cometadata/datacite-titles-descriptions-related-identifiers huggingface dataset:
DOI: 10.3535/cdm-3t1-de7
title: Carex davalliana Sm.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.15468/dl.varah4
title: Occurrence Download

description: A dataset containing 19565 species occurrences available in GBIF matching the query:
{
 "and" : [
 "TaxonKey is one of (Phylloscopus pulcher)",
 "HasCoordinate is true",
 "OccurrenceStatus is Present",
 "License is one of (CC-BY 4.0, CC0 1.0)"
 ]
}

 The dataset includes 19565 records from 16 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0064666-250717081556266/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.3535/7lj-akk-zk4
title: Lathyrus venetus (Mill.) Wohlf.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/lvk-xzq-024
title: Lemna minor L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.14457/nida.the.2014.148
title: แนวทางการส่งเสริมการท่องเที่ยวผ่านอาหารพื้นเมืองจังหวัดน่าน
DOI: 10.3535/v8v-wn6-2mx
title: Juncus articulatus L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/xpa-42r-fa6
title: Malva verticillata L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/pdl-pfq-skg
title: Salix L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.14457/nida.the.2015.254
title: แนวทางการพัฒนาแหล่งท่องเที่ยวอัญมณีของจังหวัดจันทบุรีเพื่อตอบสนองพฤติกรรมนักท่องเที่ยวชาวไทย
DOI: 10.3535/l42-ndy-gfp
title: Salix lapponum L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/8jv-zhd-ek3
title: Thalictrum flavum L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/f8n-n64-zlj
title: Salix L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/hne-6x7-81t
title: Salix L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/q0y-61p-9ap
title: Thalictrum lucidum L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.14457/nida.the.2021.136
title: อิทธิพลของจริยธรรมองค์การที่มีต่อความทุ่มเทมีใจของพนักงานโรงแรม ในเขตพื้นที่ระเบียงเศรษฐกิจพิเศษภาคตะวันออก
DOI: 10.3535/dqz-bgz-51t
title: Salix L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/npx-9jr-tjl
title: Salix L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/xl4-64v-627
title: Ranunculus acris L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.14457/nida.the.2019.195
title: พฤติกรรมนักท่องเที่ยวชาวต่างชาติต่อการท่องเที่ยวเชิงสร้างสรรค์กรณีศึกษา อำเภอเกาะสมุย จังหวัดสุราษฎร์ธานี
DOI: 10.3535/71m-zj3-acg
title: Salix L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/c8y-e4m-p92
title: Salix L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/8e9-33n-pqk
title: Salix alpina Scop.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/2py-42c-jmy
title: Salix L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/952-4ey-gle
title: Salix L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/evl-sgj-j8c
title: Salix L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/whq-fsc-3ep
title: Oreochloa disticha (Wulfen) Link

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/435-pvz-jy5
title: Salix L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/mml-hfl-ggb
title: Gymnocarpium dryopteris (L.) Newman

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/c83-wmv-3rl
title: Salix L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/mj8-vdn-02m
title: Crataegus monogyna Jacq.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/wv2-52n-zmw
title: Salix L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/35k-8ta-cg1
title: Salix L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/h6f-kxh-am3
title: Geum urbanum L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/e6g-93e-xvg
title: Potentilla micrantha Ramond ex DC.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/dy8-40e-3g7
title: Vicia cassubica L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/fvd-73g-0zk
title: Carex nigra subsp. transcaucasica (T.V.Egorova) Jim.Mejías, G.E.Rodr.-Pal., Amini Rad & Martín-Bravo

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/h8m-66r-mnx
title: Hylotelephium telephium (L.) H. Ohba

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/p7d-w7e-5vg
title: Carex phyllostachys C.A.Mey.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/c6w-sw3-src
title: Laserpitium archangelica Wulfen

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/y8l-q20-dhx
title: Salix L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/93r-k4q-y7k
title: Sedum L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/pp5-p09-sma
title: Carex tomentosa L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/1sr-dkz-0bm
title: Carex disticha Huds.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/qes-tfd-dsy
title: Laserpitium archangelica Wulfen

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/gba-x1k-j7b
title: Carex nigra subsp. transcaucasica (T.V.Egorova) Jim.Mejías, G.E.Rodr.-Pal., Amini Rad & Martín-Bravo

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/1ez-rak-8xd
title: Carex panicea L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/48y-zyr-2mc
title: Dryopteris carthusiana (Vill.) H. P. Fuchs

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.15468/dl.xh2kuz
title: Occurrence Download

description: A dataset containing 19 species occurrences available in GBIF matching the query:
{
 "and" : [
 "TaxonKey is one of (Crenicichla cincta)",
 "BasisOfRecord is one of (Specimen, Literature Occurrence, Human Observation, Observation)",
 "HasCoordinate is true",
 "HasGeospatialIssue is false",
 "Year is greater than or equal to 1991",
 "Year is less than or equal to 2025"
 ]
}

 The dataset includes 19 records from 7 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0064667-250717081556266/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.3535/h5x-s5q-s4a
title: Blysmus compressus (L.) Panz. ex Link

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/nkt-em8-td1
title: Carex umbrosa subsp. huetiana (Boiss.) Soó

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/1pm-1dp-abx
title: Carex distans L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/fre-qtx-xnf
title: Carex muricata subsp. ashokae Molina Gonz., Acedo & Llamas

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/j8s-ef5-wzl
title: Carex panicea L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/s2z-fjs-92d
title: Lepidium virginicum L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/7gt-f66-tsz
title: Carex otrubae Podp.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/gcg-f59-7f0
title: Carex divulsa Stokes

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/2qf-r68-psp
title: Poterium sanguisorba subsp. polygamum (Waldst. & Kit.) Asch. & Graebn.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/trh-93h-z5v
title: Vicia villosa Roth

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/yfd-8nv-vhf
title: Carex nigra subsp. transcaucasica (T.V.Egorova) Jim.Mejías, G.E.Rodr.-Pal., Amini Rad & Martín-Bravo

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/yrf-ahh-g1z
title: Carex spicata Huds.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/s6q-age-jkn
title: Trifolium ochroleucon subsp. ochroleucon

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/ty6-b1h-z8g
title: Rumex L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/9tj-73n-xv4
title: Myosurus minimus L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/arq-gxt-vyf
title: Trifolium incarnatum L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/fzv-adr-156
title: Saxifraga hohenwartii Vest ex Sternb.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.15468/dl.evqknv
title: Occurrence Download

description: A dataset containing 0 species occurrences available in GBIF matching the query:
{
 "and" : [
 "TaxonKey is Lemna perpusilla",
 "Country is Comoros",
 "HasCoordinate is true"
 ]
}

 The dataset includes 0 records from 0 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0064669-250717081556266/datasets/export for details.
DOI: 10.3535/40n-7na-les
title: Digitalis lanata Ehrh.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/wax-mvz-q7d
title: Rubus idaeus L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/lnl-05d-la5
title: Geranium sylvaticum L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/rwe-m2w-k97
title: Trifolium ochroleucon subsp. ochroleucon

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/em1-ntk-qh0
title: Lonicera nigra L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/f92-1m1-plm
title: Portulaca oleracea L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/a8r-nbg-mc9
title: Dactylorhiza viridis (L.) R.M.Bateman, Pridgeon & M.W.Chase

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/vwc-59g-ln5
title: Crataegus rhipidophylla Gand.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/4s1-3wd-j98
title: Agrimonia L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/klw-7mz-1hh
title: Ranunculus pilisiensis Soó

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/wnb-8k1-0xx
title: Artemisia umbelliformis Lam.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/a1j-dv7-mdc
title: Salix myrsinifolia subsp. borealis (Fr.) Hyl.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/jh8-w62-k8c
title: Cyrtochilum verstraeteanum Dalström & Deburghgr.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/869-xq2-yzt
title: Salix L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/nly-q47-nl1
title: Papaver dubium subsp. austromoravicum (Kubát) Hörandl

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/p70-hah-hve
title: Lactuca quercina L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/6jr-jjb-kd5
title: Ranunculus auricomus L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/pyh-blr-ljc
title: Salix L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/k3n-hm3-spm
title: Salix L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/wah-kxx-7m1
title: Salix myrsinifolia subsp. borealis (Fr.) Hyl.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/069-z0e-w55
title: Gentiana clusii E. P. Perrier & Songeon

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/ebr-ba7-903
title: Callitriche palustris L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/7kq-fxy-37r
title: Salix L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/g0t-bmc-k9w
title: Veronica dillenii Crantz

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/m2m-nyv-kad
title: Salix L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.15468/dl.fj9kv2
title: Occurrence Download

description: A dataset containing 223 species occurrences available in GBIF matching the query:
{
 "TaxonKey" : [
 "is Dysosma versipellis"
 ]
}

 The dataset includes 223 records from 30 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0064668-250717081556266/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.3535/0x8-knt-7xh
title: Medicago lupulina L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/rpe-sqw-knv
title: Salix L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/enq-ggj-tk0
title: Cytisus nigricans subsp. nigricans

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/hrb-hqa-9bk
title: Juncus compressus Jacq.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/494-axk-1c1
title: Circaea lutetiana L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/8rt-261-0c0
title: Campanula portenschlagiana Schult.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/faq-gwv-4ca
title: Bituminaria bituminosa (L.) C.H.Stirt.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/eee-h2r-cfg
title: Carpinus betulus L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/xwa-m56-qwj
title: Crepis biennis L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/hpm-0kc-mpb
title: Crepis biennis L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/c4w-hg0-v16
title: Carex distans L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/hnv-3kf-kh7
title: Robinia pseudoacacia L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/9cp-p6m-2zc
title: Carex stenophylla subsp. stenophylloides (V.I.Krecz.) T.V.Egorova

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/z8d-r8w-l9y
title: Salix myrsinifolia subsp. borealis (Fr.) Hyl.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.15468/dl.fhgqvp
title: Occurrence Download

description: A dataset containing 1 species occurrences available in GBIF matching the query:
{
 "and" : [
 "TaxonKey is Camelina alyssum",
 "Country is Chile",
 "HasCoordinate is true"
 ]
}

 The dataset includes 1 records from 1 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0064670-250717081556266/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.3535/5ws-9ys-yx3
title: Dianthus alpinus L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/t7l-4kd-63s
title: Carex divisa Huds.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/z87-x9n-mwf
title: Silene dioica (L.) Clairv.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/1vq-grx-kkk
title: Arenaria ciliata L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/q36-vp5-fgk
title: Danthonia alpina Vest

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/5mh-l8b-t0n
title: Sempervivum globiferum subsp. glabrescens (Sabr.) M. Werner

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/b7d-xbq-gez
title: Carex pendula Huds.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/n72-w42-hqw
title: Allium lusitanicum Lam.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/5c8-vqn-qm1
title: Inula oculus-christi L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/90s-xex-j06
title: Carex melanostachya M.Bieb. ex Willd.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/hly-6ct-ny4
title: Carex supina Willd. ex Wahlenb.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/q6j-hwg-ax0
title: Carex divulsa Stokes

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/nb9-hhv-pw2
title: Carex spicata Huds.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/d03-d4a-w30
title: Polypodium vulgare L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/kds-ya3-ryj
title: Polypodium vulgare L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/sk6-6fr-38l
title: Glechoma hirsuta Waldst. & Kit.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/zev-s7z-ybk
title: Artemisia verlotiorum Lamotte

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/gdb-9d4-6ge
title: Gymnocarpium dryopteris (L.) Newman

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/jql-p76-b71
title: Helichrysum arenarium (L.) Moench

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/nm7-k28-vf3
title: Ononis L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/wcp-8m6-lf9
title: Koeleria Pers.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/8ra-2hr-3cj
title: Trifolium Tourn. ex L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/qql-pnk-83j
title: Salix babylonica L.

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/c32-hhs-4sb
title: Alchemilla austroitalica Brullo, Scelsi & G. Spampinato

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.3535/m0c-m6j-298
title: Carex sylvatica subsp. sylvatica

description: Digital Specimen for the physical specimen hosted at University of Graz.
DOI: 10.5281/zenodo.16552425
title: galactic dark feedback higherD gravity

description: 🔷 Equation 1 — Galactic Debris Dynamics

\[

\frac{d\sigma_r}{dt} = 

\underbrace{-\frac{GM_{\text{core}}}{r^2}}_{\substack{\text{Remnant gravity} \\ \text{(Central BH/compact object)}}} 

+ \underbrace{\frac{\Lambda(t) v_p^2}{\sqrt{r^2 + r_s^2}}}_{\substack{\text{Dark feedback} \\ \text{(DM/DE coupling)}}} 

+ \underbrace{\zeta \frac{c_s^2}{r}}_{\substack{\text{Pressure support} \\ \text{(Gas turbulence)}}} 

- \underbrace{\eta \sigma_r^2}_{\substack{\text{Drag force} \\ \text{(Dynamical friction)}}}

\]

 

**Key Parameters:**

- \( r_s \): Schwarzschild radius (\(2GM_{\text{core}}/c^2\))

- \( \Lambda(t) \): Time-dependent dark sector coupling (\(\Lambda_0 e^{-t/\tau} + \Lambda_{\text{DM}}\rho_{\text{DM}}\))

- \( \zeta \): Pressure efficiency (0.1-1 for typical ISM)

 

**Observational Signatures:**

- Anomalous stellar stream kinematics (Gaia DR4)

- Non-Keplerian rotation in post-starburst galaxies (JWST/NIRSpec)

 

#### 🔷 Equation 2 — Modified Gravity with Exotic Sources

\[

G_{\mu\nu}^{(4)} + \kappa_{(4)}T_{\mu\nu}^{(4)} = 

\underbrace{e^{-\beta\phi}\left[G_{AB}^{(D)}g^{AB}_{(4)} + \mathcal{F}_{\mu\nu}\right]}_{\substack{\text{Higher-D corrections} \\ \text{(Bulk spacetime curvature)}}} 

+ \underbrace{\Lambda\left(\sqrt{\frac{3}{8\pi}}\frac{\gamma(v)v^2r_p^2\rho_g}{Gc^2}\right)g_{\mu\nu}}_{\substack{\text{Exotic BH formation} \\ \text{(Relativistic collisions)}}}

\]

 

**Novel Components:**

- \( \mathcal{F}_{\mu\nu} \): Bulk-to-brane gravity leakage (string theory motivated)

- \( \gamma(v) \): Lorentz factor (\((1-v^2/c^2)^{-1/2}\))

- Critical velocity threshold: \( v > 0.6c \) for BH formation

 

**Experimental Probes:**

- Sub-solar mass BH searches (Einstein Telescope)

- Gravitational wave echo detection (LIGO O4)

## 📈 Sample Outputs

### 1. Galactic Debris Dynamics Simulation**Input Parameters**:```pythonM_core = 1e6 * u.Msun  # Central black hole massLambda_0 = 1e-5        # Dark feedback strengthv_p = 0.2 * u.c        # Debris velocityzeta = 0.7             # Pressure efficiency```

**Radial Velocity Dispersion Evolution**:

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### 2. Modified Gravity Predictions**GW Echo Profile** (Equation 2):```pythonbeta = 0.1     # Dilaton coupling  D = 5          # Extra dimensionsM_BH = 10      # Solar masses```

*Predicted echo delay Δt ≈ 1.2 ms for LIGO O4 events*

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### 3. Observational Comparison**Palomar 5 Stream Anisotropy**:| Model | χ²/dof | Λ(t) Detection Significance ||-------|--------|-----------------------------|| Standard | 4.7 | - || **This Work** | 1.2 | 4.1σ |

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### 4. Parameter Constraints| Parameter | Best Fit | 95% CL | Instrument ||-----------|----------|--------|------------|| Λ₀ | 8.7×10⁻⁶ | [6.2, 11]×10⁻⁶ | Gaia || β | 0.12 ± 0.03 | - | LIGO-Virgo || η | (1.4 ± 0.3)×10⁻¹² cm⁻¹ | - | Chandra |```