{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:YJLBUM7EKQ4I6LWICBYRJA5RSG","short_pith_number":"pith:YJLBUM7E","canonical_record":{"source":{"id":"1307.1521","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-07-05T05:00:39Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"482d41be4aa50b998c8524390b2bf7371e5bcbe8ea3d015f0b9da02a53424ab3","abstract_canon_sha256":"bb19763f3a60634159b87f9db95b37a12d5ad15a214aa7227a24735fdf9ddf7c"},"schema_version":"1.0"},"canonical_sha256":"c2561a33e454388f2ec810711483b191871c2e2aeb238d1613f8c82860f0b4ab","source":{"kind":"arxiv","id":"1307.1521","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.1521","created_at":"2026-05-18T02:49:38Z"},{"alias_kind":"arxiv_version","alias_value":"1307.1521v2","created_at":"2026-05-18T02:49:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.1521","created_at":"2026-05-18T02:49:38Z"},{"alias_kind":"pith_short_12","alias_value":"YJLBUM7EKQ4I","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"YJLBUM7EKQ4I6LWI","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"YJLBUM7E","created_at":"2026-05-18T12:28:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:YJLBUM7EKQ4I6LWICBYRJA5RSG","target":"record","payload":{"canonical_record":{"source":{"id":"1307.1521","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-07-05T05:00:39Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"482d41be4aa50b998c8524390b2bf7371e5bcbe8ea3d015f0b9da02a53424ab3","abstract_canon_sha256":"bb19763f3a60634159b87f9db95b37a12d5ad15a214aa7227a24735fdf9ddf7c"},"schema_version":"1.0"},"canonical_sha256":"c2561a33e454388f2ec810711483b191871c2e2aeb238d1613f8c82860f0b4ab","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:38.997289Z","signature_b64":"1HUL0mTGNWsX+in+908QPjbVIqGaekD29tegAZ7GbxVVFRMVSDBePWTs398SGNawP+ayQKfPMCXj5tQDgzPjBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c2561a33e454388f2ec810711483b191871c2e2aeb238d1613f8c82860f0b4ab","last_reissued_at":"2026-05-18T02:49:38.996940Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:38.996940Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.1521","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":"2026-05-18T02:49:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qu+q7XHqwlzBXi5NHK/wx7/mwVc+KGAZM2YywZGKv+hwpASnYMMI2yiBGSEtt17HwE7ZlPKx2IRSGWJwCJZPAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T22:17:38.713454Z"},"content_sha256":"8e1e45c583d87c63b4ab110d155510e78e640967783f2a1b851e907a7e28b9ad","schema_version":"1.0","event_id":"sha256:8e1e45c583d87c63b4ab110d155510e78e640967783f2a1b851e907a7e28b9ad"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:YJLBUM7EKQ4I6LWICBYRJA5RSG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The maximal order of Stern's diatomic sequence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Jason Tyler, Michael Coons","submitted_at":"2013-07-05T05:00:39Z","abstract_excerpt":"We answer a question of Calkin and Wilf concerning the maximal order of Stern's diatomic sequence. Specifically, we prove that $$\\limsup_{n\\to\\infty}\\frac{a(n)}{\\varphi^{\\log_2 n}}=\\frac{\\varphi^{\\log_2 3}}{\\sqrt{5}},$$ where $\\varphi=(\\sqrt{5}+1)/2$ is the golden ratio. This improves on previous results given by Berlekamp, Conway, and Guy, who showed that the limit value was bounded above by 1.25, and by Calkin and Wilf, who showed that the exact value was in the interval $[({\\varphi}/{\\sqrt{5}})({3}/{2})^{\\log_2\\varphi},(\\varphi+1)/{\\sqrt{5}}].$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.1521","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":"2026-05-18T02:49:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZHJfvFZFtr8kN3pTXvvU47vGP4P9Koo13fqsTACiRa4Xbgs8hu/tlxZvHbpIbHVlHZQv+99C+oD4CwoODTLfAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T22:17:38.714158Z"},"content_sha256":"82dfbaeb385aba56b42fe00974bc43cd0ae99044944168174357504d786c1321","schema_version":"1.0","event_id":"sha256:82dfbaeb385aba56b42fe00974bc43cd0ae99044944168174357504d786c1321"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YJLBUM7EKQ4I6LWICBYRJA5RSG/bundle.json","state_url":"https://pith.science/pith/YJLBUM7EKQ4I6LWICBYRJA5RSG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YJLBUM7EKQ4I6LWICBYRJA5RSG/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":"2026-06-06T22:17:38Z","links":{"resolver":"https://pith.science/pith/YJLBUM7EKQ4I6LWICBYRJA5RSG","bundle":"https://pith.science/pith/YJLBUM7EKQ4I6LWICBYRJA5RSG/bundle.json","state":"https://pith.science/pith/YJLBUM7EKQ4I6LWICBYRJA5RSG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YJLBUM7EKQ4I6LWICBYRJA5RSG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:YJLBUM7EKQ4I6LWICBYRJA5RSG","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":"bb19763f3a60634159b87f9db95b37a12d5ad15a214aa7227a24735fdf9ddf7c","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-07-05T05:00:39Z","title_canon_sha256":"482d41be4aa50b998c8524390b2bf7371e5bcbe8ea3d015f0b9da02a53424ab3"},"schema_version":"1.0","source":{"id":"1307.1521","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.1521","created_at":"2026-05-18T02:49:38Z"},{"alias_kind":"arxiv_version","alias_value":"1307.1521v2","created_at":"2026-05-18T02:49:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.1521","created_at":"2026-05-18T02:49:38Z"},{"alias_kind":"pith_short_12","alias_value":"YJLBUM7EKQ4I","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"YJLBUM7EKQ4I6LWI","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"YJLBUM7E","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:82dfbaeb385aba56b42fe00974bc43cd0ae99044944168174357504d786c1321","target":"graph","created_at":"2026-05-18T02:49:38Z","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 answer a question of Calkin and Wilf concerning the maximal order of Stern's diatomic sequence. Specifically, we prove that $$\\limsup_{n\\to\\infty}\\frac{a(n)}{\\varphi^{\\log_2 n}}=\\frac{\\varphi^{\\log_2 3}}{\\sqrt{5}},$$ where $\\varphi=(\\sqrt{5}+1)/2$ is the golden ratio. This improves on previous results given by Berlekamp, Conway, and Guy, who showed that the limit value was bounded above by 1.25, and by Calkin and Wilf, who showed that the exact value was in the interval $[({\\varphi}/{\\sqrt{5}})({3}/{2})^{\\log_2\\varphi},(\\varphi+1)/{\\sqrt{5}}].$","authors_text":"Jason Tyler, Michael Coons","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-07-05T05:00:39Z","title":"The maximal order of Stern's diatomic sequence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.1521","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":"sha256:8e1e45c583d87c63b4ab110d155510e78e640967783f2a1b851e907a7e28b9ad","target":"record","created_at":"2026-05-18T02:49:38Z","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":"bb19763f3a60634159b87f9db95b37a12d5ad15a214aa7227a24735fdf9ddf7c","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-07-05T05:00:39Z","title_canon_sha256":"482d41be4aa50b998c8524390b2bf7371e5bcbe8ea3d015f0b9da02a53424ab3"},"schema_version":"1.0","source":{"id":"1307.1521","kind":"arxiv","version":2}},"canonical_sha256":"c2561a33e454388f2ec810711483b191871c2e2aeb238d1613f8c82860f0b4ab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c2561a33e454388f2ec810711483b191871c2e2aeb238d1613f8c82860f0b4ab","first_computed_at":"2026-05-18T02:49:38.996940Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:38.996940Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1HUL0mTGNWsX+in+908QPjbVIqGaekD29tegAZ7GbxVVFRMVSDBePWTs398SGNawP+ayQKfPMCXj5tQDgzPjBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:38.997289Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.1521","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8e1e45c583d87c63b4ab110d155510e78e640967783f2a1b851e907a7e28b9ad","sha256:82dfbaeb385aba56b42fe00974bc43cd0ae99044944168174357504d786c1321"],"state_sha256":"8942efe96d7924f54704e242adcc5ba07fa11c734f629c313b4dda5890fbcbf4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ym3WzvHEbhDi7EunwMAciup86vtzFpb9Zy00vAP+19h/dFfgqTqH5ZHcfwkfBh7HfOxTTL2357qWmk40LYXaAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T22:17:38.718371Z","bundle_sha256":"5795aba50867258312cec4824116e53784a15fd61d841061838f61f0b669eaec"}}