{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:LXLFP5XPEA3AZOUHVP7GMGMPZS","short_pith_number":"pith:LXLFP5XP","canonical_record":{"source":{"id":"1303.1395","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-03-06T17:29:28Z","cross_cats_sorted":[],"title_canon_sha256":"115bdd737a3f0757b7f9402c7eec8e9de8c1e295c6459f08497f0f88735eebde","abstract_canon_sha256":"696e05707deb055e26f0d939eae56285a23c72a96a841dc9a2350e43fa301ab0"},"schema_version":"1.0"},"canonical_sha256":"5dd657f6ef20360cba87abfe66198fccb0151110993d78de36fd907aa5b9557d","source":{"kind":"arxiv","id":"1303.1395","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.1395","created_at":"2026-05-18T03:31:43Z"},{"alias_kind":"arxiv_version","alias_value":"1303.1395v1","created_at":"2026-05-18T03:31:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.1395","created_at":"2026-05-18T03:31:43Z"},{"alias_kind":"pith_short_12","alias_value":"LXLFP5XPEA3A","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LXLFP5XPEA3AZOUH","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LXLFP5XP","created_at":"2026-05-18T12:27:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:LXLFP5XPEA3AZOUHVP7GMGMPZS","target":"record","payload":{"canonical_record":{"source":{"id":"1303.1395","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-03-06T17:29:28Z","cross_cats_sorted":[],"title_canon_sha256":"115bdd737a3f0757b7f9402c7eec8e9de8c1e295c6459f08497f0f88735eebde","abstract_canon_sha256":"696e05707deb055e26f0d939eae56285a23c72a96a841dc9a2350e43fa301ab0"},"schema_version":"1.0"},"canonical_sha256":"5dd657f6ef20360cba87abfe66198fccb0151110993d78de36fd907aa5b9557d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:31:43.599133Z","signature_b64":"rFu7vAm+QYga7UJTrC2BheOws7CFLEY6UxVoQWdVv8SjfJtdFD9R+6k7ypCYR2aAQuikm5SrylZo4wTGlpSIBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5dd657f6ef20360cba87abfe66198fccb0151110993d78de36fd907aa5b9557d","last_reissued_at":"2026-05-18T03:31:43.598325Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:31:43.598325Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.1395","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":"2026-05-18T03:31:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vkXB++MwvjcMnwgpdQXo7OMeoiY1VZVCKQhtRTwnZ5EzJ7YH6OJUbY4hej+f4cMY+4yz2HE0sZqdnCxoxxuBDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T03:17:57.200032Z"},"content_sha256":"241f413a4fec2f9ce612fb4de20560293824cf7e202e4d9aaf72586d0eac8380","schema_version":"1.0","event_id":"sha256:241f413a4fec2f9ce612fb4de20560293824cf7e202e4d9aaf72586d0eac8380"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:LXLFP5XPEA3AZOUHVP7GMGMPZS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A stack and a pop stack in series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Rebecca Smith, Vincent Vatter","submitted_at":"2013-03-06T17:29:28Z","abstract_excerpt":"We study sorting machines consisting of a stack and a pop stack in series, with or without a queue between them. While there are, a priori, four such machines, only two are essentially different: a pop stack followed directly by a stack, and a pop stack followed by a queue and then by a stack. In the former case, we obtain complete answers for the basis and enumeration of the sortable permutations. In the latter case, we present several conjectures."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.1395","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":"2026-05-18T03:31:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lGjrybEtNu3gBkNtsFH1ON5tjHjMLDLHYVyhSVmaNGtObroewuLdyGLQRdTsPqN8jH4ZEgJ0wjG3j6MevCwDBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T03:17:57.200443Z"},"content_sha256":"221c7347b828b200870755d68536c9c3b20d719ddc3ae08cdb06bad194528511","schema_version":"1.0","event_id":"sha256:221c7347b828b200870755d68536c9c3b20d719ddc3ae08cdb06bad194528511"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LXLFP5XPEA3AZOUHVP7GMGMPZS/bundle.json","state_url":"https://pith.science/pith/LXLFP5XPEA3AZOUHVP7GMGMPZS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LXLFP5XPEA3AZOUHVP7GMGMPZS/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":"2026-05-31T03:17:57Z","links":{"resolver":"https://pith.science/pith/LXLFP5XPEA3AZOUHVP7GMGMPZS","bundle":"https://pith.science/pith/LXLFP5XPEA3AZOUHVP7GMGMPZS/bundle.json","state":"https://pith.science/pith/LXLFP5XPEA3AZOUHVP7GMGMPZS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LXLFP5XPEA3AZOUHVP7GMGMPZS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:LXLFP5XPEA3AZOUHVP7GMGMPZS","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":"696e05707deb055e26f0d939eae56285a23c72a96a841dc9a2350e43fa301ab0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-03-06T17:29:28Z","title_canon_sha256":"115bdd737a3f0757b7f9402c7eec8e9de8c1e295c6459f08497f0f88735eebde"},"schema_version":"1.0","source":{"id":"1303.1395","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.1395","created_at":"2026-05-18T03:31:43Z"},{"alias_kind":"arxiv_version","alias_value":"1303.1395v1","created_at":"2026-05-18T03:31:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.1395","created_at":"2026-05-18T03:31:43Z"},{"alias_kind":"pith_short_12","alias_value":"LXLFP5XPEA3A","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LXLFP5XPEA3AZOUH","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LXLFP5XP","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:221c7347b828b200870755d68536c9c3b20d719ddc3ae08cdb06bad194528511","target":"graph","created_at":"2026-05-18T03:31:43Z","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 study sorting machines consisting of a stack and a pop stack in series, with or without a queue between them. While there are, a priori, four such machines, only two are essentially different: a pop stack followed directly by a stack, and a pop stack followed by a queue and then by a stack. In the former case, we obtain complete answers for the basis and enumeration of the sortable permutations. In the latter case, we present several conjectures.","authors_text":"Rebecca Smith, Vincent Vatter","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-03-06T17:29:28Z","title":"A stack and a pop stack in series"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.1395","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":"sha256:241f413a4fec2f9ce612fb4de20560293824cf7e202e4d9aaf72586d0eac8380","target":"record","created_at":"2026-05-18T03:31:43Z","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":"696e05707deb055e26f0d939eae56285a23c72a96a841dc9a2350e43fa301ab0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-03-06T17:29:28Z","title_canon_sha256":"115bdd737a3f0757b7f9402c7eec8e9de8c1e295c6459f08497f0f88735eebde"},"schema_version":"1.0","source":{"id":"1303.1395","kind":"arxiv","version":1}},"canonical_sha256":"5dd657f6ef20360cba87abfe66198fccb0151110993d78de36fd907aa5b9557d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5dd657f6ef20360cba87abfe66198fccb0151110993d78de36fd907aa5b9557d","first_computed_at":"2026-05-18T03:31:43.598325Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:31:43.598325Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rFu7vAm+QYga7UJTrC2BheOws7CFLEY6UxVoQWdVv8SjfJtdFD9R+6k7ypCYR2aAQuikm5SrylZo4wTGlpSIBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:31:43.599133Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.1395","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:241f413a4fec2f9ce612fb4de20560293824cf7e202e4d9aaf72586d0eac8380","sha256:221c7347b828b200870755d68536c9c3b20d719ddc3ae08cdb06bad194528511"],"state_sha256":"17be3076e26b49bba2b14d7d8b182dcfd65c78d4cdb7f82b1212590ee47f9712"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"laX2bBEKBS0RVZEkuU2YkCLL9Fp/Sa+niRhTKnFOXJg8QpKjzlb1JTBGme9XtBxVVzVQepyDNElR5bjKda7hDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T03:17:57.203724Z","bundle_sha256":"d9fea58e2faa7238414f8ce7637cbba5f43fa48f4e0eab6edbd592a5f2126926"}}