{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:KDVW2JOACGMRWAJERCNXPRW5QK","short_pith_number":"pith:KDVW2JOA","canonical_record":{"source":{"id":"2404.00700","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2024-03-31T14:36:37Z","cross_cats_sorted":[],"title_canon_sha256":"c560a79b62c9680f7e0764922cdba9103b24d772fe65642f1e9919424659db15","abstract_canon_sha256":"2ea510869f343ae7f54c7d3fb2b6cf856373193f5882a75b5d23842e43040b03"},"schema_version":"1.0"},"canonical_sha256":"50eb6d25c011991b0124889b77c6dd82a73d1fb80bdc4102e53b3e6e82f47592","source":{"kind":"arxiv","id":"2404.00700","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.00700","created_at":"2026-07-05T09:35:09Z"},{"alias_kind":"arxiv_version","alias_value":"2404.00700v2","created_at":"2026-07-05T09:35:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.00700","created_at":"2026-07-05T09:35:09Z"},{"alias_kind":"pith_short_12","alias_value":"KDVW2JOACGMR","created_at":"2026-07-05T09:35:09Z"},{"alias_kind":"pith_short_16","alias_value":"KDVW2JOACGMRWAJE","created_at":"2026-07-05T09:35:09Z"},{"alias_kind":"pith_short_8","alias_value":"KDVW2JOA","created_at":"2026-07-05T09:35:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:KDVW2JOACGMRWAJERCNXPRW5QK","target":"record","payload":{"canonical_record":{"source":{"id":"2404.00700","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2024-03-31T14:36:37Z","cross_cats_sorted":[],"title_canon_sha256":"c560a79b62c9680f7e0764922cdba9103b24d772fe65642f1e9919424659db15","abstract_canon_sha256":"2ea510869f343ae7f54c7d3fb2b6cf856373193f5882a75b5d23842e43040b03"},"schema_version":"1.0"},"canonical_sha256":"50eb6d25c011991b0124889b77c6dd82a73d1fb80bdc4102e53b3e6e82f47592","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:35:09.080915Z","signature_b64":"GKpNny63T0a+NB3S/J3sOrl4O6hN9VTDut0i9McwyC1LYuUgTGtW5FTMaVzrSr2myFz914WsiBetkKrhQ1lfAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"50eb6d25c011991b0124889b77c6dd82a73d1fb80bdc4102e53b3e6e82f47592","last_reissued_at":"2026-07-05T09:35:09.080468Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:35:09.080468Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2404.00700","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":"2026-07-05T09:35:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Sg3RSXRjp0w6RPzxoGoVAMU72M12Hu07N3rdPsR2McO7DmY39qH61PjT7VWTImnT9RsrPrjhYY88QVclGHRaBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T09:03:59.874444Z"},"content_sha256":"cebc821115633ef9d4104911f034dfa7790c16a0b45a097c6ccc8dd1d230badb","schema_version":"1.0","event_id":"sha256:cebc821115633ef9d4104911f034dfa7790c16a0b45a097c6ccc8dd1d230badb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:KDVW2JOACGMRWAJERCNXPRW5QK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Critical exponent gap and leafwise dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Omri Nisan Solan","submitted_at":"2024-03-31T14:36:37Z","abstract_excerpt":"We show that for every nonarithmetic lattice $\\Gamma<{\\rm SL}_2(\\mathbb{C})$ there is a gap $\\varepsilon_\\Gamma>0$ such that for every $g\\in {\\rm SL}_2(\\mathbb{C})$ the intersection ${\\rm SL}_2(\\mathbb{R})\\cap g\\Gamma g^{-1}$ is either a lattice in ${\\rm SL}_2(\\mathbb{R})$ or has critical exponent $\\delta({\\rm SL}_2(\\mathbb{R})\\cap g\\Gamma g^{-1}) \\leq 1 - \\varepsilon_\\Gamma$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.00700","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2404.00700/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":"2026-07-05T09:35:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qa7B9XnnigIsFAQKH34R8SwFnmGlKEsu7S73SuTYe9MFdEAqcLmkZf+Rwh6CRbcK/21GaOo0BJOImba2pSr5DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T09:03:59.875118Z"},"content_sha256":"c2d2e1acd2833e98dc0f540f562cfa32d8551f73b812ba61794e853afd008050","schema_version":"1.0","event_id":"sha256:c2d2e1acd2833e98dc0f540f562cfa32d8551f73b812ba61794e853afd008050"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KDVW2JOACGMRWAJERCNXPRW5QK/bundle.json","state_url":"https://pith.science/pith/KDVW2JOACGMRWAJERCNXPRW5QK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KDVW2JOACGMRWAJERCNXPRW5QK/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":"2026-08-10T09:03:59Z","links":{"resolver":"https://pith.science/pith/KDVW2JOACGMRWAJERCNXPRW5QK","bundle":"https://pith.science/pith/KDVW2JOACGMRWAJERCNXPRW5QK/bundle.json","state":"https://pith.science/pith/KDVW2JOACGMRWAJERCNXPRW5QK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KDVW2JOACGMRWAJERCNXPRW5QK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:KDVW2JOACGMRWAJERCNXPRW5QK","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":"2ea510869f343ae7f54c7d3fb2b6cf856373193f5882a75b5d23842e43040b03","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2024-03-31T14:36:37Z","title_canon_sha256":"c560a79b62c9680f7e0764922cdba9103b24d772fe65642f1e9919424659db15"},"schema_version":"1.0","source":{"id":"2404.00700","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.00700","created_at":"2026-07-05T09:35:09Z"},{"alias_kind":"arxiv_version","alias_value":"2404.00700v2","created_at":"2026-07-05T09:35:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.00700","created_at":"2026-07-05T09:35:09Z"},{"alias_kind":"pith_short_12","alias_value":"KDVW2JOACGMR","created_at":"2026-07-05T09:35:09Z"},{"alias_kind":"pith_short_16","alias_value":"KDVW2JOACGMRWAJE","created_at":"2026-07-05T09:35:09Z"},{"alias_kind":"pith_short_8","alias_value":"KDVW2JOA","created_at":"2026-07-05T09:35:09Z"}],"graph_snapshots":[{"event_id":"sha256:c2d2e1acd2833e98dc0f540f562cfa32d8551f73b812ba61794e853afd008050","target":"graph","created_at":"2026-07-05T09:35:09Z","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/2404.00700/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that for every nonarithmetic lattice $\\Gamma<{\\rm SL}_2(\\mathbb{C})$ there is a gap $\\varepsilon_\\Gamma>0$ such that for every $g\\in {\\rm SL}_2(\\mathbb{C})$ the intersection ${\\rm SL}_2(\\mathbb{R})\\cap g\\Gamma g^{-1}$ is either a lattice in ${\\rm SL}_2(\\mathbb{R})$ or has critical exponent $\\delta({\\rm SL}_2(\\mathbb{R})\\cap g\\Gamma g^{-1}) \\leq 1 - \\varepsilon_\\Gamma$.","authors_text":"Omri Nisan Solan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2024-03-31T14:36:37Z","title":"Critical exponent gap and leafwise dimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.00700","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:cebc821115633ef9d4104911f034dfa7790c16a0b45a097c6ccc8dd1d230badb","target":"record","created_at":"2026-07-05T09:35:09Z","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":"2ea510869f343ae7f54c7d3fb2b6cf856373193f5882a75b5d23842e43040b03","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2024-03-31T14:36:37Z","title_canon_sha256":"c560a79b62c9680f7e0764922cdba9103b24d772fe65642f1e9919424659db15"},"schema_version":"1.0","source":{"id":"2404.00700","kind":"arxiv","version":2}},"canonical_sha256":"50eb6d25c011991b0124889b77c6dd82a73d1fb80bdc4102e53b3e6e82f47592","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"50eb6d25c011991b0124889b77c6dd82a73d1fb80bdc4102e53b3e6e82f47592","first_computed_at":"2026-07-05T09:35:09.080468Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:35:09.080468Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GKpNny63T0a+NB3S/J3sOrl4O6hN9VTDut0i9McwyC1LYuUgTGtW5FTMaVzrSr2myFz914WsiBetkKrhQ1lfAg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:35:09.080915Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.00700","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cebc821115633ef9d4104911f034dfa7790c16a0b45a097c6ccc8dd1d230badb","sha256:c2d2e1acd2833e98dc0f540f562cfa32d8551f73b812ba61794e853afd008050"],"state_sha256":"10c6513722cfa9a8f9f7dd8f14d64abe8f5410a7e139abac0546bf138fd0486d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H6lJIMELjmL3Q1r1allCwykhPEumkSD5eEb5KW/0JKE6nNIW42Z2EHLcyBNR1dUYab22QHDUZNUmBYxxN5seAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T09:03:59.879651Z","bundle_sha256":"deff0cfba46b6f17d8ceaaba0a25af54d92016552e7e8caa1b0151fef26a6218"}}