{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:DPJPVFOUF7OO3YZL35PEPXKEFZ","short_pith_number":"pith:DPJPVFOU","canonical_record":{"source":{"id":"2410.15566","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2024-10-21T01:23:19Z","cross_cats_sorted":["math.FA","math.GR"],"title_canon_sha256":"b38c2bbf7e46bcafdfd6c10f3d9dba4aecc1b42ab886bdb4e974befc11965e35","abstract_canon_sha256":"ff293998a16418d97534dd914419b9f5bf68dc4ca20ab3c9735560447b1493f3"},"schema_version":"1.0"},"canonical_sha256":"1bd2fa95d42fdcede32bdf5e47dd442e5e3b1c80175b004f68828fff50e7d095","source":{"kind":"arxiv","id":"2410.15566","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.15566","created_at":"2026-07-05T09:23:21Z"},{"alias_kind":"arxiv_version","alias_value":"2410.15566v1","created_at":"2026-07-05T09:23:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.15566","created_at":"2026-07-05T09:23:21Z"},{"alias_kind":"pith_short_12","alias_value":"DPJPVFOUF7OO","created_at":"2026-07-05T09:23:21Z"},{"alias_kind":"pith_short_16","alias_value":"DPJPVFOUF7OO3YZL","created_at":"2026-07-05T09:23:21Z"},{"alias_kind":"pith_short_8","alias_value":"DPJPVFOU","created_at":"2026-07-05T09:23:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:DPJPVFOUF7OO3YZL35PEPXKEFZ","target":"record","payload":{"canonical_record":{"source":{"id":"2410.15566","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2024-10-21T01:23:19Z","cross_cats_sorted":["math.FA","math.GR"],"title_canon_sha256":"b38c2bbf7e46bcafdfd6c10f3d9dba4aecc1b42ab886bdb4e974befc11965e35","abstract_canon_sha256":"ff293998a16418d97534dd914419b9f5bf68dc4ca20ab3c9735560447b1493f3"},"schema_version":"1.0"},"canonical_sha256":"1bd2fa95d42fdcede32bdf5e47dd442e5e3b1c80175b004f68828fff50e7d095","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:23:21.413271Z","signature_b64":"dMipGuAqzk37E6At02kIjZCT+0ML2y6RKz6STE7HoeBKeBJX1qSWTrOk0HvwN7HhEEHVUemKhGIO1ZY8ojb4Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1bd2fa95d42fdcede32bdf5e47dd442e5e3b1c80175b004f68828fff50e7d095","last_reissued_at":"2026-07-05T09:23:21.412793Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:23:21.412793Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2410.15566","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":"2026-07-05T09:23:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q40DICtyTXZmH1QZ7Y/h+Y2pnOwCE831eCN6PKSSvVYHIHiK9PZa/FqQczb8+4ZJuIi/PKFg4A5JdKDlchRKAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T00:25:31.104730Z"},"content_sha256":"7f3262cd76a6d56eddec14fdc74e12c869ce72fe1973ba4b8f03c4d8b97a0220","schema_version":"1.0","event_id":"sha256:7f3262cd76a6d56eddec14fdc74e12c869ce72fe1973ba4b8f03c4d8b97a0220"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:DPJPVFOUF7OO3YZL35PEPXKEFZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sharp defective log-Sobolev inequalities on H-type groups","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.FA","math.GR"],"primary_cat":"math.AP","authors_text":"Gioacchino Antonelli, Maria Gordina, Mattia Calzi","submitted_at":"2024-10-21T01:23:19Z","abstract_excerpt":"In this paper we prove a sharp defective log-Sobolev inequality on H-type groups. Then we use such an inequality to show exponential integrability of Lipschitz functions with respect to the heat kernel measure. A defective log-Sobolev-type inequality for the Gaussian-like measure with respect to the sub-Riemannian distance is also proved on arbitrary H-type groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.15566","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/2410.15566/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":"2026-07-05T09:23:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X4Y7WeLfEhq0Sq4slZMlRLLhvKNuHQA3fF3hSOWuHDFC1VYU03xu6KPLpx9yC10UMrRQtazLVVzpGxYTo/54CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T00:25:31.105200Z"},"content_sha256":"d5131d3ce62eef990a2bad1d09bf6e2f37c03910e9549a61629f6f798b6dcc00","schema_version":"1.0","event_id":"sha256:d5131d3ce62eef990a2bad1d09bf6e2f37c03910e9549a61629f6f798b6dcc00"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DPJPVFOUF7OO3YZL35PEPXKEFZ/bundle.json","state_url":"https://pith.science/pith/DPJPVFOUF7OO3YZL35PEPXKEFZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DPJPVFOUF7OO3YZL35PEPXKEFZ/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":"2026-08-13T00:25:31Z","links":{"resolver":"https://pith.science/pith/DPJPVFOUF7OO3YZL35PEPXKEFZ","bundle":"https://pith.science/pith/DPJPVFOUF7OO3YZL35PEPXKEFZ/bundle.json","state":"https://pith.science/pith/DPJPVFOUF7OO3YZL35PEPXKEFZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DPJPVFOUF7OO3YZL35PEPXKEFZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:DPJPVFOUF7OO3YZL35PEPXKEFZ","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":"ff293998a16418d97534dd914419b9f5bf68dc4ca20ab3c9735560447b1493f3","cross_cats_sorted":["math.FA","math.GR"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2024-10-21T01:23:19Z","title_canon_sha256":"b38c2bbf7e46bcafdfd6c10f3d9dba4aecc1b42ab886bdb4e974befc11965e35"},"schema_version":"1.0","source":{"id":"2410.15566","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.15566","created_at":"2026-07-05T09:23:21Z"},{"alias_kind":"arxiv_version","alias_value":"2410.15566v1","created_at":"2026-07-05T09:23:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.15566","created_at":"2026-07-05T09:23:21Z"},{"alias_kind":"pith_short_12","alias_value":"DPJPVFOUF7OO","created_at":"2026-07-05T09:23:21Z"},{"alias_kind":"pith_short_16","alias_value":"DPJPVFOUF7OO3YZL","created_at":"2026-07-05T09:23:21Z"},{"alias_kind":"pith_short_8","alias_value":"DPJPVFOU","created_at":"2026-07-05T09:23:21Z"}],"graph_snapshots":[{"event_id":"sha256:d5131d3ce62eef990a2bad1d09bf6e2f37c03910e9549a61629f6f798b6dcc00","target":"graph","created_at":"2026-07-05T09:23:21Z","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/2410.15566/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we prove a sharp defective log-Sobolev inequality on H-type groups. Then we use such an inequality to show exponential integrability of Lipschitz functions with respect to the heat kernel measure. A defective log-Sobolev-type inequality for the Gaussian-like measure with respect to the sub-Riemannian distance is also proved on arbitrary H-type groups.","authors_text":"Gioacchino Antonelli, Maria Gordina, Mattia Calzi","cross_cats":["math.FA","math.GR"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2024-10-21T01:23:19Z","title":"Sharp defective log-Sobolev inequalities on H-type groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.15566","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":"sha256:7f3262cd76a6d56eddec14fdc74e12c869ce72fe1973ba4b8f03c4d8b97a0220","target":"record","created_at":"2026-07-05T09:23:21Z","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":"ff293998a16418d97534dd914419b9f5bf68dc4ca20ab3c9735560447b1493f3","cross_cats_sorted":["math.FA","math.GR"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AP","submitted_at":"2024-10-21T01:23:19Z","title_canon_sha256":"b38c2bbf7e46bcafdfd6c10f3d9dba4aecc1b42ab886bdb4e974befc11965e35"},"schema_version":"1.0","source":{"id":"2410.15566","kind":"arxiv","version":1}},"canonical_sha256":"1bd2fa95d42fdcede32bdf5e47dd442e5e3b1c80175b004f68828fff50e7d095","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1bd2fa95d42fdcede32bdf5e47dd442e5e3b1c80175b004f68828fff50e7d095","first_computed_at":"2026-07-05T09:23:21.412793Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:23:21.412793Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dMipGuAqzk37E6At02kIjZCT+0ML2y6RKz6STE7HoeBKeBJX1qSWTrOk0HvwN7HhEEHVUemKhGIO1ZY8ojb4Cw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:23:21.413271Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.15566","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7f3262cd76a6d56eddec14fdc74e12c869ce72fe1973ba4b8f03c4d8b97a0220","sha256:d5131d3ce62eef990a2bad1d09bf6e2f37c03910e9549a61629f6f798b6dcc00"],"state_sha256":"a85c141961898355f38ec9fc1e4abf7777aa4c02d70c1c7cc9458183bb2184da"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"grELZRlj61BFrInB3rcT2fBDEH1ERUJlfsQir8Xjf4CxI5AuEYdSF9WNv51KiXgbYxv34B2SReyDNzhjvuNtCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T00:25:31.109533Z","bundle_sha256":"14abc516ef20df7379a1b50b9185fa08aad3a1cd58060a9fd218dbab4ac77e7e"}}