{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:RPWT6GBAI7HQLU4AXXYQQAGNWS","short_pith_number":"pith:RPWT6GBA","canonical_record":{"source":{"id":"1207.2274","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-07-10T09:29:16Z","cross_cats_sorted":["math.CO","nlin.SI"],"title_canon_sha256":"19e763aab0ec54056c534093468192bdeba20a7f616ef39643ac2a128ad63301","abstract_canon_sha256":"8536cb0f38d186d5cd9f31ffa1e07b48824acfa5c7c97bca7d6ba1352cc60a88"},"schema_version":"1.0"},"canonical_sha256":"8bed3f182047cf05d380bdf10800cdb49529a22808c740d632df4078faaf714f","source":{"kind":"arxiv","id":"1207.2274","version":7},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.2274","created_at":"2026-05-18T00:09:37Z"},{"alias_kind":"arxiv_version","alias_value":"1207.2274v7","created_at":"2026-05-18T00:09:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.2274","created_at":"2026-05-18T00:09:37Z"},{"alias_kind":"pith_short_12","alias_value":"RPWT6GBAI7HQ","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"RPWT6GBAI7HQLU4A","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"RPWT6GBA","created_at":"2026-05-18T12:27:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:RPWT6GBAI7HQLU4AXXYQQAGNWS","target":"record","payload":{"canonical_record":{"source":{"id":"1207.2274","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-07-10T09:29:16Z","cross_cats_sorted":["math.CO","nlin.SI"],"title_canon_sha256":"19e763aab0ec54056c534093468192bdeba20a7f616ef39643ac2a128ad63301","abstract_canon_sha256":"8536cb0f38d186d5cd9f31ffa1e07b48824acfa5c7c97bca7d6ba1352cc60a88"},"schema_version":"1.0"},"canonical_sha256":"8bed3f182047cf05d380bdf10800cdb49529a22808c740d632df4078faaf714f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:37.091096Z","signature_b64":"XVRP27fDF4lC0zR/3E5HI2LIysONEwspzFLL4+a9dOAIjDxj/JZReSlXrUMHHqcDjUW1PsMrSV1Ai9yee0SFAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8bed3f182047cf05d380bdf10800cdb49529a22808c740d632df4078faaf714f","last_reissued_at":"2026-05-18T00:09:37.090618Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:37.090618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.2274","source_version":7,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:09:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D+5A6ada7s7w5hj0Cl7LJCOWASzZWHhJKuh1oOZrgwg6l/NFMcWTvajcU6aG6OjgCjwzrdARNorwaoOyl0qcDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T02:43:21.307152Z"},"content_sha256":"ab5d2abf58d7da59a1bac238dcf32a020ac0a80648696beb9d69c05e0866a3ed","schema_version":"1.0","event_id":"sha256:ab5d2abf58d7da59a1bac238dcf32a020ac0a80648696beb9d69c05e0866a3ed"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:RPWT6GBAI7HQLU4AXXYQQAGNWS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Critical points of master functions and integrable hierarchies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","nlin.SI"],"primary_cat":"math.AG","authors_text":"Alexander Varchenko, Daniel Wright","submitted_at":"2012-07-10T09:29:16Z","abstract_excerpt":"We consider the population of critical points generated from the trivial critical point of the master function with no variables and associated with the trivial representation of the affine Lie algebra $\\hat{\\frak{sl}}_N$. We show that the critical points of this population define rational solutions of the equations of the mKdV hierarchy associated with $\\hat{\\frak{sl}}_N$.\n  We also construct critical points from suitable $N$-tuples of tau-functions. The construction is based on a Wronskian identity for tau-functions. In particular, we construct critical points from suitable $N$-tuples of Sch"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.2274","kind":"arxiv","version":7},"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":"2026-05-18T00:09:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iUWwRqJrTtQ6qU9gGGF6kVnTEMS9EEF2nIImXwF+89yIam7++/yJGzIvoauFhVep0oGDAG74l31649QsdaeUCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T02:43:21.307510Z"},"content_sha256":"edb60fd17332653b42534c1af81e8cceac03f761d66717722b864a5ca8aab220","schema_version":"1.0","event_id":"sha256:edb60fd17332653b42534c1af81e8cceac03f761d66717722b864a5ca8aab220"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RPWT6GBAI7HQLU4AXXYQQAGNWS/bundle.json","state_url":"https://pith.science/pith/RPWT6GBAI7HQLU4AXXYQQAGNWS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RPWT6GBAI7HQLU4AXXYQQAGNWS/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":"2026-06-20T02:43:21Z","links":{"resolver":"https://pith.science/pith/RPWT6GBAI7HQLU4AXXYQQAGNWS","bundle":"https://pith.science/pith/RPWT6GBAI7HQLU4AXXYQQAGNWS/bundle.json","state":"https://pith.science/pith/RPWT6GBAI7HQLU4AXXYQQAGNWS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RPWT6GBAI7HQLU4AXXYQQAGNWS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:RPWT6GBAI7HQLU4AXXYQQAGNWS","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":"8536cb0f38d186d5cd9f31ffa1e07b48824acfa5c7c97bca7d6ba1352cc60a88","cross_cats_sorted":["math.CO","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-07-10T09:29:16Z","title_canon_sha256":"19e763aab0ec54056c534093468192bdeba20a7f616ef39643ac2a128ad63301"},"schema_version":"1.0","source":{"id":"1207.2274","kind":"arxiv","version":7}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.2274","created_at":"2026-05-18T00:09:37Z"},{"alias_kind":"arxiv_version","alias_value":"1207.2274v7","created_at":"2026-05-18T00:09:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.2274","created_at":"2026-05-18T00:09:37Z"},{"alias_kind":"pith_short_12","alias_value":"RPWT6GBAI7HQ","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"RPWT6GBAI7HQLU4A","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"RPWT6GBA","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:edb60fd17332653b42534c1af81e8cceac03f761d66717722b864a5ca8aab220","target":"graph","created_at":"2026-05-18T00:09:37Z","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 consider the population of critical points generated from the trivial critical point of the master function with no variables and associated with the trivial representation of the affine Lie algebra $\\hat{\\frak{sl}}_N$. We show that the critical points of this population define rational solutions of the equations of the mKdV hierarchy associated with $\\hat{\\frak{sl}}_N$.\n  We also construct critical points from suitable $N$-tuples of tau-functions. The construction is based on a Wronskian identity for tau-functions. In particular, we construct critical points from suitable $N$-tuples of Sch","authors_text":"Alexander Varchenko, Daniel Wright","cross_cats":["math.CO","nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-07-10T09:29:16Z","title":"Critical points of master functions and integrable hierarchies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.2274","kind":"arxiv","version":7},"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:ab5d2abf58d7da59a1bac238dcf32a020ac0a80648696beb9d69c05e0866a3ed","target":"record","created_at":"2026-05-18T00:09:37Z","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":"8536cb0f38d186d5cd9f31ffa1e07b48824acfa5c7c97bca7d6ba1352cc60a88","cross_cats_sorted":["math.CO","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-07-10T09:29:16Z","title_canon_sha256":"19e763aab0ec54056c534093468192bdeba20a7f616ef39643ac2a128ad63301"},"schema_version":"1.0","source":{"id":"1207.2274","kind":"arxiv","version":7}},"canonical_sha256":"8bed3f182047cf05d380bdf10800cdb49529a22808c740d632df4078faaf714f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8bed3f182047cf05d380bdf10800cdb49529a22808c740d632df4078faaf714f","first_computed_at":"2026-05-18T00:09:37.090618Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:37.090618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XVRP27fDF4lC0zR/3E5HI2LIysONEwspzFLL4+a9dOAIjDxj/JZReSlXrUMHHqcDjUW1PsMrSV1Ai9yee0SFAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:37.091096Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.2274","source_kind":"arxiv","source_version":7}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ab5d2abf58d7da59a1bac238dcf32a020ac0a80648696beb9d69c05e0866a3ed","sha256:edb60fd17332653b42534c1af81e8cceac03f761d66717722b864a5ca8aab220"],"state_sha256":"dc96ad4f5ecc664190f840b364ba5b9eab0e96a4dd81465338db29c98a183568"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z9ZoCFxPNx+j9i0hVA/9UM97rHpC252s9RG+dJJfPq5Hhgc4hrx+RvK9B/ULcXiUATA59++vbkWvXury4gwjAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T02:43:21.309389Z","bundle_sha256":"2ad39051cd7d72b687ef24cc9991e495d37cc4845b2ff454a73280324a6eedc3"}}