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Paper Citation Record · LEDGER

Strata of Ecological Coexistence via Grassmannians

As of 20 August 2026, this Paper Citation Record lists 27 of 27 outbound references and 1 inbound Pith citation observation for arXiv:2509.00165.

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

pith.paper-citation-record.v1
2509.00165 v1

Coverage vector

measured 27 of 27 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-05T13:58:25.748952Z

measured 28 of 28 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-16T15:56:25.366353Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-16T15:58:03.963577Z

Reference resolution

27 of 27 outbound references displayed

  • verified exact2
  • verified fuzzy14
  • unresolved11
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation b0a13f71-286f-40ee-8790-491ec95b0267 · outbound

This paper cites an unresolved cited work.

Strata of Ecological Coexistence via Grassmannians Unresolved cited work

Reference 1

Resolution
verified exact
raw_fallback, observed 2026-08-05T13:58:26.327222Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-05T13:58:22.923668Z digest=sha256:1dca14c4d7f1c4316dcae6492db56b475ce613391f5382d1cbf52958dd77eb27

Observation 4db18b86-4633-496b-aa41-4ca4c1ca040c · outbound

This paper cites an unresolved cited work.

Strata of Ecological Coexistence via Grassmannians Unresolved cited work

Reference 2

Resolution
unresolved
raw_fallback, observed 2026-08-05T13:58:32.352413Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-05T13:58:23.012868Z digest=sha256:18463920035360e1516a23d2e124cc958796669796179d32f38d90b5738c05fb

Observation a5284b72-7a4f-4f4b-9bfd-92f465c36ff2 · outbound

This paper cites Allesina and S.

Strata of Ecological Coexistence via Grassmannians Allesina and S

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T13:58:32.027108Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-05T13:58:23.096842Z digest=sha256:32ff62d99f00fa1c491c0fc5be65893899b5356ecfa9c4240342a0f4aa999577

Observation e64326f9-7eeb-4f3e-b300-03838d0bfd8d · outbound

This paper cites Allesina and S.

Strata of Ecological Coexistence via Grassmannians Allesina and S

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T13:58:31.739499Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-05T13:58:23.203277Z digest=sha256:61df5105544b97c8b836f8c70c15fd47c8df7d6daaaf8fa6b91a70a976095a9a

Observation 14978e0b-8952-4568-b790-c8ae4983556e · outbound

This paper cites Bj¨ orner, M.

Strata of Ecological Coexistence via Grassmannians Bj¨ orner, M

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T13:58:31.523963Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-05T13:58:23.294761Z digest=sha256:971602e9db9ec3a0a1aea2a0d0990cd8a87de4e0450f6d06671f93bef6d798d3

Observation 8b22a938-b54b-48f7-ae1d-fb9793651195 · outbound

This paper cites Bogoyavlensky.

Strata of Ecological Coexistence via Grassmannians Bogoyavlensky

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T13:58:31.356916Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-05T13:58:23.414430Z digest=sha256:573281c7f3fa504fdf4e4e426f22327f6893cc7b0baf1c0041f8d225c6c3435a

Observation 2c5a0b16-0e63-4f1a-9989-405340f569e4 · outbound

This paper cites Breiding, B.

Strata of Ecological Coexistence via Grassmannians Breiding, B

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T13:58:31.105627Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-05T13:58:23.512398Z digest=sha256:2521ccc7e04687e4a0db8c4aaa16603c777ea06b58f60de635268b237afb6a25

Observation 6d5e3905-3dbe-49d1-b80f-f91a6c749897 · outbound

This paper cites Butler and J.

Strata of Ecological Coexistence via Grassmannians Butler and J

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T13:58:30.898526Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-05T13:58:23.632497Z digest=sha256:71e35567565be9c1b1589927cf78da3badea658bc94ac7b1a98b17e244a15a17

Observation f56312fb-d0c2-4999-a1fb-fe185c601b8c · outbound

This paper cites an unresolved cited work.

Strata of Ecological Coexistence via Grassmannians Unresolved cited work

Reference 9

Resolution
unresolved
raw_fallback, observed 2026-08-05T13:58:30.687257Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-05T13:58:23.738692Z digest=sha256:a620e6b8a04bdd394c05421acb01e73c5e046ee1cf44bafb24a3cb95ddcb1e5c

Observation a0f1c07a-6a98-48d0-8862-40287db43973 · outbound

This paper cites Routing functions for parameter space decomposition to describe stability landscapes of ecological models.

Strata of Ecological Coexistence via Grassmannians Routing functions for parameter space decomposition to describe stability landscapes of ecological models

Reference 10

Resolution
verified exact
local_arxiv, observed 2026-08-05T13:58:25.994251Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-05T13:58:23.865795Z digest=sha256:99870f047d3924ccf9342436185d23126ef3d92f06850aad420f3b02bf8f2c2f

Observation 1e3115d7-f9ce-4b9d-b6da-9a17e5d6359c · outbound

This paper cites Cummings, J.

Strata of Ecological Coexistence via Grassmannians Cummings, J

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T13:58:30.384822Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-05T13:58:23.979776Z digest=sha256:0dd24998e771319e113c198202f6f284e69113968dea4d1e16a435249a8021ea

Observation ded239d4-349f-4de0-b7d4-6cb75021fe9d · outbound

This paper cites Curto and K.

Strata of Ecological Coexistence via Grassmannians Curto and K

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T13:58:30.042916Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-05T13:58:24.093494Z digest=sha256:915984a75b02a5f398acf8046e2f8065cc92012c7bdbd27cb2d6381cbcef9c6e

Observation 4669bcaa-8bf7-4c6d-8cae-f44ed7420b2f · outbound

This paper cites Dickenstein.

Strata of Ecological Coexistence via Grassmannians Dickenstein

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T13:58:29.790306Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-05T13:58:24.144113Z digest=sha256:487dadb9d791c4032838a3220cb4029c8ea899aa155a8c8b3c793ca5403fc52c

Observation 384fb78d-16d1-4b30-ae86-2470d38f153f · outbound

This paper cites an unresolved cited work.

Strata of Ecological Coexistence via Grassmannians Unresolved cited work

Reference 14

Resolution
unresolved
raw_fallback, observed 2026-08-05T13:58:29.479114Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-05T13:58:24.218576Z digest=sha256:8a8c29eb7a5260cf24d607df1f2a6ba437852fe447e66f5811837b194fd7433f

Observation ae884bcd-62d4-4020-99e2-b02698ff6d61 · outbound

This paper cites an unresolved cited work.

Strata of Ecological Coexistence via Grassmannians Unresolved cited work

Reference 15

Resolution
unresolved
raw_fallback, observed 2026-08-05T13:58:29.249103Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-05T13:58:24.288247Z digest=sha256:de24513b0214713689838da3daba23ed40e38db14a8ed4aad779bd0e11200701

Observation 231ef46f-46df-4363-8c46-707c4b03eedb · outbound

This paper cites Gesmundo and H.

Strata of Ecological Coexistence via Grassmannians Gesmundo and H

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T13:58:29.034024Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-05T13:58:24.368078Z digest=sha256:13f0cfc5fa9af1426ecb6109467acb4ae7bca6281654ba0be2da2fc841caff4d

Observation 967c8b4d-3bcb-4ea6-85e7-9857f19578e8 · outbound

This paper cites an unresolved cited work.

Strata of Ecological Coexistence via Grassmannians Unresolved cited work

Reference 17

Resolution
unresolved
raw_fallback, observed 2026-08-05T13:58:28.823276Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-05T13:58:24.492894Z digest=sha256:a96453bdfc748c8b40ebeb5ef2eba9153386911a1a0ed1770fe19be595963ada

Observation 09ca908c-06f0-4087-b09e-950113ff8987 · outbound

This paper cites Hofbauer and K.

Strata of Ecological Coexistence via Grassmannians Hofbauer and K

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T13:58:28.641783Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-05T13:58:24.594477Z digest=sha256:0a97304e15bf5013c7a180597d3a0eb6e966176a417506bec9ffd8787ec0e979

Observation abce353f-7c97-4022-9831-2031c8d58ca0 · outbound

This paper cites an unresolved cited work.

Strata of Ecological Coexistence via Grassmannians Unresolved cited work

Reference 19

Resolution
unresolved
raw_fallback, observed 2026-08-05T13:58:28.353915Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-05T13:58:24.720620Z digest=sha256:11ec18675dfbd45130b45ef9c3a74a3199279513a83fb90a3dedc94d45c44a00

Observation ad0648c2-cbe3-4573-8a35-22a5f3299e65 · outbound

This paper cites an unresolved cited work.

Strata of Ecological Coexistence via Grassmannians Unresolved cited work

Reference 20

Resolution
unresolved
raw_fallback, observed 2026-08-05T13:58:28.129637Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-05T13:58:24.841181Z digest=sha256:0e2baa9bc686d8208442f5cefe5a9922fa135809b4c0922beeee082e1c89bfd9

Observation 296988d5-edcc-40b4-b3fa-f0e796b6f1cc · outbound

This paper cites Micha lek and B.

Strata of Ecological Coexistence via Grassmannians Micha lek and B

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T13:58:27.951766Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-05T13:58:24.961029Z digest=sha256:5e7239e49fdacdbbd6c04878030b4e734f556bda7594bf7803e9e18c1d091181

Observation b36552db-d1f7-44bd-ad29-d926fc683cb9 · outbound

This paper cites Mougi and M.

Strata of Ecological Coexistence via Grassmannians Mougi and M

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T13:58:27.684752Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-05T13:58:25.113999Z digest=sha256:2c6042da377d1b17d19a3ee540ee643a9e0d42a4cb7efcf7072429e49c504669

Observation 95ccbe2e-88d6-4884-85e3-56b6445f0a47 · outbound

This paper cites an unresolved cited work.

Strata of Ecological Coexistence via Grassmannians Unresolved cited work

Reference 23

Resolution
unresolved
raw_fallback, observed 2026-08-05T13:58:27.474521Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-05T13:58:25.272607Z digest=sha256:efe49bf9b66012ea91fbc426a6f56079b470268b3511b7e21bdc1ca3c5ad5fc5

Observation d9fd2450-1372-4742-96ac-aa40ceb617d1 · outbound

This paper cites an unresolved cited work.

Strata of Ecological Coexistence via Grassmannians Unresolved cited work

Reference 24

Resolution
unresolved
raw_fallback, observed 2026-08-05T13:58:27.232437Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-05T13:58:25.391908Z digest=sha256:bb19e90d518edf8f7a54c02d3f23b4ab0e867af9a16b9714eca2ab3725377690

Observation 5c8dc92f-48db-49ba-841b-a04ef2bfc0da · outbound

This paper cites Scholten, K.

Strata of Ecological Coexistence via Grassmannians Scholten, K

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T13:58:27.079400Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-05T13:58:25.508081Z digest=sha256:efdf5a6f52bef737f0fb2ddf362e0436ad91fac954a597f9722c52b05b7326a8

Observation b408b752-54eb-4eea-9a9e-90fc677e1455 · outbound

This paper cites an unresolved cited work.

Strata of Ecological Coexistence via Grassmannians Unresolved cited work

Reference 26

Resolution
unresolved
raw_fallback, observed 2026-08-05T13:58:26.916305Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-05T13:58:25.657394Z digest=sha256:1925a3220c8a554b3618482eee358b632cc6b96c29a886a57c0d36791dd43bae

Observation 1ca6b4b4-4dba-4692-a26a-7e5c756a72a3 · outbound

This paper cites an unresolved cited work.

Strata of Ecological Coexistence via Grassmannians Unresolved cited work

Reference 27

Resolution
unresolved
raw_fallback, observed 2026-08-05T13:58:26.637847Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-08-05T13:58:25.748952Z digest=sha256:54c1ffe0c85ef5e28b99422716b5cb6db3323e9977695c4b14409874e0eceb6c

Pith citing papers

Observation 686dffea-2740-4a01-9a9b-e5713cd4b532 · inbound

Elimination Without Eliminating: Computing Complements of Real Hypersurfaces Using Pseudo-Witness Sets cites this paper.

Elimination Without Eliminating: Computing Complements of Real Hypersurfaces Using Pseudo-Witness Sets Strata of Ecological Coexistence via Grassmannians

Reference 54

Resolution
verified exact
arxiv_id, observed 2026-05-16T15:58:03.965689Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=pdf_text observed=2026-05-16T15:56:25.366353Z digest=sha256:cac50c0b53f81d4b229d45b20d90107d827c906a071222e574a09260d22a06e1