{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:K63SERUK2BQ3AW6Q2Q5IQKJK5G","short_pith_number":"pith:K63SERUK","canonical_record":{"source":{"id":"1509.07489","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-09-24T19:47:16Z","cross_cats_sorted":["math.RT","math.SP"],"title_canon_sha256":"859e50be561a7e3efad513f367c78d38152979f1ac7abec4866d44e07a6622f1","abstract_canon_sha256":"e47972d68b6c84c6984b28a8975d2ca213800eb625d897f9d57bab63aa059c75"},"schema_version":"1.0"},"canonical_sha256":"57b722468ad061b05bd0d43a88292ae9a68e81448c9b363da7dfb7865741d50f","source":{"kind":"arxiv","id":"1509.07489","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.07489","created_at":"2026-05-18T00:22:30Z"},{"alias_kind":"arxiv_version","alias_value":"1509.07489v4","created_at":"2026-05-18T00:22:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.07489","created_at":"2026-05-18T00:22:30Z"},{"alias_kind":"pith_short_12","alias_value":"K63SERUK2BQ3","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"K63SERUK2BQ3AW6Q","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"K63SERUK","created_at":"2026-05-18T12:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:K63SERUK2BQ3AW6Q2Q5IQKJK5G","target":"record","payload":{"canonical_record":{"source":{"id":"1509.07489","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-09-24T19:47:16Z","cross_cats_sorted":["math.RT","math.SP"],"title_canon_sha256":"859e50be561a7e3efad513f367c78d38152979f1ac7abec4866d44e07a6622f1","abstract_canon_sha256":"e47972d68b6c84c6984b28a8975d2ca213800eb625d897f9d57bab63aa059c75"},"schema_version":"1.0"},"canonical_sha256":"57b722468ad061b05bd0d43a88292ae9a68e81448c9b363da7dfb7865741d50f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:30.004038Z","signature_b64":"AjqwpyVHsf2MLRl9iHW1paZkFI8RRjPlyNIZIUgj38C7X4Gw53iFBHcr2OOMD6RAN5i5g0LpcTvLbonCKk3tBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"57b722468ad061b05bd0d43a88292ae9a68e81448c9b363da7dfb7865741d50f","last_reissued_at":"2026-05-18T00:22:30.003287Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:30.003287Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.07489","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":"2026-05-18T00:22:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ePS1mHqnWOGE4Lu3t6XPKpFruno0zalpOLpUJwpjmOU5/b91EokeuUGPv7Q+7vfbsrWVIsuRxWroY4aT+YmQCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T07:59:08.927274Z"},"content_sha256":"e86593a46652dbdf6be4805b870676b310cd92f25f14dcf356a20ba498edec32","schema_version":"1.0","event_id":"sha256:e86593a46652dbdf6be4805b870676b310cd92f25f14dcf356a20ba498edec32"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:K63SERUK2BQ3AW6Q2Q5IQKJK5G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hybrid sup-norm bounds for Maass newforms of powerful level","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT","math.SP"],"primary_cat":"math.NT","authors_text":"Abhishek Saha","submitted_at":"2015-09-24T19:47:16Z","abstract_excerpt":"Let $f$ be an $L^2$-normalized Hecke--Maass cuspidal newform of level $N$, character $\\chi$ and Laplace eigenvalue $\\lambda$. Let $N_1$ denote the smallest integer such that $N|N_1^2$ and $N_0$ denote the largest integer such that $N_0^2 |N$. Let $M$ denote the conductor of $\\chi$ and define $M_1= M/\\gcd(M,N_1)$. In this paper, we prove the bound $|f|_\\infty$ $\\ll_{\\epsilon}$ $N_0^{1/6 + \\epsilon} N_1^{1/3+\\epsilon} M_1^{1/2} \\lambda^{5/24+\\epsilon}$, which generalizes and strengthens previously known upper bounds for $|f|_\\infty$.\n  This is the first time a hybrid bound (i.e., involving both "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07489","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":"2026-05-18T00:22:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/GZG7/g7qyfMsQa5XnX3f2NhKdSNza/fFKoj+rDpCAPvDqoF4vqtcP4icQBLxOn2eThYLx94yozuj2BgzczsBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T07:59:08.927644Z"},"content_sha256":"bb3a3a328ec7216b062f27ef4435eff35f506b9b4d727d5282c7479d596e6e03","schema_version":"1.0","event_id":"sha256:bb3a3a328ec7216b062f27ef4435eff35f506b9b4d727d5282c7479d596e6e03"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K63SERUK2BQ3AW6Q2Q5IQKJK5G/bundle.json","state_url":"https://pith.science/pith/K63SERUK2BQ3AW6Q2Q5IQKJK5G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K63SERUK2BQ3AW6Q2Q5IQKJK5G/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":"2026-05-28T07:59:08Z","links":{"resolver":"https://pith.science/pith/K63SERUK2BQ3AW6Q2Q5IQKJK5G","bundle":"https://pith.science/pith/K63SERUK2BQ3AW6Q2Q5IQKJK5G/bundle.json","state":"https://pith.science/pith/K63SERUK2BQ3AW6Q2Q5IQKJK5G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K63SERUK2BQ3AW6Q2Q5IQKJK5G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:K63SERUK2BQ3AW6Q2Q5IQKJK5G","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":"e47972d68b6c84c6984b28a8975d2ca213800eb625d897f9d57bab63aa059c75","cross_cats_sorted":["math.RT","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-09-24T19:47:16Z","title_canon_sha256":"859e50be561a7e3efad513f367c78d38152979f1ac7abec4866d44e07a6622f1"},"schema_version":"1.0","source":{"id":"1509.07489","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.07489","created_at":"2026-05-18T00:22:30Z"},{"alias_kind":"arxiv_version","alias_value":"1509.07489v4","created_at":"2026-05-18T00:22:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.07489","created_at":"2026-05-18T00:22:30Z"},{"alias_kind":"pith_short_12","alias_value":"K63SERUK2BQ3","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"K63SERUK2BQ3AW6Q","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"K63SERUK","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:bb3a3a328ec7216b062f27ef4435eff35f506b9b4d727d5282c7479d596e6e03","target":"graph","created_at":"2026-05-18T00:22:30Z","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 $f$ be an $L^2$-normalized Hecke--Maass cuspidal newform of level $N$, character $\\chi$ and Laplace eigenvalue $\\lambda$. Let $N_1$ denote the smallest integer such that $N|N_1^2$ and $N_0$ denote the largest integer such that $N_0^2 |N$. Let $M$ denote the conductor of $\\chi$ and define $M_1= M/\\gcd(M,N_1)$. In this paper, we prove the bound $|f|_\\infty$ $\\ll_{\\epsilon}$ $N_0^{1/6 + \\epsilon} N_1^{1/3+\\epsilon} M_1^{1/2} \\lambda^{5/24+\\epsilon}$, which generalizes and strengthens previously known upper bounds for $|f|_\\infty$.\n  This is the first time a hybrid bound (i.e., involving both ","authors_text":"Abhishek Saha","cross_cats":["math.RT","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-09-24T19:47:16Z","title":"Hybrid sup-norm bounds for Maass newforms of powerful level"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07489","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:e86593a46652dbdf6be4805b870676b310cd92f25f14dcf356a20ba498edec32","target":"record","created_at":"2026-05-18T00:22:30Z","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":"e47972d68b6c84c6984b28a8975d2ca213800eb625d897f9d57bab63aa059c75","cross_cats_sorted":["math.RT","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-09-24T19:47:16Z","title_canon_sha256":"859e50be561a7e3efad513f367c78d38152979f1ac7abec4866d44e07a6622f1"},"schema_version":"1.0","source":{"id":"1509.07489","kind":"arxiv","version":4}},"canonical_sha256":"57b722468ad061b05bd0d43a88292ae9a68e81448c9b363da7dfb7865741d50f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"57b722468ad061b05bd0d43a88292ae9a68e81448c9b363da7dfb7865741d50f","first_computed_at":"2026-05-18T00:22:30.003287Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:30.003287Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AjqwpyVHsf2MLRl9iHW1paZkFI8RRjPlyNIZIUgj38C7X4Gw53iFBHcr2OOMD6RAN5i5g0LpcTvLbonCKk3tBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:30.004038Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.07489","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e86593a46652dbdf6be4805b870676b310cd92f25f14dcf356a20ba498edec32","sha256:bb3a3a328ec7216b062f27ef4435eff35f506b9b4d727d5282c7479d596e6e03"],"state_sha256":"24befc0e21fac6d1ba3af22f0b9d391f1077a70b556c7b3eff99a05f457c27e5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZGBojeSI1MzVdU314Rs1z0IKvhLRfzQySy/NtjfMtOw3QrsvIp9AaA5+F5+XByyt5PoN3eEOJCsTr5LZwg+oBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T07:59:08.929822Z","bundle_sha256":"6e60921b5b8c5a47507cfcc70b3fc93bebc416d9269850dd9b627fcc7bfc3467"}}