{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:WSIRPZHIAYVIHAFAXCT5CX67S6","short_pith_number":"pith:WSIRPZHI","canonical_record":{"source":{"id":"1603.07436","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-03-24T04:39:11Z","cross_cats_sorted":[],"title_canon_sha256":"9463781cb0acc03587f5bc9d12ab9bf97beae55e97fd308bcfdd450db3124e11","abstract_canon_sha256":"3b45bfdc51ecc3b96b1d19d791d9bab738f411adacc4ed40f05400ad2d0ef56d"},"schema_version":"1.0"},"canonical_sha256":"b49117e4e8062a8380a0b8a7d15fdf9788e88e797b008627934a39c42094bb87","source":{"kind":"arxiv","id":"1603.07436","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.07436","created_at":"2026-05-18T01:18:20Z"},{"alias_kind":"arxiv_version","alias_value":"1603.07436v1","created_at":"2026-05-18T01:18:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.07436","created_at":"2026-05-18T01:18:20Z"},{"alias_kind":"pith_short_12","alias_value":"WSIRPZHIAYVI","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"WSIRPZHIAYVIHAFA","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"WSIRPZHI","created_at":"2026-05-18T12:30:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:WSIRPZHIAYVIHAFAXCT5CX67S6","target":"record","payload":{"canonical_record":{"source":{"id":"1603.07436","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-03-24T04:39:11Z","cross_cats_sorted":[],"title_canon_sha256":"9463781cb0acc03587f5bc9d12ab9bf97beae55e97fd308bcfdd450db3124e11","abstract_canon_sha256":"3b45bfdc51ecc3b96b1d19d791d9bab738f411adacc4ed40f05400ad2d0ef56d"},"schema_version":"1.0"},"canonical_sha256":"b49117e4e8062a8380a0b8a7d15fdf9788e88e797b008627934a39c42094bb87","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:20.956055Z","signature_b64":"dOaprZZg3R2qP6jeqpJ3sYmoSkDaLhz5pb175G7FVaoOXUxHYDhXOYLPzUTI5s3Pvxvci6kZXk5YVZvU4fQJAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b49117e4e8062a8380a0b8a7d15fdf9788e88e797b008627934a39c42094bb87","last_reissued_at":"2026-05-18T01:18:20.955533Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:20.955533Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.07436","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":"2026-05-18T01:18:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OSyrrgkf7D+cGt4x90kZbtpWRlK2XeQ1WPkZ1oSisQRm5qnKtK6T98yJQORfi8sJZBb3A+rkQPk8aaQXvCKcBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T14:27:23.525521Z"},"content_sha256":"8023da6f590ec2af74b4b04ebb2c04cc762405acb7cef32e3e1c718dd2a1e83d","schema_version":"1.0","event_id":"sha256:8023da6f590ec2af74b4b04ebb2c04cc762405acb7cef32e3e1c718dd2a1e83d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:WSIRPZHIAYVIHAFAXCT5CX67S6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the value-distribution of the difference between logarithms of two symmetric power $L$-functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Kohji Matsumoto, Yumiko Umegaki","submitted_at":"2016-03-24T04:39:11Z","abstract_excerpt":"We consider the value distribution of the difference between logarithms of two symmetric power $L$-functions at $s=\\sigma > 1/2$. We prove that certain averages of those values can be written as integrals involving a density function which is constructed explicitly."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07436","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":"2026-05-18T01:18:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4qbZWNy90nAd3eubHhoC5jtdkKr40sd8X9q0llcfBzTkT9AMEqqYWM6UG3YjjOY+G+hGTmhzQccU0Lo6fnlVBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T14:27:23.525867Z"},"content_sha256":"d27ee15b3b34b2df74860be66039f15195815ec4ced9ec344a6fd79f17248d04","schema_version":"1.0","event_id":"sha256:d27ee15b3b34b2df74860be66039f15195815ec4ced9ec344a6fd79f17248d04"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WSIRPZHIAYVIHAFAXCT5CX67S6/bundle.json","state_url":"https://pith.science/pith/WSIRPZHIAYVIHAFAXCT5CX67S6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WSIRPZHIAYVIHAFAXCT5CX67S6/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":"2026-06-11T14:27:23Z","links":{"resolver":"https://pith.science/pith/WSIRPZHIAYVIHAFAXCT5CX67S6","bundle":"https://pith.science/pith/WSIRPZHIAYVIHAFAXCT5CX67S6/bundle.json","state":"https://pith.science/pith/WSIRPZHIAYVIHAFAXCT5CX67S6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WSIRPZHIAYVIHAFAXCT5CX67S6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:WSIRPZHIAYVIHAFAXCT5CX67S6","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":"3b45bfdc51ecc3b96b1d19d791d9bab738f411adacc4ed40f05400ad2d0ef56d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-03-24T04:39:11Z","title_canon_sha256":"9463781cb0acc03587f5bc9d12ab9bf97beae55e97fd308bcfdd450db3124e11"},"schema_version":"1.0","source":{"id":"1603.07436","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.07436","created_at":"2026-05-18T01:18:20Z"},{"alias_kind":"arxiv_version","alias_value":"1603.07436v1","created_at":"2026-05-18T01:18:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.07436","created_at":"2026-05-18T01:18:20Z"},{"alias_kind":"pith_short_12","alias_value":"WSIRPZHIAYVI","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"WSIRPZHIAYVIHAFA","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"WSIRPZHI","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:d27ee15b3b34b2df74860be66039f15195815ec4ced9ec344a6fd79f17248d04","target":"graph","created_at":"2026-05-18T01:18:20Z","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 consider the value distribution of the difference between logarithms of two symmetric power $L$-functions at $s=\\sigma > 1/2$. We prove that certain averages of those values can be written as integrals involving a density function which is constructed explicitly.","authors_text":"Kohji Matsumoto, Yumiko Umegaki","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-03-24T04:39:11Z","title":"On the value-distribution of the difference between logarithms of two symmetric power $L$-functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07436","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":"sha256:8023da6f590ec2af74b4b04ebb2c04cc762405acb7cef32e3e1c718dd2a1e83d","target":"record","created_at":"2026-05-18T01:18:20Z","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":"3b45bfdc51ecc3b96b1d19d791d9bab738f411adacc4ed40f05400ad2d0ef56d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-03-24T04:39:11Z","title_canon_sha256":"9463781cb0acc03587f5bc9d12ab9bf97beae55e97fd308bcfdd450db3124e11"},"schema_version":"1.0","source":{"id":"1603.07436","kind":"arxiv","version":1}},"canonical_sha256":"b49117e4e8062a8380a0b8a7d15fdf9788e88e797b008627934a39c42094bb87","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b49117e4e8062a8380a0b8a7d15fdf9788e88e797b008627934a39c42094bb87","first_computed_at":"2026-05-18T01:18:20.955533Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:20.955533Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dOaprZZg3R2qP6jeqpJ3sYmoSkDaLhz5pb175G7FVaoOXUxHYDhXOYLPzUTI5s3Pvxvci6kZXk5YVZvU4fQJAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:20.956055Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.07436","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8023da6f590ec2af74b4b04ebb2c04cc762405acb7cef32e3e1c718dd2a1e83d","sha256:d27ee15b3b34b2df74860be66039f15195815ec4ced9ec344a6fd79f17248d04"],"state_sha256":"d009eb5cd7118a0066a0e26f64c08dd453636391f6809b1a4d1f2b017d8773ef"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7n7Ncrv9JdSV7+eX4g3C+DftqJCrHWdxNvyOP36w9z6nIQ4BMJLEI+TubViT9iTQLhzdaaNPbvEw3UzM7TFzDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T14:27:23.527775Z","bundle_sha256":"966ced61ba7f7e95cd984fe3a15f10c69c432480e856f97117884fde2ea6e283"}}