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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 2026-08-19T06:32:44.657259+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 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-05T13:58:22.923668Z digest=sha256:a6ab54e8b079088ba3114aead759c3389944ebccf7a55f2558a735f54421309d

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 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-05T13:58:23.012868Z digest=sha256:681e03098617f0f34556f9c6c967d87ee9a656de641fb219e46ebb5b5c764906

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 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-05T13:58:23.096842Z digest=sha256:27ed83daa0cb8716457dba7e60cee80800314d789fc4959fc49e8db342578772

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 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-05T13:58:23.203277Z digest=sha256:04d8f68ee6f6d2e5349abf5110a8e9f861146bb85cab0027f5b7070ddaba0461

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 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-05T13:58:23.294761Z digest=sha256:a1d372d2915760c5823d8527db221291a375881b9d93b7e7a8554aac5af61008

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 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-05T13:58:23.414430Z digest=sha256:be3949d048c1b8951adc017f0a720875c3a9efed6d8301509d3a5696ce8719c8

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 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-05T13:58:23.512398Z digest=sha256:44915943e576aff19a7fc9719ae828ee5a71447eba960864e54e2451e4192b98

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 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-05T13:58:23.632497Z digest=sha256:c85f29a7082a8987300d424dc7908b6d4a8f62c850e34b6958584dc9c6381655

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 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-05T13:58:23.738692Z digest=sha256:ecc800c9497d3477c0a662a5226829a7014aae1bd5f7159b102a1210f1782447

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 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-05T13:58:23.865795Z digest=sha256:b5a3b399fb4774a6ee58aefe6dcd2bf194613811fe1f683064da5715b2a0af85

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 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-05T13:58:23.979776Z digest=sha256:099c8919c9465851034f5a10324a3700251cfde61c90cb7ec2657e88e6d520ec

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 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-05T13:58:24.093494Z digest=sha256:ba02182d5428535ce2c9ee12f39a57fd419eb718958cc4ebd5f63af605ffc4ba

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 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-05T13:58:24.144113Z digest=sha256:e4ac87216146525ba465e03d75efd79f745e14467d457b662fe549f6e3b42591

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 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-05T13:58:24.218576Z digest=sha256:bfdace60c89cfcf7650f345c4250ab326e4e9dc23a32ece01cc1a3313dfa1e3e

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 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-05T13:58:24.288247Z digest=sha256:eaf9fd5046b7898571b85cfe481d9ab358837e28addb10470c6a1e12d33782f9

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 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-05T13:58:24.368078Z digest=sha256:b573e2058b3ff1a45fd776eb84aa33078cba824c001f3d18e6bee3998dbf7df5

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 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-05T13:58:24.492894Z digest=sha256:ed3e2c6669477f6739583c69a323d88a8e3126a47d3b2cc75488686bba1e421b

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 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-05T13:58:24.594477Z digest=sha256:9f19785f82e43a4f5a75b2eb24267e2c287039ad46f86354792be8bcea7dcbdc

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 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-05T13:58:24.720620Z digest=sha256:37476cd4ee7fe952b944401f4a4775c837163a0a2e2d3ef924a1a4f291e256b8

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 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-05T13:58:24.841181Z digest=sha256:deb292dd8d50747849850984e21a29c1e506a493c022fef80cc89de891ae002e

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 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-05T13:58:24.961029Z digest=sha256:3811c416f073f9c2b057364329369ed4033992cffdf9bcabd879bd9fd0e295e1

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 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-05T13:58:25.113999Z digest=sha256:ac35fd9de466cca7e9ae13d6c6e1ad884d90b8bd8bf2930708d170fac2db79a2

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 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-05T13:58:25.272607Z digest=sha256:97fc8caf434be9f9d7023e3ce144e26e5ba56dd6bbd9859a75fb8bee774df609

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 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-05T13:58:25.391908Z digest=sha256:e042a4a00708b234babd62eb925af75873bdee8fd703639ccb4cda9db653a3a0

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 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-05T13:58:25.508081Z digest=sha256:094115185fc4b265e4fa99ede697776128eafcc751fb856dd3710054876615be

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 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-05T13:58:25.657394Z digest=sha256:268402d20dce96fef96d30b6b839eeb4cf063c7ff3e25a3cf9917bc65f4988bb

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 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-05T13:58:25.748952Z digest=sha256:3e85f29f54331762242f2de72703b9bb0ebf46ac0811e0fabf8b6cf2c4126cf4

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 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-05-16T15:56:25.366353Z digest=sha256:ac5858274076b1ead9a1786654f7ab5add67758d61663b6fb5f46dbdc84f391f