{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:K2X5FCATPAQNSQN4RKZ23QGODJ","short_pith_number":"pith:K2X5FCAT","canonical_record":{"source":{"id":"1701.01915","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-01-08T06:03:04Z","cross_cats_sorted":[],"title_canon_sha256":"4645bd49d0134c532fecf68b25894a4ee855a5a1b83907cb235783cfb591ca52","abstract_canon_sha256":"ea083f91b230c18118b72694a9c4363cc583471321de007638bcbd4cb9b0def6"},"schema_version":"1.0"},"canonical_sha256":"56afd288137820d941bc8ab3adc0ce1a7126d563483e1f614470ed00a389d528","source":{"kind":"arxiv","id":"1701.01915","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.01915","created_at":"2026-05-17T23:53:12Z"},{"alias_kind":"arxiv_version","alias_value":"1701.01915v4","created_at":"2026-05-17T23:53:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.01915","created_at":"2026-05-17T23:53:12Z"},{"alias_kind":"pith_short_12","alias_value":"K2X5FCATPAQN","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"K2X5FCATPAQNSQN4","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"K2X5FCAT","created_at":"2026-05-18T12:31:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:K2X5FCATPAQNSQN4RKZ23QGODJ","target":"record","payload":{"canonical_record":{"source":{"id":"1701.01915","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-01-08T06:03:04Z","cross_cats_sorted":[],"title_canon_sha256":"4645bd49d0134c532fecf68b25894a4ee855a5a1b83907cb235783cfb591ca52","abstract_canon_sha256":"ea083f91b230c18118b72694a9c4363cc583471321de007638bcbd4cb9b0def6"},"schema_version":"1.0"},"canonical_sha256":"56afd288137820d941bc8ab3adc0ce1a7126d563483e1f614470ed00a389d528","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:12.893063Z","signature_b64":"vCz1hRrnqlYoG0f9o4exYWbS7ZlVMaF9QNSgfopuhGNwCh7d2oOM8dZN4G2Px2bE1DJkaTEMQtgVsIkN3hsRDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"56afd288137820d941bc8ab3adc0ce1a7126d563483e1f614470ed00a389d528","last_reissued_at":"2026-05-17T23:53:12.891974Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:12.891974Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.01915","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:53:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qzAjqH1LNVmG3Ah1+5d6EEY9syTe6iqLgxHEE62VgqKy5/iZO8/NwH2FUWwtAQiHlERG8poL2f61qxSk0TTtDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:25:39.151521Z"},"content_sha256":"bc3c36a7ce0fcd53fb351e6ab941e46e481758c83f8b2edce788580c02450166","schema_version":"1.0","event_id":"sha256:bc3c36a7ce0fcd53fb351e6ab941e46e481758c83f8b2edce788580c02450166"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:K2X5FCATPAQNSQN4RKZ23QGODJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Random ordering in modulus of consecutive Hecke eigenvalues of primitive forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Florian Luca, Jean-Marc Deshouillers, Sanoli Gun, Yuri Bilu","submitted_at":"2017-01-08T06:03:04Z","abstract_excerpt":"Let \\tau(.) be the Ramanujan \\tau-function, and let k be a positive integer such that \\tau(n) is not 0 for n=1,...,[k/2]. (This is known to be true for k < 10^{23}, and, conjecturally, for all k.) Further, let s be a permutation of the set {1,...,k}. Then there exist infinitely many positive integers m such that |\\tau(m+s(1))|<\\tau(m+s(2))|<...<|\\tau(m+s(k))|. We also obtain a similar result for Fourier-coefficients of general newforms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.01915","kind":"arxiv","version":4},"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":"2026-05-17T23:53:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j/yBZZ3hgxfVTqoQv5W/QPm0JWiE6cXyDK1yEYAACrevr9qk2H98+fQeNbOHcP/x+Zw1gYZ/thKi4+ESwjnuBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:25:39.151903Z"},"content_sha256":"e58424a382b6227439d0521f694a3db2013ec6be0567e94418511f9df19c1760","schema_version":"1.0","event_id":"sha256:e58424a382b6227439d0521f694a3db2013ec6be0567e94418511f9df19c1760"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K2X5FCATPAQNSQN4RKZ23QGODJ/bundle.json","state_url":"https://pith.science/pith/K2X5FCATPAQNSQN4RKZ23QGODJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K2X5FCATPAQNSQN4RKZ23QGODJ/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":"2026-05-27T11:25:39Z","links":{"resolver":"https://pith.science/pith/K2X5FCATPAQNSQN4RKZ23QGODJ","bundle":"https://pith.science/pith/K2X5FCATPAQNSQN4RKZ23QGODJ/bundle.json","state":"https://pith.science/pith/K2X5FCATPAQNSQN4RKZ23QGODJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K2X5FCATPAQNSQN4RKZ23QGODJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:K2X5FCATPAQNSQN4RKZ23QGODJ","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":"ea083f91b230c18118b72694a9c4363cc583471321de007638bcbd4cb9b0def6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-01-08T06:03:04Z","title_canon_sha256":"4645bd49d0134c532fecf68b25894a4ee855a5a1b83907cb235783cfb591ca52"},"schema_version":"1.0","source":{"id":"1701.01915","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.01915","created_at":"2026-05-17T23:53:12Z"},{"alias_kind":"arxiv_version","alias_value":"1701.01915v4","created_at":"2026-05-17T23:53:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.01915","created_at":"2026-05-17T23:53:12Z"},{"alias_kind":"pith_short_12","alias_value":"K2X5FCATPAQN","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"K2X5FCATPAQNSQN4","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"K2X5FCAT","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:e58424a382b6227439d0521f694a3db2013ec6be0567e94418511f9df19c1760","target":"graph","created_at":"2026-05-17T23:53:12Z","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":"Let \\tau(.) be the Ramanujan \\tau-function, and let k be a positive integer such that \\tau(n) is not 0 for n=1,...,[k/2]. (This is known to be true for k < 10^{23}, and, conjecturally, for all k.) Further, let s be a permutation of the set {1,...,k}. Then there exist infinitely many positive integers m such that |\\tau(m+s(1))|<\\tau(m+s(2))|<...<|\\tau(m+s(k))|. We also obtain a similar result for Fourier-coefficients of general newforms.","authors_text":"Florian Luca, Jean-Marc Deshouillers, Sanoli Gun, Yuri Bilu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-01-08T06:03:04Z","title":"Random ordering in modulus of consecutive Hecke eigenvalues of primitive forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.01915","kind":"arxiv","version":4},"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:bc3c36a7ce0fcd53fb351e6ab941e46e481758c83f8b2edce788580c02450166","target":"record","created_at":"2026-05-17T23:53:12Z","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":"ea083f91b230c18118b72694a9c4363cc583471321de007638bcbd4cb9b0def6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-01-08T06:03:04Z","title_canon_sha256":"4645bd49d0134c532fecf68b25894a4ee855a5a1b83907cb235783cfb591ca52"},"schema_version":"1.0","source":{"id":"1701.01915","kind":"arxiv","version":4}},"canonical_sha256":"56afd288137820d941bc8ab3adc0ce1a7126d563483e1f614470ed00a389d528","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"56afd288137820d941bc8ab3adc0ce1a7126d563483e1f614470ed00a389d528","first_computed_at":"2026-05-17T23:53:12.891974Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:12.891974Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vCz1hRrnqlYoG0f9o4exYWbS7ZlVMaF9QNSgfopuhGNwCh7d2oOM8dZN4G2Px2bE1DJkaTEMQtgVsIkN3hsRDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:12.893063Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.01915","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bc3c36a7ce0fcd53fb351e6ab941e46e481758c83f8b2edce788580c02450166","sha256:e58424a382b6227439d0521f694a3db2013ec6be0567e94418511f9df19c1760"],"state_sha256":"fa7dd1c4865333973c1f6352d725d76471eff721bc473d46e2b69afbe239de83"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5C4WIK205tWaJRLRN6ai43IepuXTXWVu+WOsT5vnwjlCpFMoXJptRcW6rDa+uWkYc9nkKCarqo+wtvrk/W3KCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T11:25:39.154191Z","bundle_sha256":"5d642b3bb0757c936c37933dc955c9f5b763940641b8473eb783254ace2b99a1"}}