{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:L2LSN5USUMKHSHURMTOSF3D2XB","short_pith_number":"pith:L2LSN5US","canonical_record":{"source":{"id":"2606.03423","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.OA","submitted_at":"2026-06-02T10:09:13Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"1cfa0104d74943613d35ea2bc425e453325f4f2e63485f2a7158682e683fb9a4","abstract_canon_sha256":"1e6bb251aa17e6ce254499846cdf21bcd40978c8d735142002b1920f3afe6be5"},"schema_version":"1.0"},"canonical_sha256":"5e9726f692a314791e9164dd22ec7ab87397f20290267c04f18718062bb60963","source":{"kind":"arxiv","id":"2606.03423","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.03423","created_at":"2026-06-03T01:05:57Z"},{"alias_kind":"arxiv_version","alias_value":"2606.03423v1","created_at":"2026-06-03T01:05:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.03423","created_at":"2026-06-03T01:05:57Z"},{"alias_kind":"pith_short_12","alias_value":"L2LSN5USUMKH","created_at":"2026-06-03T01:05:57Z"},{"alias_kind":"pith_short_16","alias_value":"L2LSN5USUMKHSHUR","created_at":"2026-06-03T01:05:57Z"},{"alias_kind":"pith_short_8","alias_value":"L2LSN5US","created_at":"2026-06-03T01:05:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:L2LSN5USUMKHSHURMTOSF3D2XB","target":"record","payload":{"canonical_record":{"source":{"id":"2606.03423","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.OA","submitted_at":"2026-06-02T10:09:13Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"1cfa0104d74943613d35ea2bc425e453325f4f2e63485f2a7158682e683fb9a4","abstract_canon_sha256":"1e6bb251aa17e6ce254499846cdf21bcd40978c8d735142002b1920f3afe6be5"},"schema_version":"1.0"},"canonical_sha256":"5e9726f692a314791e9164dd22ec7ab87397f20290267c04f18718062bb60963","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T01:05:57.455238Z","signature_b64":"OKyXwAoQrv5JpblJVDkqyLzCNzwv2FuwM7DHO7GuPZPoDZp4sc/Kp1W9XsRDfUZTE3N/3h1AyWRjVqRVot8jBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5e9726f692a314791e9164dd22ec7ab87397f20290267c04f18718062bb60963","last_reissued_at":"2026-06-03T01:05:57.454803Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T01:05:57.454803Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.03423","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":"2026-06-03T01:05:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i0OuTxkxHtFdaMuiYpD8/kHu1xv4ahcEFJg4EnzIkWYlmOf7r+DZx3W0RL7VXg428w+AZemoE7HO/BT485ODAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T06:01:25.801846Z"},"content_sha256":"e35d677c48e10b9f595917c65994dfefaddeb9c7c8d79938e1a2619c2afa4981","schema_version":"1.0","event_id":"sha256:e35d677c48e10b9f595917c65994dfefaddeb9c7c8d79938e1a2619c2afa4981"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:L2LSN5USUMKHSHURMTOSF3D2XB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sharp hypercontractivity for free group von Neumann algebras","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Haonan Zhang, Xinyuan Xie","submitted_at":"2026-06-02T10:09:13Z","abstract_excerpt":"We prove that the Poisson semigroup on free group von Neumann algebras satisfies hypercontractivity with optimal time."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.03423","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/2606.03423/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":"2026-06-03T01:05:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XnAlEoQRAZaPQZitbSKgQuVs9R0e3XNiTRhzki9ao3LNgmwA2NozBBkYYFrimCQGnII4qR7blZpNGGu1c41pCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T06:01:25.802654Z"},"content_sha256":"646c2f9cada1b219131d655e53a9e08e1035854be3bf386088503fcb093a3d8c","schema_version":"1.0","event_id":"sha256:646c2f9cada1b219131d655e53a9e08e1035854be3bf386088503fcb093a3d8c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L2LSN5USUMKHSHURMTOSF3D2XB/bundle.json","state_url":"https://pith.science/pith/L2LSN5USUMKHSHURMTOSF3D2XB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L2LSN5USUMKHSHURMTOSF3D2XB/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":"2026-06-11T06:01:25Z","links":{"resolver":"https://pith.science/pith/L2LSN5USUMKHSHURMTOSF3D2XB","bundle":"https://pith.science/pith/L2LSN5USUMKHSHURMTOSF3D2XB/bundle.json","state":"https://pith.science/pith/L2LSN5USUMKHSHURMTOSF3D2XB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L2LSN5USUMKHSHURMTOSF3D2XB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:L2LSN5USUMKHSHURMTOSF3D2XB","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":"1e6bb251aa17e6ce254499846cdf21bcd40978c8d735142002b1920f3afe6be5","cross_cats_sorted":["math.FA"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.OA","submitted_at":"2026-06-02T10:09:13Z","title_canon_sha256":"1cfa0104d74943613d35ea2bc425e453325f4f2e63485f2a7158682e683fb9a4"},"schema_version":"1.0","source":{"id":"2606.03423","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.03423","created_at":"2026-06-03T01:05:57Z"},{"alias_kind":"arxiv_version","alias_value":"2606.03423v1","created_at":"2026-06-03T01:05:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.03423","created_at":"2026-06-03T01:05:57Z"},{"alias_kind":"pith_short_12","alias_value":"L2LSN5USUMKH","created_at":"2026-06-03T01:05:57Z"},{"alias_kind":"pith_short_16","alias_value":"L2LSN5USUMKHSHUR","created_at":"2026-06-03T01:05:57Z"},{"alias_kind":"pith_short_8","alias_value":"L2LSN5US","created_at":"2026-06-03T01:05:57Z"}],"graph_snapshots":[{"event_id":"sha256:646c2f9cada1b219131d655e53a9e08e1035854be3bf386088503fcb093a3d8c","target":"graph","created_at":"2026-06-03T01:05:57Z","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/2606.03423/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that the Poisson semigroup on free group von Neumann algebras satisfies hypercontractivity with optimal time.","authors_text":"Haonan Zhang, Xinyuan Xie","cross_cats":["math.FA"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.OA","submitted_at":"2026-06-02T10:09:13Z","title":"Sharp hypercontractivity for free group von Neumann algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.03423","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:e35d677c48e10b9f595917c65994dfefaddeb9c7c8d79938e1a2619c2afa4981","target":"record","created_at":"2026-06-03T01:05:57Z","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":"1e6bb251aa17e6ce254499846cdf21bcd40978c8d735142002b1920f3afe6be5","cross_cats_sorted":["math.FA"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.OA","submitted_at":"2026-06-02T10:09:13Z","title_canon_sha256":"1cfa0104d74943613d35ea2bc425e453325f4f2e63485f2a7158682e683fb9a4"},"schema_version":"1.0","source":{"id":"2606.03423","kind":"arxiv","version":1}},"canonical_sha256":"5e9726f692a314791e9164dd22ec7ab87397f20290267c04f18718062bb60963","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5e9726f692a314791e9164dd22ec7ab87397f20290267c04f18718062bb60963","first_computed_at":"2026-06-03T01:05:57.454803Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T01:05:57.454803Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OKyXwAoQrv5JpblJVDkqyLzCNzwv2FuwM7DHO7GuPZPoDZp4sc/Kp1W9XsRDfUZTE3N/3h1AyWRjVqRVot8jBQ==","signature_status":"signed_v1","signed_at":"2026-06-03T01:05:57.455238Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.03423","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e35d677c48e10b9f595917c65994dfefaddeb9c7c8d79938e1a2619c2afa4981","sha256:646c2f9cada1b219131d655e53a9e08e1035854be3bf386088503fcb093a3d8c"],"state_sha256":"071396dfe1613d7fd135db1ec326b9f0e63781ebfe37db12dd2daa50f7bfc02b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8V98rawFXkadonhaAAUHKx05s4z28yb0xZO0Jjl0TZMvUMmWk+mnw+qeCkK7pyiKWQI85G3Tp4lVd9S2uKPnDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T06:01:25.807505Z","bundle_sha256":"bc146e8c82f85107e8eb22e6041be9840c35619d58e6597888612d792eb55c78"}}