{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1996:IRZV2D5SQYKFT5KV6CKCEUQMDH","short_pith_number":"pith:IRZV2D5S","canonical_record":{"source":{"id":"math/9606224","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"1996-06-03T19:29:36Z","cross_cats_sorted":[],"title_canon_sha256":"0494226c1a335aba374de645dfe2b8aa13c760fb28540494bc6038f26ee8fe79","abstract_canon_sha256":"c387ccab7971df454f8b98b90ab8b11dd4c8c0338b2c189d3b19edd4a98c09dd"},"schema_version":"1.0"},"canonical_sha256":"44735d0fb2861459f555f09422520c19e5cd302d099264091029bdddc8524f76","source":{"kind":"arxiv","id":"math/9606224","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9606224","created_at":"2026-07-04T15:08:59Z"},{"alias_kind":"arxiv_version","alias_value":"math/9606224v1","created_at":"2026-07-04T15:08:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9606224","created_at":"2026-07-04T15:08:59Z"},{"alias_kind":"pith_short_12","alias_value":"IRZV2D5SQYKF","created_at":"2026-07-04T15:08:59Z"},{"alias_kind":"pith_short_16","alias_value":"IRZV2D5SQYKFT5KV","created_at":"2026-07-04T15:08:59Z"},{"alias_kind":"pith_short_8","alias_value":"IRZV2D5S","created_at":"2026-07-04T15:08:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1996:IRZV2D5SQYKFT5KV6CKCEUQMDH","target":"record","payload":{"canonical_record":{"source":{"id":"math/9606224","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"1996-06-03T19:29:36Z","cross_cats_sorted":[],"title_canon_sha256":"0494226c1a335aba374de645dfe2b8aa13c760fb28540494bc6038f26ee8fe79","abstract_canon_sha256":"c387ccab7971df454f8b98b90ab8b11dd4c8c0338b2c189d3b19edd4a98c09dd"},"schema_version":"1.0"},"canonical_sha256":"44735d0fb2861459f555f09422520c19e5cd302d099264091029bdddc8524f76","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:08:59.213935Z","signature_b64":"Wc9nXDUo4+6Luhaxv8eN4G3Jw5r00D0oeDdneeJ9wP97zWc3wv7u6Acr/lLSM7n3eQjkS9TEoV1fpfRFyb5YBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"44735d0fb2861459f555f09422520c19e5cd302d099264091029bdddc8524f76","last_reissued_at":"2026-07-04T15:08:59.213584Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:08:59.213584Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/9606224","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T15:08:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qcGPihR3HhBS0LLa7WdN8laYMFJ9HCmRFie+Y06KKlDB8K8Wn7sAwX5S/13eCQ07HF1WGtiEqUEW1ubWXgYJBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T17:00:49.516643Z"},"content_sha256":"b8133d786ef7fe8cc1ec7114f79afa9fa13c0fff03b1e489fc682d3f4a3e7d09","schema_version":"1.0","event_id":"sha256:b8133d786ef7fe8cc1ec7114f79afa9fa13c0fff03b1e489fc682d3f4a3e7d09"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1996:IRZV2D5SQYKFT5KV6CKCEUQMDH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Proof of the Refined Alternating Sign Matrix Conjecture","license":"","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Doron Zeilberger (Temple University)","submitted_at":"1996-06-03T19:29:36Z","abstract_excerpt":"Mills, Robbins, and Rumsey conjectured, and Zeilberger proved, that the number of alternating sign matrices of order $n$ equals $A(n):={{1!4!7! ... (3n-2)!} \\over {n!(n+1)! ... (2n-1)!}}$. Mills, Robbins, and Rumsey also made the stronger conjecture that the number of such matrices whose (unique) `1' of the first row is at the $r^{th}$ column, equals $A(n) {{n+r-2} \\choose {n-1}}{{2n-1-r} \\choose {n-1}}/ {{3n-2} \\choose {n-1}}$. Standing on the shoulders of A.G. Izergin, V. E. Korepin, and G. Kuperberg, and using in addition orthogonal polynomials and $q$-calculus, this stronger conjecture is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9606224","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/9606224/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T15:08:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z/XnKI+vns5c8JUz2EU+bXezE3GNnht8Hee1fwKa92iwz8g/o06pt0+m1+Zfi10Zi0vclhV+kI+wVUXbrYRnCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T17:00:49.517605Z"},"content_sha256":"faa364f6f9588f094f831800e3800e19b86e63744598c14c3b2e60d96bc2b6fa","schema_version":"1.0","event_id":"sha256:faa364f6f9588f094f831800e3800e19b86e63744598c14c3b2e60d96bc2b6fa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IRZV2D5SQYKFT5KV6CKCEUQMDH/bundle.json","state_url":"https://pith.science/pith/IRZV2D5SQYKFT5KV6CKCEUQMDH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IRZV2D5SQYKFT5KV6CKCEUQMDH/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":"2026-08-09T17:00:49Z","links":{"resolver":"https://pith.science/pith/IRZV2D5SQYKFT5KV6CKCEUQMDH","bundle":"https://pith.science/pith/IRZV2D5SQYKFT5KV6CKCEUQMDH/bundle.json","state":"https://pith.science/pith/IRZV2D5SQYKFT5KV6CKCEUQMDH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IRZV2D5SQYKFT5KV6CKCEUQMDH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1996:IRZV2D5SQYKFT5KV6CKCEUQMDH","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":"c387ccab7971df454f8b98b90ab8b11dd4c8c0338b2c189d3b19edd4a98c09dd","cross_cats_sorted":[],"license":"","primary_cat":"math.CO","submitted_at":"1996-06-03T19:29:36Z","title_canon_sha256":"0494226c1a335aba374de645dfe2b8aa13c760fb28540494bc6038f26ee8fe79"},"schema_version":"1.0","source":{"id":"math/9606224","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9606224","created_at":"2026-07-04T15:08:59Z"},{"alias_kind":"arxiv_version","alias_value":"math/9606224v1","created_at":"2026-07-04T15:08:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9606224","created_at":"2026-07-04T15:08:59Z"},{"alias_kind":"pith_short_12","alias_value":"IRZV2D5SQYKF","created_at":"2026-07-04T15:08:59Z"},{"alias_kind":"pith_short_16","alias_value":"IRZV2D5SQYKFT5KV","created_at":"2026-07-04T15:08:59Z"},{"alias_kind":"pith_short_8","alias_value":"IRZV2D5S","created_at":"2026-07-04T15:08:59Z"}],"graph_snapshots":[{"event_id":"sha256:faa364f6f9588f094f831800e3800e19b86e63744598c14c3b2e60d96bc2b6fa","target":"graph","created_at":"2026-07-04T15:08:59Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/9606224/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Mills, Robbins, and Rumsey conjectured, and Zeilberger proved, that the number of alternating sign matrices of order $n$ equals $A(n):={{1!4!7! ... (3n-2)!} \\over {n!(n+1)! ... (2n-1)!}}$. Mills, Robbins, and Rumsey also made the stronger conjecture that the number of such matrices whose (unique) `1' of the first row is at the $r^{th}$ column, equals $A(n) {{n+r-2} \\choose {n-1}}{{2n-1-r} \\choose {n-1}}/ {{3n-2} \\choose {n-1}}$. Standing on the shoulders of A.G. Izergin, V. E. Korepin, and G. Kuperberg, and using in addition orthogonal polynomials and $q$-calculus, this stronger conjecture is ","authors_text":"Doron Zeilberger (Temple University)","cross_cats":[],"headline":"","license":"","primary_cat":"math.CO","submitted_at":"1996-06-03T19:29:36Z","title":"Proof of the Refined Alternating Sign Matrix Conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9606224","kind":"arxiv","version":1},"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:b8133d786ef7fe8cc1ec7114f79afa9fa13c0fff03b1e489fc682d3f4a3e7d09","target":"record","created_at":"2026-07-04T15:08:59Z","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":"c387ccab7971df454f8b98b90ab8b11dd4c8c0338b2c189d3b19edd4a98c09dd","cross_cats_sorted":[],"license":"","primary_cat":"math.CO","submitted_at":"1996-06-03T19:29:36Z","title_canon_sha256":"0494226c1a335aba374de645dfe2b8aa13c760fb28540494bc6038f26ee8fe79"},"schema_version":"1.0","source":{"id":"math/9606224","kind":"arxiv","version":1}},"canonical_sha256":"44735d0fb2861459f555f09422520c19e5cd302d099264091029bdddc8524f76","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"44735d0fb2861459f555f09422520c19e5cd302d099264091029bdddc8524f76","first_computed_at":"2026-07-04T15:08:59.213584Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:08:59.213584Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Wc9nXDUo4+6Luhaxv8eN4G3Jw5r00D0oeDdneeJ9wP97zWc3wv7u6Acr/lLSM7n3eQjkS9TEoV1fpfRFyb5YBg==","signature_status":"signed_v1","signed_at":"2026-07-04T15:08:59.213935Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9606224","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b8133d786ef7fe8cc1ec7114f79afa9fa13c0fff03b1e489fc682d3f4a3e7d09","sha256:faa364f6f9588f094f831800e3800e19b86e63744598c14c3b2e60d96bc2b6fa"],"state_sha256":"9cbad26904b6ab5223cb9e247603b75e62800029b7dfea1f37ade0a448fb4315"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KwCaz3SqhmbZfjxX0qwUQfwaiFdYfWzBxzBZOrtdVdepGriPg5hfRXppOqmak8/lKdZEx2Q//tViA6O2iKIoDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T17:00:49.525167Z","bundle_sha256":"04ffbb928af87fe56405e18fb8265e99a1c1ed77d1f3e7a046ef9b68ef026c00"}}