{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:KLKHPADXGDOAO5DZS3M5VONURL","short_pith_number":"pith:KLKHPADX","canonical_record":{"source":{"id":"1802.01740","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-02-06T00:26:04Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"fc928ed4ae9c11d3da9655f125f7ca538fb0fc7092307988c344cda2269f4b5c","abstract_canon_sha256":"a0ecae141a5032d701cea27f5d5ebbdb4909843b279d6ef19ecf844e064d3cfb"},"schema_version":"1.0"},"canonical_sha256":"52d477807730dc07747996d9dab9b48ae1fe5f5083af18c71978b44a83fa6c57","source":{"kind":"arxiv","id":"1802.01740","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.01740","created_at":"2026-05-18T00:23:44Z"},{"alias_kind":"arxiv_version","alias_value":"1802.01740v2","created_at":"2026-05-18T00:23:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.01740","created_at":"2026-05-18T00:23:44Z"},{"alias_kind":"pith_short_12","alias_value":"KLKHPADXGDOA","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"KLKHPADXGDOAO5DZ","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"KLKHPADX","created_at":"2026-05-18T12:32:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:KLKHPADXGDOAO5DZS3M5VONURL","target":"record","payload":{"canonical_record":{"source":{"id":"1802.01740","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-02-06T00:26:04Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"fc928ed4ae9c11d3da9655f125f7ca538fb0fc7092307988c344cda2269f4b5c","abstract_canon_sha256":"a0ecae141a5032d701cea27f5d5ebbdb4909843b279d6ef19ecf844e064d3cfb"},"schema_version":"1.0"},"canonical_sha256":"52d477807730dc07747996d9dab9b48ae1fe5f5083af18c71978b44a83fa6c57","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:44.740143Z","signature_b64":"5D7PlIBcoPYvL+9LmnkBIxCdPQYoqa4WWG8SDc+zw2+dNG3OF8kBwVRK7Ik1lTEzIiiEdzJY2rZZqK9RcencDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"52d477807730dc07747996d9dab9b48ae1fe5f5083af18c71978b44a83fa6c57","last_reissued_at":"2026-05-18T00:23:44.739586Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:44.739586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.01740","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":"2026-05-18T00:23:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tkyuv3lTUzJLytZPG3xsbEPxqwXY3vf0hLecLHl415i1DSkHawRuropWdwrCTK8s4NAANB47yKQPSxQK3WxqCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T14:46:38.940584Z"},"content_sha256":"dfa950758f5fff6ae11b5744251cdb3f4d0fcd2743f96fe64a9434664453bea1","schema_version":"1.0","event_id":"sha256:dfa950758f5fff6ae11b5744251cdb3f4d0fcd2743f96fe64a9434664453bea1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:KLKHPADXGDOAO5DZS3M5VONURL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gagliardo-Nirenberg-Sobolev inequalities for convex domains in $\\mathbb{R}^d$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Cristobal Vallejos, Hanne Van Den Bosch, Rafael D. Benguria","submitted_at":"2018-02-06T00:26:04Z","abstract_excerpt":"A special type of Gagliardo-Nirenberg-Sobolev (GNS) inequalities in $\\mathbb{R}^d$ has played a key role in several proofs of Lieb-Thirring inequalities. Recently, a need for GNS inequalities in convex domains of $\\mathbb{R}^d$, in particular for cubes, has arised. The purpose of this manuscript is two-fold. First we prove a GNS inequality for convex domains, with explicit constants which depend on the geometry of the domain. Later, using the discrete version of Rumin's method, we prove GNS inequalities on cubes with improved constants."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.01740","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":"2026-05-18T00:23:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WWZzpET+2djZLwMx+ixOS7kPIFldsGLT7WHdzuWQY5O/UL6ZMcm5LB5b9WL1UhSilrhWmeBM0na8Osb0iSJIDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T14:46:38.940933Z"},"content_sha256":"8dbd0e74a99a140234fb52b257a22c9889c80fb6fbf96cf4fd7b67ae74a3d012","schema_version":"1.0","event_id":"sha256:8dbd0e74a99a140234fb52b257a22c9889c80fb6fbf96cf4fd7b67ae74a3d012"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KLKHPADXGDOAO5DZS3M5VONURL/bundle.json","state_url":"https://pith.science/pith/KLKHPADXGDOAO5DZS3M5VONURL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KLKHPADXGDOAO5DZS3M5VONURL/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":"2026-06-21T14:46:38Z","links":{"resolver":"https://pith.science/pith/KLKHPADXGDOAO5DZS3M5VONURL","bundle":"https://pith.science/pith/KLKHPADXGDOAO5DZS3M5VONURL/bundle.json","state":"https://pith.science/pith/KLKHPADXGDOAO5DZS3M5VONURL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KLKHPADXGDOAO5DZS3M5VONURL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:KLKHPADXGDOAO5DZS3M5VONURL","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":"a0ecae141a5032d701cea27f5d5ebbdb4909843b279d6ef19ecf844e064d3cfb","cross_cats_sorted":["math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-02-06T00:26:04Z","title_canon_sha256":"fc928ed4ae9c11d3da9655f125f7ca538fb0fc7092307988c344cda2269f4b5c"},"schema_version":"1.0","source":{"id":"1802.01740","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.01740","created_at":"2026-05-18T00:23:44Z"},{"alias_kind":"arxiv_version","alias_value":"1802.01740v2","created_at":"2026-05-18T00:23:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.01740","created_at":"2026-05-18T00:23:44Z"},{"alias_kind":"pith_short_12","alias_value":"KLKHPADXGDOA","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"KLKHPADXGDOAO5DZ","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"KLKHPADX","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:8dbd0e74a99a140234fb52b257a22c9889c80fb6fbf96cf4fd7b67ae74a3d012","target":"graph","created_at":"2026-05-18T00:23:44Z","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":"A special type of Gagliardo-Nirenberg-Sobolev (GNS) inequalities in $\\mathbb{R}^d$ has played a key role in several proofs of Lieb-Thirring inequalities. Recently, a need for GNS inequalities in convex domains of $\\mathbb{R}^d$, in particular for cubes, has arised. The purpose of this manuscript is two-fold. First we prove a GNS inequality for convex domains, with explicit constants which depend on the geometry of the domain. Later, using the discrete version of Rumin's method, we prove GNS inequalities on cubes with improved constants.","authors_text":"Cristobal Vallejos, Hanne Van Den Bosch, Rafael D. Benguria","cross_cats":["math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-02-06T00:26:04Z","title":"Gagliardo-Nirenberg-Sobolev inequalities for convex domains in $\\mathbb{R}^d$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.01740","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:dfa950758f5fff6ae11b5744251cdb3f4d0fcd2743f96fe64a9434664453bea1","target":"record","created_at":"2026-05-18T00:23:44Z","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":"a0ecae141a5032d701cea27f5d5ebbdb4909843b279d6ef19ecf844e064d3cfb","cross_cats_sorted":["math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-02-06T00:26:04Z","title_canon_sha256":"fc928ed4ae9c11d3da9655f125f7ca538fb0fc7092307988c344cda2269f4b5c"},"schema_version":"1.0","source":{"id":"1802.01740","kind":"arxiv","version":2}},"canonical_sha256":"52d477807730dc07747996d9dab9b48ae1fe5f5083af18c71978b44a83fa6c57","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"52d477807730dc07747996d9dab9b48ae1fe5f5083af18c71978b44a83fa6c57","first_computed_at":"2026-05-18T00:23:44.739586Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:44.739586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5D7PlIBcoPYvL+9LmnkBIxCdPQYoqa4WWG8SDc+zw2+dNG3OF8kBwVRK7Ik1lTEzIiiEdzJY2rZZqK9RcencDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:44.740143Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.01740","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dfa950758f5fff6ae11b5744251cdb3f4d0fcd2743f96fe64a9434664453bea1","sha256:8dbd0e74a99a140234fb52b257a22c9889c80fb6fbf96cf4fd7b67ae74a3d012"],"state_sha256":"c2f8aea27bb22345d37eb1913524f2409ae5426fa0e79f02511998db62491d1e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zdmMG0fVbVMfxRjN5n8eTJ0svBxB2YRvMpGPn2Zt+3sHVf6NrNVdM2wSk0yL218KfZTSgcGWXpBPy0w7DmefCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T14:46:38.942939Z","bundle_sha256":"336d7e487bf64e171f674ada370a314177565b17b0c6f3a74377172dd8f405b7"}}