{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:QK2ADUGLQA2SHQRHIAKGZKXYQK","short_pith_number":"pith:QK2ADUGL","canonical_record":{"source":{"id":"1709.03644","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-12T01:33:06Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"502ee85c74192b27dabb2f0e48c9d013482e3ed5db557e1d3c257e3c416e03cd","abstract_canon_sha256":"3b87b9c1c57093f368bcf11a14ad905b40dd080caeafef8e63944a0d56ad1342"},"schema_version":"1.0"},"canonical_sha256":"82b401d0cb803523c22740146caaf882b1a7b1a1e49cec21eb74c67fc66d9732","source":{"kind":"arxiv","id":"1709.03644","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.03644","created_at":"2026-05-18T00:34:28Z"},{"alias_kind":"arxiv_version","alias_value":"1709.03644v2","created_at":"2026-05-18T00:34:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.03644","created_at":"2026-05-18T00:34:28Z"},{"alias_kind":"pith_short_12","alias_value":"QK2ADUGLQA2S","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"QK2ADUGLQA2SHQRH","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"QK2ADUGL","created_at":"2026-05-18T12:31:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:QK2ADUGLQA2SHQRHIAKGZKXYQK","target":"record","payload":{"canonical_record":{"source":{"id":"1709.03644","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-12T01:33:06Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"502ee85c74192b27dabb2f0e48c9d013482e3ed5db557e1d3c257e3c416e03cd","abstract_canon_sha256":"3b87b9c1c57093f368bcf11a14ad905b40dd080caeafef8e63944a0d56ad1342"},"schema_version":"1.0"},"canonical_sha256":"82b401d0cb803523c22740146caaf882b1a7b1a1e49cec21eb74c67fc66d9732","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:28.795025Z","signature_b64":"lQBsdP4itaQ8TSRDxFYLnfx74AsfYQgOOz3fHPwp2NHHeeaWrr5b6OSPHi5GGcJsrbPESIlMEiYyHcRAb1kkAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"82b401d0cb803523c22740146caaf882b1a7b1a1e49cec21eb74c67fc66d9732","last_reissued_at":"2026-05-18T00:34:28.794587Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:28.794587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.03644","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:34:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aul3O2m5fIQsMqMlH5V9Z+/8Qzk20ZZawmcaNceM2UWM6mJJp/MdR46w3S1jX8Swaqqm/ZiipEdgfi/B2mqoDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T03:25:10.006726Z"},"content_sha256":"5db7ba07c044d8ff2e39410b5659da979b8044a2f530c1bcb11f6affe064ee3d","schema_version":"1.0","event_id":"sha256:5db7ba07c044d8ff2e39410b5659da979b8044a2f530c1bcb11f6affe064ee3d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:QK2ADUGLQA2SHQRHIAKGZKXYQK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the isoperimetric quotient over scalar-flat conformal classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Jingang Xiong, Tianling Jin","submitted_at":"2017-09-12T01:33:06Z","abstract_excerpt":"Let $(M,g)$ be a smooth compact Riemannian manifold of dimension $n$ with smooth boundary $\\partial M$. Suppose that $(M,g)$ admits a scalar-flat conformal metric. We prove that the supremum of the isoperimetric quotient over the scalar-flat conformal class is strictly larger than the best constant of the isoperimetric inequality in the Euclidean space, and consequently is achieved, if either (i) $n\\ge 12$ and $\\partial M$ has a nonumbilic point; or (ii) $n\\ge 10$, $\\partial M$ is umbilic and the Weyl tensor does not vanish at some boundary point."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.03644","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T00:34:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dEzf7W/AKaoKBR4RbKSwBouzHQ74H/nTfX3dOFqhbWThKcYKJlt2jBLm2E8xgmOiqsNbZZJdUMaocui3CTbcBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T03:25:10.007062Z"},"content_sha256":"f611a1a141f763b61fd5462e4d64bb65cb8c4a9dd8ed072633b508e1d61da733","schema_version":"1.0","event_id":"sha256:f611a1a141f763b61fd5462e4d64bb65cb8c4a9dd8ed072633b508e1d61da733"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QK2ADUGLQA2SHQRHIAKGZKXYQK/bundle.json","state_url":"https://pith.science/pith/QK2ADUGLQA2SHQRHIAKGZKXYQK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QK2ADUGLQA2SHQRHIAKGZKXYQK/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":"2026-06-27T03:25:10Z","links":{"resolver":"https://pith.science/pith/QK2ADUGLQA2SHQRHIAKGZKXYQK","bundle":"https://pith.science/pith/QK2ADUGLQA2SHQRHIAKGZKXYQK/bundle.json","state":"https://pith.science/pith/QK2ADUGLQA2SHQRHIAKGZKXYQK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QK2ADUGLQA2SHQRHIAKGZKXYQK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:QK2ADUGLQA2SHQRHIAKGZKXYQK","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":"3b87b9c1c57093f368bcf11a14ad905b40dd080caeafef8e63944a0d56ad1342","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-12T01:33:06Z","title_canon_sha256":"502ee85c74192b27dabb2f0e48c9d013482e3ed5db557e1d3c257e3c416e03cd"},"schema_version":"1.0","source":{"id":"1709.03644","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.03644","created_at":"2026-05-18T00:34:28Z"},{"alias_kind":"arxiv_version","alias_value":"1709.03644v2","created_at":"2026-05-18T00:34:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.03644","created_at":"2026-05-18T00:34:28Z"},{"alias_kind":"pith_short_12","alias_value":"QK2ADUGLQA2S","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"QK2ADUGLQA2SHQRH","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"QK2ADUGL","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:f611a1a141f763b61fd5462e4d64bb65cb8c4a9dd8ed072633b508e1d61da733","target":"graph","created_at":"2026-05-18T00:34:28Z","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"},"paper":{"abstract_excerpt":"Let $(M,g)$ be a smooth compact Riemannian manifold of dimension $n$ with smooth boundary $\\partial M$. Suppose that $(M,g)$ admits a scalar-flat conformal metric. We prove that the supremum of the isoperimetric quotient over the scalar-flat conformal class is strictly larger than the best constant of the isoperimetric inequality in the Euclidean space, and consequently is achieved, if either (i) $n\\ge 12$ and $\\partial M$ has a nonumbilic point; or (ii) $n\\ge 10$, $\\partial M$ is umbilic and the Weyl tensor does not vanish at some boundary point.","authors_text":"Jingang Xiong, Tianling Jin","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-12T01:33:06Z","title":"On the isoperimetric quotient over scalar-flat conformal classes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.03644","kind":"arxiv","version":2},"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":"sha256:5db7ba07c044d8ff2e39410b5659da979b8044a2f530c1bcb11f6affe064ee3d","target":"record","created_at":"2026-05-18T00:34:28Z","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":"3b87b9c1c57093f368bcf11a14ad905b40dd080caeafef8e63944a0d56ad1342","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-12T01:33:06Z","title_canon_sha256":"502ee85c74192b27dabb2f0e48c9d013482e3ed5db557e1d3c257e3c416e03cd"},"schema_version":"1.0","source":{"id":"1709.03644","kind":"arxiv","version":2}},"canonical_sha256":"82b401d0cb803523c22740146caaf882b1a7b1a1e49cec21eb74c67fc66d9732","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"82b401d0cb803523c22740146caaf882b1a7b1a1e49cec21eb74c67fc66d9732","first_computed_at":"2026-05-18T00:34:28.794587Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:28.794587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lQBsdP4itaQ8TSRDxFYLnfx74AsfYQgOOz3fHPwp2NHHeeaWrr5b6OSPHi5GGcJsrbPESIlMEiYyHcRAb1kkAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:28.795025Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.03644","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5db7ba07c044d8ff2e39410b5659da979b8044a2f530c1bcb11f6affe064ee3d","sha256:f611a1a141f763b61fd5462e4d64bb65cb8c4a9dd8ed072633b508e1d61da733"],"state_sha256":"42b98073d93aaff4e5b0b405fa719beab57c67f06d5b7705418b9b107c95f1d3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O6mQR8ClhcEhQgoDpPMGJJLQ5MSqPmzEp5WgKpUYCqKBX8ZOdVrJMCPh7jq7mi2hu+H+U7EfNhsdt0d/aCsHCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T03:25:10.009005Z","bundle_sha256":"8eb5a91aa3fb46c49981c0066d7e48a5935b780d7beddde3e0524e5550ff8c20"}}