{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:55YFFJ5YDGAY6NVWE5ORYTD42S","short_pith_number":"pith:55YFFJ5Y","canonical_record":{"source":{"id":"1612.09040","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-12-29T05:32:40Z","cross_cats_sorted":["math.AP","math.DS","math.SP","nlin.CD"],"title_canon_sha256":"16c8b79d563c5a83f2ca1dfd6316a70aed8fb932d6a6b4903cca1c5eb6e6a6f1","abstract_canon_sha256":"3b6a7a613290878f99d99541c97dd7c691818a781c7b6852c4d05c9345a208d4"},"schema_version":"1.0"},"canonical_sha256":"ef7052a7b819818f36b6275d1c4c7cd4a1391479f0178075a0546a3ba227f3c8","source":{"kind":"arxiv","id":"1612.09040","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.09040","created_at":"2026-05-18T00:18:05Z"},{"alias_kind":"arxiv_version","alias_value":"1612.09040v2","created_at":"2026-05-18T00:18:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.09040","created_at":"2026-05-18T00:18:05Z"},{"alias_kind":"pith_short_12","alias_value":"55YFFJ5YDGAY","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"55YFFJ5YDGAY6NVW","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"55YFFJ5Y","created_at":"2026-05-18T12:29:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:55YFFJ5YDGAY6NVWE5ORYTD42S","target":"record","payload":{"canonical_record":{"source":{"id":"1612.09040","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-12-29T05:32:40Z","cross_cats_sorted":["math.AP","math.DS","math.SP","nlin.CD"],"title_canon_sha256":"16c8b79d563c5a83f2ca1dfd6316a70aed8fb932d6a6b4903cca1c5eb6e6a6f1","abstract_canon_sha256":"3b6a7a613290878f99d99541c97dd7c691818a781c7b6852c4d05c9345a208d4"},"schema_version":"1.0"},"canonical_sha256":"ef7052a7b819818f36b6275d1c4c7cd4a1391479f0178075a0546a3ba227f3c8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:05.421342Z","signature_b64":"1zMx+/HPGhy4SQQc3UY+MK8e9qpnB7zaXgTwCdfeT6jInxI5jSFn9wge/toZU7SVtePXErRg7AoNJOO5/RgDDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ef7052a7b819818f36b6275d1c4c7cd4a1391479f0178075a0546a3ba227f3c8","last_reissued_at":"2026-05-18T00:18:05.420674Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:05.420674Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.09040","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":"2026-05-18T00:18:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hE7NszDlKm26ztDv0S5IdzdK6REYftBWxIvyp6SFajD3IcyNj5UcoH3vj52Ko1d77HgpS5PbXd8N91sNNCAODg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T18:54:01.221421Z"},"content_sha256":"d8a01d63dbf3d83852210b8f4598b64aac732ba8b39a1dee175808edee2895f2","schema_version":"1.0","event_id":"sha256:d8a01d63dbf3d83852210b8f4598b64aac732ba8b39a1dee175808edee2895f2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:55YFFJ5YDGAY6NVWE5ORYTD42S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectral gaps without the pressure condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.DS","math.SP","nlin.CD"],"primary_cat":"math.CA","authors_text":"Jean Bourgain, Semyon Dyatlov","submitted_at":"2016-12-29T05:32:40Z","abstract_excerpt":"For all convex co-compact hyperbolic surfaces, we prove the existence of an essential spectral gap, that is a strip beyond the unitarity axis in which the Selberg zeta function has only finitely many zeroes. We make no assumption on the dimension $\\delta$ of the limit set, in particular we do not require the pressure condition $\\delta\\leq {1\\over 2}$. This is the first result of this kind for quantum Hamiltonians.\n  Our proof follows the strategy developed by Dyatlov-Zahl [arXiv:1504.06589]. The main new ingredient is the fractal uncertainty principle for $\\delta$-regular sets with $\\delta<1$,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.09040","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":"2026-05-18T00:18:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6x/PD/mYU+TXp+jMcZDst0/ysWJ6++QYeXXQv7MJHLPB8PpD6Kw6OlQIJfZYUlIaQ3qQA936QVmmR17Q37qrBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T18:54:01.222125Z"},"content_sha256":"b1c6b8515669102cd10987cc34ab91df9cb16e2e665b5e25cc511ad1774d5148","schema_version":"1.0","event_id":"sha256:b1c6b8515669102cd10987cc34ab91df9cb16e2e665b5e25cc511ad1774d5148"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/55YFFJ5YDGAY6NVWE5ORYTD42S/bundle.json","state_url":"https://pith.science/pith/55YFFJ5YDGAY6NVWE5ORYTD42S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/55YFFJ5YDGAY6NVWE5ORYTD42S/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":"2026-05-28T18:54:01Z","links":{"resolver":"https://pith.science/pith/55YFFJ5YDGAY6NVWE5ORYTD42S","bundle":"https://pith.science/pith/55YFFJ5YDGAY6NVWE5ORYTD42S/bundle.json","state":"https://pith.science/pith/55YFFJ5YDGAY6NVWE5ORYTD42S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/55YFFJ5YDGAY6NVWE5ORYTD42S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:55YFFJ5YDGAY6NVWE5ORYTD42S","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":"3b6a7a613290878f99d99541c97dd7c691818a781c7b6852c4d05c9345a208d4","cross_cats_sorted":["math.AP","math.DS","math.SP","nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-12-29T05:32:40Z","title_canon_sha256":"16c8b79d563c5a83f2ca1dfd6316a70aed8fb932d6a6b4903cca1c5eb6e6a6f1"},"schema_version":"1.0","source":{"id":"1612.09040","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.09040","created_at":"2026-05-18T00:18:05Z"},{"alias_kind":"arxiv_version","alias_value":"1612.09040v2","created_at":"2026-05-18T00:18:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.09040","created_at":"2026-05-18T00:18:05Z"},{"alias_kind":"pith_short_12","alias_value":"55YFFJ5YDGAY","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"55YFFJ5YDGAY6NVW","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"55YFFJ5Y","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:b1c6b8515669102cd10987cc34ab91df9cb16e2e665b5e25cc511ad1774d5148","target":"graph","created_at":"2026-05-18T00:18:05Z","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":"For all convex co-compact hyperbolic surfaces, we prove the existence of an essential spectral gap, that is a strip beyond the unitarity axis in which the Selberg zeta function has only finitely many zeroes. We make no assumption on the dimension $\\delta$ of the limit set, in particular we do not require the pressure condition $\\delta\\leq {1\\over 2}$. This is the first result of this kind for quantum Hamiltonians.\n  Our proof follows the strategy developed by Dyatlov-Zahl [arXiv:1504.06589]. The main new ingredient is the fractal uncertainty principle for $\\delta$-regular sets with $\\delta<1$,","authors_text":"Jean Bourgain, Semyon Dyatlov","cross_cats":["math.AP","math.DS","math.SP","nlin.CD"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-12-29T05:32:40Z","title":"Spectral gaps without the pressure condition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.09040","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:d8a01d63dbf3d83852210b8f4598b64aac732ba8b39a1dee175808edee2895f2","target":"record","created_at":"2026-05-18T00:18:05Z","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":"3b6a7a613290878f99d99541c97dd7c691818a781c7b6852c4d05c9345a208d4","cross_cats_sorted":["math.AP","math.DS","math.SP","nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-12-29T05:32:40Z","title_canon_sha256":"16c8b79d563c5a83f2ca1dfd6316a70aed8fb932d6a6b4903cca1c5eb6e6a6f1"},"schema_version":"1.0","source":{"id":"1612.09040","kind":"arxiv","version":2}},"canonical_sha256":"ef7052a7b819818f36b6275d1c4c7cd4a1391479f0178075a0546a3ba227f3c8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ef7052a7b819818f36b6275d1c4c7cd4a1391479f0178075a0546a3ba227f3c8","first_computed_at":"2026-05-18T00:18:05.420674Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:05.420674Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1zMx+/HPGhy4SQQc3UY+MK8e9qpnB7zaXgTwCdfeT6jInxI5jSFn9wge/toZU7SVtePXErRg7AoNJOO5/RgDDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:05.421342Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.09040","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d8a01d63dbf3d83852210b8f4598b64aac732ba8b39a1dee175808edee2895f2","sha256:b1c6b8515669102cd10987cc34ab91df9cb16e2e665b5e25cc511ad1774d5148"],"state_sha256":"8b709cc7128fc8b59303bbc7807f138622d3f6b978db1b4509b7c62ab4524ee6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xK2OjwQihaEo9ohFD8sahZSQprcD2q8PYlakA41GN6uzCJxzJZtAJCv/65gzIVWoXqQK6pPqQn/HkUXffRcVBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T18:54:01.225845Z","bundle_sha256":"c1063c9b23270a7a1f65574b3956a9520147e3771534c29e43d5d50b42d369f9"}}