{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:LD6IUSJ4KXBRAMQCLLGTNHV2NJ","short_pith_number":"pith:LD6IUSJ4","canonical_record":{"source":{"id":"1805.12535","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-05-31T16:14:01Z","cross_cats_sorted":[],"title_canon_sha256":"061c1e01d1bcd67748776a280192fc9bf945a8b3d5f6a22a32cf11ebbdae66c8","abstract_canon_sha256":"d11492f12d4477369111df899e2488bc935cb6f4226c384ab236f2707c862139"},"schema_version":"1.0"},"canonical_sha256":"58fc8a493c55c31032025acd369eba6a684ee054ef02b3c04beadfffeae23183","source":{"kind":"arxiv","id":"1805.12535","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.12535","created_at":"2026-05-18T00:14:29Z"},{"alias_kind":"arxiv_version","alias_value":"1805.12535v1","created_at":"2026-05-18T00:14:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.12535","created_at":"2026-05-18T00:14:29Z"},{"alias_kind":"pith_short_12","alias_value":"LD6IUSJ4KXBR","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"LD6IUSJ4KXBRAMQC","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"LD6IUSJ4","created_at":"2026-05-18T12:32:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:LD6IUSJ4KXBRAMQCLLGTNHV2NJ","target":"record","payload":{"canonical_record":{"source":{"id":"1805.12535","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-05-31T16:14:01Z","cross_cats_sorted":[],"title_canon_sha256":"061c1e01d1bcd67748776a280192fc9bf945a8b3d5f6a22a32cf11ebbdae66c8","abstract_canon_sha256":"d11492f12d4477369111df899e2488bc935cb6f4226c384ab236f2707c862139"},"schema_version":"1.0"},"canonical_sha256":"58fc8a493c55c31032025acd369eba6a684ee054ef02b3c04beadfffeae23183","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:29.980889Z","signature_b64":"ltkFGyTzVyi6dgKEGkrmXZdMkvLUsiqaoBerXhqrRkpAbKrno27dZUhzHSlnMbfWk9Mh0jKKxRjAznzE/n/5CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"58fc8a493c55c31032025acd369eba6a684ee054ef02b3c04beadfffeae23183","last_reissued_at":"2026-05-18T00:14:29.980121Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:29.980121Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.12535","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":"2026-05-18T00:14:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"berKKJRe69gWUPj6E4181L5KTdIMHvsD0xrhXoJ1K6op55PRTko+ud6HEP701UKuOjgmSXoGYE7pBR7a3rNHDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T09:14:25.450795Z"},"content_sha256":"96ee37f95e822149f6becdcb3f95125422678a85acae8a8e8ad7d143c86675a5","schema_version":"1.0","event_id":"sha256:96ee37f95e822149f6becdcb3f95125422678a85acae8a8e8ad7d143c86675a5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:LD6IUSJ4KXBRAMQCLLGTNHV2NJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sharp Gagliardo--Nirenberg trace inequalities via mass transportion method and their affine versions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Van Hoang Nguyen","submitted_at":"2018-05-31T16:14:01Z","abstract_excerpt":"Exploiting the mass transportation method, we prove a dual principle which implies directly the sharp Gagliardo-Nirenberg trace inequalities which was recently proved by Bolley et al. [BCFGG17]. Moreover, we determine all optimal functions for these obtained sharp Gagliardo-Nirenberg trace inequalities. This settles a question left open in [BCFGG17]. Finally, we use the sharp Gagliardo--Nirenberg trace inequality to establish their affine versions (i.e., the sharp affine Gagliardo-Nirenberg trace inequalities) which generalize a recent result of De N\\'apoli et al. [DeNapoli]. It was shown that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.12535","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":""},"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":"2026-05-18T00:14:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YIysRHqepWfBawYy8Li+SZTkoL7LrGhVPt5FmRktzOT9yJQDYYCSVkGiV4WTOGNRBmOAhadi6tbzERLQ9uBaBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T09:14:25.451138Z"},"content_sha256":"fb267c5782a42ba26f60a20dac1d0e8d57cd71c7e5aa54cbea46982d4ad36dd5","schema_version":"1.0","event_id":"sha256:fb267c5782a42ba26f60a20dac1d0e8d57cd71c7e5aa54cbea46982d4ad36dd5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LD6IUSJ4KXBRAMQCLLGTNHV2NJ/bundle.json","state_url":"https://pith.science/pith/LD6IUSJ4KXBRAMQCLLGTNHV2NJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LD6IUSJ4KXBRAMQCLLGTNHV2NJ/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":"2026-06-25T09:14:25Z","links":{"resolver":"https://pith.science/pith/LD6IUSJ4KXBRAMQCLLGTNHV2NJ","bundle":"https://pith.science/pith/LD6IUSJ4KXBRAMQCLLGTNHV2NJ/bundle.json","state":"https://pith.science/pith/LD6IUSJ4KXBRAMQCLLGTNHV2NJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LD6IUSJ4KXBRAMQCLLGTNHV2NJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:LD6IUSJ4KXBRAMQCLLGTNHV2NJ","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":"d11492f12d4477369111df899e2488bc935cb6f4226c384ab236f2707c862139","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-05-31T16:14:01Z","title_canon_sha256":"061c1e01d1bcd67748776a280192fc9bf945a8b3d5f6a22a32cf11ebbdae66c8"},"schema_version":"1.0","source":{"id":"1805.12535","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.12535","created_at":"2026-05-18T00:14:29Z"},{"alias_kind":"arxiv_version","alias_value":"1805.12535v1","created_at":"2026-05-18T00:14:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.12535","created_at":"2026-05-18T00:14:29Z"},{"alias_kind":"pith_short_12","alias_value":"LD6IUSJ4KXBR","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"LD6IUSJ4KXBRAMQC","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"LD6IUSJ4","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:fb267c5782a42ba26f60a20dac1d0e8d57cd71c7e5aa54cbea46982d4ad36dd5","target":"graph","created_at":"2026-05-18T00:14:29Z","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":"Exploiting the mass transportation method, we prove a dual principle which implies directly the sharp Gagliardo-Nirenberg trace inequalities which was recently proved by Bolley et al. [BCFGG17]. Moreover, we determine all optimal functions for these obtained sharp Gagliardo-Nirenberg trace inequalities. This settles a question left open in [BCFGG17]. Finally, we use the sharp Gagliardo--Nirenberg trace inequality to establish their affine versions (i.e., the sharp affine Gagliardo-Nirenberg trace inequalities) which generalize a recent result of De N\\'apoli et al. [DeNapoli]. It was shown that","authors_text":"Van Hoang Nguyen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-05-31T16:14:01Z","title":"Sharp Gagliardo--Nirenberg trace inequalities via mass transportion method and their affine versions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.12535","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":"sha256:96ee37f95e822149f6becdcb3f95125422678a85acae8a8e8ad7d143c86675a5","target":"record","created_at":"2026-05-18T00:14:29Z","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":"d11492f12d4477369111df899e2488bc935cb6f4226c384ab236f2707c862139","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-05-31T16:14:01Z","title_canon_sha256":"061c1e01d1bcd67748776a280192fc9bf945a8b3d5f6a22a32cf11ebbdae66c8"},"schema_version":"1.0","source":{"id":"1805.12535","kind":"arxiv","version":1}},"canonical_sha256":"58fc8a493c55c31032025acd369eba6a684ee054ef02b3c04beadfffeae23183","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"58fc8a493c55c31032025acd369eba6a684ee054ef02b3c04beadfffeae23183","first_computed_at":"2026-05-18T00:14:29.980121Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:29.980121Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ltkFGyTzVyi6dgKEGkrmXZdMkvLUsiqaoBerXhqrRkpAbKrno27dZUhzHSlnMbfWk9Mh0jKKxRjAznzE/n/5CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:29.980889Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.12535","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:96ee37f95e822149f6becdcb3f95125422678a85acae8a8e8ad7d143c86675a5","sha256:fb267c5782a42ba26f60a20dac1d0e8d57cd71c7e5aa54cbea46982d4ad36dd5"],"state_sha256":"f2ac2a96faec8b951d82226153568d9ec0fafff9d978b9947dcfcdb9f3ea1009"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7Txk/X9f0TEN6ZU4Jn0qTtz4J2cgvMKxVGg6nuh1lQE/6NmluJKA8nzvxDE/hlV9tzwFpkxrWmS6Q7gaZ5t+Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T09:14:25.453101Z","bundle_sha256":"32d0a9acc8b5bcb57d3a8de3da557cd9c604b832425ebf6ea27057a3573a64ef"}}