{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:KG5DRQSX7RN45Y4JGUYJMCS3S5","short_pith_number":"pith:KG5DRQSX","canonical_record":{"source":{"id":"1411.2044","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-11-07T21:56:25Z","cross_cats_sorted":["math.NT","math.QA"],"title_canon_sha256":"d7c18427f203c5005a799f3d56feb3164d83198c019a66a255bdb38b5258d00c","abstract_canon_sha256":"f1ee056e07170ac08fe6cdb61c5039f65121a4855d9a4495610e8645f3a6ff3c"},"schema_version":"1.0"},"canonical_sha256":"51ba38c257fc5bcee3893530960a5b9756b97f99cf3408a302868a5c74d248d8","source":{"kind":"arxiv","id":"1411.2044","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.2044","created_at":"2026-05-18T02:34:44Z"},{"alias_kind":"arxiv_version","alias_value":"1411.2044v2","created_at":"2026-05-18T02:34:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.2044","created_at":"2026-05-18T02:34:44Z"},{"alias_kind":"pith_short_12","alias_value":"KG5DRQSX7RN4","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KG5DRQSX7RN45Y4J","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KG5DRQSX","created_at":"2026-05-18T12:28:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:KG5DRQSX7RN45Y4JGUYJMCS3S5","target":"record","payload":{"canonical_record":{"source":{"id":"1411.2044","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-11-07T21:56:25Z","cross_cats_sorted":["math.NT","math.QA"],"title_canon_sha256":"d7c18427f203c5005a799f3d56feb3164d83198c019a66a255bdb38b5258d00c","abstract_canon_sha256":"f1ee056e07170ac08fe6cdb61c5039f65121a4855d9a4495610e8645f3a6ff3c"},"schema_version":"1.0"},"canonical_sha256":"51ba38c257fc5bcee3893530960a5b9756b97f99cf3408a302868a5c74d248d8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:34:44.611337Z","signature_b64":"dga2/bu1UY36FGtQU5tXPOIIRhwe+Xvk0VH84tABVEj2S9RPBRRtkVd77wdtC/mKw1K73OIDgkHgC2l3TRZUAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"51ba38c257fc5bcee3893530960a5b9756b97f99cf3408a302868a5c74d248d8","last_reissued_at":"2026-05-18T02:34:44.610947Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:34:44.610947Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.2044","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":"2026-05-18T02:34:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"04pmu0Vh8QG3ycBEOZVK3bftIl7JoIlSXXIbi9OkVhb4IKo6tiNdIiR9sS9dUzi0T4rHFfNWj7t4aF2xiqDbCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T06:54:15.795569Z"},"content_sha256":"f8f61a93ae02a73ec9234fdfc91f19c11dfb9e05458f2f732a228ef10dbdea99","schema_version":"1.0","event_id":"sha256:f8f61a93ae02a73ec9234fdfc91f19c11dfb9e05458f2f732a228ef10dbdea99"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:KG5DRQSX7RN45Y4JGUYJMCS3S5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A motivated proof of the G\\\"ollnitz-Gordon-Andrews identities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT","math.QA"],"primary_cat":"math.CO","authors_text":"Bud Coulson, Christopher Sadowski, Fei Qi, James Lepowsky, Matthew C. Russell, Robert McRae, Shashank Kanade","submitted_at":"2014-11-07T21:56:25Z","abstract_excerpt":"We present what we call a \"motivated proof\" of the G\\\"{o}llnitz-Gordon-Andrews identities. A similar motivated proof of the Rogers-Ramanujan identities was previously given by G. E. Andrews and R. J. Baxter, and was subsequently generalized to Gordon's identities by J. Lepowsky and M. Zhu. We anticipate that the present proof of the G\\\"{o}llnitz-Gordon-Andrews identities will illuminate certain twisted vertex-algebraic constructions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2044","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":"2026-05-18T02:34:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ntAsqLK0TeAMNHFui8BdoVxCrtURgqfPcyybgVV3VumytOBY1urU1k8veWfge0Lw5i9DG1lWb1IiDwC+UvmPAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T06:54:15.795919Z"},"content_sha256":"868332ae3e78df4e03b80aca94085552d65dfd838f087be5d2e3f31ef2d14df7","schema_version":"1.0","event_id":"sha256:868332ae3e78df4e03b80aca94085552d65dfd838f087be5d2e3f31ef2d14df7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KG5DRQSX7RN45Y4JGUYJMCS3S5/bundle.json","state_url":"https://pith.science/pith/KG5DRQSX7RN45Y4JGUYJMCS3S5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KG5DRQSX7RN45Y4JGUYJMCS3S5/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":"2026-06-02T06:54:15Z","links":{"resolver":"https://pith.science/pith/KG5DRQSX7RN45Y4JGUYJMCS3S5","bundle":"https://pith.science/pith/KG5DRQSX7RN45Y4JGUYJMCS3S5/bundle.json","state":"https://pith.science/pith/KG5DRQSX7RN45Y4JGUYJMCS3S5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KG5DRQSX7RN45Y4JGUYJMCS3S5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:KG5DRQSX7RN45Y4JGUYJMCS3S5","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":"f1ee056e07170ac08fe6cdb61c5039f65121a4855d9a4495610e8645f3a6ff3c","cross_cats_sorted":["math.NT","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-11-07T21:56:25Z","title_canon_sha256":"d7c18427f203c5005a799f3d56feb3164d83198c019a66a255bdb38b5258d00c"},"schema_version":"1.0","source":{"id":"1411.2044","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.2044","created_at":"2026-05-18T02:34:44Z"},{"alias_kind":"arxiv_version","alias_value":"1411.2044v2","created_at":"2026-05-18T02:34:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.2044","created_at":"2026-05-18T02:34:44Z"},{"alias_kind":"pith_short_12","alias_value":"KG5DRQSX7RN4","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KG5DRQSX7RN45Y4J","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KG5DRQSX","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:868332ae3e78df4e03b80aca94085552d65dfd838f087be5d2e3f31ef2d14df7","target":"graph","created_at":"2026-05-18T02:34:44Z","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 present what we call a \"motivated proof\" of the G\\\"{o}llnitz-Gordon-Andrews identities. A similar motivated proof of the Rogers-Ramanujan identities was previously given by G. E. Andrews and R. J. Baxter, and was subsequently generalized to Gordon's identities by J. Lepowsky and M. Zhu. We anticipate that the present proof of the G\\\"{o}llnitz-Gordon-Andrews identities will illuminate certain twisted vertex-algebraic constructions.","authors_text":"Bud Coulson, Christopher Sadowski, Fei Qi, James Lepowsky, Matthew C. Russell, Robert McRae, Shashank Kanade","cross_cats":["math.NT","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-11-07T21:56:25Z","title":"A motivated proof of the G\\\"ollnitz-Gordon-Andrews identities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2044","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:f8f61a93ae02a73ec9234fdfc91f19c11dfb9e05458f2f732a228ef10dbdea99","target":"record","created_at":"2026-05-18T02:34:44Z","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":"f1ee056e07170ac08fe6cdb61c5039f65121a4855d9a4495610e8645f3a6ff3c","cross_cats_sorted":["math.NT","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-11-07T21:56:25Z","title_canon_sha256":"d7c18427f203c5005a799f3d56feb3164d83198c019a66a255bdb38b5258d00c"},"schema_version":"1.0","source":{"id":"1411.2044","kind":"arxiv","version":2}},"canonical_sha256":"51ba38c257fc5bcee3893530960a5b9756b97f99cf3408a302868a5c74d248d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"51ba38c257fc5bcee3893530960a5b9756b97f99cf3408a302868a5c74d248d8","first_computed_at":"2026-05-18T02:34:44.610947Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:34:44.610947Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dga2/bu1UY36FGtQU5tXPOIIRhwe+Xvk0VH84tABVEj2S9RPBRRtkVd77wdtC/mKw1K73OIDgkHgC2l3TRZUAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:34:44.611337Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.2044","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f8f61a93ae02a73ec9234fdfc91f19c11dfb9e05458f2f732a228ef10dbdea99","sha256:868332ae3e78df4e03b80aca94085552d65dfd838f087be5d2e3f31ef2d14df7"],"state_sha256":"efcd12b94612c41ae8c823da09a53acb4ec3408e996e1cf570db07c9d30965e9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vKmhHboclIQNYQvJ3Jz4z64Pw770R626rDaH0j7dGaN+bsDNGmqpRa7xU7OgRhKhxzymhw5WkM8mcMqnAOslCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T06:54:15.797853Z","bundle_sha256":"8ee0d6534da09b14f52aa936fbce863730d5906a990f9ab3e40dd1a908865b92"}}