{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:D2U7MQWNNVXLEAFUUVWD5COKLN","short_pith_number":"pith:D2U7MQWN","canonical_record":{"source":{"id":"1408.6506","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-08-27T19:40:49Z","cross_cats_sorted":[],"title_canon_sha256":"b15877adbb5198d98765416ecda94ff42efb5552e7ace3812f8d786a08189358","abstract_canon_sha256":"4955bf972a6e1f41450b924089327e0919a4945f673e6d593106e1fe06b775a7"},"schema_version":"1.0"},"canonical_sha256":"1ea9f642cd6d6eb200b4a56c3e89ca5b6e92fa3620967d41ccc2b1ce24b037ab","source":{"kind":"arxiv","id":"1408.6506","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.6506","created_at":"2026-05-18T01:22:21Z"},{"alias_kind":"arxiv_version","alias_value":"1408.6506v2","created_at":"2026-05-18T01:22:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.6506","created_at":"2026-05-18T01:22:21Z"},{"alias_kind":"pith_short_12","alias_value":"D2U7MQWNNVXL","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"D2U7MQWNNVXLEAFU","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"D2U7MQWN","created_at":"2026-05-18T12:28:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:D2U7MQWNNVXLEAFUUVWD5COKLN","target":"record","payload":{"canonical_record":{"source":{"id":"1408.6506","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-08-27T19:40:49Z","cross_cats_sorted":[],"title_canon_sha256":"b15877adbb5198d98765416ecda94ff42efb5552e7ace3812f8d786a08189358","abstract_canon_sha256":"4955bf972a6e1f41450b924089327e0919a4945f673e6d593106e1fe06b775a7"},"schema_version":"1.0"},"canonical_sha256":"1ea9f642cd6d6eb200b4a56c3e89ca5b6e92fa3620967d41ccc2b1ce24b037ab","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:21.826196Z","signature_b64":"YNCpBwJKpTEiNj3O2r1y4H1w3Qrr29CaPyJV5QpA/5JdagG0S2qHF398c6BWkrmxIwX/tj3Dqnc5KzKrld1ZAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ea9f642cd6d6eb200b4a56c3e89ca5b6e92fa3620967d41ccc2b1ce24b037ab","last_reissued_at":"2026-05-18T01:22:21.825660Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:21.825660Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.6506","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:22:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rltWoqSr4Q9RU1zdWLuR5fUaYLVljDPpuVNAcqPu30F1/rGqqpdWZyyU2r1c6QFR8qFqjBJtX+WCZRYhYGK4DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T17:16:55.922893Z"},"content_sha256":"840edb9b44b3ce15dde5ba2d410045cd47027e3bccc7e8fbb8253991d124d61c","schema_version":"1.0","event_id":"sha256:840edb9b44b3ce15dde5ba2d410045cd47027e3bccc7e8fbb8253991d124d61c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:D2U7MQWNNVXLEAFUUVWD5COKLN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The image of Carmichael's $\\lambda$-function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Carl Pomerance, Florian Luca, Kevin Ford","submitted_at":"2014-08-27T19:40:49Z","abstract_excerpt":"We show that the counting function of the set of values of the Carmichael $\\lambda$-function is $x/(\\log x)^{\\eta+o(1)}$, where $\\eta=1-(1+\\log\\log 2)/(\\log 2)=0.08607...$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.6506","kind":"arxiv","version":2},"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":"2026-05-18T01:22:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4B7np9lUCtE/TB2n3DnIsmwEVV1WZmV/K+7wDtLGCS2r1rF9i0B86Vigq/rViulWy4TZxznP7wIHFQGU7V8FBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T17:16:55.923581Z"},"content_sha256":"bdd0992925b8495eb02ab482f484dc11c2a9173d97e0f32e43cdd2efd3c599ce","schema_version":"1.0","event_id":"sha256:bdd0992925b8495eb02ab482f484dc11c2a9173d97e0f32e43cdd2efd3c599ce"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D2U7MQWNNVXLEAFUUVWD5COKLN/bundle.json","state_url":"https://pith.science/pith/D2U7MQWNNVXLEAFUUVWD5COKLN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D2U7MQWNNVXLEAFUUVWD5COKLN/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":"2026-05-25T17:16:55Z","links":{"resolver":"https://pith.science/pith/D2U7MQWNNVXLEAFUUVWD5COKLN","bundle":"https://pith.science/pith/D2U7MQWNNVXLEAFUUVWD5COKLN/bundle.json","state":"https://pith.science/pith/D2U7MQWNNVXLEAFUUVWD5COKLN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D2U7MQWNNVXLEAFUUVWD5COKLN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:D2U7MQWNNVXLEAFUUVWD5COKLN","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":"4955bf972a6e1f41450b924089327e0919a4945f673e6d593106e1fe06b775a7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-08-27T19:40:49Z","title_canon_sha256":"b15877adbb5198d98765416ecda94ff42efb5552e7ace3812f8d786a08189358"},"schema_version":"1.0","source":{"id":"1408.6506","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.6506","created_at":"2026-05-18T01:22:21Z"},{"alias_kind":"arxiv_version","alias_value":"1408.6506v2","created_at":"2026-05-18T01:22:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.6506","created_at":"2026-05-18T01:22:21Z"},{"alias_kind":"pith_short_12","alias_value":"D2U7MQWNNVXL","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"D2U7MQWNNVXLEAFU","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"D2U7MQWN","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:bdd0992925b8495eb02ab482f484dc11c2a9173d97e0f32e43cdd2efd3c599ce","target":"graph","created_at":"2026-05-18T01:22:21Z","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 show that the counting function of the set of values of the Carmichael $\\lambda$-function is $x/(\\log x)^{\\eta+o(1)}$, where $\\eta=1-(1+\\log\\log 2)/(\\log 2)=0.08607...$.","authors_text":"Carl Pomerance, Florian Luca, Kevin Ford","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-08-27T19:40:49Z","title":"The image of Carmichael's $\\lambda$-function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.6506","kind":"arxiv","version":2},"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":"sha256:840edb9b44b3ce15dde5ba2d410045cd47027e3bccc7e8fbb8253991d124d61c","target":"record","created_at":"2026-05-18T01:22:21Z","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":"4955bf972a6e1f41450b924089327e0919a4945f673e6d593106e1fe06b775a7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-08-27T19:40:49Z","title_canon_sha256":"b15877adbb5198d98765416ecda94ff42efb5552e7ace3812f8d786a08189358"},"schema_version":"1.0","source":{"id":"1408.6506","kind":"arxiv","version":2}},"canonical_sha256":"1ea9f642cd6d6eb200b4a56c3e89ca5b6e92fa3620967d41ccc2b1ce24b037ab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ea9f642cd6d6eb200b4a56c3e89ca5b6e92fa3620967d41ccc2b1ce24b037ab","first_computed_at":"2026-05-18T01:22:21.825660Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:21.825660Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YNCpBwJKpTEiNj3O2r1y4H1w3Qrr29CaPyJV5QpA/5JdagG0S2qHF398c6BWkrmxIwX/tj3Dqnc5KzKrld1ZAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:21.826196Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.6506","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:840edb9b44b3ce15dde5ba2d410045cd47027e3bccc7e8fbb8253991d124d61c","sha256:bdd0992925b8495eb02ab482f484dc11c2a9173d97e0f32e43cdd2efd3c599ce"],"state_sha256":"af10dfb44e5813348de96a5c13663e6af2d4f001656734f6f6283cf094427fbc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JGjmPEwNErFPlfebPrKaARHLAkles400jnw+nAINmC7+eujC+Uc07UmcOF+ochkN7qS52CxpA1nqmTf5MUfzBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T17:16:55.927354Z","bundle_sha256":"48977af165ba3e8b7f6cff60cbe70df4774536eff8d4be0d82148d4208394d5f"}}