{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:ELP7SSG3WOTM6Z6DV6EDZCNLRZ","short_pith_number":"pith:ELP7SSG3","canonical_record":{"source":{"id":"1804.07054","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-04-19T09:33:17Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"7961224c210428302f5fa38daa80f028a02e83692b2af47ba5b5b0f64af694d2","abstract_canon_sha256":"a8fe0787faae463f2a11e9a5b33a4a22fa0e5411960be9436558258ceb76209c"},"schema_version":"1.0"},"canonical_sha256":"22dff948dbb3a6cf67c3af883c89ab8e4e511e6d67e9e196d1f0239c3c659ba3","source":{"kind":"arxiv","id":"1804.07054","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.07054","created_at":"2026-05-18T00:18:03Z"},{"alias_kind":"arxiv_version","alias_value":"1804.07054v1","created_at":"2026-05-18T00:18:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.07054","created_at":"2026-05-18T00:18:03Z"},{"alias_kind":"pith_short_12","alias_value":"ELP7SSG3WOTM","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"ELP7SSG3WOTM6Z6D","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"ELP7SSG3","created_at":"2026-05-18T12:32:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:ELP7SSG3WOTM6Z6DV6EDZCNLRZ","target":"record","payload":{"canonical_record":{"source":{"id":"1804.07054","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-04-19T09:33:17Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"7961224c210428302f5fa38daa80f028a02e83692b2af47ba5b5b0f64af694d2","abstract_canon_sha256":"a8fe0787faae463f2a11e9a5b33a4a22fa0e5411960be9436558258ceb76209c"},"schema_version":"1.0"},"canonical_sha256":"22dff948dbb3a6cf67c3af883c89ab8e4e511e6d67e9e196d1f0239c3c659ba3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:03.558126Z","signature_b64":"j5O0GySE0Nq3aWYtGFU8qJVvFPFC0IdrYbbje4gCw94hkGb9VkkH47oUPSQsO9K0BLQYY4MnVLKY6D8AdCOTCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"22dff948dbb3a6cf67c3af883c89ab8e4e511e6d67e9e196d1f0239c3c659ba3","last_reissued_at":"2026-05-18T00:18:03.557612Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:03.557612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.07054","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":"2026-05-18T00:18:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KZvRL/xhn+Tp9N5o0/jDGIZEurtnwSNJgB8lkQnM3dsEmCzO7Nn918KAMa5kjrJwnBZaQXTqxmiJBGrQpCOaDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T12:48:10.114378Z"},"content_sha256":"7ef6f09c1ab0b6712839ba88690defc3935076be9bb912aea5905213ad7b2440","schema_version":"1.0","event_id":"sha256:7ef6f09c1ab0b6712839ba88690defc3935076be9bb912aea5905213ad7b2440"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:ELP7SSG3WOTM6Z6DV6EDZCNLRZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Constant term formulas for refined enumerations of Gog and Magog trapezoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.CO","authors_text":"Ilse Fischer","submitted_at":"2018-04-19T09:33:17Z","abstract_excerpt":"Gog and Magog trapezoids are certain arrays of positive integers that generalize alternating sign matrices (ASMs) and totally symmetric self-complementary plane partitions (TSSCPPs) respectively. Zeilberger used constant term formulas to prove that there is the same number of (n,k)-Gog trapezoids as there is of (n,k)-Magog trapezoids, thereby providing so far the only proof for a weak version of a conjecture by Mills, Robbins and Rumsey from 1986. About 20 years ago, Krattenthaler generalized Gog and Magog trapezoids and formulated an extension of their conjecture, and, recently, Biane and Che"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.07054","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":""},"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":"2026-05-18T00:18:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U1rEn9BH0g5dqVghLWR/BKL2aGabGDd0+CFDjh3W70VDFQzB9H9Dv7PM4N8vh13ARVu9t6Xg3SdYpq2/uKQEBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T12:48:10.114735Z"},"content_sha256":"6606d6816bf9fdf1748115aee9aa4bfe0c11443a32ba3b45b95de7e5cb8504b0","schema_version":"1.0","event_id":"sha256:6606d6816bf9fdf1748115aee9aa4bfe0c11443a32ba3b45b95de7e5cb8504b0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ELP7SSG3WOTM6Z6DV6EDZCNLRZ/bundle.json","state_url":"https://pith.science/pith/ELP7SSG3WOTM6Z6DV6EDZCNLRZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ELP7SSG3WOTM6Z6DV6EDZCNLRZ/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":"2026-06-22T12:48:10Z","links":{"resolver":"https://pith.science/pith/ELP7SSG3WOTM6Z6DV6EDZCNLRZ","bundle":"https://pith.science/pith/ELP7SSG3WOTM6Z6DV6EDZCNLRZ/bundle.json","state":"https://pith.science/pith/ELP7SSG3WOTM6Z6DV6EDZCNLRZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ELP7SSG3WOTM6Z6DV6EDZCNLRZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ELP7SSG3WOTM6Z6DV6EDZCNLRZ","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":"a8fe0787faae463f2a11e9a5b33a4a22fa0e5411960be9436558258ceb76209c","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-04-19T09:33:17Z","title_canon_sha256":"7961224c210428302f5fa38daa80f028a02e83692b2af47ba5b5b0f64af694d2"},"schema_version":"1.0","source":{"id":"1804.07054","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.07054","created_at":"2026-05-18T00:18:03Z"},{"alias_kind":"arxiv_version","alias_value":"1804.07054v1","created_at":"2026-05-18T00:18:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.07054","created_at":"2026-05-18T00:18:03Z"},{"alias_kind":"pith_short_12","alias_value":"ELP7SSG3WOTM","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"ELP7SSG3WOTM6Z6D","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"ELP7SSG3","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:6606d6816bf9fdf1748115aee9aa4bfe0c11443a32ba3b45b95de7e5cb8504b0","target":"graph","created_at":"2026-05-18T00:18:03Z","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":"Gog and Magog trapezoids are certain arrays of positive integers that generalize alternating sign matrices (ASMs) and totally symmetric self-complementary plane partitions (TSSCPPs) respectively. Zeilberger used constant term formulas to prove that there is the same number of (n,k)-Gog trapezoids as there is of (n,k)-Magog trapezoids, thereby providing so far the only proof for a weak version of a conjecture by Mills, Robbins and Rumsey from 1986. About 20 years ago, Krattenthaler generalized Gog and Magog trapezoids and formulated an extension of their conjecture, and, recently, Biane and Che","authors_text":"Ilse Fischer","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-04-19T09:33:17Z","title":"Constant term formulas for refined enumerations of Gog and Magog trapezoids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.07054","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":"sha256:7ef6f09c1ab0b6712839ba88690defc3935076be9bb912aea5905213ad7b2440","target":"record","created_at":"2026-05-18T00:18:03Z","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":"a8fe0787faae463f2a11e9a5b33a4a22fa0e5411960be9436558258ceb76209c","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-04-19T09:33:17Z","title_canon_sha256":"7961224c210428302f5fa38daa80f028a02e83692b2af47ba5b5b0f64af694d2"},"schema_version":"1.0","source":{"id":"1804.07054","kind":"arxiv","version":1}},"canonical_sha256":"22dff948dbb3a6cf67c3af883c89ab8e4e511e6d67e9e196d1f0239c3c659ba3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"22dff948dbb3a6cf67c3af883c89ab8e4e511e6d67e9e196d1f0239c3c659ba3","first_computed_at":"2026-05-18T00:18:03.557612Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:03.557612Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j5O0GySE0Nq3aWYtGFU8qJVvFPFC0IdrYbbje4gCw94hkGb9VkkH47oUPSQsO9K0BLQYY4MnVLKY6D8AdCOTCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:03.558126Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.07054","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7ef6f09c1ab0b6712839ba88690defc3935076be9bb912aea5905213ad7b2440","sha256:6606d6816bf9fdf1748115aee9aa4bfe0c11443a32ba3b45b95de7e5cb8504b0"],"state_sha256":"85fc8a5d2b75d1fe1f5363dc60fe2413e80df10006928ca4101a8d82c6ea43a6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hRtBUsvLPGSi4n5+pDs3b3whdsMSgzzTt7aI0Y2xMGjNCg0AFfz4Yzv6Myl5dkDfj6IWLhH29BDSmB/Xu0yzBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T12:48:10.116873Z","bundle_sha256":"8f67a4d098b7fb212636119d724c450b635f29ed392e9f7b06046a1336512059"}}