{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:YTGXP7QOG4OTO5UXAIGFXRGTQ2","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":"4bd42dda51d7a430ec0da302243d333450f60f8637fadad2a323fc2125f2c9f8","cross_cats_sorted":["cs.DM"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2026-01-14T12:49:26Z","title_canon_sha256":"be23c34f3a0c2e051dfc5541cda4df0bae96c6bfb4e7171696f8a1f1b6bdca37"},"schema_version":"1.0","source":{"id":"2601.09447","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2601.09447","created_at":"2026-05-28T01:04:35Z"},{"alias_kind":"arxiv_version","alias_value":"2601.09447v2","created_at":"2026-05-28T01:04:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.09447","created_at":"2026-05-28T01:04:35Z"},{"alias_kind":"pith_short_12","alias_value":"YTGXP7QOG4OT","created_at":"2026-05-28T01:04:35Z"},{"alias_kind":"pith_short_16","alias_value":"YTGXP7QOG4OTO5UX","created_at":"2026-05-28T01:04:35Z"},{"alias_kind":"pith_short_8","alias_value":"YTGXP7QO","created_at":"2026-05-28T01:04:35Z"}],"graph_snapshots":[{"event_id":"sha256:70ee13edf9a16efe892d6bb8830604e735312d9fd2967e12f9d8fd6d2f48bf87","target":"graph","created_at":"2026-05-28T01:04:35Z","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/2601.09447/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this work, we consider the burnt pancake problem, which is a well-studied problem going back to a work of Gates and Papadimitriou from 1979.The problem is to sort a stack of~$n$ one-sided burnt pancakes of different sizes, by a sequence of flips of the top pancakes, such that at the end of the flipping sequence the pancakes have increasing size and the burnt sides of all pancakes are face-down. The pancakes are denoted by $ 1,2,\\dots,n$, and a number is multiplied by $-1$, if the corresponding pancake has burnt side face-up.\n  Let $T(n)$ be the minimum number of flips to sort a special stac","authors_text":"Gerold J\\\"ager, Nacim Oijid","cross_cats":["cs.DM"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2026-01-14T12:49:26Z","title":"Exact number of flips required to sort a burnt stack of pancakes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.09447","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":"sha256:4594c2b1329d700b45d75c9df95ab0f65ee158ec7b7417b38047390b20a3784a","target":"record","created_at":"2026-05-28T01:04:35Z","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":"4bd42dda51d7a430ec0da302243d333450f60f8637fadad2a323fc2125f2c9f8","cross_cats_sorted":["cs.DM"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2026-01-14T12:49:26Z","title_canon_sha256":"be23c34f3a0c2e051dfc5541cda4df0bae96c6bfb4e7171696f8a1f1b6bdca37"},"schema_version":"1.0","source":{"id":"2601.09447","kind":"arxiv","version":2}},"canonical_sha256":"c4cd77fe0e371d377697020c5bc4d3868e009fbff7550f2519fadb10217f718e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c4cd77fe0e371d377697020c5bc4d3868e009fbff7550f2519fadb10217f718e","first_computed_at":"2026-05-28T01:04:35.285821Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-28T01:04:35.285821Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WDWJuB2+2dE7yQr/BnhAUE/VYCu8I/uw1U8GHZ3nyODpht7v1khsN6jrsUSPCYNmWZXEW8qBIvFKhB4PBQLODA==","signature_status":"signed_v1","signed_at":"2026-05-28T01:04:35.286262Z","signed_message":"canonical_sha256_bytes"},"source_id":"2601.09447","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4594c2b1329d700b45d75c9df95ab0f65ee158ec7b7417b38047390b20a3784a","sha256:70ee13edf9a16efe892d6bb8830604e735312d9fd2967e12f9d8fd6d2f48bf87"],"state_sha256":"0d4ed76d8e9e3ca076e6650aee741f1de985707198fa8fb02aef8f4e3c0fc2cb"}