{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:GJUFAWSRG7QISJTZ23BEVSN2QQ","short_pith_number":"pith:GJUFAWSR","canonical_record":{"source":{"id":"2501.12347","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-01-21T18:25:31Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"f35566a393a652d4b35f12803853eae296d8f1c6f27f23ea12b4dc75823a626b","abstract_canon_sha256":"b0ce53e9c300088fc93d6ccfdea0fb174e5fbe75ee1a0467bfe3bb8ab33bb8aa"},"schema_version":"1.0"},"canonical_sha256":"3268505a5137e0892679d6c24ac9ba843c555f50b38a304f4c6356f1aafed55b","source":{"kind":"arxiv","id":"2501.12347","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.12347","created_at":"2026-07-05T10:03:34Z"},{"alias_kind":"arxiv_version","alias_value":"2501.12347v1","created_at":"2026-07-05T10:03:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.12347","created_at":"2026-07-05T10:03:34Z"},{"alias_kind":"pith_short_12","alias_value":"GJUFAWSRG7QI","created_at":"2026-07-05T10:03:34Z"},{"alias_kind":"pith_short_16","alias_value":"GJUFAWSRG7QISJTZ","created_at":"2026-07-05T10:03:34Z"},{"alias_kind":"pith_short_8","alias_value":"GJUFAWSR","created_at":"2026-07-05T10:03:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:GJUFAWSRG7QISJTZ23BEVSN2QQ","target":"record","payload":{"canonical_record":{"source":{"id":"2501.12347","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-01-21T18:25:31Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"f35566a393a652d4b35f12803853eae296d8f1c6f27f23ea12b4dc75823a626b","abstract_canon_sha256":"b0ce53e9c300088fc93d6ccfdea0fb174e5fbe75ee1a0467bfe3bb8ab33bb8aa"},"schema_version":"1.0"},"canonical_sha256":"3268505a5137e0892679d6c24ac9ba843c555f50b38a304f4c6356f1aafed55b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:03:34.931521Z","signature_b64":"zMUiUtUGOeZHnxjUC2QaVhEO13qsvfh7lNUgsjarBQIPlAoDJlBEC4kA7Bs9hTy3PAhrjQGPaHuspQYvwIXxDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3268505a5137e0892679d6c24ac9ba843c555f50b38a304f4c6356f1aafed55b","last_reissued_at":"2026-07-05T10:03:34.931102Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:03:34.931102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2501.12347","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:03:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GQCpQmxGRMGJ6BwsBU3qs1snRiDZyBT+5TKv4oLalatsmtKESWIZbLjv3BCD1/GIXZdlr+pwoLqtFzRnghJABA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T06:39:46.115708Z"},"content_sha256":"3db6f7cbabc214b84fe388a017cce1de86e8784cf27a0874e451b13e21d05489","schema_version":"1.0","event_id":"sha256:3db6f7cbabc214b84fe388a017cce1de86e8784cf27a0874e451b13e21d05489"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:GJUFAWSRG7QISJTZ23BEVSN2QQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Euclidean Domains with Nearly Maximal Yamabe Quotient","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Liam Mazurowski, Xuan Yao","submitted_at":"2025-01-21T18:25:31Z","abstract_excerpt":"Let $\\Omega$ be a smooth, bounded domain in $\\mathbb R^3$ with connected boundary. It follows from work of Escobar that the Yamabe quotient of $\\Omega$ is at most the Yamabe quotient of a ball, and equality holds if and only if $\\Omega$ is a ball. We show that if equality almost holds then the following things are true:\n  (i)$\\Omega$ is diffeomorphic to a ball;\n  (ii) There is a small number $\\epsilon > 0$ such that $B(x,r) \\subset \\Omega \\subset B(x,r(1+\\epsilon))$; (iii) After suitable scaling, $\\Omega$ is Gromov-Hausdorff close to the unit ball when considered as a metric space with its ind"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.12347","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.12347/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:03:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WyQnGb0xx70gdcesjoTd27PonfWKyLePbIHV882u9bNdFSCde6Jn58Ucwc6DlZkA5PW7WiEhhd0dUEn3Djm6BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T06:39:46.116312Z"},"content_sha256":"f065633fac0b106a8b7a2c76a0b6b766a64c09e103d2d4a1d64f26352e8f8568","schema_version":"1.0","event_id":"sha256:f065633fac0b106a8b7a2c76a0b6b766a64c09e103d2d4a1d64f26352e8f8568"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GJUFAWSRG7QISJTZ23BEVSN2QQ/bundle.json","state_url":"https://pith.science/pith/GJUFAWSRG7QISJTZ23BEVSN2QQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GJUFAWSRG7QISJTZ23BEVSN2QQ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-12T06:39:46Z","links":{"resolver":"https://pith.science/pith/GJUFAWSRG7QISJTZ23BEVSN2QQ","bundle":"https://pith.science/pith/GJUFAWSRG7QISJTZ23BEVSN2QQ/bundle.json","state":"https://pith.science/pith/GJUFAWSRG7QISJTZ23BEVSN2QQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GJUFAWSRG7QISJTZ23BEVSN2QQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:GJUFAWSRG7QISJTZ23BEVSN2QQ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"b0ce53e9c300088fc93d6ccfdea0fb174e5fbe75ee1a0467bfe3bb8ab33bb8aa","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-01-21T18:25:31Z","title_canon_sha256":"f35566a393a652d4b35f12803853eae296d8f1c6f27f23ea12b4dc75823a626b"},"schema_version":"1.0","source":{"id":"2501.12347","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.12347","created_at":"2026-07-05T10:03:34Z"},{"alias_kind":"arxiv_version","alias_value":"2501.12347v1","created_at":"2026-07-05T10:03:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.12347","created_at":"2026-07-05T10:03:34Z"},{"alias_kind":"pith_short_12","alias_value":"GJUFAWSRG7QI","created_at":"2026-07-05T10:03:34Z"},{"alias_kind":"pith_short_16","alias_value":"GJUFAWSRG7QISJTZ","created_at":"2026-07-05T10:03:34Z"},{"alias_kind":"pith_short_8","alias_value":"GJUFAWSR","created_at":"2026-07-05T10:03:34Z"}],"graph_snapshots":[{"event_id":"sha256:f065633fac0b106a8b7a2c76a0b6b766a64c09e103d2d4a1d64f26352e8f8568","target":"graph","created_at":"2026-07-05T10:03:34Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2501.12347/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\Omega$ be a smooth, bounded domain in $\\mathbb R^3$ with connected boundary. It follows from work of Escobar that the Yamabe quotient of $\\Omega$ is at most the Yamabe quotient of a ball, and equality holds if and only if $\\Omega$ is a ball. We show that if equality almost holds then the following things are true:\n  (i)$\\Omega$ is diffeomorphic to a ball;\n  (ii) There is a small number $\\epsilon > 0$ such that $B(x,r) \\subset \\Omega \\subset B(x,r(1+\\epsilon))$; (iii) After suitable scaling, $\\Omega$ is Gromov-Hausdorff close to the unit ball when considered as a metric space with its ind","authors_text":"Liam Mazurowski, Xuan Yao","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-01-21T18:25:31Z","title":"Euclidean Domains with Nearly Maximal Yamabe Quotient"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.12347","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:3db6f7cbabc214b84fe388a017cce1de86e8784cf27a0874e451b13e21d05489","target":"record","created_at":"2026-07-05T10:03:34Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"b0ce53e9c300088fc93d6ccfdea0fb174e5fbe75ee1a0467bfe3bb8ab33bb8aa","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-01-21T18:25:31Z","title_canon_sha256":"f35566a393a652d4b35f12803853eae296d8f1c6f27f23ea12b4dc75823a626b"},"schema_version":"1.0","source":{"id":"2501.12347","kind":"arxiv","version":1}},"canonical_sha256":"3268505a5137e0892679d6c24ac9ba843c555f50b38a304f4c6356f1aafed55b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3268505a5137e0892679d6c24ac9ba843c555f50b38a304f4c6356f1aafed55b","first_computed_at":"2026-07-05T10:03:34.931102Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:03:34.931102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zMUiUtUGOeZHnxjUC2QaVhEO13qsvfh7lNUgsjarBQIPlAoDJlBEC4kA7Bs9hTy3PAhrjQGPaHuspQYvwIXxDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:03:34.931521Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.12347","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3db6f7cbabc214b84fe388a017cce1de86e8784cf27a0874e451b13e21d05489","sha256:f065633fac0b106a8b7a2c76a0b6b766a64c09e103d2d4a1d64f26352e8f8568"],"state_sha256":"4a37211e83cc55fb22a5fecfdf50391ddd758b8b014ffd32bd346f3bba1930aa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+LVjUUBnEKykpjDZlqe8wwmZdORC5By03b28ZNxZ7klGkQXtG1oOuP83GOVN1Hmwojpj+d1kadPPFm9BRF7+BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T06:39:46.121509Z","bundle_sha256":"8dc145d17cb6c8e2967c2158a6dc1e20cb88cf5b436e8cb23fd7647929ab757e"}}