{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:RHKE2IC5L4RFRF6SDTRDOX7RNP","short_pith_number":"pith:RHKE2IC5","canonical_record":{"source":{"id":"1401.0770","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-01-04T02:37:27Z","cross_cats_sorted":[],"title_canon_sha256":"4233a9fa94795ca5258afc0c49204a1d11c23edf5a8f58da49af6d200b6d8e23","abstract_canon_sha256":"6418d0522602a92d922ee6443a9597d6880f81e322e8e5aba1aebaa91f646418"},"schema_version":"1.0"},"canonical_sha256":"89d44d205d5f225897d21ce2375ff16bef1b19a25b340dcc38ba79f848251444","source":{"kind":"arxiv","id":"1401.0770","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.0770","created_at":"2026-05-18T03:03:12Z"},{"alias_kind":"arxiv_version","alias_value":"1401.0770v1","created_at":"2026-05-18T03:03:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0770","created_at":"2026-05-18T03:03:12Z"},{"alias_kind":"pith_short_12","alias_value":"RHKE2IC5L4RF","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"RHKE2IC5L4RFRF6S","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"RHKE2IC5","created_at":"2026-05-18T12:28:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:RHKE2IC5L4RFRF6SDTRDOX7RNP","target":"record","payload":{"canonical_record":{"source":{"id":"1401.0770","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-01-04T02:37:27Z","cross_cats_sorted":[],"title_canon_sha256":"4233a9fa94795ca5258afc0c49204a1d11c23edf5a8f58da49af6d200b6d8e23","abstract_canon_sha256":"6418d0522602a92d922ee6443a9597d6880f81e322e8e5aba1aebaa91f646418"},"schema_version":"1.0"},"canonical_sha256":"89d44d205d5f225897d21ce2375ff16bef1b19a25b340dcc38ba79f848251444","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:03:12.049025Z","signature_b64":"+2baNwPFWC8XSVKp45nu7Q9Y06DyDC0bMl0ULQtSTNJPSfidv2bLoB2a126FRs6wjteX573JcWgXn/ylhTVBAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"89d44d205d5f225897d21ce2375ff16bef1b19a25b340dcc38ba79f848251444","last_reissued_at":"2026-05-18T03:03:12.048233Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:03:12.048233Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.0770","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":"2026-05-18T03:03:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+Hv8FjCk9t9uIwBxIJOlVH2JM3W4sSr34NC0shnNpEKVYO7frbLZFYKc1HqAo8XmVvXhcLgFC3zWHOdgsVg0CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T10:18:02.620251Z"},"content_sha256":"713c41cf168ac5c6aa096bf21b81c4542e07d60c8a1203389b24e7d19c1a342a","schema_version":"1.0","event_id":"sha256:713c41cf168ac5c6aa096bf21b81c4542e07d60c8a1203389b24e7d19c1a342a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:RHKE2IC5L4RFRF6SDTRDOX7RNP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Expected Shape of Random Doubly Alternating Baxter Permutations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Igor Pak, Theodore Dokos","submitted_at":"2014-01-04T02:37:27Z","abstract_excerpt":"Guibert and Linusson introduced the family of doubly alternating Baxter permutations, i.e. Baxter permutations $\\sigma \\in S_n$, such that $\\sigma$ and $\\sigma^{-1}$ are alternating. They proved that the number of such permutations in $S_{2n}$ and $S_{2n+1}$ is the Catalan number $C_n$. In this paper we explore the expected limit shape of such permutations, following the approach by Miner and Pak."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0770","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":"2026-05-18T03:03:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0aBwyHB7zjMCUYJWiVO2YAsw6Htbfi5qPMJmSuYBoe97E9d6+6cv7TE7c85pI/nld7Y+7VWT0JeHTnpc5z0ADA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T10:18:02.620906Z"},"content_sha256":"631b6e0b3b76256b4e7e760be11e3a51b22e0687ac66453a3097b5e59d30bcea","schema_version":"1.0","event_id":"sha256:631b6e0b3b76256b4e7e760be11e3a51b22e0687ac66453a3097b5e59d30bcea"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RHKE2IC5L4RFRF6SDTRDOX7RNP/bundle.json","state_url":"https://pith.science/pith/RHKE2IC5L4RFRF6SDTRDOX7RNP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RHKE2IC5L4RFRF6SDTRDOX7RNP/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":"2026-05-31T10:18:02Z","links":{"resolver":"https://pith.science/pith/RHKE2IC5L4RFRF6SDTRDOX7RNP","bundle":"https://pith.science/pith/RHKE2IC5L4RFRF6SDTRDOX7RNP/bundle.json","state":"https://pith.science/pith/RHKE2IC5L4RFRF6SDTRDOX7RNP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RHKE2IC5L4RFRF6SDTRDOX7RNP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:RHKE2IC5L4RFRF6SDTRDOX7RNP","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":"6418d0522602a92d922ee6443a9597d6880f81e322e8e5aba1aebaa91f646418","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-01-04T02:37:27Z","title_canon_sha256":"4233a9fa94795ca5258afc0c49204a1d11c23edf5a8f58da49af6d200b6d8e23"},"schema_version":"1.0","source":{"id":"1401.0770","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.0770","created_at":"2026-05-18T03:03:12Z"},{"alias_kind":"arxiv_version","alias_value":"1401.0770v1","created_at":"2026-05-18T03:03:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0770","created_at":"2026-05-18T03:03:12Z"},{"alias_kind":"pith_short_12","alias_value":"RHKE2IC5L4RF","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"RHKE2IC5L4RFRF6S","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"RHKE2IC5","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:631b6e0b3b76256b4e7e760be11e3a51b22e0687ac66453a3097b5e59d30bcea","target":"graph","created_at":"2026-05-18T03:03:12Z","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":"Guibert and Linusson introduced the family of doubly alternating Baxter permutations, i.e. Baxter permutations $\\sigma \\in S_n$, such that $\\sigma$ and $\\sigma^{-1}$ are alternating. They proved that the number of such permutations in $S_{2n}$ and $S_{2n+1}$ is the Catalan number $C_n$. In this paper we explore the expected limit shape of such permutations, following the approach by Miner and Pak.","authors_text":"Igor Pak, Theodore Dokos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-01-04T02:37:27Z","title":"The Expected Shape of Random Doubly Alternating Baxter Permutations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0770","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":"sha256:713c41cf168ac5c6aa096bf21b81c4542e07d60c8a1203389b24e7d19c1a342a","target":"record","created_at":"2026-05-18T03:03:12Z","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":"6418d0522602a92d922ee6443a9597d6880f81e322e8e5aba1aebaa91f646418","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-01-04T02:37:27Z","title_canon_sha256":"4233a9fa94795ca5258afc0c49204a1d11c23edf5a8f58da49af6d200b6d8e23"},"schema_version":"1.0","source":{"id":"1401.0770","kind":"arxiv","version":1}},"canonical_sha256":"89d44d205d5f225897d21ce2375ff16bef1b19a25b340dcc38ba79f848251444","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"89d44d205d5f225897d21ce2375ff16bef1b19a25b340dcc38ba79f848251444","first_computed_at":"2026-05-18T03:03:12.048233Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:03:12.048233Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+2baNwPFWC8XSVKp45nu7Q9Y06DyDC0bMl0ULQtSTNJPSfidv2bLoB2a126FRs6wjteX573JcWgXn/ylhTVBAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:03:12.049025Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.0770","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:713c41cf168ac5c6aa096bf21b81c4542e07d60c8a1203389b24e7d19c1a342a","sha256:631b6e0b3b76256b4e7e760be11e3a51b22e0687ac66453a3097b5e59d30bcea"],"state_sha256":"3cbebd42e65e68d45c1ef64e99d08ebb8f7137801cf8779869f4c2d4eb52761c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"neONVBaXWscWmCgQIPllAYtZkDt+u5wAVRWnMR7g/y35duF74dW6+AsF8KPYGYQjOSd1lcTo90lAMmMtqLYQBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T10:18:02.624284Z","bundle_sha256":"0d0bffdde24a7d931da2ad08bf5e06cc6f5acb0258187020da4881035bc6d60f"}}