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Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"annotates":["heading","list_item","table","paragraph","furniture"],"attribution":{"arxiv_id":"2608.10424","authors":"Au Kwok Chun, Abhigyan Acherjee, Amrutha Rao, Zaiqian Chen, Kazem Meidani, C. Bayan Bruss, Micah Goldblum","title":"Recovering Wasted Compute in Autoresearch Agents","url":"https://arxiv.org/abs/2608.1... | CC-BY-4.0 | assets/b9a7da7d72418354505d6e330eec28ceeed205542b444e1a90145a637a0e3db2.pdf | b9a7da7d72418354505d6e330eec28ceeed205542b444e1a90145a637a0e3db2 | arxiv:2608.10424 | page | 18 | {"arxiv_id":"2608.10424","authors":"Au Kwok Chun, Abhigyan Acherjee, Amrutha Rao, Zaiqian Chen, Kazem Meidani, C. Bayan Bruss, Micah Goldblum","title":"Recovering Wasted Compute in Autoresearch Agents","url":"https://arxiv.org/abs/2608.10424v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"annotates":["heading","list_item","table","paragraph","furniture"],"attribution":{"arxiv_id":"2608.10424","authors":"Au Kwok Chun, Abhigyan Acherjee, Amrutha Rao, Zaiqian Chen, Kazem Meidani, C. Bayan Bruss, Micah Goldblum","title":"Recovering Wasted Compute in Autoresearch Agents","url":"https://arxiv.org/abs/2608.1... | CC-BY-4.0 | assets/51230eb62fcbf72a70353ed2610c4d1d669b0c9284da76ab7d1042f2d351fc04.pdf | 51230eb62fcbf72a70353ed2610c4d1d669b0c9284da76ab7d1042f2d351fc04 | arxiv:2608.10424 | page | 20 | {"arxiv_id":"2608.10424","authors":"Au Kwok Chun, Abhigyan Acherjee, Amrutha Rao, Zaiqian Chen, Kazem Meidani, C. Bayan Bruss, Micah Goldblum","title":"Recovering Wasted Compute in Autoresearch Agents","url":"https://arxiv.org/abs/2608.10424v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"annotates":["heading","list_item","table","paragraph","furniture"],"attribution":{"arxiv_id":"2608.10424","authors":"Au Kwok Chun, Abhigyan Acherjee, Amrutha Rao, Zaiqian Chen, Kazem Meidani, C. Bayan Bruss, Micah Goldblum","title":"Recovering Wasted Compute in Autoresearch Agents","url":"https://arxiv.org/abs/2608.1... | CC-BY-4.0 | assets/2faf314f263a0660069f7a244ee468ab9f13a4255e2984df01a0705abaf9966f.pdf | 2faf314f263a0660069f7a244ee468ab9f13a4255e2984df01a0705abaf9966f | arxiv:2608.10424 | page | 32 | {"arxiv_id":"2608.10424","authors":"Au Kwok Chun, Abhigyan Acherjee, Amrutha Rao, Zaiqian Chen, Kazem Meidani, C. Bayan Bruss, Micah Goldblum","title":"Recovering Wasted Compute in Autoresearch Agents","url":"https://arxiv.org/abs/2608.10424v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"annotates":["heading","list_item","table","paragraph","furniture"],"attribution":{"arxiv_id":"2608.10424","authors":"Au Kwok Chun, Abhigyan Acherjee, Amrutha Rao, Zaiqian Chen, Kazem Meidani, C. Bayan Bruss, Micah Goldblum","title":"Recovering Wasted Compute in Autoresearch Agents","url":"https://arxiv.org/abs/2608.1... | CC-BY-4.0 | assets/ac81e19443222cd01561d1de452dda762624a450811f5d57e93a2a9c8f2eb5d1.pdf | ac81e19443222cd01561d1de452dda762624a450811f5d57e93a2a9c8f2eb5d1 | arxiv:2608.10424 | page | 38 | {"arxiv_id":"2608.10424","authors":"Au Kwok Chun, Abhigyan Acherjee, Amrutha Rao, Zaiqian Chen, Kazem Meidani, C. Bayan Bruss, Micah Goldblum","title":"Recovering Wasted Compute in Autoresearch Agents","url":"https://arxiv.org/abs/2608.10424v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"annotates":["heading","list_item","table","paragraph","furniture"],"attribution":{"arxiv_id":"2608.10428","authors":"Abhishek Raghav (1 and 2), Kousuke Nakano (2 and 3), Marco Cherubini (1), Ryotaro Arita (2 and 4) and Michele Casula (1) ((1) Institut de Min\\'eralogie, de Physique des Mat\\'eriaux et de Cosmochimie,... | CC-BY-4.0 | assets/3f9bfbf6ae62194cf5c5f6a9e25119ef9ad6ad29783633bcbf0641e83a77416d.pdf | 3f9bfbf6ae62194cf5c5f6a9e25119ef9ad6ad29783633bcbf0641e83a77416d | arxiv:2608.10428 | page | 3 | {"arxiv_id":"2608.10428","authors":"Abhishek Raghav (1 and 2), Kousuke Nakano (2 and 3), Marco Cherubini (1), Ryotaro Arita (2 and 4) and Michele Casula (1) ((1) Institut de Min\\'eralogie, de Physique des Mat\\'eriaux et de Cosmochimie, Sorbonne Universit\\'e, CNRS UMR 7590, Paris, France, (2) Center for Emergent Matt... | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"annotates":["heading","list_item","table","paragraph","furniture"],"attribution":{"arxiv_id":"2608.10428","authors":"Abhishek Raghav (1 and 2), Kousuke Nakano (2 and 3), Marco Cherubini (1), Ryotaro Arita (2 and 4) and Michele Casula (1) ((1) Institut de Min\\'eralogie, de Physique des Mat\\'eriaux et de Cosmochimie,... | CC-BY-4.0 | assets/33723819bc0ca3a62528fb4c528feaf02738d7e21404ba6f19617d8c5bd27afb.pdf | 33723819bc0ca3a62528fb4c528feaf02738d7e21404ba6f19617d8c5bd27afb | arxiv:2608.10428 | page | 6 | {"arxiv_id":"2608.10428","authors":"Abhishek Raghav (1 and 2), Kousuke Nakano (2 and 3), Marco Cherubini (1), Ryotaro Arita (2 and 4) and Michele Casula (1) ((1) Institut de Min\\'eralogie, de Physique des Mat\\'eriaux et de Cosmochimie, Sorbonne Universit\\'e, CNRS UMR 7590, Paris, France, (2) Center for Emergent Matt... | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"annotates":["heading","list_item","table","paragraph","furniture"],"attribution":{"arxiv_id":"2608.10428","authors":"Abhishek Raghav (1 and 2), Kousuke Nakano (2 and 3), Marco Cherubini (1), Ryotaro Arita (2 and 4) and Michele Casula (1) ((1) Institut de Min\\'eralogie, de Physique des Mat\\'eriaux et de Cosmochimie,... | CC-BY-4.0 | assets/df87f2d0ae4f5cddf70b48f284abf6ef525124b3ad9c4c586adeba39d9262e6b.pdf | df87f2d0ae4f5cddf70b48f284abf6ef525124b3ad9c4c586adeba39d9262e6b | arxiv:2608.10428 | page | 7 | {"arxiv_id":"2608.10428","authors":"Abhishek Raghav (1 and 2), Kousuke Nakano (2 and 3), Marco Cherubini (1), Ryotaro Arita (2 and 4) and Michele Casula (1) ((1) Institut de Min\\'eralogie, de Physique des Mat\\'eriaux et de Cosmochimie, Sorbonne Universit\\'e, CNRS UMR 7590, Paris, France, (2) Center for Emergent Matt... | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"annotates":["heading","list_item","table","paragraph","furniture"],"attribution":{"arxiv_id":"2608.10428","authors":"Abhishek Raghav (1 and 2), Kousuke Nakano (2 and 3), Marco Cherubini (1), Ryotaro Arita (2 and 4) and Michele Casula (1) ((1) Institut de Min\\'eralogie, de Physique des Mat\\'eriaux et de Cosmochimie,... | CC-BY-4.0 | assets/b3d88b033d185a2dfa419df225e43533d8ccd7f98ff0fff08bcfd3da9427d9a9.pdf | b3d88b033d185a2dfa419df225e43533d8ccd7f98ff0fff08bcfd3da9427d9a9 | arxiv:2608.10428 | page | 9 | {"arxiv_id":"2608.10428","authors":"Abhishek Raghav (1 and 2), Kousuke Nakano (2 and 3), Marco Cherubini (1), Ryotaro Arita (2 and 4) and Michele Casula (1) ((1) Institut de Min\\'eralogie, de Physique des Mat\\'eriaux et de Cosmochimie, Sorbonne Universit\\'e, CNRS UMR 7590, Paris, France, (2) Center for Emergent Matt... | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"annotates":["heading","list_item","table","paragraph","furniture"],"attribution":{"arxiv_id":"2608.10428","authors":"Abhishek Raghav (1 and 2), Kousuke Nakano (2 and 3), Marco Cherubini (1), Ryotaro Arita (2 and 4) and Michele Casula (1) ((1) Institut de Min\\'eralogie, de Physique des Mat\\'eriaux et de Cosmochimie,... | CC-BY-4.0 | assets/84fa0b7a89e4ebf99d04172cc59bb3fe29e3d7f94d1552766088e232a23368a0.pdf | 84fa0b7a89e4ebf99d04172cc59bb3fe29e3d7f94d1552766088e232a23368a0 | arxiv:2608.10428 | page | 10 | {"arxiv_id":"2608.10428","authors":"Abhishek Raghav (1 and 2), Kousuke Nakano (2 and 3), Marco Cherubini (1), Ryotaro Arita (2 and 4) and Michele Casula (1) ((1) Institut de Min\\'eralogie, de Physique des Mat\\'eriaux et de Cosmochimie, Sorbonne Universit\\'e, CNRS UMR 7590, Paris, France, (2) Center for Emergent Matt... | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"annotates":["heading","list_item","table","paragraph","furniture"],"attribution":{"arxiv_id":"2608.10428","authors":"Abhishek Raghav (1 and 2), Kousuke Nakano (2 and 3), Marco Cherubini (1), Ryotaro Arita (2 and 4) and Michele Casula (1) ((1) Institut de Min\\'eralogie, de Physique des Mat\\'eriaux et de Cosmochimie,... | CC-BY-4.0 | assets/63637c1ae3215dffeaed079c15590b2cefbc3cb72e244fea1c06c1e06417b9f5.pdf | 63637c1ae3215dffeaed079c15590b2cefbc3cb72e244fea1c06c1e06417b9f5 | arxiv:2608.10428 | page | 11 | {"arxiv_id":"2608.10428","authors":"Abhishek Raghav (1 and 2), Kousuke Nakano (2 and 3), Marco Cherubini (1), Ryotaro Arita (2 and 4) and Michele Casula (1) ((1) Institut de Min\\'eralogie, de Physique des Mat\\'eriaux et de Cosmochimie, Sorbonne Universit\\'e, CNRS UMR 7590, Paris, France, (2) Center for Emergent Matt... | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"annotates":["heading","list_item","table","paragraph","furniture"],"attribution":{"arxiv_id":"2608.10428","authors":"Abhishek Raghav (1 and 2), Kousuke Nakano (2 and 3), Marco Cherubini (1), Ryotaro Arita (2 and 4) and Michele Casula (1) ((1) Institut de Min\\'eralogie, de Physique des Mat\\'eriaux et de Cosmochimie,... | CC-BY-4.0 | assets/6f8ef347da281d2e94f29d65e4e440553495c785b45ff86a49ca812aabd3bc63.pdf | 6f8ef347da281d2e94f29d65e4e440553495c785b45ff86a49ca812aabd3bc63 | arxiv:2608.10428 | page | 12 | {"arxiv_id":"2608.10428","authors":"Abhishek Raghav (1 and 2), Kousuke Nakano (2 and 3), Marco Cherubini (1), Ryotaro Arita (2 and 4) and Michele Casula (1) ((1) Institut de Min\\'eralogie, de Physique des Mat\\'eriaux et de Cosmochimie, Sorbonne Universit\\'e, CNRS UMR 7590, Paris, France, (2) Center for Emergent Matt... | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"annotates":["heading","list_item","table","paragraph","furniture"],"attribution":{"arxiv_id":"2608.10428","authors":"Abhishek Raghav (1 and 2), Kousuke Nakano (2 and 3), Marco Cherubini (1), Ryotaro Arita (2 and 4) and Michele Casula (1) ((1) Institut de Min\\'eralogie, de Physique des Mat\\'eriaux et de Cosmochimie,... | CC-BY-4.0 | assets/db8acda3768b422a9592f5aa286850597af7e4c8bca742cdc6a54b0e832b304b.pdf | db8acda3768b422a9592f5aa286850597af7e4c8bca742cdc6a54b0e832b304b | arxiv:2608.10428 | page | 13 | {"arxiv_id":"2608.10428","authors":"Abhishek Raghav (1 and 2), Kousuke Nakano (2 and 3), Marco Cherubini (1), Ryotaro Arita (2 and 4) and Michele Casula (1) ((1) Institut de Min\\'eralogie, de Physique des Mat\\'eriaux et de Cosmochimie, Sorbonne Universit\\'e, CNRS UMR 7590, Paris, France, (2) Center for Emergent Matt... | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[179.03,331.85,291.65,28.56],"bbox_pdf":[179.03,481.48,470.68,510.04],"fragments":[{"bbox_pdf":[179.03,481.48,470.68,510.04],"words":[5365,5366,5367,5368,5369,5370,5371,5372,5373,5375,5376,5377,5379,5380,5381,5382,5383]}],"html":null,"kind":"paragraph","latex":"M_{pq}^{(\\mu)}\\equiv\\sqrt{\\frac{4\\pi... | CC-BY-4.0 | assets/db8acda3768b422a9592f5aa286850597af7e4c8bca742cdc6a54b0e832b304b.pdf | db8acda3768b422a9592f5aa286850597af7e4c8bca742cdc6a54b0e832b304b | arxiv:2608.10428 | formula | 13 | {"arxiv_id":"2608.10428","authors":"Abhishek Raghav (1 and 2), Kousuke Nakano (2 and 3), Marco Cherubini (1), Ryotaro Arita (2 and 4) and Michele Casula (1) ((1) Institut de Min\\'eralogie, de Physique des Mat\\'eriaux et de Cosmochimie, Sorbonne Universit\\'e, CNRS UMR 7590, Paris, France, (2) Center for Emergent Matt... | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[220.18,495.18,250.5,118.49],"bbox_pdf":[220.18,228.22,470.68,346.71],"fragments":[{"bbox_pdf":[220.18,228.22,470.68,346.71],"words":[5532,5533,5534,5535,5536,5537,5538,5539,5540,5541,5542,5543,5544,5545,5546,5547,5548,5549,5550,5551,5552,5553,5554,5555,5556,5557,5558,5559,5560,5561,5562,5563,5564,5565... | CC-BY-4.0 | assets/db8acda3768b422a9592f5aa286850597af7e4c8bca742cdc6a54b0e832b304b.pdf | db8acda3768b422a9592f5aa286850597af7e4c8bca742cdc6a54b0e832b304b | arxiv:2608.10428 | formula | 13 | {"arxiv_id":"2608.10428","authors":"Abhishek Raghav (1 and 2), Kousuke Nakano (2 and 3), Marco Cherubini (1), Ryotaro Arita (2 and 4) and Michele Casula (1) ((1) Institut de Min\\'eralogie, de Physique des Mat\\'eriaux et de Cosmochimie, Sorbonne Universit\\'e, CNRS UMR 7590, Paris, France, (2) Center for Emergent Matt... | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"annotates":["heading","list_item","table","paragraph","furniture"],"attribution":{"arxiv_id":"2608.10428","authors":"Abhishek Raghav (1 and 2), Kousuke Nakano (2 and 3), Marco Cherubini (1), Ryotaro Arita (2 and 4) and Michele Casula (1) ((1) Institut de Min\\'eralogie, de Physique des Mat\\'eriaux et de Cosmochimie,... | CC-BY-4.0 | assets/09c65f20706587277f5681e1124873ad29ca7c16ae7f4747741459d9d45c2635.pdf | 09c65f20706587277f5681e1124873ad29ca7c16ae7f4747741459d9d45c2635 | arxiv:2608.10428 | page | 14 | {"arxiv_id":"2608.10428","authors":"Abhishek Raghav (1 and 2), Kousuke Nakano (2 and 3), Marco Cherubini (1), Ryotaro Arita (2 and 4) and Michele Casula (1) ((1) Institut de Min\\'eralogie, de Physique des Mat\\'eriaux et de Cosmochimie, Sorbonne Universit\\'e, CNRS UMR 7590, Paris, France, (2) Center for Emergent Matt... | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[244.57,116.86,250.64,26.73],"bbox_pdf":[244.57,698.3,495.21,725.03],"fragments":[{"bbox_pdf":[244.57,698.3,495.21,725.03],"words":[5602,5603,5604,5605,5606,5607,5608,5609,5610,5611,5612,5613,5614,5615]}],"html":null,"kind":"paragraph","latex":"\\Delta_{l}=\\left\\langle\\frac{1}{N_{\\text{cube}}}\\sum... | CC-BY-4.0 | assets/09c65f20706587277f5681e1124873ad29ca7c16ae7f4747741459d9d45c2635.pdf | 09c65f20706587277f5681e1124873ad29ca7c16ae7f4747741459d9d45c2635 | arxiv:2608.10428 | formula | 14 | {"arxiv_id":"2608.10428","authors":"Abhishek Raghav (1 and 2), Kousuke Nakano (2 and 3), Marco Cherubini (1), Ryotaro Arita (2 and 4) and Michele Casula (1) ((1) Institut de Min\\'eralogie, de Physique des Mat\\'eriaux et de Cosmochimie, Sorbonne Universit\\'e, CNRS UMR 7590, Paris, France, (2) Center for Emergent Matt... | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"annotates":["heading","list_item","table","paragraph","furniture"],"attribution":{"arxiv_id":"2608.10428","authors":"Abhishek Raghav (1 and 2), Kousuke Nakano (2 and 3), Marco Cherubini (1), Ryotaro Arita (2 and 4) and Michele Casula (1) ((1) Institut de Min\\'eralogie, de Physique des Mat\\'eriaux et de Cosmochimie,... | CC-BY-4.0 | assets/889cf962480c1d11f3374dbeca02bb928ef9ef0ec5725e9c2b313be735d15ac2.pdf | 889cf962480c1d11f3374dbeca02bb928ef9ef0ec5725e9c2b313be735d15ac2 | arxiv:2608.10428 | page | 15 | {"arxiv_id":"2608.10428","authors":"Abhishek Raghav (1 and 2), Kousuke Nakano (2 and 3), Marco Cherubini (1), Ryotaro Arita (2 and 4) and Michele Casula (1) ((1) Institut de Min\\'eralogie, de Physique des Mat\\'eriaux et de Cosmochimie, Sorbonne Universit\\'e, CNRS UMR 7590, Paris, France, (2) Center for Emergent Matt... | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"annotates":["heading","list_item","table","paragraph","furniture"],"attribution":{"arxiv_id":"2608.10428","authors":"Abhishek Raghav (1 and 2), Kousuke Nakano (2 and 3), Marco Cherubini (1), Ryotaro Arita (2 and 4) and Michele Casula (1) ((1) Institut de Min\\'eralogie, de Physique des Mat\\'eriaux et de Cosmochimie,... | CC-BY-4.0 | assets/eb79b4475afb660ba80c774d65fb1a3b5355920f5028cd10b4761ea67fd69092.pdf | eb79b4475afb660ba80c774d65fb1a3b5355920f5028cd10b4761ea67fd69092 | arxiv:2608.10428 | page | 17 | {"arxiv_id":"2608.10428","authors":"Abhishek Raghav (1 and 2), Kousuke Nakano (2 and 3), Marco Cherubini (1), Ryotaro Arita (2 and 4) and Michele Casula (1) ((1) Institut de Min\\'eralogie, de Physique des Mat\\'eriaux et de Cosmochimie, Sorbonne Universit\\'e, CNRS UMR 7590, Paris, France, (2) Center for Emergent Matt... | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"annotates":["heading","list_item","table","paragraph","furniture"],"attribution":{"arxiv_id":"2608.10451","authors":"Lindsey A. Kwok, St\\'ephane Blondin, Adam A. Miller, Saurabh W. Jha, Willem B. Hoogendam, Cameron M. Pfeffer, Eyouel Z. Abate, Jennifer E. Andrews, Moira Andrews, Chris Ashall, Katie Auchettl, K. Azal... | CC-BY-4.0 | assets/80f1a25c1b1eafe071960de834b0a01815c7c435ac5905b0a1df0d1c38589990.pdf | 80f1a25c1b1eafe071960de834b0a01815c7c435ac5905b0a1df0d1c38589990 | arxiv:2608.10451 | page | 8 | {"arxiv_id":"2608.10451","authors":"Lindsey A. Kwok, St\\'ephane Blondin, Adam A. Miller, Saurabh W. Jha, Willem B. Hoogendam, Cameron M. Pfeffer, Eyouel Z. Abate, Jennifer E. Andrews, Moira Andrews, Chris Ashall, Katie Auchettl, K. Azalee Bostroem, Thomas G. Brink, Fionntan P. Callan, Collin T. Christy, Joseph R. Fara... | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"annotates":["heading","list_item","table","paragraph","furniture"],"attribution":{"arxiv_id":"2608.10451","authors":"Lindsey A. Kwok, St\\'ephane Blondin, Adam A. Miller, Saurabh W. Jha, Willem B. Hoogendam, Cameron M. Pfeffer, Eyouel Z. Abate, Jennifer E. Andrews, Moira Andrews, Chris Ashall, Katie Auchettl, K. Azal... | CC-BY-4.0 | assets/277112df089fc9738d1d9585add71a487d6a72e8c88d5c7106f77d1fae4f3e46.pdf | 277112df089fc9738d1d9585add71a487d6a72e8c88d5c7106f77d1fae4f3e46 | arxiv:2608.10451 | page | 9 | {"arxiv_id":"2608.10451","authors":"Lindsey A. Kwok, St\\'ephane Blondin, Adam A. Miller, Saurabh W. Jha, Willem B. Hoogendam, Cameron M. Pfeffer, Eyouel Z. Abate, Jennifer E. Andrews, Moira Andrews, Chris Ashall, Katie Auchettl, K. Azalee Bostroem, Thomas G. Brink, Fionntan P. Callan, Collin T. Christy, Joseph R. Fara... | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"annotates":["heading","list_item","table","paragraph","furniture"],"attribution":{"arxiv_id":"2608.10451","authors":"Lindsey A. Kwok, St\\'ephane Blondin, Adam A. Miller, Saurabh W. Jha, Willem B. Hoogendam, Cameron M. Pfeffer, Eyouel Z. Abate, Jennifer E. Andrews, Moira Andrews, Chris Ashall, Katie Auchettl, K. Azal... | CC-BY-4.0 | assets/ae3b0674b1c4780f60d818ec2e3439b5586d94ce12eb2e9256ede6f22fcbcb98.pdf | ae3b0674b1c4780f60d818ec2e3439b5586d94ce12eb2e9256ede6f22fcbcb98 | arxiv:2608.10451 | page | 13 | {"arxiv_id":"2608.10451","authors":"Lindsey A. Kwok, St\\'ephane Blondin, Adam A. Miller, Saurabh W. Jha, Willem B. Hoogendam, Cameron M. Pfeffer, Eyouel Z. Abate, Jennifer E. Andrews, Moira Andrews, Chris Ashall, Katie Auchettl, K. Azalee Bostroem, Thomas G. Brink, Fionntan P. Callan, Collin T. Christy, Joseph R. Fara... | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[400.09,434.84,82.33,34.6],"bbox_pdf":[400.09,322.56,482.43,357.16],"fragments":[{"bbox_pdf":[400.09,322.56,482.43,357.16],"words":[9536,9537,9538,9539,9540,9541,9542,9543,9544]}],"html":null,"kind":"paragraph","latex":"\\epsilon\\equiv\\frac{\\left\\langle\\delta F_{\\rm hp}(v)^{2}\\right\\rangle^{1/2... | CC-BY-4.0 | assets/ae3b0674b1c4780f60d818ec2e3439b5586d94ce12eb2e9256ede6f22fcbcb98.pdf | ae3b0674b1c4780f60d818ec2e3439b5586d94ce12eb2e9256ede6f22fcbcb98 | arxiv:2608.10451 | formula | 13 | {"arxiv_id":"2608.10451","authors":"Lindsey A. Kwok, St\\'ephane Blondin, Adam A. Miller, Saurabh W. Jha, Willem B. Hoogendam, Cameron M. Pfeffer, Eyouel Z. Abate, Jennifer E. Andrews, Moira Andrews, Chris Ashall, Katie Auchettl, K. Azalee Bostroem, Thomas G. Brink, Fionntan P. Callan, Collin T. Christy, Joseph R. Fara... | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"annotates":["heading","list_item","table","paragraph","furniture"],"attribution":{"arxiv_id":"2608.10451","authors":"Lindsey A. Kwok, St\\'ephane Blondin, Adam A. Miller, Saurabh W. Jha, Willem B. Hoogendam, Cameron M. Pfeffer, Eyouel Z. Abate, Jennifer E. Andrews, Moira Andrews, Chris Ashall, Katie Auchettl, K. Azal... | CC-BY-4.0 | assets/77553ab29edfe2524b6ea21d1f08e93e73ae17ab9274bb2fa87a19bc4afd23ca.pdf | 77553ab29edfe2524b6ea21d1f08e93e73ae17ab9274bb2fa87a19bc4afd23ca | arxiv:2608.10451 | page | 15 | {"arxiv_id":"2608.10451","authors":"Lindsey A. Kwok, St\\'ephane Blondin, Adam A. Miller, Saurabh W. Jha, Willem B. Hoogendam, Cameron M. Pfeffer, Eyouel Z. Abate, Jennifer E. Andrews, Moira Andrews, Chris Ashall, Katie Auchettl, K. Azalee Bostroem, Thomas G. Brink, Fionntan P. Callan, Collin T. Christy, Joseph R. Fara... | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"annotates":["heading","list_item","table","paragraph","furniture"],"attribution":{"arxiv_id":"2608.10451","authors":"Lindsey A. Kwok, St\\'ephane Blondin, Adam A. Miller, Saurabh W. Jha, Willem B. Hoogendam, Cameron M. Pfeffer, Eyouel Z. Abate, Jennifer E. Andrews, Moira Andrews, Chris Ashall, Katie Auchettl, K. Azal... | CC-BY-4.0 | assets/396217e4b2da5cab21cf896f13846b2bcdf92a01233a8ae58d2eb52656288cd9.pdf | 396217e4b2da5cab21cf896f13846b2bcdf92a01233a8ae58d2eb52656288cd9 | arxiv:2608.10451 | page | 17 | {"arxiv_id":"2608.10451","authors":"Lindsey A. Kwok, St\\'ephane Blondin, Adam A. Miller, Saurabh W. Jha, Willem B. Hoogendam, Cameron M. Pfeffer, Eyouel Z. Abate, Jennifer E. Andrews, Moira Andrews, Chris Ashall, Katie Auchettl, K. Azalee Bostroem, Thomas G. Brink, Fionntan P. Callan, Collin T. Christy, Joseph R. Fara... | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"annotates":["heading","list_item","table","paragraph","furniture"],"attribution":{"arxiv_id":"2608.10451","authors":"Lindsey A. Kwok, St\\'ephane Blondin, Adam A. Miller, Saurabh W. Jha, Willem B. Hoogendam, Cameron M. Pfeffer, Eyouel Z. Abate, Jennifer E. Andrews, Moira Andrews, Chris Ashall, Katie Auchettl, K. Azal... | CC-BY-4.0 | assets/f7eafcff8a00e4e1ae4b85456f2ef9d49c27db0c42d5bc248d321767ae0d605a.pdf | f7eafcff8a00e4e1ae4b85456f2ef9d49c27db0c42d5bc248d321767ae0d605a | arxiv:2608.10451 | page | 18 | {"arxiv_id":"2608.10451","authors":"Lindsey A. Kwok, St\\'ephane Blondin, Adam A. Miller, Saurabh W. Jha, Willem B. Hoogendam, Cameron M. Pfeffer, Eyouel Z. Abate, Jennifer E. Andrews, Moira Andrews, Chris Ashall, Katie Auchettl, K. Azalee Bostroem, Thomas G. Brink, Fionntan P. Callan, Collin T. Christy, Joseph R. Fara... | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"annotates":["heading","list_item","table","paragraph","furniture"],"attribution":{"arxiv_id":"2608.10451","authors":"Lindsey A. Kwok, St\\'ephane Blondin, Adam A. Miller, Saurabh W. Jha, Willem B. Hoogendam, Cameron M. Pfeffer, Eyouel Z. Abate, Jennifer E. Andrews, Moira Andrews, Chris Ashall, Katie Auchettl, K. Azal... | CC-BY-4.0 | assets/783b3094168ae0c02fa048f87fa7b96f93930fe3b259ae41c2657c78775131e9.pdf | 783b3094168ae0c02fa048f87fa7b96f93930fe3b259ae41c2657c78775131e9 | arxiv:2608.10451 | page | 19 | {"arxiv_id":"2608.10451","authors":"Lindsey A. Kwok, St\\'ephane Blondin, Adam A. Miller, Saurabh W. Jha, Willem B. Hoogendam, Cameron M. Pfeffer, Eyouel Z. Abate, Jennifer E. Andrews, Moira Andrews, Chris Ashall, Katie Auchettl, K. Azalee Bostroem, Thomas G. Brink, Fionntan P. Callan, Collin T. Christy, Joseph R. Fara... | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"annotates":["heading","list_item","table","paragraph","furniture"],"attribution":{"arxiv_id":"2608.10463","authors":"Idrees Qasim, Ovaisa Jan","title":"On Turan Type inequality for Quaternionic Canonical Generalized Polynomials","url":"https://arxiv.org/abs/2608.10463v1","version":1},"blocks":[{"bbox":[97.45,44.79,45... | CC-BY-4.0 | assets/84071b26aca105acd382f0346d3e275d3e25c7dda52cfca280cf787d6a727533.pdf | 84071b26aca105acd382f0346d3e275d3e25c7dda52cfca280cf787d6a727533 | arxiv:2608.10463 | page | 2 | {"arxiv_id":"2608.10463","authors":"Idrees Qasim, Ovaisa Jan","title":"On Turan Type inequality for Quaternionic Canonical Generalized Polynomials","url":"https://arxiv.org/abs/2608.10463v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[259.44,80.31,291.56,26.09],"bbox_pdf":[259.44,685.6,551.0,711.69],"fragments":[{"bbox_pdf":[259.44,685.6,551.0,711.69],"words":[373,374,375,376,377,378,379,380,381,382,383,384]}],"html":null,"kind":"paragraph","latex":"\\max_{|z|=1}|p^{\\prime}(z)|\\;\\geq\\;\\frac{n}{2}\\max_{|z|=1}|p(z)|","level":nu... | CC-BY-4.0 | assets/84071b26aca105acd382f0346d3e275d3e25c7dda52cfca280cf787d6a727533.pdf | 84071b26aca105acd382f0346d3e275d3e25c7dda52cfca280cf787d6a727533 | arxiv:2608.10463 | formula | 2 | {"arxiv_id":"2608.10463","authors":"Idrees Qasim, Ovaisa Jan","title":"On Turan Type inequality for Quaternionic Canonical Generalized Polynomials","url":"https://arxiv.org/abs/2608.10463v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[284.04,160.1,266.95,25.77],"bbox_pdf":[284.04,606.13,550.99,631.9],"fragments":[{"bbox_pdf":[284.04,606.13,550.99,631.9],"words":[439,440,441,442,443,444,445,446,447,448]}],"html":null,"kind":"paragraph","latex":"\\|p^{\\prime}\\|\\geq\\frac{n}{1+k}\\|p\\|.","level":null,"list_depth":null,"match":{"sr... | CC-BY-4.0 | assets/84071b26aca105acd382f0346d3e275d3e25c7dda52cfca280cf787d6a727533.pdf | 84071b26aca105acd382f0346d3e275d3e25c7dda52cfca280cf787d6a727533 | arxiv:2608.10463 | formula | 2 | {"arxiv_id":"2608.10463","authors":"Idrees Qasim, Ovaisa Jan","title":"On Turan Type inequality for Quaternionic Canonical Generalized Polynomials","url":"https://arxiv.org/abs/2608.10463v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[281.22,224.91,269.78,25.77],"bbox_pdf":[281.22,541.31,551.0,567.09],"fragments":[{"bbox_pdf":[281.22,541.31,551.0,567.09],"words":[472,473,474,475,476,477,478,479,480,481]}],"html":null,"kind":"paragraph","latex":"\\|p^{\\prime}\\|\\geq\\frac{n}{1+k^{n}}\\|p\\|.","level":null,"list_depth":null,"match"... | CC-BY-4.0 | assets/84071b26aca105acd382f0346d3e275d3e25c7dda52cfca280cf787d6a727533.pdf | 84071b26aca105acd382f0346d3e275d3e25c7dda52cfca280cf787d6a727533 | arxiv:2608.10463 | formula | 2 | {"arxiv_id":"2608.10463","authors":"Idrees Qasim, Ovaisa Jan","title":"On Turan Type inequality for Quaternionic Canonical Generalized Polynomials","url":"https://arxiv.org/abs/2608.10463v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"annotates":["heading","list_item","table","paragraph","furniture"],"attribution":{"arxiv_id":"2608.10463","authors":"Idrees Qasim, Ovaisa Jan","title":"On Turan Type inequality for Quaternionic Canonical Generalized Polynomials","url":"https://arxiv.org/abs/2608.10463v1","version":1},"blocks":[{"bbox":[97.45,44.79,45... | CC-BY-4.0 | assets/72f9c0219bbc96f67da3f5f875a26799e6377a71f3dcf827a2204908a99b5b2d.pdf | 72f9c0219bbc96f67da3f5f875a26799e6377a71f3dcf827a2204908a99b5b2d | arxiv:2608.10463 | page | 3 | {"arxiv_id":"2608.10463","authors":"Idrees Qasim, Ovaisa Jan","title":"On Turan Type inequality for Quaternionic Canonical Generalized Polynomials","url":"https://arxiv.org/abs/2608.10463v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[267.67,360.95,112.77,12.55],"bbox_pdf":[267.67,418.5,380.44,431.05],"fragments":[{"bbox_pdf":[267.67,418.5,380.44,431.05],"words":[1169,1170,1171,1172,1173,1174,1175,1176,1177]}],"html":null,"kind":"paragraph","latex":"q=q_{0}+q_{1}{i}+q_{2}{j}+q_{3}{k}","level":null,"list_depth":null,"match":{"src_pl... | CC-BY-4.0 | assets/72f9c0219bbc96f67da3f5f875a26799e6377a71f3dcf827a2204908a99b5b2d.pdf | 72f9c0219bbc96f67da3f5f875a26799e6377a71f3dcf827a2204908a99b5b2d | arxiv:2608.10463 | formula | 3 | {"arxiv_id":"2608.10463","authors":"Idrees Qasim, Ovaisa Jan","title":"On Turan Type inequality for Quaternionic Canonical Generalized Polynomials","url":"https://arxiv.org/abs/2608.10463v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[266.17,406.51,116.11,12.47],"bbox_pdf":[266.17,373.02,382.28,385.49],"fragments":[{"bbox_pdf":[266.17,373.02,382.28,385.49],"words":[1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202]}],"html":null,"kind":"paragraph","latex":"{i}^{2}={j}^{2}={k}^{2}={i}{j}{k}=-1","level":null,"list_depth":nu... | CC-BY-4.0 | assets/72f9c0219bbc96f67da3f5f875a26799e6377a71f3dcf827a2204908a99b5b2d.pdf | 72f9c0219bbc96f67da3f5f875a26799e6377a71f3dcf827a2204908a99b5b2d | arxiv:2608.10463 | formula | 3 | {"arxiv_id":"2608.10463","authors":"Idrees Qasim, Ovaisa Jan","title":"On Turan Type inequality for Quaternionic Canonical Generalized Polynomials","url":"https://arxiv.org/abs/2608.10463v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[263.79,467.18,120.88,14.11],"bbox_pdf":[263.79,310.71,384.67,324.82],"fragments":[{"bbox_pdf":[263.79,310.71,384.67,324.82],"words":[1238,1239,1240,1241,1242,1243,1244,1245,1246,1247]}],"html":null,"kind":"paragraph","latex":"q^{*}=q_{0}-q_{1}{i}-q_{2}{j}-q_{3}{k}.","level":null,"list_depth":null,"mat... | CC-BY-4.0 | assets/72f9c0219bbc96f67da3f5f875a26799e6377a71f3dcf827a2204908a99b5b2d.pdf | 72f9c0219bbc96f67da3f5f875a26799e6377a71f3dcf827a2204908a99b5b2d | arxiv:2608.10463 | formula | 3 | {"arxiv_id":"2608.10463","authors":"Idrees Qasim, Ovaisa Jan","title":"On Turan Type inequality for Quaternionic Canonical Generalized Polynomials","url":"https://arxiv.org/abs/2608.10463v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[254.04,527.86,139.88,15.17],"bbox_pdf":[254.04,248.97,393.91,264.14],"fragments":[{"bbox_pdf":[254.04,248.97,393.91,264.14],"words":[1266,1267,1268,1269,1270,1271,1272,1273,1274,1275,1276,1277,1278,1279,1280,1281,1282,1283]}],"html":null,"kind":"paragraph","latex":"|q|^{2}=q{q^{*}}=q_{0}^{2}+q_{1}^{2}... | CC-BY-4.0 | assets/72f9c0219bbc96f67da3f5f875a26799e6377a71f3dcf827a2204908a99b5b2d.pdf | 72f9c0219bbc96f67da3f5f875a26799e6377a71f3dcf827a2204908a99b5b2d | arxiv:2608.10463 | formula | 3 | {"arxiv_id":"2608.10463","authors":"Idrees Qasim, Ovaisa Jan","title":"On Turan Type inequality for Quaternionic Canonical Generalized Polynomials","url":"https://arxiv.org/abs/2608.10463v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"annotates":["heading","list_item","table","paragraph","furniture"],"attribution":{"arxiv_id":"2608.10463","authors":"Idrees Qasim, Ovaisa Jan","title":"On Turan Type inequality for Quaternionic Canonical Generalized Polynomials","url":"https://arxiv.org/abs/2608.10463v1","version":1},"blocks":[{"bbox":[97.45,44.79,15... | CC-BY-4.0 | assets/20880d3055258194a3eae614f5031f2bff95f75112b91ade56564f6e96368a05.pdf | 20880d3055258194a3eae614f5031f2bff95f75112b91ade56564f6e96368a05 | arxiv:2608.10463 | page | 8 | {"arxiv_id":"2608.10463","authors":"Idrees Qasim, Ovaisa Jan","title":"On Turan Type inequality for Quaternionic Canonical Generalized Polynomials","url":"https://arxiv.org/abs/2608.10463v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[243.33,66.66,161.29,12.47],"bbox_pdf":[243.33,712.87,404.62,725.34],"fragments":[{"bbox_pdf":[243.33,712.87,404.62,725.34],"words":[2905,2906,2907,2908,2909,2910,2911,2912,2913,2914,2915,2917,2918,2919]}],"html":null,"kind":"paragraph","latex":"3k^{3}+(k^{3}-2)(|\\alpha|^{2}+k^{2})\\geq 3|\\alpha|k^{2... | CC-BY-4.0 | assets/20880d3055258194a3eae614f5031f2bff95f75112b91ade56564f6e96368a05.pdf | 20880d3055258194a3eae614f5031f2bff95f75112b91ade56564f6e96368a05 | arxiv:2608.10463 | formula | 8 | {"arxiv_id":"2608.10463","authors":"Idrees Qasim, Ovaisa Jan","title":"On Turan Type inequality for Quaternionic Canonical Generalized Polynomials","url":"https://arxiv.org/abs/2608.10463v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[204.83,113.52,346.16,12.48],"bbox_pdf":[204.83,666.0,551.0,678.48],"fragments":[{"bbox_pdf":[204.83,666.0,551.0,678.48],"words":[2927,2928,2929,2930,2931,2932,2933,2934,2935,2936,2937,2938,2939,2940,2941,2942,2943,2944,2945,2946,2947,2948,2949,2950,2951]}],"html":null,"kind":"paragraph","latex":"(k^{3... | CC-BY-4.0 | assets/20880d3055258194a3eae614f5031f2bff95f75112b91ade56564f6e96368a05.pdf | 20880d3055258194a3eae614f5031f2bff95f75112b91ade56564f6e96368a05 | arxiv:2608.10463 | formula | 8 | {"arxiv_id":"2608.10463","authors":"Idrees Qasim, Ovaisa Jan","title":"On Turan Type inequality for Quaternionic Canonical Generalized Polynomials","url":"https://arxiv.org/abs/2608.10463v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[226.01,150.5,324.98,12.47],"bbox_pdf":[226.01,629.02,550.99,641.5],"fragments":[{"bbox_pdf":[226.01,629.02,550.99,641.5],"words":[2955,2956,2957,2958,2959,2960,2961,2962,2963,2964,2965,2966,2967,2968,2969,2970,2971,2972,2973,2974,2975,2976,2977]}],"html":null,"kind":"paragraph","latex":"(2-k^{3})x^{2}... | CC-BY-4.0 | assets/20880d3055258194a3eae614f5031f2bff95f75112b91ade56564f6e96368a05.pdf | 20880d3055258194a3eae614f5031f2bff95f75112b91ade56564f6e96368a05 | arxiv:2608.10463 | formula | 8 | {"arxiv_id":"2608.10463","authors":"Idrees Qasim, Ovaisa Jan","title":"On Turan Type inequality for Quaternionic Canonical Generalized Polynomials","url":"https://arxiv.org/abs/2608.10463v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[215.57,193.42,216.82,14.25],"bbox_pdf":[215.57,584.33,432.38,598.58],"fragments":[{"bbox_pdf":[215.57,584.33,432.38,598.58],"words":[2982,2983,2984,2985,2986,2987,2988,2989,2990,2991,2992,2993,2994,2995,2996,2997,2998,2999,3000,3001,3002,3003]}],"html":null,"kind":"paragraph","latex":"\\phi_{k}(x)=(2-... | CC-BY-4.0 | assets/20880d3055258194a3eae614f5031f2bff95f75112b91ade56564f6e96368a05.pdf | 20880d3055258194a3eae614f5031f2bff95f75112b91ade56564f6e96368a05 | arxiv:2608.10463 | formula | 8 | {"arxiv_id":"2608.10463","authors":"Idrees Qasim, Ovaisa Jan","title":"On Turan Type inequality for Quaternionic Canonical Generalized Polynomials","url":"https://arxiv.org/abs/2608.10463v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[201.24,262.52,244.78,35.3],"bbox_pdf":[201.24,494.18,446.02,529.48],"fragments":[{"bbox_pdf":[201.24,494.18,446.02,529.48],"words":[3055,3056,3057,3058,3059,3060,3061,3062,3063,3064,3065,3066,3067,3068,3069,3070,3071,3072,3073]}],"html":null,"kind":"paragraph","latex":"A(k)=\\dfrac{-3k^{2}+\\sqrt{9k^{... | CC-BY-4.0 | assets/20880d3055258194a3eae614f5031f2bff95f75112b91ade56564f6e96368a05.pdf | 20880d3055258194a3eae614f5031f2bff95f75112b91ade56564f6e96368a05 | arxiv:2608.10463 | formula | 8 | {"arxiv_id":"2608.10463","authors":"Idrees Qasim, Ovaisa Jan","title":"On Turan Type inequality for Quaternionic Canonical Generalized Polynomials","url":"https://arxiv.org/abs/2608.10463v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[257.74,399.62,132.98,14.25],"bbox_pdf":[257.74,378.13,390.71,392.38],"fragments":[{"bbox_pdf":[257.74,378.13,390.71,392.38],"words":[3180,3181,3182,3183,3184,3185,3186,3187,3188,3189,3190,3191,3192]}],"html":null,"kind":"paragraph","latex":"\\phi_{k}(0)=(2-k^{3})k^{2}-k^{3}<0","level":null,"list_depth... | CC-BY-4.0 | assets/20880d3055258194a3eae614f5031f2bff95f75112b91ade56564f6e96368a05.pdf | 20880d3055258194a3eae614f5031f2bff95f75112b91ade56564f6e96368a05 | arxiv:2608.10463 | formula | 8 | {"arxiv_id":"2608.10463","authors":"Idrees Qasim, Ovaisa Jan","title":"On Turan Type inequality for Quaternionic Canonical Generalized Polynomials","url":"https://arxiv.org/abs/2608.10463v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[251.51,441.31,145.44,25.77],"bbox_pdf":[251.51,324.92,396.94,350.69],"fragments":[{"bbox_pdf":[251.51,324.92,396.94,350.69],"words":[3210,3211,3212,3213,3214,3215,3216,3217,3218,3219,3220,3221,3222,3223,3224]}],"html":null,"kind":"paragraph","latex":"\\|P^{\\prime}\\|=3+|B|\\;\\geq\\;\\frac{3}{1+k^{3}... | CC-BY-4.0 | assets/20880d3055258194a3eae614f5031f2bff95f75112b91ade56564f6e96368a05.pdf | 20880d3055258194a3eae614f5031f2bff95f75112b91ade56564f6e96368a05 | arxiv:2608.10463 | formula | 8 | {"arxiv_id":"2608.10463","authors":"Idrees Qasim, Ovaisa Jan","title":"On Turan Type inequality for Quaternionic Canonical Generalized Polynomials","url":"https://arxiv.org/abs/2608.10463v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[223.01,511.21,202.42,10.91],"bbox_pdf":[223.01,269.88,425.43,280.79],"fragments":[{"bbox_pdf":[223.01,269.88,425.43,280.79],"words":[3228,3229,3230,3231,3232,3233,3234,3235,3236,3237,3238,3239,3240,3241,3242,3243,3244,3245]}],"html":null,"kind":"paragraph","latex":"P(q)=(q-\\alpha)*(q-\\beta)*(q-\\gam... | CC-BY-4.0 | assets/20880d3055258194a3eae614f5031f2bff95f75112b91ade56564f6e96368a05.pdf | 20880d3055258194a3eae614f5031f2bff95f75112b91ade56564f6e96368a05 | arxiv:2608.10463 | formula | 8 | {"arxiv_id":"2608.10463","authors":"Idrees Qasim, Ovaisa Jan","title":"On Turan Type inequality for Quaternionic Canonical Generalized Polynomials","url":"https://arxiv.org/abs/2608.10463v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[250.77,554.13,146.92,10.91],"bbox_pdf":[250.77,226.97,397.69,237.87],"fragments":[{"bbox_pdf":[250.77,226.97,397.69,237.87],"words":[3254,3255,3256,3257,3258,3259,3260,3261,3262]}],"html":null,"kind":"paragraph","latex":"|\\alpha|,\\,|\\beta|,\\,|\\gamma|,\\,|\\lambda|\\leq k,\\qquad k\\geq 1.","level... | CC-BY-4.0 | assets/20880d3055258194a3eae614f5031f2bff95f75112b91ade56564f6e96368a05.pdf | 20880d3055258194a3eae614f5031f2bff95f75112b91ade56564f6e96368a05 | arxiv:2608.10463 | formula | 8 | {"arxiv_id":"2608.10463","authors":"Idrees Qasim, Ovaisa Jan","title":"On Turan Type inequality for Quaternionic Canonical Generalized Polynomials","url":"https://arxiv.org/abs/2608.10463v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[183.28,600.99,281.9,10.91],"bbox_pdf":[183.28,180.1,465.18,191.01],"fragments":[{"bbox_pdf":[183.28,180.1,465.18,191.01],"words":[3271,3272,3273,3274,3275,3276,3277,3278,3279,3280,3281,3282,3283,3284,3285,3286,3287,3288,3289]}],"html":null,"kind":"paragraph","latex":"\\alpha+\\beta+\\gamma+\\lambda=0,... | CC-BY-4.0 | assets/20880d3055258194a3eae614f5031f2bff95f75112b91ade56564f6e96368a05.pdf | 20880d3055258194a3eae614f5031f2bff95f75112b91ade56564f6e96368a05 | arxiv:2608.10463 | formula | 8 | {"arxiv_id":"2608.10463","authors":"Idrees Qasim, Ovaisa Jan","title":"On Turan Type inequality for Quaternionic Canonical Generalized Polynomials","url":"https://arxiv.org/abs/2608.10463v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[213.44,637.97,221.58,10.91],"bbox_pdf":[213.44,143.12,435.02,154.03],"fragments":[{"bbox_pdf":[213.44,143.12,435.02,154.03],"words":[3291,3292,3293,3294,3295,3296,3297,3298,3299,3300,3301,3302]}],"html":null,"kind":"paragraph","latex":"E=\\alpha\\beta\\gamma+\\alpha\\beta\\lambda+\\alpha\\gamma\\lambd... | CC-BY-4.0 | assets/20880d3055258194a3eae614f5031f2bff95f75112b91ade56564f6e96368a05.pdf | 20880d3055258194a3eae614f5031f2bff95f75112b91ade56564f6e96368a05 | arxiv:2608.10463 | formula | 8 | {"arxiv_id":"2608.10463","authors":"Idrees Qasim, Ovaisa Jan","title":"On Turan Type inequality for Quaternionic Canonical Generalized Polynomials","url":"https://arxiv.org/abs/2608.10463v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"annotates":["heading","list_item","table","paragraph","furniture"],"attribution":{"arxiv_id":"2608.10463","authors":"Idrees Qasim, Ovaisa Jan","title":"On Turan Type inequality for Quaternionic Canonical Generalized Polynomials","url":"https://arxiv.org/abs/2608.10463v1","version":1},"blocks":[{"bbox":[97.45,41.36,75... | CC-BY-4.0 | assets/246f2503a7e6d4aae88a5c18459b093f7a40233fd9c4da824266474803c459d1.pdf | 246f2503a7e6d4aae88a5c18459b093f7a40233fd9c4da824266474803c459d1 | arxiv:2608.10463 | page | 11 | {"arxiv_id":"2608.10463","authors":"Idrees Qasim, Ovaisa Jan","title":"On Turan Type inequality for Quaternionic Canonical Generalized Polynomials","url":"https://arxiv.org/abs/2608.10463v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"annotates":["heading","list_item","table","paragraph","furniture"],"attribution":{"arxiv_id":"2608.10463","authors":"Idrees Qasim, Ovaisa Jan","title":"On Turan Type inequality for Quaternionic Canonical Generalized Polynomials","url":"https://arxiv.org/abs/2608.10463v1","version":1},"blocks":[{"bbox":[102.91,42.04,4... | CC-BY-4.0 | assets/52757518a3044164f019e5aaae457ae458c609737a4fd6b1f055fb47bd9f4da5.pdf | 52757518a3044164f019e5aaae457ae458c609737a4fd6b1f055fb47bd9f4da5 | arxiv:2608.10463 | page | 12 | {"arxiv_id":"2608.10463","authors":"Idrees Qasim, Ovaisa Jan","title":"On Turan Type inequality for Quaternionic Canonical Generalized Polynomials","url":"https://arxiv.org/abs/2608.10463v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"annotates":["heading","list_item","table","paragraph","furniture"],"attribution":{"arxiv_id":"2608.10468","authors":"Pooja Singla","title":"A canonical section method for conjugacy classes of GL_n(O_2)","url":"https://arxiv.org/abs/2608.10468v1","version":1},"blocks":[{"bbox":[273.59,50.08,64.82,7.97],"bbox_pdf":[273... | CC-BY-4.0 | assets/e53c2461e240a432e854aa19332747f29624bbe84befe68e33ae95b709948aa7.pdf | e53c2461e240a432e854aa19332747f29624bbe84befe68e33ae95b709948aa7 | arxiv:2608.10468 | page | 4 | {"arxiv_id":"2608.10468","authors":"Pooja Singla","title":"A canonical section method for conjugacy classes of GL_n(O_2)","url":"https://arxiv.org/abs/2608.10468v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[146.0,199.42,319.99,21.43],"bbox_pdf":[146.0,571.14,466.0,592.58],"fragments":[{"bbox_pdf":[146.0,571.14,466.0,592.58],"words":[2107,2108,2109,2110,2111,2112,2113,2114,2116,2117,2118,2119,2120,2121,2122,2124,2125,2126,2127,2128,2129,2130]}],"html":null,"kind":"paragraph","latex":"g\\,s_{X}(X)\\,i(Y)\\... | CC-BY-4.0 | assets/e53c2461e240a432e854aa19332747f29624bbe84befe68e33ae95b709948aa7.pdf | e53c2461e240a432e854aa19332747f29624bbe84befe68e33ae95b709948aa7 | arxiv:2608.10468 | formula | 4 | {"arxiv_id":"2608.10468","authors":"Pooja Singla","title":"A canonical section method for conjugacy classes of GL_n(O_2)","url":"https://arxiv.org/abs/2608.10468v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"annotates":["heading","list_item","table","paragraph","furniture"],"attribution":{"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1},"blocks":[{"bbox":[142.62,49.09,326... | CC-BY-4.0 | assets/836daf79aeebc2c6981d8fcd63c109ccd24dda28b46dd6f73991f0129f16b4a1.pdf | 836daf79aeebc2c6981d8fcd63c109ccd24dda28b46dd6f73991f0129f16b4a1 | arxiv:2608.10476 | page | 3 | {"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[262.49,320.86,87.02,24.77],"bbox_pdf":[262.49,446.37,349.51,471.14],"fragments":[{"bbox_pdf":[262.49,446.37,349.51,471.14],"words":[1130,1131,1132,1133,1134,1135,1136]}],"html":null,"kind":"paragraph","latex":"\\mathcal{H}^{1}\\big{(}\\varphi_{j_{E}}(E)\\big{)}>0.","level":null,"list_depth":null,"matc... | CC-BY-4.0 | assets/836daf79aeebc2c6981d8fcd63c109ccd24dda28b46dd6f73991f0129f16b4a1.pdf | 836daf79aeebc2c6981d8fcd63c109ccd24dda28b46dd6f73991f0129f16b4a1 | arxiv:2608.10476 | formula | 3 | {"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[264.11,546.13,83.79,13.75],"bbox_pdf":[264.11,232.12,347.89,245.87],"fragments":[{"bbox_pdf":[264.11,232.12,347.89,245.87],"words":[1283,1284,1285,1286]}],"html":null,"kind":"paragraph","latex":"(\\alpha,x)\\longmapsto\\varphi_{\\alpha}(x)","level":null,"list_depth":null,"match":{"src_placed":1.0,"ver... | CC-BY-4.0 | assets/836daf79aeebc2c6981d8fcd63c109ccd24dda28b46dd6f73991f0129f16b4a1.pdf | 836daf79aeebc2c6981d8fcd63c109ccd24dda28b46dd6f73991f0129f16b4a1 | arxiv:2608.10476 | formula | 3 | {"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[227.21,588.06,157.58,24.84],"bbox_pdf":[227.21,179.1,384.79,203.94],"fragments":[{"bbox_pdf":[227.21,179.1,384.79,203.94],"words":[1319,1320,1321,1322,1323,1327,1328]}],"html":null,"kind":"paragraph","latex":"\\mathsf{H}_{\\boldsymbol{\\alpha}}(x):=\\big{(}\\varphi_{\\alpha_{1}}(x),\\ldots,%\n\\varphi... | CC-BY-4.0 | assets/836daf79aeebc2c6981d8fcd63c109ccd24dda28b46dd6f73991f0129f16b4a1.pdf | 836daf79aeebc2c6981d8fcd63c109ccd24dda28b46dd6f73991f0129f16b4a1 | arxiv:2608.10476 | formula | 3 | {"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[112.72,635.42,386.55,13.75],"bbox_pdf":[112.72,142.83,499.28,156.58],"fragments":[{"bbox_pdf":[112.72,142.83,499.28,156.58],"words":[1332,1333,1334,1335,1336,1337,1338,1339,1341,1342,1343,1344,1345,1346,1347,1348,1349,1350,1351,1352]}],"html":null,"kind":"paragraph","latex":"\\Sigma_{\\boldsymbol{\\al... | CC-BY-4.0 | assets/836daf79aeebc2c6981d8fcd63c109ccd24dda28b46dd6f73991f0129f16b4a1.pdf | 836daf79aeebc2c6981d8fcd63c109ccd24dda28b46dd6f73991f0129f16b4a1 | arxiv:2608.10476 | formula | 3 | {"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"annotates":["heading","list_item","table","paragraph","furniture"],"attribution":{"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1},"blocks":[{"bbox":[142.62,49.09,326... | CC-BY-4.0 | assets/a3c26b17af30e66c37457af383376dc572563d1fe0cbc9cd476074522df9d2a6.pdf | a3c26b17af30e66c37457af383376dc572563d1fe0cbc9cd476074522df9d2a6 | arxiv:2608.10476 | page | 5 | {"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[264.16,143.41,83.68,24.65],"bbox_pdf":[264.16,623.94,347.84,648.59],"fragments":[{"bbox_pdf":[264.16,623.94,347.84,648.59],"words":[1983,1984,1985,1986,1987,1988,1989]}],"html":null,"kind":"paragraph","latex":"\\mathcal{H}^{1}\\big{(}P_{L_{j}}(E)\\big{)}>0","level":null,"list_depth":null,"match":{"src... | CC-BY-4.0 | assets/a3c26b17af30e66c37457af383376dc572563d1fe0cbc9cd476074522df9d2a6.pdf | a3c26b17af30e66c37457af383376dc572563d1fe0cbc9cd476074522df9d2a6 | arxiv:2608.10476 | formula | 5 | {"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[234.38,188.44,143.25,23.43],"bbox_pdf":[234.38,580.13,377.62,603.56],"fragments":[{"bbox_pdf":[234.38,580.13,377.62,603.56],"words":[2011,2012,2013,2014,2015,2016,2017,2021,2022]}],"html":null,"kind":"paragraph","latex":"T(x):=\\big{(}\\langle x,e_{1}\\rangle,\\ldots,\\langle x,e_{d}\\rangle\\big{)}",... | CC-BY-4.0 | assets/a3c26b17af30e66c37457af383376dc572563d1fe0cbc9cd476074522df9d2a6.pdf | a3c26b17af30e66c37457af383376dc572563d1fe0cbc9cd476074522df9d2a6 | arxiv:2608.10476 | formula | 5 | {"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[232.76,355.83,146.48,28.24],"bbox_pdf":[232.76,407.92,379.24,436.17],"fragments":[{"bbox_pdf":[232.76,407.92,379.24,436.17],"words":[2125,2126,2127,2128,2129,2130,2131,2132,2133,2134,2135]}],"html":null,"kind":"paragraph","latex":"(\\alpha;x,y)\\longmapsto\\frac{\\Pi_{\\alpha}(x)-\\Pi_{\\alpha}(y)}{|x... | CC-BY-4.0 | assets/a3c26b17af30e66c37457af383376dc572563d1fe0cbc9cd476074522df9d2a6.pdf | a3c26b17af30e66c37457af383376dc572563d1fe0cbc9cd476074522df9d2a6 | arxiv:2608.10476 | formula | 5 | {"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"annotates":["heading","list_item","table","paragraph","furniture"],"attribution":{"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1},"blocks":[{"bbox":[142.62,49.09,326... | CC-BY-4.0 | assets/5abb2f13d99b82e562f1c2b50b153bf8ea29ab14057a1add21dd1edf6d892cac.pdf | 5abb2f13d99b82e562f1c2b50b153bf8ea29ab14057a1add21dd1edf6d892cac | arxiv:2608.10476 | page | 9 | {"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[260.45,173.42,91.11,13.75],"bbox_pdf":[260.45,604.83,351.56,618.58],"fragments":[{"bbox_pdf":[260.45,604.83,351.56,618.58],"words":[3704,3705,3706,3707]}],"html":null,"kind":"paragraph","latex":"L_{\\mathcal{Q}}:=\\operatorname{Aff}\\{q_{1},q_{2}\\}.","level":null,"list_depth":null,"match":{"src_place... | CC-BY-4.0 | assets/5abb2f13d99b82e562f1c2b50b153bf8ea29ab14057a1add21dd1edf6d892cac.pdf | 5abb2f13d99b82e562f1c2b50b153bf8ea29ab14057a1add21dd1edf6d892cac | arxiv:2608.10476 | formula | 9 | {"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[208.28,210.14,195.44,30.04],"bbox_pdf":[208.28,551.82,403.72,581.86],"fragments":[{"bbox_pdf":[208.28,551.82,403.72,581.86],"words":[3715,3716,3717,3718,3719,3720,3721,3722,3723,3724,3725,3726,3727,3728,3729]}],"html":null,"kind":"paragraph","latex":"\\pi_{q_{j}}(x):=\\frac{x-q_{j}}{|x-q_{j}|},\\qquad... | CC-BY-4.0 | assets/5abb2f13d99b82e562f1c2b50b153bf8ea29ab14057a1add21dd1edf6d892cac.pdf | 5abb2f13d99b82e562f1c2b50b153bf8ea29ab14057a1add21dd1edf6d892cac | arxiv:2608.10476 | formula | 9 | {"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[227.29,254.8,157.42,24.65],"bbox_pdf":[227.29,512.56,384.71,537.2],"fragments":[{"bbox_pdf":[227.29,512.56,384.71,537.2],"words":[3748,3749,3750,3751,3752,3753,3754,3755,3756]}],"html":null,"kind":"paragraph","latex":"\\pi_{q_{j}}(x)=\\big{(}\\cos\\varphi_{j}(x),\\sin\\varphi_{j}(x)\\big{)}.","level":... | CC-BY-4.0 | assets/5abb2f13d99b82e562f1c2b50b153bf8ea29ab14057a1add21dd1edf6d892cac.pdf | 5abb2f13d99b82e562f1c2b50b153bf8ea29ab14057a1add21dd1edf6d892cac | arxiv:2608.10476 | formula | 9 | {"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[242.93,294.15,126.14,23.43],"bbox_pdf":[242.93,474.42,369.07,497.85],"fragments":[{"bbox_pdf":[242.93,474.42,369.07,497.85],"words":[3767,3768,3769,3770,3771,3772,3773]}],"html":null,"kind":"paragraph","latex":"\\mathsf{H}_{\\mathcal{Q}}(x):=\\big{(}\\varphi_{1}(x),\\varphi_{2}(x)\\big{)},","level":nu... | CC-BY-4.0 | assets/5abb2f13d99b82e562f1c2b50b153bf8ea29ab14057a1add21dd1edf6d892cac.pdf | 5abb2f13d99b82e562f1c2b50b153bf8ea29ab14057a1add21dd1edf6d892cac | arxiv:2608.10476 | formula | 9 | {"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[259.05,409.95,93.91,13.75],"bbox_pdf":[259.05,368.3,352.96,382.05],"fragments":[{"bbox_pdf":[259.05,368.3,352.96,382.05],"words":[3831,3832,3833,3834,3835,3836,3837]}],"html":null,"kind":"paragraph","latex":"\\Sigma_{\\mathcal{Q}}\\cap U=L_{\\mathcal{Q}}\\cap U.","level":null,"list_depth":null,"match"... | CC-BY-4.0 | assets/5abb2f13d99b82e562f1c2b50b153bf8ea29ab14057a1add21dd1edf6d892cac.pdf | 5abb2f13d99b82e562f1c2b50b153bf8ea29ab14057a1add21dd1edf6d892cac | arxiv:2608.10476 | formula | 9 | {"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[239.52,448.69,132.96,24.77],"bbox_pdf":[239.52,318.54,372.48,343.31],"fragments":[{"bbox_pdf":[239.52,318.54,372.48,343.31],"words":[3859,3860,3861,3862,3863,3864]}],"html":null,"kind":"paragraph","latex":"\\operatorname{rank}\\big{(}D_{x}\\mathsf{H}_{\\mathcal{Q}}(x)|_{T_{x}L_{\\mathcal{%\nQ}}}\\big{... | CC-BY-4.0 | assets/5abb2f13d99b82e562f1c2b50b153bf8ea29ab14057a1add21dd1edf6d892cac.pdf | 5abb2f13d99b82e562f1c2b50b153bf8ea29ab14057a1add21dd1edf6d892cac | arxiv:2608.10476 | formula | 9 | {"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[218.51,541.12,174.97,30.04],"bbox_pdf":[218.51,220.85,393.48,250.88],"fragments":[{"bbox_pdf":[218.51,220.85,393.48,250.88],"words":[3900,3901,3902,3903,3904,3905,3906,3907,3908,3909,3910,3911,3912]}],"html":null,"kind":"paragraph","latex":"\\nabla\\varphi_{j}(x)=\\frac{R(x-q_{j})}{|x-q_{j}|^{2}},\\qq... | CC-BY-4.0 | assets/5abb2f13d99b82e562f1c2b50b153bf8ea29ab14057a1add21dd1edf6d892cac.pdf | 5abb2f13d99b82e562f1c2b50b153bf8ea29ab14057a1add21dd1edf6d892cac | arxiv:2608.10476 | formula | 9 | {"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[72.0,597.12,347.81,21.95],"bbox_pdf":[72.0,172.93,419.81,194.88],"fragments":[{"bbox_pdf":[72.0,172.93,419.81,194.88],"words":[3916,3917,3918,3919,3920,3921,3922,3923,3924,3925,3926,3927,3928,3929,3930,3931,3932,3933]}],"html":null,"kind":"paragraph","latex":"J_{\\mathcal{Q}}(x):=\\det D_{x}\\mathsf{H... | CC-BY-4.0 | assets/5abb2f13d99b82e562f1c2b50b153bf8ea29ab14057a1add21dd1edf6d892cac.pdf | 5abb2f13d99b82e562f1c2b50b153bf8ea29ab14057a1add21dd1edf6d892cac | arxiv:2608.10476 | formula | 9 | {"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[257.54,688.37,96.92,15.09],"bbox_pdf":[257.54,88.55,354.46,103.63],"fragments":[{"bbox_pdf":[257.54,88.55,354.46,103.63],"words":[3997,3998,3999]}],"html":null,"kind":"paragraph","latex":"D_{x}\\mathsf{H}_{\\mathcal{Q}}(x)|_{T_{x}L_{\\mathcal{Q}}}=0.","level":null,"list_depth":null,"match":{"src_place... | CC-BY-4.0 | assets/5abb2f13d99b82e562f1c2b50b153bf8ea29ab14057a1add21dd1edf6d892cac.pdf | 5abb2f13d99b82e562f1c2b50b153bf8ea29ab14057a1add21dd1edf6d892cac | arxiv:2608.10476 | formula | 9 | {"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"annotates":["heading","list_item","table","paragraph","furniture"],"attribution":{"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1},"blocks":[{"bbox":[72.0,49.09,9.22,... | CC-BY-4.0 | assets/8e73ca7bd1ccb02dd8c028dbc4c026a4b0c209e0c52907bd4a73ce0ad46a9261.pdf | 8e73ca7bd1ccb02dd8c028dbc4c026a4b0c209e0c52907bd4a73ce0ad46a9261 | arxiv:2608.10476 | page | 20 | {"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[238.22,89.19,135.57,13.75],"bbox_pdf":[238.22,689.06,373.79,702.81],"fragments":[{"bbox_pdf":[238.22,689.06,373.79,702.81],"words":[8493,8494,8495,8496]}],"html":null,"kind":"paragraph","latex":"\\ker D_{x}\\mathsf{H}_{\\boldsymbol{\\beta}}(y)=\\operatorname{span}\\{v_{%\n\\boldsymbol{\\beta},y}\\}.",... | CC-BY-4.0 | assets/8e73ca7bd1ccb02dd8c028dbc4c026a4b0c209e0c52907bd4a73ce0ad46a9261.pdf | 8e73ca7bd1ccb02dd8c028dbc4c026a4b0c209e0c52907bd4a73ce0ad46a9261 | arxiv:2608.10476 | formula | 20 | {"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[254.2,181.97,103.6,13.96],"bbox_pdf":[254.2,596.07,357.8,610.03],"fragments":[{"bbox_pdf":[254.2,596.07,357.8,610.03],"words":[8557,8559,8560]}],"html":null,"kind":"paragraph","latex":"D_{x}J_{\\boldsymbol{\\alpha}^{0}}(x)[v_{\\boldsymbol{\\alpha}^{0},x}]\\neq 0.","level":null,"list_depth":null,"match... | CC-BY-4.0 | assets/8e73ca7bd1ccb02dd8c028dbc4c026a4b0c209e0c52907bd4a73ce0ad46a9261.pdf | 8e73ca7bd1ccb02dd8c028dbc4c026a4b0c209e0c52907bd4a73ce0ad46a9261 | arxiv:2608.10476 | formula | 20 | {"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[257.16,217.97,97.69,13.75],"bbox_pdf":[257.16,560.29,354.85,574.03],"fragments":[{"bbox_pdf":[257.16,560.29,354.85,574.03],"words":[8576,8577,8578,8579]}],"html":null,"kind":"paragraph","latex":"(\\boldsymbol{\\beta},y)\\longmapsto D_{x}J_{\\boldsymbol{\\beta}}(y)","level":null,"list_depth":null,"matc... | CC-BY-4.0 | assets/8e73ca7bd1ccb02dd8c028dbc4c026a4b0c209e0c52907bd4a73ce0ad46a9261.pdf | 8e73ca7bd1ccb02dd8c028dbc4c026a4b0c209e0c52907bd4a73ce0ad46a9261 | arxiv:2608.10476 | formula | 20 | {"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[244.51,256.33,122.99,13.75],"bbox_pdf":[244.51,521.93,367.49,535.67],"fragments":[{"bbox_pdf":[244.51,521.93,367.49,535.67],"words":[8594,8595,8596,8597]}],"html":null,"kind":"paragraph","latex":"(\\boldsymbol{\\beta},y)\\longmapsto D_{x}J_{\\boldsymbol{\\beta}}(y)[v_{%\n\\boldsymbol{\\beta},y}]","lev... | CC-BY-4.0 | assets/8e73ca7bd1ccb02dd8c028dbc4c026a4b0c209e0c52907bd4a73ce0ad46a9261.pdf | 8e73ca7bd1ccb02dd8c028dbc4c026a4b0c209e0c52907bd4a73ce0ad46a9261 | arxiv:2608.10476 | formula | 20 | {"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[72.0,308.63,278.96,13.75],"bbox_pdf":[72.0,469.62,350.96,483.37],"fragments":[{"bbox_pdf":[72.0,469.62,350.96,483.37],"words":[8616,8617,8619,8620,8621,8622,8624]}],"html":null,"kind":"paragraph","latex":"D_{x}J_{\\boldsymbol{\\beta}}(y)[v_{\\boldsymbol{\\beta},y}]\\neq 0","level":null,"list_depth":nu... | CC-BY-4.0 | assets/8e73ca7bd1ccb02dd8c028dbc4c026a4b0c209e0c52907bd4a73ce0ad46a9261.pdf | 8e73ca7bd1ccb02dd8c028dbc4c026a4b0c209e0c52907bd4a73ce0ad46a9261 | arxiv:2608.10476 | formula | 20 | {"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[238.22,373.52,135.57,13.75],"bbox_pdf":[238.22,404.73,373.79,418.48],"fragments":[{"bbox_pdf":[238.22,404.73,373.79,418.48],"words":[8648,8649,8650,8651]}],"html":null,"kind":"paragraph","latex":"\\ker D_{x}\\mathsf{H}_{\\boldsymbol{\\beta}}(y)=\\operatorname{span}\\{v_{%\n\\boldsymbol{\\beta},y}\\},"... | CC-BY-4.0 | assets/8e73ca7bd1ccb02dd8c028dbc4c026a4b0c209e0c52907bd4a73ce0ad46a9261.pdf | 8e73ca7bd1ccb02dd8c028dbc4c026a4b0c209e0c52907bd4a73ce0ad46a9261 | arxiv:2608.10476 | formula | 20 | {"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[280.97,409.44,49.28,13.75],"bbox_pdf":[280.97,368.81,330.25,382.56],"fragments":[{"bbox_pdf":[280.97,368.81,330.25,382.56],"words":[8662,8663,8664]}],"html":null,"kind":"paragraph","latex":"w=\\lambda v_{\\boldsymbol{\\beta},y}","level":null,"list_depth":null,"match":{"src_placed":1.0,"verified":true}... | CC-BY-4.0 | assets/8e73ca7bd1ccb02dd8c028dbc4c026a4b0c209e0c52907bd4a73ce0ad46a9261.pdf | 8e73ca7bd1ccb02dd8c028dbc4c026a4b0c209e0c52907bd4a73ce0ad46a9261 | arxiv:2608.10476 | formula | 20 | {"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[219.03,447.8,173.93,13.75],"bbox_pdf":[219.03,330.45,392.96,344.2],"fragments":[{"bbox_pdf":[219.03,330.45,392.96,344.2],"words":[8676,8677,8678,8680,8681]}],"html":null,"kind":"paragraph","latex":"D_{x}J_{\\boldsymbol{\\beta}}(y)[w]=\\lambda D_{x}J_{\\boldsymbol{\\beta}}(y)[v_{%\n\\boldsymbol{\\beta}... | CC-BY-4.0 | assets/8e73ca7bd1ccb02dd8c028dbc4c026a4b0c209e0c52907bd4a73ce0ad46a9261.pdf | 8e73ca7bd1ccb02dd8c028dbc4c026a4b0c209e0c52907bd4a73ce0ad46a9261 | arxiv:2608.10476 | formula | 20 | {"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[253.3,531.52,103.76,15.09],"bbox_pdf":[253.3,245.39,357.06,260.48],"fragments":[{"bbox_pdf":[253.3,245.39,357.06,260.48],"words":[8738,8739,8740,8741,8745]}],"html":null,"kind":"paragraph","latex":"Z\\subseteq G_{x_{1}}\\cup\\cdots\\cup G_{x_{N}}","level":null,"list_depth":null,"match":{"src_placed":1... | CC-BY-4.0 | assets/8e73ca7bd1ccb02dd8c028dbc4c026a4b0c209e0c52907bd4a73ce0ad46a9261.pdf | 8e73ca7bd1ccb02dd8c028dbc4c026a4b0c209e0c52907bd4a73ce0ad46a9261 | arxiv:2608.10476 | formula | 20 | {"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[181.72,565.0,248.55,15.09],"bbox_pdf":[181.72,211.92,430.28,227.0],"fragments":[{"bbox_pdf":[181.72,211.92,430.28,227.0],"words":[8748,8749,8750,8751,8755,8756,8757,8758,8759,8760,8764,8765]}],"html":null,"kind":"paragraph","latex":"G:=G_{x_{1}}\\cup\\cdots\\cup G_{x_{N}},\\qquad\\mathcal{V}_{0}:=\\ma... | CC-BY-4.0 | assets/8e73ca7bd1ccb02dd8c028dbc4c026a4b0c209e0c52907bd4a73ce0ad46a9261.pdf | 8e73ca7bd1ccb02dd8c028dbc4c026a4b0c209e0c52907bd4a73ce0ad46a9261 | arxiv:2608.10476 | formula | 20 | {"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[234.56,650.26,142.88,24.12],"bbox_pdf":[234.56,117.62,377.44,141.74],"fragments":[{"bbox_pdf":[234.56,117.62,377.44,141.74],"words":[8845,8846,8847,8848,8849,8850,8851,8852,8854]}],"html":null,"kind":"paragraph","latex":"\\big{|}J_{\\boldsymbol{\\alpha}^{0}}(y)\\big{|}\\geq\\delta,\\qquad y\\in L\\set... | CC-BY-4.0 | assets/8e73ca7bd1ccb02dd8c028dbc4c026a4b0c209e0c52907bd4a73ce0ad46a9261.pdf | 8e73ca7bd1ccb02dd8c028dbc4c026a4b0c209e0c52907bd4a73ce0ad46a9261 | arxiv:2608.10476 | formula | 20 | {"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[273.63,707.09,64.25,14.7],"bbox_pdf":[273.63,70.21,337.87,84.91],"fragments":[{"bbox_pdf":[273.63,70.21,337.87,84.91],"words":[8876,8877,8878,8879,8880,8881]}],"html":null,"kind":"paragraph","latex":"\\boldsymbol{\\alpha}^{0}\\in\\mathcal{V}\\subseteq\\mathcal{V}_{0}","level":null,"list_depth":null,"m... | CC-BY-4.0 | assets/8e73ca7bd1ccb02dd8c028dbc4c026a4b0c209e0c52907bd4a73ce0ad46a9261.pdf | 8e73ca7bd1ccb02dd8c028dbc4c026a4b0c209e0c52907bd4a73ce0ad46a9261 | arxiv:2608.10476 | formula | 20 | {"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"annotates":["heading","list_item","table","paragraph","furniture"],"attribution":{"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1},"blocks":[{"bbox":[142.62,49.09,326... | CC-BY-4.0 | assets/c1eac61368311ce5526756657052df62242511c7bb6fedc1687f5a33f719a9e8.pdf | c1eac61368311ce5526756657052df62242511c7bb6fedc1687f5a33f719a9e8 | arxiv:2608.10476 | page | 27 | {"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[216.55,93.82,178.4,27.02],"bbox_pdf":[216.55,671.16,394.95,698.18],"fragments":[{"bbox_pdf":[216.55,671.16,394.95,698.18],"words":[11443,11444,11445,11446,11447,11448,11449,11450,11451,11452]}],"html":null,"kind":"paragraph","latex":"\\det\\Big{(}D_{\\alpha}\\Phi_{\\alpha}(x,y)D_{\\alpha}\\Phi_{\\alph... | CC-BY-4.0 | assets/c1eac61368311ce5526756657052df62242511c7bb6fedc1687f5a33f719a9e8.pdf | c1eac61368311ce5526756657052df62242511c7bb6fedc1687f5a33f719a9e8 | arxiv:2608.10476 | formula | 27 | {"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[190.88,210.22,230.24,13.75],"bbox_pdf":[190.88,568.03,421.12,581.78],"fragments":[{"bbox_pdf":[190.88,568.03,421.12,581.78],"words":[11523,11525,11526,11527,11528,11529,11530,11532]}],"html":null,"kind":"paragraph","latex":"D_{x}J_{\\boldsymbol{\\alpha}}(x)[v]\\neq 0,\\qquad\\forall v\\in\\ker D_{x}\\... | CC-BY-4.0 | assets/c1eac61368311ce5526756657052df62242511c7bb6fedc1687f5a33f719a9e8.pdf | c1eac61368311ce5526756657052df62242511c7bb6fedc1687f5a33f719a9e8 | arxiv:2608.10476 | formula | 27 | {"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[197.23,253.58,217.54,37.49],"bbox_pdf":[197.23,500.93,414.77,538.42],"fragments":[{"bbox_pdf":[197.23,500.93,414.77,538.42],"words":[11548,11549,11550,11551,11552,11553,11554,11555,11556,11557,11558,11559,11560,11561,11562,11564,11565,11566,11567,11568,11569,11570,11571,11572]}],"html":null,"kind":"pa... | CC-BY-4.0 | assets/c1eac61368311ce5526756657052df62242511c7bb6fedc1687f5a33f719a9e8.pdf | c1eac61368311ce5526756657052df62242511c7bb6fedc1687f5a33f719a9e8 | arxiv:2608.10476 | formula | 27 | {"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[212.94,331.32,193.1,14.7],"bbox_pdf":[212.94,445.98,406.04,460.68],"fragments":[{"bbox_pdf":[212.94,445.98,406.04,460.68],"words":[11597,11598,11599,11600,11601,11602,11603,11604,11606,11607,11608,11609,11610]}],"html":null,"kind":"paragraph","latex":"\\big{\\{}(\\boldsymbol{\\alpha},x)\\in\\mathcal{A... | CC-BY-4.0 | assets/c1eac61368311ce5526756657052df62242511c7bb6fedc1687f5a33f719a9e8.pdf | c1eac61368311ce5526756657052df62242511c7bb6fedc1687f5a33f719a9e8 | arxiv:2608.10476 | formula | 27 | {"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[193.75,416.71,224.5,12.91],"bbox_pdf":[193.75,362.38,418.25,375.29],"fragments":[{"bbox_pdf":[193.75,362.38,418.25,375.29],"words":[11657,11658,11659,11660,11661,11663,11664,11665,11666,11667,11668,11669,11671,11672,11673,11675,11676]}],"html":null,"kind":"paragraph","latex":"(x^{\\prime},g(x^{\\prime... | CC-BY-4.0 | assets/c1eac61368311ce5526756657052df62242511c7bb6fedc1687f5a33f719a9e8.pdf | c1eac61368311ce5526756657052df62242511c7bb6fedc1687f5a33f719a9e8 | arxiv:2608.10476 | formula | 27 | {"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[262.6,484.64,86.31,14.7],"bbox_pdf":[262.6,292.66,348.9,307.36],"fragments":[{"bbox_pdf":[262.6,292.66,348.9,307.36],"words":[11716,11717,11718,11719,11720,11721]}],"html":null,"kind":"paragraph","latex":"\\Pi_{p}(x):=|x-p|^{2}","level":null,"list_depth":null,"match":{"src_placed":1.0,"verified":true}... | CC-BY-4.0 | assets/c1eac61368311ce5526756657052df62242511c7bb6fedc1687f5a33f719a9e8.pdf | c1eac61368311ce5526756657052df62242511c7bb6fedc1687f5a33f719a9e8 | arxiv:2608.10476 | formula | 27 | {"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[205.37,515.0,136.97,37.49],"bbox_pdf":[205.37,239.51,342.33,277.0],"fragments":[{"bbox_pdf":[205.37,239.51,342.33,277.0],"words":[11728,11729,11730,11731,11732,11733,11734,11735,11736,11737,11738,11739,11740,11741,11742,11743,11744]}],"html":null,"kind":"paragraph","latex":"\\left|\\nabla_{p}\\bigg{(}... | CC-BY-4.0 | assets/c1eac61368311ce5526756657052df62242511c7bb6fedc1687f5a33f719a9e8.pdf | c1eac61368311ce5526756657052df62242511c7bb6fedc1687f5a33f719a9e8 | arxiv:2608.10476 | formula | 27 | {"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[365.74,532.34,40.89,11.96],"bbox_pdf":[365.74,247.71,406.63,259.66],"fragments":[{"bbox_pdf":[365.74,247.71,406.63,259.66],"words":[11745,11747,11748]}],"html":null,"kind":"paragraph","latex":"\\left|\\nabla_{p}\\bigg{(}\\frac{\\Pi_{p}(x)-\\Pi_{p}(y)}{|x-y|}\\bigg{)}\\right|=2%\n\\qquad(x\\neq y).","l... | CC-BY-4.0 | assets/c1eac61368311ce5526756657052df62242511c7bb6fedc1687f5a33f719a9e8.pdf | c1eac61368311ce5526756657052df62242511c7bb6fedc1687f5a33f719a9e8 | arxiv:2608.10476 | formula | 27 | {"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[269.81,662.57,72.39,13.75],"bbox_pdf":[269.81,115.68,342.19,129.43],"fragments":[{"bbox_pdf":[269.81,115.68,342.19,129.43],"words":[11824,11825,11826]}],"html":null,"kind":"paragraph","latex":"\\nu_{\\alpha}:=(\\Pi_{\\alpha})_{\\#}\\mu.","level":null,"list_depth":null,"match":{"src_placed":1.0,"verifi... | CC-BY-4.0 | assets/c1eac61368311ce5526756657052df62242511c7bb6fedc1687f5a33f719a9e8.pdf | c1eac61368311ce5526756657052df62242511c7bb6fedc1687f5a33f719a9e8 | arxiv:2608.10476 | formula | 27 | {"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"annotates":["heading","list_item","table","paragraph","furniture"],"attribution":{"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1},"blocks":[{"bbox":[72.0,49.09,9.22,... | CC-BY-4.0 | assets/38177f7ee41f1e0b8d9ae416a311081c8441c33893063882f6381a70001a8c35.pdf | 38177f7ee41f1e0b8d9ae416a311081c8441c33893063882f6381a70001a8c35 | arxiv:2608.10476 | page | 28 | {"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[72.0,96.05,343.74,23.43],"bbox_pdf":[72.0,672.52,415.74,695.95],"fragments":[{"bbox_pdf":[72.0,672.52,415.74,695.95],"words":[11897,11898,11899,11900,11901,11902,11903,11905,11906,11907,11908,11909,11910,11911,11912]}],"html":null,"kind":"paragraph","latex":"\\dim\\big{\\{}\\alpha\\in\\mathcal{A}:\\di... | CC-BY-4.0 | assets/38177f7ee41f1e0b8d9ae416a311081c8441c33893063882f6381a70001a8c35.pdf | 38177f7ee41f1e0b8d9ae416a311081c8441c33893063882f6381a70001a8c35 | arxiv:2608.10476 | formula | 28 | {"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"annotates":["heading","list_item","table","paragraph","furniture"],"attribution":{"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1},"blocks":[{"bbox":[142.62,49.09,326... | CC-BY-4.0 | assets/e300bfa84fdefa43387898b3502b811e51103f964fc863d371992264ec3cd1ce.pdf | e300bfa84fdefa43387898b3502b811e51103f964fc863d371992264ec3cd1ce | arxiv:2608.10476 | page | 29 | {"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[207.94,124.57,196.11,24.6],"bbox_pdf":[207.94,642.83,404.06,667.43],"fragments":[{"bbox_pdf":[207.94,642.83,404.06,667.43],"words":[12450,12451,12452,12453,12454,12455,12456,12457,12458,12459,12460,12461,12462,12463,12464,12465,12466]}],"html":null,"kind":"paragraph","latex":"\\varphi_{q}^{A,\\eta}(x)... | CC-BY-4.0 | assets/e300bfa84fdefa43387898b3502b811e51103f964fc863d371992264ec3cd1ce.pdf | e300bfa84fdefa43387898b3502b811e51103f964fc863d371992264ec3cd1ce | arxiv:2608.10476 | formula | 29 | {"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[243.09,213.14,125.82,26.27],"bbox_pdf":[243.09,552.59,368.91,578.86],"fragments":[{"bbox_pdf":[243.09,552.59,368.91,578.86],"words":[12523,12524,12525,12526,12527,12528,12529,12530,12531,12535,12536,12537,12538]}],"html":null,"kind":"paragraph","latex":"\\mathsf{\\Phi}_{\\mathcal{Q}}^{A,\\eta}:=\\big{... | CC-BY-4.0 | assets/e300bfa84fdefa43387898b3502b811e51103f964fc863d371992264ec3cd1ce.pdf | e300bfa84fdefa43387898b3502b811e51103f964fc863d371992264ec3cd1ce | arxiv:2608.10476 | formula | 29 | {"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[250.12,302.42,111.26,14.7],"bbox_pdf":[250.12,474.88,361.38,489.58],"fragments":[{"bbox_pdf":[250.12,474.88,361.38,489.58],"words":[12581,12582,12583,12584,12585,12586,12587,12588]}],"html":null,"kind":"paragraph","latex":"s_{j}(x):=|A(x-q^{(j)})|^{2}","level":null,"list_depth":null,"match":{"src_plac... | CC-BY-4.0 | assets/e300bfa84fdefa43387898b3502b811e51103f964fc863d371992264ec3cd1ce.pdf | e300bfa84fdefa43387898b3502b811e51103f964fc863d371992264ec3cd1ce | arxiv:2608.10476 | formula | 29 | {"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
Innovation Trigger B.V., PDFluent ground-truth annotations (2026) | {"block":{"bbox":[231.53,331.97,148.95,24.88],"bbox_pdf":[231.53,435.15,380.47,460.03],"fragments":[{"bbox_pdf":[231.53,435.15,380.47,460.03],"words":[12597,12598,12599,12600,12601,12602,12603,12607,12608]}],"html":null,"kind":"paragraph","latex":"\\mathsf{H}_{\\mathcal{Q}}^{A,2}(x):=\\big{(}s_{1}(x),\\ldots,s_{d}(x)\\... | CC-BY-4.0 | assets/e300bfa84fdefa43387898b3502b811e51103f964fc863d371992264ec3cd1ce.pdf | e300bfa84fdefa43387898b3502b811e51103f964fc863d371992264ec3cd1ce | arxiv:2608.10476 | formula | 29 | {"arxiv_id":"2608.10476","authors":"Caleb Marshall","title":"Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint","url":"https://arxiv.org/abs/2608.10476v1","version":1} | CC-BY-4.0 | arxiv-aligned/dev |
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