{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:EPNFC4FGCOLTVGETDUOHO34H27","short_pith_number":"pith:EPNFC4FG","canonical_record":{"source":{"id":"1612.05935","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-12-18T15:45:00Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"059e1cf53bc3d5b1f6e9a4086214cf6ccbb2637ee01251f8a0c208c3f6f00908","abstract_canon_sha256":"c076738b8171a8f4b7a7de22bd36633080b971d5030ba3a53de63826a66ed035"},"schema_version":"1.0"},"canonical_sha256":"23da5170a613973a98931d1c776f87d7e9efab85adc08cb6c813879e8acb95bf","source":{"kind":"arxiv","id":"1612.05935","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.05935","created_at":"2026-05-18T00:54:46Z"},{"alias_kind":"arxiv_version","alias_value":"1612.05935v1","created_at":"2026-05-18T00:54:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.05935","created_at":"2026-05-18T00:54:46Z"},{"alias_kind":"pith_short_12","alias_value":"EPNFC4FGCOLT","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"EPNFC4FGCOLTVGET","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"EPNFC4FG","created_at":"2026-05-18T12:30:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:EPNFC4FGCOLTVGETDUOHO34H27","target":"record","payload":{"canonical_record":{"source":{"id":"1612.05935","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-12-18T15:45:00Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"059e1cf53bc3d5b1f6e9a4086214cf6ccbb2637ee01251f8a0c208c3f6f00908","abstract_canon_sha256":"c076738b8171a8f4b7a7de22bd36633080b971d5030ba3a53de63826a66ed035"},"schema_version":"1.0"},"canonical_sha256":"23da5170a613973a98931d1c776f87d7e9efab85adc08cb6c813879e8acb95bf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:46.315810Z","signature_b64":"8TiPqFOtQyuLjQ6IWB0CCXW72QeuOSbQLDbEBZpGdD9841KTQO3/h96jq/GPmXxbh/F1uUnXY0GRLQVApKqhBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"23da5170a613973a98931d1c776f87d7e9efab85adc08cb6c813879e8acb95bf","last_reissued_at":"2026-05-18T00:54:46.315218Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:46.315218Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.05935","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":"2026-05-18T00:54:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"szhmC8U8UTHzk8KNuPyBC5YfA3GT0CsGYqq6myAJVtCqT0NMpz+7gGlio8bONqvRR8hpMjAROkH2u6b+5YXqBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T10:01:57.148087Z"},"content_sha256":"4f391c031d89f67263aa178f7bdb78f9886d25f322ace0ba21fbb76666aacbd2","schema_version":"1.0","event_id":"sha256:4f391c031d89f67263aa178f7bdb78f9886d25f322ace0ba21fbb76666aacbd2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:EPNFC4FGCOLTVGETDUOHO34H27","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Salem numbers and the spectrum of hyperbolic surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.NT","authors_text":"Bertrand Deroin, Emmanuel Breuillard","submitted_at":"2016-12-18T15:45:00Z","abstract_excerpt":"We give a reformulation of Salem's conjecture about the absence of Salem numbers near one in terms of a uniform spectral gap for certain arithmetic hyperbolic surfaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.05935","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":""},"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":"2026-05-18T00:54:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mmuBArKnHSvb7Iuwj9iMmfYY1/aJwY5bWO5OY3/HX/AWmySFORsvB/GuNRhVNLDtPaxaOgayKcFFL0quhFULBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T10:01:57.148450Z"},"content_sha256":"8113baab41b2f80fe9efb1330e00dd0cce00e72ba30561f77924cc89d0e3cebd","schema_version":"1.0","event_id":"sha256:8113baab41b2f80fe9efb1330e00dd0cce00e72ba30561f77924cc89d0e3cebd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EPNFC4FGCOLTVGETDUOHO34H27/bundle.json","state_url":"https://pith.science/pith/EPNFC4FGCOLTVGETDUOHO34H27/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EPNFC4FGCOLTVGETDUOHO34H27/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":"2026-06-04T10:01:57Z","links":{"resolver":"https://pith.science/pith/EPNFC4FGCOLTVGETDUOHO34H27","bundle":"https://pith.science/pith/EPNFC4FGCOLTVGETDUOHO34H27/bundle.json","state":"https://pith.science/pith/EPNFC4FGCOLTVGETDUOHO34H27/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EPNFC4FGCOLTVGETDUOHO34H27/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:EPNFC4FGCOLTVGETDUOHO34H27","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":"c076738b8171a8f4b7a7de22bd36633080b971d5030ba3a53de63826a66ed035","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-12-18T15:45:00Z","title_canon_sha256":"059e1cf53bc3d5b1f6e9a4086214cf6ccbb2637ee01251f8a0c208c3f6f00908"},"schema_version":"1.0","source":{"id":"1612.05935","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.05935","created_at":"2026-05-18T00:54:46Z"},{"alias_kind":"arxiv_version","alias_value":"1612.05935v1","created_at":"2026-05-18T00:54:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.05935","created_at":"2026-05-18T00:54:46Z"},{"alias_kind":"pith_short_12","alias_value":"EPNFC4FGCOLT","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"EPNFC4FGCOLTVGET","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"EPNFC4FG","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:8113baab41b2f80fe9efb1330e00dd0cce00e72ba30561f77924cc89d0e3cebd","target":"graph","created_at":"2026-05-18T00:54:46Z","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":"We give a reformulation of Salem's conjecture about the absence of Salem numbers near one in terms of a uniform spectral gap for certain arithmetic hyperbolic surfaces.","authors_text":"Bertrand Deroin, Emmanuel Breuillard","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-12-18T15:45:00Z","title":"Salem numbers and the spectrum of hyperbolic surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.05935","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":"sha256:4f391c031d89f67263aa178f7bdb78f9886d25f322ace0ba21fbb76666aacbd2","target":"record","created_at":"2026-05-18T00:54:46Z","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":"c076738b8171a8f4b7a7de22bd36633080b971d5030ba3a53de63826a66ed035","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-12-18T15:45:00Z","title_canon_sha256":"059e1cf53bc3d5b1f6e9a4086214cf6ccbb2637ee01251f8a0c208c3f6f00908"},"schema_version":"1.0","source":{"id":"1612.05935","kind":"arxiv","version":1}},"canonical_sha256":"23da5170a613973a98931d1c776f87d7e9efab85adc08cb6c813879e8acb95bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"23da5170a613973a98931d1c776f87d7e9efab85adc08cb6c813879e8acb95bf","first_computed_at":"2026-05-18T00:54:46.315218Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:46.315218Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8TiPqFOtQyuLjQ6IWB0CCXW72QeuOSbQLDbEBZpGdD9841KTQO3/h96jq/GPmXxbh/F1uUnXY0GRLQVApKqhBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:46.315810Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.05935","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4f391c031d89f67263aa178f7bdb78f9886d25f322ace0ba21fbb76666aacbd2","sha256:8113baab41b2f80fe9efb1330e00dd0cce00e72ba30561f77924cc89d0e3cebd"],"state_sha256":"f91c58a966c41c69b6dfc5e1a39c1af9832f75609c4d7e6658191692831f105d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rl7KE2oesD9HPQ79sLcIxC5rZ+KRobZYaYgB54cALuniNtfg5Fv3DjZHDDBSIIxqAh4XQxGUbf3olTQ0jNqiCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T10:01:57.150478Z","bundle_sha256":"15d5e3b64ae883db4f5edc68d744e88af37d5f1a18116cfee9895dc0c60d8a35"}}