{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:TE23BENNDL2QNZKAL2PKBPEOPX","short_pith_number":"pith:TE23BENN","canonical_record":{"source":{"id":"1611.09279","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-28T18:38:39Z","cross_cats_sorted":[],"title_canon_sha256":"2b40758f5fb76e3e9474262bcd59e2c3122de4b913f94fdc913c1469814ae31f","abstract_canon_sha256":"5d3919a36c4ccc1d7d6a41e7b9b2640c3d076f47fbb83666c829d6c1544d693b"},"schema_version":"1.0"},"canonical_sha256":"9935b091ad1af506e5405e9ea0bc8e7de14467d275f58684147a4972754de68a","source":{"kind":"arxiv","id":"1611.09279","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.09279","created_at":"2026-05-18T00:23:56Z"},{"alias_kind":"arxiv_version","alias_value":"1611.09279v2","created_at":"2026-05-18T00:23:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.09279","created_at":"2026-05-18T00:23:56Z"},{"alias_kind":"pith_short_12","alias_value":"TE23BENNDL2Q","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"TE23BENNDL2QNZKA","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"TE23BENN","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:TE23BENNDL2QNZKAL2PKBPEOPX","target":"record","payload":{"canonical_record":{"source":{"id":"1611.09279","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-28T18:38:39Z","cross_cats_sorted":[],"title_canon_sha256":"2b40758f5fb76e3e9474262bcd59e2c3122de4b913f94fdc913c1469814ae31f","abstract_canon_sha256":"5d3919a36c4ccc1d7d6a41e7b9b2640c3d076f47fbb83666c829d6c1544d693b"},"schema_version":"1.0"},"canonical_sha256":"9935b091ad1af506e5405e9ea0bc8e7de14467d275f58684147a4972754de68a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:56.930308Z","signature_b64":"xljp24pkzdd6xu/8fXDHrrSKT8wArHf6rels409/+D4RxCY46lJ7yNpTHixDY/XDExdeEhHuqv7YrA2SkereCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9935b091ad1af506e5405e9ea0bc8e7de14467d275f58684147a4972754de68a","last_reissued_at":"2026-05-18T00:23:56.929579Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:56.929579Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.09279","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:23:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jg5cYZC/xVjT/74dM15AbQyeCzi8HyLSjfD+ctlUw7ggbYg+aEI/bmpqEfckl2iGn8PqeqOpz9giwZ5k3NvEBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T06:54:21.316186Z"},"content_sha256":"c750444f57bc973d210b4be934ae58a09e5af75ef39dd10e9775d58b3e5e751a","schema_version":"1.0","event_id":"sha256:c750444f57bc973d210b4be934ae58a09e5af75ef39dd10e9775d58b3e5e751a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:TE23BENNDL2QNZKAL2PKBPEOPX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dyck Paths and Positroids from Unit Interval Orders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Anastasia Chavez, Felix Gotti","submitted_at":"2016-11-28T18:38:39Z","abstract_excerpt":"It is well known that the number of non-isomorphic unit interval orders on $[n]$ equals the $n$-th Catalan number. Using work of Skandera and Reed and work of Postnikov, we show that each unit interval order on $[n]$ naturally induces a rank $n$ positroid on $[2n]$. We call the positroids produced in this fashion unit interval positroids. We characterize the unit interval positroids by describing their associated decorated permutations, showing that each one must be a $2n$-cycle encoding a Dyck path of length $2n$. We also provide recipes to read the decorated permutation of a unit interval po"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.09279","kind":"arxiv","version":2},"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":"2026-05-18T00:23:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+7m8MBnSTyzbJJYUCRZGIK9zOZIpzZxbNr6DhlVvuveJ/mWDfKU9yBuA4jCsytACOh58dl4kWfufnC7jDlv/AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T06:54:21.316540Z"},"content_sha256":"2e1555f2c3bdb9f113a1bae0a662ef22c07cd1c7a4228b67329c2a3248fa18de","schema_version":"1.0","event_id":"sha256:2e1555f2c3bdb9f113a1bae0a662ef22c07cd1c7a4228b67329c2a3248fa18de"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TE23BENNDL2QNZKAL2PKBPEOPX/bundle.json","state_url":"https://pith.science/pith/TE23BENNDL2QNZKAL2PKBPEOPX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TE23BENNDL2QNZKAL2PKBPEOPX/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":"2026-06-27T06:54:21Z","links":{"resolver":"https://pith.science/pith/TE23BENNDL2QNZKAL2PKBPEOPX","bundle":"https://pith.science/pith/TE23BENNDL2QNZKAL2PKBPEOPX/bundle.json","state":"https://pith.science/pith/TE23BENNDL2QNZKAL2PKBPEOPX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TE23BENNDL2QNZKAL2PKBPEOPX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TE23BENNDL2QNZKAL2PKBPEOPX","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":"5d3919a36c4ccc1d7d6a41e7b9b2640c3d076f47fbb83666c829d6c1544d693b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-28T18:38:39Z","title_canon_sha256":"2b40758f5fb76e3e9474262bcd59e2c3122de4b913f94fdc913c1469814ae31f"},"schema_version":"1.0","source":{"id":"1611.09279","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.09279","created_at":"2026-05-18T00:23:56Z"},{"alias_kind":"arxiv_version","alias_value":"1611.09279v2","created_at":"2026-05-18T00:23:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.09279","created_at":"2026-05-18T00:23:56Z"},{"alias_kind":"pith_short_12","alias_value":"TE23BENNDL2Q","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"TE23BENNDL2QNZKA","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"TE23BENN","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:2e1555f2c3bdb9f113a1bae0a662ef22c07cd1c7a4228b67329c2a3248fa18de","target":"graph","created_at":"2026-05-18T00:23:56Z","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":"It is well known that the number of non-isomorphic unit interval orders on $[n]$ equals the $n$-th Catalan number. Using work of Skandera and Reed and work of Postnikov, we show that each unit interval order on $[n]$ naturally induces a rank $n$ positroid on $[2n]$. We call the positroids produced in this fashion unit interval positroids. We characterize the unit interval positroids by describing their associated decorated permutations, showing that each one must be a $2n$-cycle encoding a Dyck path of length $2n$. We also provide recipes to read the decorated permutation of a unit interval po","authors_text":"Anastasia Chavez, Felix Gotti","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-28T18:38:39Z","title":"Dyck Paths and Positroids from Unit Interval Orders"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.09279","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:c750444f57bc973d210b4be934ae58a09e5af75ef39dd10e9775d58b3e5e751a","target":"record","created_at":"2026-05-18T00:23:56Z","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":"5d3919a36c4ccc1d7d6a41e7b9b2640c3d076f47fbb83666c829d6c1544d693b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-28T18:38:39Z","title_canon_sha256":"2b40758f5fb76e3e9474262bcd59e2c3122de4b913f94fdc913c1469814ae31f"},"schema_version":"1.0","source":{"id":"1611.09279","kind":"arxiv","version":2}},"canonical_sha256":"9935b091ad1af506e5405e9ea0bc8e7de14467d275f58684147a4972754de68a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9935b091ad1af506e5405e9ea0bc8e7de14467d275f58684147a4972754de68a","first_computed_at":"2026-05-18T00:23:56.929579Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:56.929579Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xljp24pkzdd6xu/8fXDHrrSKT8wArHf6rels409/+D4RxCY46lJ7yNpTHixDY/XDExdeEhHuqv7YrA2SkereCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:56.930308Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.09279","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c750444f57bc973d210b4be934ae58a09e5af75ef39dd10e9775d58b3e5e751a","sha256:2e1555f2c3bdb9f113a1bae0a662ef22c07cd1c7a4228b67329c2a3248fa18de"],"state_sha256":"08bd434ab3a28fe9b60c008cba074f10fc666456e8eaf76070406587c8b31e4c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qmAYB9BU+PsI0wqsu6OCzdoo9q60gWZBkRhYeYpRGiixEFWrqcmsbeesbFQi1G6TeDwtwJK8hCZ3KFNChsXHBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T06:54:21.318436Z","bundle_sha256":"3e46a0d432074cfe1d22900d9c5ccfb75e843d8e28de3b8aa98d78aff1d750b2"}}