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Paper Citation Record · LEDGER

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex

As of 17 August 2026, this Paper Citation Record lists 65 of 65 outbound references and 0 inbound Pith citation observations for arXiv:2606.11646.

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

pith.paper-citation-record.v1
2606.11646 v1

Coverage vector

measured 65 of 65 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-06-27T11:07:10.751182Z

measured 65 of 65 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-17T06:30:58.91139+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

65 of 65 outbound references displayed

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  • verified fuzzy0
  • unresolved63
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 04f55d4f-581c-4882-bacc-6704570a4341 · outbound

This paper cites Mathematical Geology , volume=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex Mathematical Geology , volume=

Reference 1

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:5c8886f463b62313b8a57325b61a0ec13d3c55d0d87ff667dd92b25ed436d2f6

Observation 7b7835b6-5813-4a1c-a6ad-3e0a28ec1398 · outbound

This paper cites Journal of Scientific Computing , volume=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex Journal of Scientific Computing , volume=

Reference 2

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:b460f8e13139532e1e4c71c8e181809ba98a1e5d42028d7bcc498f5bb0d2ca63

Observation daddf9bc-e088-4ae6-a878-c230dbae1951 · outbound

This paper cites Austrian Journal of Statistics , volume=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex Austrian Journal of Statistics , volume=

Reference 3

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:a2624608b2a8291f69ba1c5bcfa86ccd8967c1ed2801bd55e1d750a2fff046cd

Observation c80c9854-205e-4f71-8fe6-7aadda4645e0 · outbound

This paper cites elife , volume=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex elife , volume=

Reference 4

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:e50ffd24d082a07093f458a622acf1f167da6fb41761c23d1f14f90ec17e3ac8

Observation 41252dd0-28ec-4527-bd86-a8e97f16ad76 · outbound

This paper cites PeerJ , volume=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex PeerJ , volume=

Reference 5

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:a547a4ba755863f53b5c18b9e052c3c9d97d067194a09cca7dbafd8507daf996

Observation 19551b54-45f4-40b3-9d65-14b5e2315b85 · outbound

This paper cites Mathematical Geology , volume=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex Mathematical Geology , volume=

Reference 6

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:6a031e46a2a0f22e1f3af30bb167fee42871c13a80a7e94815c2a5aecac34741

Observation 0e560802-a6a5-4af0-a360-399a64724302 · outbound

This paper cites Advances in Neural Information Processing Systems , volume=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex Advances in Neural Information Processing Systems , volume=

Reference 7

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:02902f51e1b5b5ea408adf60ee3b0d4614fbfb8376b02783fe0fad06e4c9a112

Observation 33ed8fe9-ec83-4dc5-b90d-b64c868bd97a · outbound

This paper cites Simplex-to-euclidean bijections for categorical flow matching.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex Simplex-to-euclidean bijections for categorical flow matching

Reference 8

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arxiv_id, observed 2026-07-03T08:07:45.322066Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:7524bf143acb3774beebc8f05119acea240aea6f9d8786699a19872e88a7ff7c

Observation 73b9bbba-2dc0-443f-952e-5635d48cc86e · outbound

This paper cites Journal of the Royal Statistical Society: Series B (Methodological) , volume=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex Journal of the Royal Statistical Society: Series B (Methodological) , volume=

Reference 9

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:8e12206edbc5d62967f5379a7338d8e457930406eddec5bcce38188d4dc6f0b4

Observation c90c216b-f97b-4927-9fc9-73fbb3ee7e02 · outbound

This paper cites Stochastic Environmental Research and Risk Assessment , volume=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex Stochastic Environmental Research and Risk Assessment , volume=

Reference 10

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:8e99e2e33b0fe6976910df2da9836b77fe3a979a52c7cf0dd13aa4af4945c045

Observation 28a9e9d0-57c4-4d94-b850-b0b2872f46ed · outbound

This paper cites Journal of the American Statistical Association , volume=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex Journal of the American Statistical Association , volume=

Reference 11

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:d5fa78bcb79c83b7d3d38cf06d1f7634625da4e5734ff9252d35b0bfc713dd23

Observation db4d4416-f700-4bf6-9004-16bc0f54183d · outbound

This paper cites 2018 , publisher=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex 2018 , publisher=

Reference 12

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:193f211a48ab6c18d5dc657135b940d73324ac32fa6ac477bbf40aa7175168ec

Observation 96fe097f-79d5-4a6a-8d40-5919b410d00a · outbound

This paper cites Frontiers in Microbiology , volume=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex Frontiers in Microbiology , volume=

Reference 13

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:e6bf414d3a9eef9245c925c90ac849b2b5c56a0e9f9f90533d3191f82f99f4a2

Observation 9d20e872-46b4-459a-87a9-c92ce8c8a5fc · outbound

This paper cites Ecology , volume=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex Ecology , volume=

Reference 14

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:9ea190abdd8913cf960b3c380082594387e249118a90801a97dbc16147872bab

Observation f52bc945-8a29-4e4c-a70d-7d35ded55c5c · outbound

This paper cites Earth and Planetary Science Letters , volume=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex Earth and Planetary Science Letters , volume=

Reference 15

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:42aa6d563eda5355ef412123db7bc0d3d4890bb5a2d4465cec6cd902a3a21e8b

Observation ccb53493-5e60-44bd-91f3-ab641801c422 · outbound

This paper cites 2019 , publisher=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex 2019 , publisher=

Reference 16

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:552ed6da1d8c4e846895de5ee4adb9bd432e42b5a56addf02ad2cc499ccefa2e

Observation 81ecf0fb-889c-495a-8e00-1103371be07b · outbound

This paper cites The ISME Journal , volume=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex The ISME Journal , volume=

Reference 17

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:4312d5f3db03643e1830bb3ece7787fa32b864f9c390ce01195c6bf6c2a04610

Observation 6ef048ef-c5c0-4179-a301-75c38689363b · outbound

This paper cites an unresolved cited work.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex Unresolved cited work

Reference 18

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:c22da1eed566402631cb8e072c017962f06bc897d41f302b27f9f61f970ee8a0

Observation b143bd7a-45fb-455e-bd69-b8a79771c0f7 · outbound

This paper cites Biometrika , volume=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex Biometrika , volume=

Reference 19

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:39f567b0e38be2aa9256453d28c41e90b382802029cd8a8ba1ec23f9292859bf

Observation f96297f5-0ca6-4c1d-b713-edd41b387d7c · outbound

This paper cites Microbial ecology in health and disease , volume=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex Microbial ecology in health and disease , volume=

Reference 20

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:623effadd9862ff6864002ef393f28dd05d1e0b96c63fcfb8200e32ba05c0b43

Observation 549fb91f-49e4-4f8f-968f-d9019bfe4ccb · outbound

This paper cites MSystems , volume=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex MSystems , volume=

Reference 21

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:78b108b960effbdc6458af1a8ae0dce223fa7b0cbbf8b4fc2553dea9c9194ef1

Observation 3a415bb7-9d36-46a5-9fbe-97d9514d1f7d · outbound

This paper cites MSystems , volume=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex MSystems , volume=

Reference 22

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:0f9f8afc845356591a08f29308ccf948fb2c5f89880d48c911beeb72173485db

Observation fde0986f-ee78-442e-9d8c-a6f9b90cc877 · outbound

This paper cites Ecological Monographs , volume=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex Ecological Monographs , volume=

Reference 23

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:5e1f808a9535dce762bf5604e84b4c4b26e2740fb1cb4c6b3fec4d651680148a

Observation ee85aba1-6acd-40e5-9019-bf73874dd749 · outbound

This paper cites 2021 , publisher=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex 2021 , publisher=

Reference 24

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:8db7a3260a6a49afc0594800013f4a9afaea6b3d156cd2e69bdcd86b4f55d4dc

Observation bc17464e-2f1d-4dc3-9e26-268e3c627227 · outbound

This paper cites an unresolved cited work.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex Unresolved cited work

Reference 25

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:4add00d9eb7d395f24e0bff193be41e0a649a7fa6ddc59a013e9d02202985b69

Observation 4752ac04-7b20-4fe0-8937-c44d0bf3d984 · outbound

This paper cites 2002 , publisher=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex 2002 , publisher=

Reference 26

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:5797abe5de110128242a602bde9cca6f3365a159122866fa4f6d30c17ae637c8

Observation ad75520f-dfa0-4f23-ba11-28fd6273eccf · outbound

This paper cites Nature Methods , volume=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex Nature Methods , volume=

Reference 27

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:d598dbe808923d5e3fd3f882c9d18bc9da0df0bde7e379fa54ea2e2c5eeec8b6

Observation 9c347709-3721-4476-a270-b9562aa777f0 · outbound

This paper cites Nature , volume=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex Nature , volume=

Reference 28

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:c38531e8f0132fb3b87300493689ee33c1f0a1ec8cde28edb44eb6f8f4ee4d55

Observation 910695b7-cc65-43dd-84f8-b8e8655aaef9 · outbound

This paper cites BMC systems Biology , volume=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex BMC systems Biology , volume=

Reference 29

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:76a813b0b1bdffb37e1c1616e93cf4d9f50db725ffb8a420456cc48a9c881068

Observation 113b947d-c24f-4359-be3e-1e87cba0e3e6 · outbound

This paper cites Journal of Bacteriology , volume=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex Journal of Bacteriology , volume=

Reference 30

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:b94f5e1cca610a813ad3be791a354625f6c128a4d371ce00e1eb71d2f94a35cf

Observation df0020f3-68f1-41a7-8e05-4aa2bf662b55 · outbound

This paper cites Proceedings of the National Academy of Sciences , volume=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex Proceedings of the National Academy of Sciences , volume=

Reference 31

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:cbdc9283e04d25033cafbb0333fd00ce080c0dc66250ac2efb7c462c5297d693

Observation 76219920-c614-47ce-a6d5-cd4c16106233 · outbound

This paper cites Nature , volume=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex Nature , volume=

Reference 32

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:4d28433ae3c0555ac975ec2014b8a241f6f28952487e23d091d617c9c88fe950

Observation 7a13b119-4b60-4d8d-8a09-293f5908a1bf · outbound

This paper cites NPJ Biofilms and Microbiomes , volume=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex NPJ Biofilms and Microbiomes , volume=

Reference 33

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:36af6de4dce0d71c785e3ddb308863c8f62b04c20e2635d5c98bfa4ac82e3b0a

Observation 75c2a2f6-5ef1-4c9c-8e63-a6a24fd8e765 · outbound

This paper cites Gut , volume=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex Gut , volume=

Reference 34

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:6afe055dad6ac6be08a2624dc3fbeda99cf176bf05c0a1ed79a9de7dae368f14

Observation 3d40a081-defe-40f6-8308-8464f8c36bd1 · outbound

This paper cites Science , volume=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex Science , volume=

Reference 35

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:3e2f9a4f76756829cef83dc1bf994ff765f3aeb4041f8771e295307a02c3ec7a

Observation b35c4415-c34b-4b97-9049-dda5346eab2c · outbound

This paper cites core microbiome.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex core microbiome

Reference 36

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:12c9e489ecc21408e48f4def61ec6b823094fa454c9e7da1d146f2d1190af2c9

Observation 42af08c8-5034-4182-b512-b77f4801749c · outbound

This paper cites Nature , volume=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex Nature , volume=

Reference 37

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:964f493db54bd97018cc718674c820a2e238345fa21a3e7e09cef5726ee7564c

Observation 34629e03-a3e6-46d9-984d-c25b8e251fd0 · outbound

This paper cites Forty-second International Conference on Machine Learning , year=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex Forty-second International Conference on Machine Learning , year=

Reference 38

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:47418c0f21bc35ca09b642e68599fe4951a34304446ecf087667f4adce4a52d7

Observation 94141778-fae9-4221-acad-253ec9aacf0c · outbound

This paper cites Applied and environmental microbiology , volume=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex Applied and environmental microbiology , volume=

Reference 39

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:a1f0097b619bf69c052eb16648afa5af0bbb4b30e0f6874f4cea9f8ad6e1f57b

Observation 9a4bb73a-339d-44c0-85a5-e5048bc17135 · outbound

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Tree-Structured Orthonormal Decomposition of the Aitchison Simplex Unresolved cited work

Reference 40

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Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:4b48c4ce1fda86e048a3024164b63cd3480b442bb1f1e2d108f7bb01fe437472

Observation 309cd2ab-c9de-410a-a888-68db7c87fb95 · outbound

This paper cites Nature Genetics , volume=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex Nature Genetics , volume=

Reference 41

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:b2cd47177b0150b02e29698f320789a107a25cde52e7adef71c9cf876bbfa745

Observation eb3d4d58-bc99-4675-9374-101dd104574f · outbound

This paper cites Nature Machine Intelligence , volume=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex Nature Machine Intelligence , volume=

Reference 42

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no resolver link, observed 2026-06-27T11:07:10.751182Z

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:d8dc88402d45960673d4716ed9988a3c72892ab28dc251d90f741aa0d2867776

Observation 7e9dd170-53bb-48b4-81f9-e3c952986565 · outbound

This paper cites Frontiers in Microbiology , volume=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex Frontiers in Microbiology , volume=

Reference 43

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no resolver link, observed 2026-06-27T11:07:10.751182Z

Source-reported events for the cited work

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:7143c52b266cc98c2a1d253bbde8657d59426dd06d7939a54a876184d9e9d64d

Observation 41442941-f499-4689-a644-ad913ccd8a53 · outbound

This paper cites 2009 , organization=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex 2009 , organization=

Reference 44

Resolution
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no resolver link, observed 2026-06-27T11:07:10.751182Z

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:b7ba18b86173764ee28734aede9e9c183cc0c6bbe4e804e60cef03a6642aff31

Observation 16f7bdd3-3e71-4686-82b1-9eba498919dc · outbound

This paper cites 1995 , publisher=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex 1995 , publisher=

Reference 45

Resolution
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no resolver link, observed 2026-06-27T11:07:10.751182Z

Source-reported events for the cited work

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:49636e23326a5f396eb187c7f862b04a8c1f5a16e07e9adbfdf77866c5eac45b

Observation 53684918-c047-469e-8b73-82123979cc1e · outbound

This paper cites 2009 , publisher=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex 2009 , publisher=

Reference 46

Resolution
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no resolver link, observed 2026-06-27T11:07:10.751182Z

Source-reported events for the cited work

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:348bcbb9be621d9ec4c53db2af6c64a9ccb0ea19f0bbdf6c8eb10c878fe1cf26

Observation 14b21b64-e31f-402f-926c-6b7fed2bd5a0 · outbound

This paper cites Frontiers in microbiology , volume=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex Frontiers in microbiology , volume=

Reference 47

Resolution
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no resolver link, observed 2026-06-27T11:07:10.751182Z

Source-reported events for the cited work

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:9c49ab5312624f794d2377edcca25e9b073c5258ecbc4e8abc3fe6a93a83c8e8

Observation d29e29c7-9e79-4977-a31e-44e6c5c8cc34 · outbound

This paper cites 2022 , publisher=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex 2022 , publisher=

Reference 48

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no resolver link, observed 2026-06-27T11:07:10.751182Z

Source-reported events for the cited work

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:ef9ab0aebf02f69aa5b7f70202dcde83370b9f93119cbc7bc3f086506cbe351d

Observation f0767625-4ee2-4ec6-8d92-3e47aa02adc5 · outbound

This paper cites 2022 , publisher=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex 2022 , publisher=

Reference 49

Resolution
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no resolver link, observed 2026-06-27T11:07:10.751182Z

Source-reported events for the cited work

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:0716cbc19a991ce5b96241a8ee8c6b1fddd00f5bc8e2306541e9c26b070d2c86

Observation b3a4d116-e44a-4659-bce2-60e067f5d4ee · outbound

This paper cites New England Journal of Medicine , volume=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex New England Journal of Medicine , volume=

Reference 50

Resolution
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no resolver link, observed 2026-06-27T11:07:10.751182Z

Source-reported events for the cited work

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:e5e1f397e13d4b6893116579b8774ed39dea4d918e51cea4c990033c46f4f084

Observation 5325738c-c53a-4c08-b273-9361d51708e2 · outbound

This paper cites Comprehensive Physiology , volume=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex Comprehensive Physiology , volume=

Reference 51

Resolution
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no resolver link, observed 2026-06-27T11:07:10.751182Z

Source-reported events for the cited work

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:a459122cecd35a4cb2721bf4cfd3501594f16f6093b61d7c588a8435d5ba794e

Observation b3bce94b-7cf5-4e21-a9e1-66e2589261ef · outbound

This paper cites 2022 , publisher=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex 2022 , publisher=

Reference 52

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no resolver link, observed 2026-06-27T11:07:10.751182Z

Source-reported events for the cited work

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:bcaf90f9b66fda830621e81d35b1cda659848ced09cea1700bb343925eb6efd5

Observation 1161301c-8c37-4048-936b-50b6df237505 · outbound

This paper cites The 28th International Conference on Artificial Intelligence and Statistics , year=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex The 28th International Conference on Artificial Intelligence and Statistics , year=

Reference 53

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no resolver link, observed 2026-06-27T11:07:10.751182Z

Source-reported events for the cited work

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:669ee0fbb73b3644b2865f1417f63324746d149576f8fbd8373247ac1c906d03

Observation 940ea72c-f4f4-4b37-8403-dd6923f10368 · outbound

This paper cites an unresolved cited work.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex Unresolved cited work

Reference 54

Resolution
unresolved
no resolver link, observed 2026-06-27T11:07:10.751182Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:9f9d0b5950b9d44863011376fb36aef5bd304b663b92a14f36572a24eb05b5d8

Observation 150ae1ee-9346-4013-a0b1-6d5f7554f4c0 · outbound

This paper cites Advances in neural information processing systems , volume=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex Advances in neural information processing systems , volume=

Reference 55

Resolution
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Source-reported events for the cited work

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:e61b70baa9f14a4dcb7dd9d1fe81969c994d24b14b559fcedd0da2db255b1f2e

Observation ed6f162d-c4c9-4cc7-a6ee-673e734fd5c7 · outbound

This paper cites Advances in Applied Mathematics , volume=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex Advances in Applied Mathematics , volume=

Reference 56

Resolution
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no resolver link, observed 2026-06-27T11:07:10.751182Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:bd3f66247890ea6676acd6cd744c190f0cae8d001481e3a12335a401a22c696f

Observation ebda350f-0c13-45d0-9710-674add656aa7 · outbound

This paper cites IEEE/ACM Transactions on Computational Biology and Bioinformatics , volume=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex IEEE/ACM Transactions on Computational Biology and Bioinformatics , volume=

Reference 57

Resolution
unresolved
no resolver link, observed 2026-06-27T11:07:10.751182Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:cd604641ba81c276f9e8d93ee623324c5c2643c998ba0fcc8ff41ad2d417be9c

Observation 20eb4bb0-82e5-4c86-b917-d1d8984310cd · outbound

This paper cites Tropical Geometry of Phylogenetic Tree Space: A Statistical Perspective.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex Tropical Geometry of Phylogenetic Tree Space: A Statistical Perspective

Reference 58

Resolution
verified exact
arxiv_id, observed 2026-07-03T08:07:45.324717Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:86c0045621fa002df51712930852370679ebe8633598da32a7762275ee85ae2a

Observation 7314527f-69bc-4c6e-9d23-c01bbbc3986b · outbound

This paper cites Data mining and knowledge discovery , volume=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex Data mining and knowledge discovery , volume=

Reference 59

Resolution
unresolved
no resolver link, observed 2026-06-27T11:07:10.751182Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:0f6002721677a4643436f7ee7b8f49a87d3fc29e0af4adbe0fa975bbd1bda36d

Observation f9668ec6-e760-4348-b283-69e6f8f811da · outbound

This paper cites International Conference on Machine Learning , pages=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex International Conference on Machine Learning , pages=

Reference 60

Resolution
unresolved
no resolver link, observed 2026-06-27T11:07:10.751182Z

Source-reported events for the cited work

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:f3b0ec1458860a792666030393d9da938635454756c0ece85428b3c606a60d6f

Observation 9c4c7abf-4d96-45a2-855f-d3f2779cdf8e · outbound

This paper cites Signal Transduction and Targeted Therapy , volume=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex Signal Transduction and Targeted Therapy , volume=

Reference 61

Resolution
unresolved
no resolver link, observed 2026-06-27T11:07:10.751182Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:32e380c6f486a5d1a91a9709d70fbf446dd053516e99b88bd2d0276f58e1c90a

Observation 30f44c02-2606-4afe-b357-a505fee870ba · outbound

This paper cites Cladistics , volume=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex Cladistics , volume=

Reference 62

Resolution
unresolved
no resolver link, observed 2026-06-27T11:07:10.751182Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:8fe40ac0a5e3ea32f72b9a0dadd2b66519f82e785bb2711ea984883c3c0d2599

Observation 0c293047-6203-416a-a262-f043aac24dfc · outbound

This paper cites an unresolved cited work.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex Unresolved cited work

Reference 63

Resolution
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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:582b039d275cc6dbecb7af7490d3ca9eca3b2b42a0db1f2d9e1fee205da597fe

Observation 25311cb6-e9f5-46a7-a044-db1d0d5633e0 · outbound

This paper cites Nature Communications , volume=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex Nature Communications , volume=

Reference 64

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source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:382467cae589a8c9d68460761a876c876712251edfbbb801d2af297433cb8145

Observation 7ab5edd0-ca51-40df-b825-7a9d653972ad · outbound

This paper cites Microbiome , volume=.

Tree-Structured Orthonormal Decomposition of the Aitchison Simplex Microbiome , volume=

Reference 65

Resolution
unresolved
no resolver link, observed 2026-06-27T11:07:10.751182Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-06-27T11:07:10.751182Z digest=sha256:e7617399b93d92015fe164aa6f1e62fc765c73b26ef6fc2b6d5efb2ee63b7003

Pith citing papers

No inbound Pith citation observations are available.