{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:OFUWIDQMEWIREK2BUYGCRDYWYZ","short_pith_number":"pith:OFUWIDQM","canonical_record":{"source":{"id":"1308.2698","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-08-12T20:59:13Z","cross_cats_sorted":[],"title_canon_sha256":"5b5ba072e5e452c30ab77b5b12a2a9f4635dc635b5ed30901bb85b0111b7ccd5","abstract_canon_sha256":"4718392fbd465dbcb33832c674246d491a29e96888c21169dd1dba33ad5400ae"},"schema_version":"1.0"},"canonical_sha256":"7169640e0c2591122b41a60c288f16c664e163c393f93101897bdb453ed37cb3","source":{"kind":"arxiv","id":"1308.2698","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.2698","created_at":"2026-05-18T03:13:21Z"},{"alias_kind":"arxiv_version","alias_value":"1308.2698v2","created_at":"2026-05-18T03:13:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.2698","created_at":"2026-05-18T03:13:21Z"},{"alias_kind":"pith_short_12","alias_value":"OFUWIDQMEWIR","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OFUWIDQMEWIREK2B","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OFUWIDQM","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:OFUWIDQMEWIREK2BUYGCRDYWYZ","target":"record","payload":{"canonical_record":{"source":{"id":"1308.2698","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-08-12T20:59:13Z","cross_cats_sorted":[],"title_canon_sha256":"5b5ba072e5e452c30ab77b5b12a2a9f4635dc635b5ed30901bb85b0111b7ccd5","abstract_canon_sha256":"4718392fbd465dbcb33832c674246d491a29e96888c21169dd1dba33ad5400ae"},"schema_version":"1.0"},"canonical_sha256":"7169640e0c2591122b41a60c288f16c664e163c393f93101897bdb453ed37cb3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:13:21.197614Z","signature_b64":"qCz1yg75TMmTgrWzxcmxdR+SIrGbp+37ZuzRbdabtjFk9e5bDjhrObhhT2QTfOtxm9omW0N4eOmCc/89bOnDDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7169640e0c2591122b41a60c288f16c664e163c393f93101897bdb453ed37cb3","last_reissued_at":"2026-05-18T03:13:21.197145Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:13:21.197145Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.2698","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":"2026-05-18T03:13:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1Xum3khA8f24QlWvX80L1JjF/BdvpbYDvXAp+lEe/IXcZznauTLSykzEdeV3+xPKzVoV7zhWLdpeLCG6swP9CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T10:30:19.498973Z"},"content_sha256":"c1d21469d189b43d56f3cb41c2836e5457970f5db445d4c8b425583ba4b1315c","schema_version":"1.0","event_id":"sha256:c1d21469d189b43d56f3cb41c2836e5457970f5db445d4c8b425583ba4b1315c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:OFUWIDQMEWIREK2BUYGCRDYWYZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Positroids and non-crossing partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Federico Ardila, Felipe Rinc\\'on, Lauren Williams","submitted_at":"2013-08-12T20:59:13Z","abstract_excerpt":"We investigate the role that non-crossing partitions play in the study of positroids, a class of matroids introduced by Postnikov. We prove that every positroid can be constructed uniquely by choosing a non-crossing partition on the ground set, and then freely placing the structure of a connected positroid on each of the blocks of the partition. This structural result yields several combinatorial facts about positroids. We show that the face poset of a positroid polytope embeds in a poset of weighted non-crossing partitions. We enumerate connected positroids, and show how they arise naturally "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.2698","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":"2026-05-18T03:13:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u23OBGw9NsI654bLPp7MAKkr1a8gXRsLOdaNNZ+Hr+gor17ys0Hyx0KbfKZCsNqdhyEgaGqACGwm5i46A/dvCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T10:30:19.499341Z"},"content_sha256":"685f1f472f6fa50deebe5897fe23a7a9891443b65f81da862fa19a743229a694","schema_version":"1.0","event_id":"sha256:685f1f472f6fa50deebe5897fe23a7a9891443b65f81da862fa19a743229a694"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OFUWIDQMEWIREK2BUYGCRDYWYZ/bundle.json","state_url":"https://pith.science/pith/OFUWIDQMEWIREK2BUYGCRDYWYZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OFUWIDQMEWIREK2BUYGCRDYWYZ/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":"2026-06-01T10:30:19Z","links":{"resolver":"https://pith.science/pith/OFUWIDQMEWIREK2BUYGCRDYWYZ","bundle":"https://pith.science/pith/OFUWIDQMEWIREK2BUYGCRDYWYZ/bundle.json","state":"https://pith.science/pith/OFUWIDQMEWIREK2BUYGCRDYWYZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OFUWIDQMEWIREK2BUYGCRDYWYZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:OFUWIDQMEWIREK2BUYGCRDYWYZ","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":"4718392fbd465dbcb33832c674246d491a29e96888c21169dd1dba33ad5400ae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-08-12T20:59:13Z","title_canon_sha256":"5b5ba072e5e452c30ab77b5b12a2a9f4635dc635b5ed30901bb85b0111b7ccd5"},"schema_version":"1.0","source":{"id":"1308.2698","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.2698","created_at":"2026-05-18T03:13:21Z"},{"alias_kind":"arxiv_version","alias_value":"1308.2698v2","created_at":"2026-05-18T03:13:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.2698","created_at":"2026-05-18T03:13:21Z"},{"alias_kind":"pith_short_12","alias_value":"OFUWIDQMEWIR","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OFUWIDQMEWIREK2B","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OFUWIDQM","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:685f1f472f6fa50deebe5897fe23a7a9891443b65f81da862fa19a743229a694","target":"graph","created_at":"2026-05-18T03:13:21Z","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 investigate the role that non-crossing partitions play in the study of positroids, a class of matroids introduced by Postnikov. We prove that every positroid can be constructed uniquely by choosing a non-crossing partition on the ground set, and then freely placing the structure of a connected positroid on each of the blocks of the partition. This structural result yields several combinatorial facts about positroids. We show that the face poset of a positroid polytope embeds in a poset of weighted non-crossing partitions. We enumerate connected positroids, and show how they arise naturally ","authors_text":"Federico Ardila, Felipe Rinc\\'on, Lauren Williams","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-08-12T20:59:13Z","title":"Positroids and non-crossing partitions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.2698","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:c1d21469d189b43d56f3cb41c2836e5457970f5db445d4c8b425583ba4b1315c","target":"record","created_at":"2026-05-18T03:13:21Z","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":"4718392fbd465dbcb33832c674246d491a29e96888c21169dd1dba33ad5400ae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-08-12T20:59:13Z","title_canon_sha256":"5b5ba072e5e452c30ab77b5b12a2a9f4635dc635b5ed30901bb85b0111b7ccd5"},"schema_version":"1.0","source":{"id":"1308.2698","kind":"arxiv","version":2}},"canonical_sha256":"7169640e0c2591122b41a60c288f16c664e163c393f93101897bdb453ed37cb3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7169640e0c2591122b41a60c288f16c664e163c393f93101897bdb453ed37cb3","first_computed_at":"2026-05-18T03:13:21.197145Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:13:21.197145Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qCz1yg75TMmTgrWzxcmxdR+SIrGbp+37ZuzRbdabtjFk9e5bDjhrObhhT2QTfOtxm9omW0N4eOmCc/89bOnDDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:13:21.197614Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.2698","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c1d21469d189b43d56f3cb41c2836e5457970f5db445d4c8b425583ba4b1315c","sha256:685f1f472f6fa50deebe5897fe23a7a9891443b65f81da862fa19a743229a694"],"state_sha256":"07234255272ee7b0f659a297aab4db405f8a4158c586ed65330667cc86c16c59"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EsN0iamhUMUtWxfCo/ttm/Yd3JrK4XpiQCGyJOX/a+WbsrYaPTnXoPx7shMgK6MuHaB6rnCMQ3vwHn7XJbtcAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T10:30:19.501409Z","bundle_sha256":"cf9351010aece0e93fe50260437b25c729da6d33392c523c41ad9adb5452ce56"}}