{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:KJFAVBAJADUTRQQSKII5W6C36C","short_pith_number":"pith:KJFAVBAJ","canonical_record":{"source":{"id":"1702.03611","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-02-13T02:44:28Z","cross_cats_sorted":[],"title_canon_sha256":"8b22de1db2659d3c072e32f4f181446004b1dfb93aed60687172a74002695079","abstract_canon_sha256":"dea928b35ed16ed4a8a98d03d5731fb63485745e5b6522726c6391d27d38382a"},"schema_version":"1.0"},"canonical_sha256":"524a0a840900e938c2125211db785bf0bf9cb3baf8947925104d99924ff05f86","source":{"kind":"arxiv","id":"1702.03611","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.03611","created_at":"2026-05-18T00:19:47Z"},{"alias_kind":"arxiv_version","alias_value":"1702.03611v2","created_at":"2026-05-18T00:19:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.03611","created_at":"2026-05-18T00:19:47Z"},{"alias_kind":"pith_short_12","alias_value":"KJFAVBAJADUT","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"KJFAVBAJADUTRQQS","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"KJFAVBAJ","created_at":"2026-05-18T12:31:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:KJFAVBAJADUTRQQSKII5W6C36C","target":"record","payload":{"canonical_record":{"source":{"id":"1702.03611","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-02-13T02:44:28Z","cross_cats_sorted":[],"title_canon_sha256":"8b22de1db2659d3c072e32f4f181446004b1dfb93aed60687172a74002695079","abstract_canon_sha256":"dea928b35ed16ed4a8a98d03d5731fb63485745e5b6522726c6391d27d38382a"},"schema_version":"1.0"},"canonical_sha256":"524a0a840900e938c2125211db785bf0bf9cb3baf8947925104d99924ff05f86","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:19:47.693254Z","signature_b64":"QfejjO4dJObJkl3SRFvv4/OVOle0eAgWmD2mk/FUJ8ETjPzr+bC9LwfhJX9CjsVj3tUKEc66Rftcrg3af+2IDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"524a0a840900e938c2125211db785bf0bf9cb3baf8947925104d99924ff05f86","last_reissued_at":"2026-05-18T00:19:47.692564Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:19:47.692564Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.03611","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":"2026-05-18T00:19:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/GJ4XZABRteScEoKjdllNREvFiXp1QMtkEND9NArUEIJHUHhUwJIql/wwayv2A6eZk6OLyxp/xbkF453HQAICQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T03:01:51.758278Z"},"content_sha256":"82e0d5cf8ce20bf6c5c9c6f5b2d1c0fe7ad1e6a1bcb90f83e1f9f9041b099fdc","schema_version":"1.0","event_id":"sha256:82e0d5cf8ce20bf6c5c9c6f5b2d1c0fe7ad1e6a1bcb90f83e1f9f9041b099fdc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:KJFAVBAJADUTRQQSKII5W6C36C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Partitions and Sylvester waves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Cormac O'Sullivan","submitted_at":"2017-02-13T02:44:28Z","abstract_excerpt":"The restricted partition function $p_N(n)$ counts the partitions of the integer $n$ into at most $N$ parts. In the nineteenth century Sylvester described these partitions as a sum of waves. We give detailed descriptions of these waves and, for the first time, show the asymptotics of the initial waves as $N$ and $n$ both go to infinity at about the same rate. This allows us to see when the initial waves are a good approximation to $p_N(n)$ in this situation. Our proofs employ the saddle-point method of Perron and the dilogarithm."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03611","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":"2026-05-18T00:19:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C5ec/g1GS1hHeCcb+prmtn6a+SHtw5mdzQbhfhMUjBm+R53ajwRBFb3xHeUUZADm9fs6fD5Ijf6MD7J9AyksCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T03:01:51.758636Z"},"content_sha256":"4a2c84861fa34803c5e70b93f3692406a16129cf7e6c6ee8964b5aaeb6ee449d","schema_version":"1.0","event_id":"sha256:4a2c84861fa34803c5e70b93f3692406a16129cf7e6c6ee8964b5aaeb6ee449d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KJFAVBAJADUTRQQSKII5W6C36C/bundle.json","state_url":"https://pith.science/pith/KJFAVBAJADUTRQQSKII5W6C36C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KJFAVBAJADUTRQQSKII5W6C36C/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":"2026-06-23T03:01:51Z","links":{"resolver":"https://pith.science/pith/KJFAVBAJADUTRQQSKII5W6C36C","bundle":"https://pith.science/pith/KJFAVBAJADUTRQQSKII5W6C36C/bundle.json","state":"https://pith.science/pith/KJFAVBAJADUTRQQSKII5W6C36C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KJFAVBAJADUTRQQSKII5W6C36C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:KJFAVBAJADUTRQQSKII5W6C36C","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":"dea928b35ed16ed4a8a98d03d5731fb63485745e5b6522726c6391d27d38382a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-02-13T02:44:28Z","title_canon_sha256":"8b22de1db2659d3c072e32f4f181446004b1dfb93aed60687172a74002695079"},"schema_version":"1.0","source":{"id":"1702.03611","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.03611","created_at":"2026-05-18T00:19:47Z"},{"alias_kind":"arxiv_version","alias_value":"1702.03611v2","created_at":"2026-05-18T00:19:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.03611","created_at":"2026-05-18T00:19:47Z"},{"alias_kind":"pith_short_12","alias_value":"KJFAVBAJADUT","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"KJFAVBAJADUTRQQS","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"KJFAVBAJ","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:4a2c84861fa34803c5e70b93f3692406a16129cf7e6c6ee8964b5aaeb6ee449d","target":"graph","created_at":"2026-05-18T00:19:47Z","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":"The restricted partition function $p_N(n)$ counts the partitions of the integer $n$ into at most $N$ parts. In the nineteenth century Sylvester described these partitions as a sum of waves. We give detailed descriptions of these waves and, for the first time, show the asymptotics of the initial waves as $N$ and $n$ both go to infinity at about the same rate. This allows us to see when the initial waves are a good approximation to $p_N(n)$ in this situation. Our proofs employ the saddle-point method of Perron and the dilogarithm.","authors_text":"Cormac O'Sullivan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-02-13T02:44:28Z","title":"Partitions and Sylvester waves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03611","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":"sha256:82e0d5cf8ce20bf6c5c9c6f5b2d1c0fe7ad1e6a1bcb90f83e1f9f9041b099fdc","target":"record","created_at":"2026-05-18T00:19:47Z","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":"dea928b35ed16ed4a8a98d03d5731fb63485745e5b6522726c6391d27d38382a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-02-13T02:44:28Z","title_canon_sha256":"8b22de1db2659d3c072e32f4f181446004b1dfb93aed60687172a74002695079"},"schema_version":"1.0","source":{"id":"1702.03611","kind":"arxiv","version":2}},"canonical_sha256":"524a0a840900e938c2125211db785bf0bf9cb3baf8947925104d99924ff05f86","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"524a0a840900e938c2125211db785bf0bf9cb3baf8947925104d99924ff05f86","first_computed_at":"2026-05-18T00:19:47.692564Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:47.692564Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QfejjO4dJObJkl3SRFvv4/OVOle0eAgWmD2mk/FUJ8ETjPzr+bC9LwfhJX9CjsVj3tUKEc66Rftcrg3af+2IDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:47.693254Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.03611","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:82e0d5cf8ce20bf6c5c9c6f5b2d1c0fe7ad1e6a1bcb90f83e1f9f9041b099fdc","sha256:4a2c84861fa34803c5e70b93f3692406a16129cf7e6c6ee8964b5aaeb6ee449d"],"state_sha256":"e1f201016869749c9e1655002dfbda68e235c8131e34cb9b7c46c3bf54296249"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0uK3ITsgZvlxlCgzVNW4L8xWRrpiHW7Qe0uu4UrEN8bnJk0ojXGrB7IMsihKYQaIXfLll1YtKyJrau2391XbAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T03:01:51.760503Z","bundle_sha256":"9ed847a121d345a89ba78340018bd1b34988f963b498793d8c632f1c8b445c58"}}