{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:7FKUEJ5ZQ4G47FRDPP4A3X3ZZG","short_pith_number":"pith:7FKUEJ5Z","canonical_record":{"source":{"id":"1702.04631","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-02-15T14:45:22Z","cross_cats_sorted":["hep-th","math-ph","math.MP"],"title_canon_sha256":"241b9634ce89a437f73c4751dbef94c261bf86c1f8700cc767393113cc43da6d","abstract_canon_sha256":"6fd3405893fe70f2272d862a5f3a7e75568062d1990498affcc585240e78cbde"},"schema_version":"1.0"},"canonical_sha256":"f9554227b9870dcf96237bf80ddf79c99ee41c54e28301e41395891a9e807eb5","source":{"kind":"arxiv","id":"1702.04631","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.04631","created_at":"2026-05-18T00:49:41Z"},{"alias_kind":"arxiv_version","alias_value":"1702.04631v3","created_at":"2026-05-18T00:49:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.04631","created_at":"2026-05-18T00:49:41Z"},{"alias_kind":"pith_short_12","alias_value":"7FKUEJ5ZQ4G4","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7FKUEJ5ZQ4G47FRD","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7FKUEJ5Z","created_at":"2026-05-18T12:31:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:7FKUEJ5ZQ4G47FRDPP4A3X3ZZG","target":"record","payload":{"canonical_record":{"source":{"id":"1702.04631","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-02-15T14:45:22Z","cross_cats_sorted":["hep-th","math-ph","math.MP"],"title_canon_sha256":"241b9634ce89a437f73c4751dbef94c261bf86c1f8700cc767393113cc43da6d","abstract_canon_sha256":"6fd3405893fe70f2272d862a5f3a7e75568062d1990498affcc585240e78cbde"},"schema_version":"1.0"},"canonical_sha256":"f9554227b9870dcf96237bf80ddf79c99ee41c54e28301e41395891a9e807eb5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:41.699531Z","signature_b64":"Wri4fTsWpTI60EXsXadIMznG5kGVO1lCqCzHZ+HFexwnofuOwgWVMknCq3QAeNwh+StJvteovQoSR7EVkSiOBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f9554227b9870dcf96237bf80ddf79c99ee41c54e28301e41395891a9e807eb5","last_reissued_at":"2026-05-18T00:49:41.698991Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:41.698991Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.04631","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:49:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XUkO7nfPfBJmrRqVXsrveUPYdywGvHr1ChLufGt34eoPY35mY2hfEkpU2zQXH7vpn3VPH+729UR+1E/eu4AMAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T04:11:04.087980Z"},"content_sha256":"91244315aee965bede85954f9b6b54fdb84b2653b4408c04b1881e6ee0957bfc","schema_version":"1.0","event_id":"sha256:91244315aee965bede85954f9b6b54fdb84b2653b4408c04b1881e6ee0957bfc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:7FKUEJ5ZQ4G47FRDPP4A3X3ZZG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Analytic Formula for Numbers of Restricted Partitions from Conformal Field Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"math.NT","authors_text":"Dimitri Polyakov","submitted_at":"2017-02-15T14:45:22Z","abstract_excerpt":"We study the correlators of irregular vertex operators in two-dimensional conformal field theory (CFT) in order to propose an exact analytic formula for calculating numbers of partitions, that is:\n  1) for given $N,k$, finding the total number $\\lambda(N|k)$ of length $k$ partitions of $N$: $N=n_1+...+n_k;0<n_1\\leq{n_2}...\\leq{n_k}$.\n  2) finding the total number $\\lambda(N)=\\sum_{k=1}^N\\lambda(N|k)$ of partitions of a natural number $N$\n  We propose an exact analytic expression for $\\lambda(N|k)$ by relating two-point short-distance correlation functions of irregular vertex operators in $c=1$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.04631","kind":"arxiv","version":3},"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":"2026-05-18T00:49:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Cf7g+sZiLibS+8kTYTd4NVQ0qGS+l/v98tk6xGJiky35h6WotyswZ5G5sIeV8EdjTHcOndT2ND4rzvTp3sNJDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T04:11:04.088688Z"},"content_sha256":"861afd9f30bfa27c4a7cd5e949b66a71291f0c0b3d1b820bbe5232133aae9605","schema_version":"1.0","event_id":"sha256:861afd9f30bfa27c4a7cd5e949b66a71291f0c0b3d1b820bbe5232133aae9605"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7FKUEJ5ZQ4G47FRDPP4A3X3ZZG/bundle.json","state_url":"https://pith.science/pith/7FKUEJ5ZQ4G47FRDPP4A3X3ZZG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7FKUEJ5ZQ4G47FRDPP4A3X3ZZG/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":"2026-05-27T04:11:04Z","links":{"resolver":"https://pith.science/pith/7FKUEJ5ZQ4G47FRDPP4A3X3ZZG","bundle":"https://pith.science/pith/7FKUEJ5ZQ4G47FRDPP4A3X3ZZG/bundle.json","state":"https://pith.science/pith/7FKUEJ5ZQ4G47FRDPP4A3X3ZZG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7FKUEJ5ZQ4G47FRDPP4A3X3ZZG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:7FKUEJ5ZQ4G47FRDPP4A3X3ZZG","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":"6fd3405893fe70f2272d862a5f3a7e75568062d1990498affcc585240e78cbde","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-02-15T14:45:22Z","title_canon_sha256":"241b9634ce89a437f73c4751dbef94c261bf86c1f8700cc767393113cc43da6d"},"schema_version":"1.0","source":{"id":"1702.04631","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.04631","created_at":"2026-05-18T00:49:41Z"},{"alias_kind":"arxiv_version","alias_value":"1702.04631v3","created_at":"2026-05-18T00:49:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.04631","created_at":"2026-05-18T00:49:41Z"},{"alias_kind":"pith_short_12","alias_value":"7FKUEJ5ZQ4G4","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7FKUEJ5ZQ4G47FRD","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7FKUEJ5Z","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:861afd9f30bfa27c4a7cd5e949b66a71291f0c0b3d1b820bbe5232133aae9605","target":"graph","created_at":"2026-05-18T00:49:41Z","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 study the correlators of irregular vertex operators in two-dimensional conformal field theory (CFT) in order to propose an exact analytic formula for calculating numbers of partitions, that is:\n  1) for given $N,k$, finding the total number $\\lambda(N|k)$ of length $k$ partitions of $N$: $N=n_1+...+n_k;0<n_1\\leq{n_2}...\\leq{n_k}$.\n  2) finding the total number $\\lambda(N)=\\sum_{k=1}^N\\lambda(N|k)$ of partitions of a natural number $N$\n  We propose an exact analytic expression for $\\lambda(N|k)$ by relating two-point short-distance correlation functions of irregular vertex operators in $c=1$","authors_text":"Dimitri Polyakov","cross_cats":["hep-th","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-02-15T14:45:22Z","title":"An Analytic Formula for Numbers of Restricted Partitions from Conformal Field Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.04631","kind":"arxiv","version":3},"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":"sha256:91244315aee965bede85954f9b6b54fdb84b2653b4408c04b1881e6ee0957bfc","target":"record","created_at":"2026-05-18T00:49:41Z","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":"6fd3405893fe70f2272d862a5f3a7e75568062d1990498affcc585240e78cbde","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-02-15T14:45:22Z","title_canon_sha256":"241b9634ce89a437f73c4751dbef94c261bf86c1f8700cc767393113cc43da6d"},"schema_version":"1.0","source":{"id":"1702.04631","kind":"arxiv","version":3}},"canonical_sha256":"f9554227b9870dcf96237bf80ddf79c99ee41c54e28301e41395891a9e807eb5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f9554227b9870dcf96237bf80ddf79c99ee41c54e28301e41395891a9e807eb5","first_computed_at":"2026-05-18T00:49:41.698991Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:41.698991Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Wri4fTsWpTI60EXsXadIMznG5kGVO1lCqCzHZ+HFexwnofuOwgWVMknCq3QAeNwh+StJvteovQoSR7EVkSiOBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:41.699531Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.04631","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:91244315aee965bede85954f9b6b54fdb84b2653b4408c04b1881e6ee0957bfc","sha256:861afd9f30bfa27c4a7cd5e949b66a71291f0c0b3d1b820bbe5232133aae9605"],"state_sha256":"37345ef3e851f2c37747066630a2eb1c139463a0b49c559ef9c85ac4156e57d9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wa9xP01MVjGhQhLAFlRW7ugjgXuWaz+n+iISiGicY5UEMQWsBrW3PrIYa4t5oebewSETkxQ8PvDY03w1aoYzCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T04:11:04.092368Z","bundle_sha256":"733f2ca6ef8be9d18ded6c5d28647b02e758145f006544be5ad147ba7249a6f1"}}