{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:RUQ5HN53S3G3QEQF25NKEG5UH6","short_pith_number":"pith:RUQ5HN53","canonical_record":{"source":{"id":"2608.05366","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2026-08-05T19:37:32Z","cross_cats_sorted":[],"title_canon_sha256":"dd6e555e302ca3f99798525000a13daf53cd8b25a55c8f5329eea01656145ba1","abstract_canon_sha256":"26d36732ffd7e149c85ffe9caa25c14a1e0d4d389f13f3161bdf8e1b8643e56f"},"schema_version":"1.0"},"canonical_sha256":"8d21d3b7bb96cdb81205d75aa21bb43f900b94279aac3b0ea57463e41568cab1","source":{"kind":"arxiv","id":"2608.05366","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.05366","created_at":"2026-08-07T00:47:29Z"},{"alias_kind":"arxiv_version","alias_value":"2608.05366v1","created_at":"2026-08-07T00:47:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.05366","created_at":"2026-08-07T00:47:29Z"},{"alias_kind":"pith_short_12","alias_value":"RUQ5HN53S3G3","created_at":"2026-08-07T00:47:29Z"},{"alias_kind":"pith_short_16","alias_value":"RUQ5HN53S3G3QEQF","created_at":"2026-08-07T00:47:29Z"},{"alias_kind":"pith_short_8","alias_value":"RUQ5HN53","created_at":"2026-08-07T00:47:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:RUQ5HN53S3G3QEQF25NKEG5UH6","target":"record","payload":{"canonical_record":{"source":{"id":"2608.05366","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2026-08-05T19:37:32Z","cross_cats_sorted":[],"title_canon_sha256":"dd6e555e302ca3f99798525000a13daf53cd8b25a55c8f5329eea01656145ba1","abstract_canon_sha256":"26d36732ffd7e149c85ffe9caa25c14a1e0d4d389f13f3161bdf8e1b8643e56f"},"schema_version":"1.0"},"canonical_sha256":"8d21d3b7bb96cdb81205d75aa21bb43f900b94279aac3b0ea57463e41568cab1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-07T00:47:29.974154Z","signature_b64":"Vch/F9PUlcn8M1475rSIHEdGDJkPUVfC902LMQvDxOcRs33hqysrWe08CGKK8+KA9jfgZUZpISzesPDeeEzcBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8d21d3b7bb96cdb81205d75aa21bb43f900b94279aac3b0ea57463e41568cab1","last_reissued_at":"2026-08-07T00:47:29.972481Z","signature_status":"signed_v1","first_computed_at":"2026-08-07T00:47:29.972481Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.05366","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":"2026-08-07T00:47:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LDPg7O31+EBxl6unM1+AGFlcClqoRocz2aFIPvehEQre5WdYpOuuIn8TwYDo+NP5kvF3WHgO4/cs4BXLu8nnAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T16:22:18.442422Z"},"content_sha256":"e25b37f2304d940116aa5bae875b21d34cc7f60b4ab32f189f98b1f4d9470522","schema_version":"1.0","event_id":"sha256:e25b37f2304d940116aa5bae875b21d34cc7f60b4ab32f189f98b1f4d9470522"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:RUQ5HN53S3G3QEQF25NKEG5UH6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Subexponential Bohnenblust-Hille Inequalities on Finite Cyclic Groups","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Anselmo Raposo Jr, Daniel M. Pellegrino","submitted_at":"2026-08-05T19:37:32Z","abstract_excerpt":"Slote, Volberg and Zhang proved a dimension-free Bohnenblust--Hille inequality on products of finite cyclic groups for functions of bounded total degree. Later, Becker, Klein, Slote, Volberg and Zhang proved $\\BHdeg{d}{q}\\leq(C\\log q)^{2d}$ and asked whether the optimal constants are subexponential in the degree. More recently, Defant, Galicer, Mansilla, Masty\\l o and Muro established an exponential Bohnenblust--Hille estimate for the larger support-sensitive class governed by the number of active coordinates. We prove that the optimal constants for this larger class grow subexponentially. Mor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.05366","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/2608.05366/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":"2026-08-07T00:47:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FoaI8NfNrOl8BKhNS3gZupRc7ADdFeBw+bDhh7Hc/wYw/4qv+Qmn+nngHZaBrZO0bHXgVId/bVRo/IFBVjwPCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T16:22:18.443030Z"},"content_sha256":"65070476b66bd2f927fb5f22b9fb6e5f8b74d5c09ff7fb5b0e775db8181f4b13","schema_version":"1.0","event_id":"sha256:65070476b66bd2f927fb5f22b9fb6e5f8b74d5c09ff7fb5b0e775db8181f4b13"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RUQ5HN53S3G3QEQF25NKEG5UH6/bundle.json","state_url":"https://pith.science/pith/RUQ5HN53S3G3QEQF25NKEG5UH6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RUQ5HN53S3G3QEQF25NKEG5UH6/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":"2026-08-21T16:22:18Z","links":{"resolver":"https://pith.science/pith/RUQ5HN53S3G3QEQF25NKEG5UH6","bundle":"https://pith.science/pith/RUQ5HN53S3G3QEQF25NKEG5UH6/bundle.json","state":"https://pith.science/pith/RUQ5HN53S3G3QEQF25NKEG5UH6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RUQ5HN53S3G3QEQF25NKEG5UH6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:RUQ5HN53S3G3QEQF25NKEG5UH6","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":"26d36732ffd7e149c85ffe9caa25c14a1e0d4d389f13f3161bdf8e1b8643e56f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2026-08-05T19:37:32Z","title_canon_sha256":"dd6e555e302ca3f99798525000a13daf53cd8b25a55c8f5329eea01656145ba1"},"schema_version":"1.0","source":{"id":"2608.05366","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.05366","created_at":"2026-08-07T00:47:29Z"},{"alias_kind":"arxiv_version","alias_value":"2608.05366v1","created_at":"2026-08-07T00:47:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.05366","created_at":"2026-08-07T00:47:29Z"},{"alias_kind":"pith_short_12","alias_value":"RUQ5HN53S3G3","created_at":"2026-08-07T00:47:29Z"},{"alias_kind":"pith_short_16","alias_value":"RUQ5HN53S3G3QEQF","created_at":"2026-08-07T00:47:29Z"},{"alias_kind":"pith_short_8","alias_value":"RUQ5HN53","created_at":"2026-08-07T00:47:29Z"}],"graph_snapshots":[{"event_id":"sha256:65070476b66bd2f927fb5f22b9fb6e5f8b74d5c09ff7fb5b0e775db8181f4b13","target":"graph","created_at":"2026-08-07T00:47:29Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2608.05366/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Slote, Volberg and Zhang proved a dimension-free Bohnenblust--Hille inequality on products of finite cyclic groups for functions of bounded total degree. Later, Becker, Klein, Slote, Volberg and Zhang proved $\\BHdeg{d}{q}\\leq(C\\log q)^{2d}$ and asked whether the optimal constants are subexponential in the degree. More recently, Defant, Galicer, Mansilla, Masty\\l o and Muro established an exponential Bohnenblust--Hille estimate for the larger support-sensitive class governed by the number of active coordinates. We prove that the optimal constants for this larger class grow subexponentially. Mor","authors_text":"Anselmo Raposo Jr, Daniel M. Pellegrino","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2026-08-05T19:37:32Z","title":"Subexponential Bohnenblust-Hille Inequalities on Finite Cyclic Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.05366","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:e25b37f2304d940116aa5bae875b21d34cc7f60b4ab32f189f98b1f4d9470522","target":"record","created_at":"2026-08-07T00:47:29Z","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":"26d36732ffd7e149c85ffe9caa25c14a1e0d4d389f13f3161bdf8e1b8643e56f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2026-08-05T19:37:32Z","title_canon_sha256":"dd6e555e302ca3f99798525000a13daf53cd8b25a55c8f5329eea01656145ba1"},"schema_version":"1.0","source":{"id":"2608.05366","kind":"arxiv","version":1}},"canonical_sha256":"8d21d3b7bb96cdb81205d75aa21bb43f900b94279aac3b0ea57463e41568cab1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d21d3b7bb96cdb81205d75aa21bb43f900b94279aac3b0ea57463e41568cab1","first_computed_at":"2026-08-07T00:47:29.972481Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-07T00:47:29.972481Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Vch/F9PUlcn8M1475rSIHEdGDJkPUVfC902LMQvDxOcRs33hqysrWe08CGKK8+KA9jfgZUZpISzesPDeeEzcBA==","signature_status":"signed_v1","signed_at":"2026-08-07T00:47:29.974154Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.05366","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e25b37f2304d940116aa5bae875b21d34cc7f60b4ab32f189f98b1f4d9470522","sha256:65070476b66bd2f927fb5f22b9fb6e5f8b74d5c09ff7fb5b0e775db8181f4b13"],"state_sha256":"ed0b176e34098389aff7bf9b70eb7f491ba86b79ff03e274a7c57f021258562e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f11/Hr6QxqiL6YEjUMBgQhW7W+utPjVSyFQ2wrZEs6yB0Lov+cwiELQxfMrGyzusrr0QcG/YgoxjshSv8/0OBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T16:22:18.447539Z","bundle_sha256":"32cfd1ef11037c80873a7c9b16e3da4040db520930af838b2380eb2726f364ec"}}