{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:FV2WFS5OUOOT7QE2VTPYQ7FJV4","short_pith_number":"pith:FV2WFS5O","canonical_record":{"source":{"id":"1703.04953","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-03-15T06:21:18Z","cross_cats_sorted":[],"title_canon_sha256":"f41f21114a8cda0deb138a8711ed46ce810291f100f81b765e0dbb52f9654cae","abstract_canon_sha256":"63bb0a9c859f94f781d31f9e42084f174bdaf8aa5839bf881f41360161bbeeea"},"schema_version":"1.0"},"canonical_sha256":"2d7562cbaea39d3fc09aacdf887ca9af272ba2f067a42d271f93c6f70a8488c0","source":{"kind":"arxiv","id":"1703.04953","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.04953","created_at":"2026-05-18T00:48:38Z"},{"alias_kind":"arxiv_version","alias_value":"1703.04953v1","created_at":"2026-05-18T00:48:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.04953","created_at":"2026-05-18T00:48:38Z"},{"alias_kind":"pith_short_12","alias_value":"FV2WFS5OUOOT","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FV2WFS5OUOOT7QE2","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FV2WFS5O","created_at":"2026-05-18T12:31:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:FV2WFS5OUOOT7QE2VTPYQ7FJV4","target":"record","payload":{"canonical_record":{"source":{"id":"1703.04953","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-03-15T06:21:18Z","cross_cats_sorted":[],"title_canon_sha256":"f41f21114a8cda0deb138a8711ed46ce810291f100f81b765e0dbb52f9654cae","abstract_canon_sha256":"63bb0a9c859f94f781d31f9e42084f174bdaf8aa5839bf881f41360161bbeeea"},"schema_version":"1.0"},"canonical_sha256":"2d7562cbaea39d3fc09aacdf887ca9af272ba2f067a42d271f93c6f70a8488c0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:38.755570Z","signature_b64":"UgQvM5Uy9bPl3Kpd0tCXe+m+Km+uKHW600pCYzTUFQUTn4pOd8HpjTm6Wd/xuT3jzKXhHIdiU6dbh4lUmkpZDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2d7562cbaea39d3fc09aacdf887ca9af272ba2f067a42d271f93c6f70a8488c0","last_reissued_at":"2026-05-18T00:48:38.754831Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:38.754831Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.04953","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":"2026-05-18T00:48:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"upnPCXx3CCl57GmEKWSQa1AZV3UExkSDuReo//Q3eDBzysdsTOlYtRqVzy/F4OP4aqORCM2F3LX94L0d0+mNAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T01:26:53.336297Z"},"content_sha256":"d4d820ad5cc5d20f53d20319a20aaf7bf1e446d12b124c838f5fd9d028861b03","schema_version":"1.0","event_id":"sha256:d4d820ad5cc5d20f53d20319a20aaf7bf1e446d12b124c838f5fd9d028861b03"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:FV2WFS5OUOOT7QE2VTPYQ7FJV4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Square-full primitive roots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Marc Munsch, Tim Trudgian","submitted_at":"2017-03-15T06:21:18Z","abstract_excerpt":"We use character sum estimates to give a bound on the least square-full primitive root modulo a prime. Specifically, we show that there is a square-full primitive root mod $p$ less than $p^{2/3 + 3/(4 \\sqrt{e})+ \\epsilon}$, and we give some conditional bounds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.04953","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":"2026-05-18T00:48:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GbrZDTg9SOiyC1tdHCPLR7izNQYqdt1a4nL3dNM93bX7yX5fJNC2jRaFfQ8+fU8Hv68yNFS4Qlud5RgI7IdLDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T01:26:53.336656Z"},"content_sha256":"ee75cf198f1e1148ac687274cff567d7e6f83fb1e0b58d624ae4f83973731348","schema_version":"1.0","event_id":"sha256:ee75cf198f1e1148ac687274cff567d7e6f83fb1e0b58d624ae4f83973731348"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FV2WFS5OUOOT7QE2VTPYQ7FJV4/bundle.json","state_url":"https://pith.science/pith/FV2WFS5OUOOT7QE2VTPYQ7FJV4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FV2WFS5OUOOT7QE2VTPYQ7FJV4/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":"2026-06-01T01:26:53Z","links":{"resolver":"https://pith.science/pith/FV2WFS5OUOOT7QE2VTPYQ7FJV4","bundle":"https://pith.science/pith/FV2WFS5OUOOT7QE2VTPYQ7FJV4/bundle.json","state":"https://pith.science/pith/FV2WFS5OUOOT7QE2VTPYQ7FJV4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FV2WFS5OUOOT7QE2VTPYQ7FJV4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:FV2WFS5OUOOT7QE2VTPYQ7FJV4","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":"63bb0a9c859f94f781d31f9e42084f174bdaf8aa5839bf881f41360161bbeeea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-03-15T06:21:18Z","title_canon_sha256":"f41f21114a8cda0deb138a8711ed46ce810291f100f81b765e0dbb52f9654cae"},"schema_version":"1.0","source":{"id":"1703.04953","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.04953","created_at":"2026-05-18T00:48:38Z"},{"alias_kind":"arxiv_version","alias_value":"1703.04953v1","created_at":"2026-05-18T00:48:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.04953","created_at":"2026-05-18T00:48:38Z"},{"alias_kind":"pith_short_12","alias_value":"FV2WFS5OUOOT","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FV2WFS5OUOOT7QE2","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FV2WFS5O","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:ee75cf198f1e1148ac687274cff567d7e6f83fb1e0b58d624ae4f83973731348","target":"graph","created_at":"2026-05-18T00:48:38Z","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 use character sum estimates to give a bound on the least square-full primitive root modulo a prime. Specifically, we show that there is a square-full primitive root mod $p$ less than $p^{2/3 + 3/(4 \\sqrt{e})+ \\epsilon}$, and we give some conditional bounds.","authors_text":"Marc Munsch, Tim Trudgian","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-03-15T06:21:18Z","title":"Square-full primitive roots"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.04953","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:d4d820ad5cc5d20f53d20319a20aaf7bf1e446d12b124c838f5fd9d028861b03","target":"record","created_at":"2026-05-18T00:48:38Z","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":"63bb0a9c859f94f781d31f9e42084f174bdaf8aa5839bf881f41360161bbeeea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-03-15T06:21:18Z","title_canon_sha256":"f41f21114a8cda0deb138a8711ed46ce810291f100f81b765e0dbb52f9654cae"},"schema_version":"1.0","source":{"id":"1703.04953","kind":"arxiv","version":1}},"canonical_sha256":"2d7562cbaea39d3fc09aacdf887ca9af272ba2f067a42d271f93c6f70a8488c0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2d7562cbaea39d3fc09aacdf887ca9af272ba2f067a42d271f93c6f70a8488c0","first_computed_at":"2026-05-18T00:48:38.754831Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:38.754831Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UgQvM5Uy9bPl3Kpd0tCXe+m+Km+uKHW600pCYzTUFQUTn4pOd8HpjTm6Wd/xuT3jzKXhHIdiU6dbh4lUmkpZDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:38.755570Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.04953","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d4d820ad5cc5d20f53d20319a20aaf7bf1e446d12b124c838f5fd9d028861b03","sha256:ee75cf198f1e1148ac687274cff567d7e6f83fb1e0b58d624ae4f83973731348"],"state_sha256":"4eafdedf63ba2e7611ea429e342add94f8cc6cb92d1a838d2872585a7b648655"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HP7dav8gThKwc0LLchNOu7uTAqy8WKeJKbwHAZzrsfuFA8o6ybpxW6iaNNvYW125esOznfhJXah3a0SEtxuTDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T01:26:53.338951Z","bundle_sha256":"59e9e6e239cf789511559d3d1f48c91ee511cfdf9fd3ec8c1839ad5c4be2edfc"}}