting

Reference 17

Resolution: metadata mismatch; local_arxiv, observed 2026-07-02T20:57:23.398592Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation a976b7cc-8984-4d7b-896c-eb64f2a60185 · outbound

This paper cites The Illusion of State in State-Space Models.

SPDM: Geometry-Modulated State Space Modeling with Manifold Constraints for Time Series Forecasting The Illusion of State in State-Space Models

Reference 18

Resolution: metadata mismatch; arxiv_id, observed 2026-07-02T20:57:23.401162Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation e6e03d72-e93f-4891-a032-b6f08662ccf6 · outbound

This paper cites Ridge regression for manifold-valued time-series with application to meteo- rological forecast.

SPDM: Geometry-Modulated State Space Modeling with Manifold Constraints for Time Series Forecasting Ridge regression for manifold-valued time-series with application to meteo- rological forecast

Reference 19

Resolution: verified exact; arxiv_id, observed 2026-07-02T20:57:23.406924Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation fd95c662-0ae8-4a16-a0d4-a97edae5660f · outbound

This paper cites Adaptive sliding window normalization.

SPDM: Geometry-Modulated State Space Modeling with Manifold Constraints for Time Series Forecasting Adaptive sliding window normalization

Reference 20

Resolution: unresolved; no resolver link, observed 2026-06-27T20:01:38.433950Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bdf0c32d-3a7e-475b-b3fb-a0b372f8193f · outbound

This paper cites Clus- tering brain-network time series by riemannian geometry.

SPDM: Geometry-Modulated State Space Modeling with Manifold Constraints for Time Series Forecasting Clus- tering brain-network time series by riemannian geometry

Reference 21

Resolution: unresolved; no resolver link, observed 2026-06-27T20:01:38.433950Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fc23cecb-260c-4b22-b1de-b121d17d7a57 · outbound

This paper cites Attention is all you need.

SPDM: Geometry-Modulated State Space Modeling with Manifold Constraints for Time Series Forecasting Attention is all you need

Reference 22

Resolution: unresolved; no resolver link, observed 2026-06-27T20:01:38.433950Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6cacad90-83f7-4c40-ae27-ada612d27a65 · outbound

This paper cites Koopman Neural Forecaster for Time Series with Temporal Distribution Shifts.

SPDM: Geometry-Modulated State Space Modeling with Manifold Constraints for Time Series Forecasting Koopman Neural Forecaster for Time Series with Temporal Distribution Shifts

Reference 23

Resolution: verified exact; arxiv_id, observed 2026-07-02T20:57:23.409719Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 16978b48-cb58-4424-8631-c7944ca7bec3 · outbound

This paper cites Contrastive learning enhanced by graph neural networks for universal multivariate time series representation.

SPDM: Geometry-Modulated State Space Modeling with Manifold Constraints for Time Series Forecasting Contrastive learning enhanced by graph neural networks for universal multivariate time series representation

Reference 24

Resolution: unresolved; no resolver link, observed 2026-06-27T20:01:38.433950Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bc40f4e6-1789-4a79-bd80-2e50bd97d409 · outbound

This paper cites Is mamba effective for time series forecasting? Neurocomputing 619, 129178.

SPDM: Geometry-Modulated State Space Modeling with Manifold Constraints for Time Series Forecasting Is mamba effective for time series forecasting? Neurocomputing 619, 129178

Reference 25

Resolution: unresolved; no resolver link, observed 2026-06-27T20:01:38.433950Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cbe434a8-5794-4cbc-9686-192f7867486a · outbound

This paper cites URL:https://openreview.net/forum?id=ju_Uqw384Oq.

SPDM: Geometry-Modulated State Space Modeling with Manifold Constraints for Time Series Forecasting URL:https://openreview.net/forum?id=ju_Uqw384Oq

Reference 26

Resolution: unresolved; no resolver link, observed 2026-06-27T20:01:38.433950Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 545aab85-a21c-4653-b110-3d698c3fe60f · outbound

This paper cites Advancesinneuralinformationprocessingsystems34,22419–22430.

SPDM: Geometry-Modulated State Space Modeling with Manifold Constraints for Time Series Forecasting Advancesinneuralinformationprocessingsystems34,22419–22430

Reference 27

Resolution: unresolved; no resolver link, observed 2026-06-27T20:01:38.433950Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d96e01ec-c85a-4f3d-af52-c365221d85f8 · outbound

This paper cites Repetitive contrastive learning enhances mamba’s selectivity in time series prediction.

SPDM: Geometry-Modulated State Space Modeling with Manifold Constraints for Time Series Forecasting Repetitive contrastive learning enhances mamba’s selectivity in time series prediction

Reference 28

Resolution: unresolved; no resolver link, observed 2026-06-27T20:01:38.433950Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 064ef2a9-d8cf-457d-9c30-2dbd6f41a2ac · outbound

This paper cites Fa- mamba: Frequency attention driven mamba for multimodal remote sensing classification.

SPDM: Geometry-Modulated State Space Modeling with Manifold Constraints for Time Series Forecasting Fa- mamba: Frequency attention driven mamba for multimodal remote sensing classification

Reference 29

Resolution: unresolved; no resolver link, observed 2026-06-27T20:01:38.433950Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c0e7c2e0-a218-4f4c-a92b-486cc1ed8ea9 · outbound

This paper cites Fast sequential clustering in Riemannian manifolds for dynamic and time-series-annotated multilayer networks.

SPDM: Geometry-Modulated State Space Modeling with Manifold Constraints for Time Series Forecasting Fast sequential clustering in Riemannian manifolds for dynamic and time-series-annotated multilayer networks

Reference 30

Resolution: unresolved; no resolver link, observed 2026-06-27T20:01:38.433950Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 178b65fd-7f38-4412-ad00-9231c402082e · outbound

This paper cites Are transformers effective for time series forecasting?, in: Proceedings of the AAAI conference on artificial intelligence, pp.

SPDM: Geometry-Modulated State Space Modeling with Manifold Constraints for Time Series Forecasting Are transformers effective for time series forecasting?, in: Proceedings of the AAAI conference on artificial intelligence, pp

Reference 31

Resolution: unresolved; no resolver link, observed 2026-06-27T20:01:38.433950Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fed63f9f-83af-467c-857f-d732a76fd698 · outbound

This paper cites Multivariate time series forecasting under hyperbolic space hierarchical constraints URL:https://openreview.

SPDM: Geometry-Modulated State Space Modeling with Manifold Constraints for Time Series Forecasting Multivariate time series forecasting under hyperbolic space hierarchical constraints URL:https://openreview

Reference 32

Resolution: unresolved; no resolver link, observed 2026-06-27T20:01:38.433950Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d13bc8df-75e6-4411-be04-d3251803706b · outbound

This paper cites Crossformer: Transformer utilizing cross- dimension dependency for multivariate time series forecasting, in: The Eleventh International Conference on Learning Representations.

SPDM: Geometry-Modulated State Space Modeling with Manifold Constraints for Time Series Forecasting Crossformer: Transformer utilizing cross- dimension dependency for multivariate time series forecasting, in: The Eleventh International Conference on Learning Representations

Reference 33

Resolution: unresolved; no resolver link, observed 2026-06-27T20:01:38.433950Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b0388bac-9bcf-47d2-aed6-61b39bdbaf47 · outbound

This paper cites FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting.

SPDM: Geometry-Modulated State Space Modeling with Manifold Constraints for Time Series Forecasting FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting

Reference 34

Resolution: verified exact; arxiv_id, observed 2026-07-02T20:57:23.408788Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Pith citing papers

Observation c8e9304d-203e-4d98-92d4-f19b5d6c699c · inbound

Structured Latent Space Modeling over Multi-Scale Temporal Patches for Multivariate Time Series Forecasting cites this paper.

Structured Latent Space Modeling over Multi-Scale Temporal Patches for Multivariate Time Series Forecasting SPDM: Geometry-Modulated State Space Modeling with Manifold Constraints for Time Series Forecasting

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-02T08:17:30.688149Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.