{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:5KVDDZQJRQM2K3FHRE3F4K2NJB","short_pith_number":"pith:5KVDDZQJ","canonical_record":{"source":{"id":"2102.11306","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2021-02-22T19:01:30Z","cross_cats_sorted":[],"title_canon_sha256":"d4ce4db1e82e950ca77877c576de971e343b3c03bb2526c2f86e91eb24a36892","abstract_canon_sha256":"8b0081bfe9ceafc1374e30430ee118be63e3ad8ee27fc58d0efc927b90ef155f"},"schema_version":"1.0"},"canonical_sha256":"eaaa31e6098c19a56ca789365e2b4d486a919dec1a2b5b3c52ef83628e5895dd","source":{"kind":"arxiv","id":"2102.11306","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.11306","created_at":"2026-07-05T02:30:14Z"},{"alias_kind":"arxiv_version","alias_value":"2102.11306v2","created_at":"2026-07-05T02:30:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.11306","created_at":"2026-07-05T02:30:14Z"},{"alias_kind":"pith_short_12","alias_value":"5KVDDZQJRQM2","created_at":"2026-07-05T02:30:14Z"},{"alias_kind":"pith_short_16","alias_value":"5KVDDZQJRQM2K3FH","created_at":"2026-07-05T02:30:14Z"},{"alias_kind":"pith_short_8","alias_value":"5KVDDZQJ","created_at":"2026-07-05T02:30:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:5KVDDZQJRQM2K3FHRE3F4K2NJB","target":"record","payload":{"canonical_record":{"source":{"id":"2102.11306","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2021-02-22T19:01:30Z","cross_cats_sorted":[],"title_canon_sha256":"d4ce4db1e82e950ca77877c576de971e343b3c03bb2526c2f86e91eb24a36892","abstract_canon_sha256":"8b0081bfe9ceafc1374e30430ee118be63e3ad8ee27fc58d0efc927b90ef155f"},"schema_version":"1.0"},"canonical_sha256":"eaaa31e6098c19a56ca789365e2b4d486a919dec1a2b5b3c52ef83628e5895dd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:30:14.962340Z","signature_b64":"0OcHDXr6yktptbd2gr76yap4JVg619LdjNcmKO+emSsxHbNB4Fu4VvM5B08Yr7ieEqoZf2nRIE0FtcHRMR3/CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eaaa31e6098c19a56ca789365e2b4d486a919dec1a2b5b3c52ef83628e5895dd","last_reissued_at":"2026-07-05T02:30:14.961906Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:30:14.961906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2102.11306","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":"2026-07-05T02:30:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W7xMaCxdWUenwbG1MmRJ8Qk7RpaODu95hoxWH+ZQh/ck2VvJpp9A7Lk4/WGZx6EWasy3+/kwQZ4D5YYpVNwsBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T04:38:54.682008Z"},"content_sha256":"6e74e03c285d5648d74d6c7c02231e6e0ed9872b4330d059e7542c4b311c1c61","schema_version":"1.0","event_id":"sha256:6e74e03c285d5648d74d6c7c02231e6e0ed9872b4330d059e7542c4b311c1c61"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:5KVDDZQJRQM2K3FHRE3F4K2NJB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Triangulations, order polytopes, and generalized snake posets","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andr\\'es R. Vindas-Mel\\'endez, Benjamin Braun, Derek Hanely, Julianne Vega, Khrystyna Serhiyenko, Martha Yip, Matias von Bell","submitted_at":"2021-02-22T19:01:30Z","abstract_excerpt":"This work regards the order polytopes arising from the class of generalized snake posets and their posets of meet-irreducible elements. Among generalized snake posets of the same rank, we characterize those whose order polytopes have minimal and maximal volume. We give a combinatorial characterization of the circuits in these order polytopes and then conclude that every triangulation is unimodular. For a generalized snake word, we count the number of flips for the canonical triangulation of these order polytopes. We determine that the flip graph of the order polytope of the poset whose lattice"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.11306","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2102.11306/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T02:30:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+DnRKD0CjWnSTzdRrQF/1w5lmnItcJTVm6TTs17MjdHkMnEJ7Ou7sDA103hB+8hjDynhcTiacNA/+yL5EPYIDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T04:38:54.682669Z"},"content_sha256":"a76196eaa7bb9527e827871bccaba00ce54e9b3dd5b09d3afd6c3c7fef5dd6d2","schema_version":"1.0","event_id":"sha256:a76196eaa7bb9527e827871bccaba00ce54e9b3dd5b09d3afd6c3c7fef5dd6d2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5KVDDZQJRQM2K3FHRE3F4K2NJB/bundle.json","state_url":"https://pith.science/pith/5KVDDZQJRQM2K3FHRE3F4K2NJB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5KVDDZQJRQM2K3FHRE3F4K2NJB/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":"2026-07-07T04:38:54Z","links":{"resolver":"https://pith.science/pith/5KVDDZQJRQM2K3FHRE3F4K2NJB","bundle":"https://pith.science/pith/5KVDDZQJRQM2K3FHRE3F4K2NJB/bundle.json","state":"https://pith.science/pith/5KVDDZQJRQM2K3FHRE3F4K2NJB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5KVDDZQJRQM2K3FHRE3F4K2NJB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:5KVDDZQJRQM2K3FHRE3F4K2NJB","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":"8b0081bfe9ceafc1374e30430ee118be63e3ad8ee27fc58d0efc927b90ef155f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2021-02-22T19:01:30Z","title_canon_sha256":"d4ce4db1e82e950ca77877c576de971e343b3c03bb2526c2f86e91eb24a36892"},"schema_version":"1.0","source":{"id":"2102.11306","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.11306","created_at":"2026-07-05T02:30:14Z"},{"alias_kind":"arxiv_version","alias_value":"2102.11306v2","created_at":"2026-07-05T02:30:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.11306","created_at":"2026-07-05T02:30:14Z"},{"alias_kind":"pith_short_12","alias_value":"5KVDDZQJRQM2","created_at":"2026-07-05T02:30:14Z"},{"alias_kind":"pith_short_16","alias_value":"5KVDDZQJRQM2K3FH","created_at":"2026-07-05T02:30:14Z"},{"alias_kind":"pith_short_8","alias_value":"5KVDDZQJ","created_at":"2026-07-05T02:30:14Z"}],"graph_snapshots":[{"event_id":"sha256:a76196eaa7bb9527e827871bccaba00ce54e9b3dd5b09d3afd6c3c7fef5dd6d2","target":"graph","created_at":"2026-07-05T02:30:14Z","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/2102.11306/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This work regards the order polytopes arising from the class of generalized snake posets and their posets of meet-irreducible elements. Among generalized snake posets of the same rank, we characterize those whose order polytopes have minimal and maximal volume. We give a combinatorial characterization of the circuits in these order polytopes and then conclude that every triangulation is unimodular. For a generalized snake word, we count the number of flips for the canonical triangulation of these order polytopes. We determine that the flip graph of the order polytope of the poset whose lattice","authors_text":"Andr\\'es R. Vindas-Mel\\'endez, Benjamin Braun, Derek Hanely, Julianne Vega, Khrystyna Serhiyenko, Martha Yip, Matias von Bell","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2021-02-22T19:01:30Z","title":"Triangulations, order polytopes, and generalized snake posets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.11306","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":"sha256:6e74e03c285d5648d74d6c7c02231e6e0ed9872b4330d059e7542c4b311c1c61","target":"record","created_at":"2026-07-05T02:30:14Z","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":"8b0081bfe9ceafc1374e30430ee118be63e3ad8ee27fc58d0efc927b90ef155f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2021-02-22T19:01:30Z","title_canon_sha256":"d4ce4db1e82e950ca77877c576de971e343b3c03bb2526c2f86e91eb24a36892"},"schema_version":"1.0","source":{"id":"2102.11306","kind":"arxiv","version":2}},"canonical_sha256":"eaaa31e6098c19a56ca789365e2b4d486a919dec1a2b5b3c52ef83628e5895dd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eaaa31e6098c19a56ca789365e2b4d486a919dec1a2b5b3c52ef83628e5895dd","first_computed_at":"2026-07-05T02:30:14.961906Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:30:14.961906Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0OcHDXr6yktptbd2gr76yap4JVg619LdjNcmKO+emSsxHbNB4Fu4VvM5B08Yr7ieEqoZf2nRIE0FtcHRMR3/CQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:30:14.962340Z","signed_message":"canonical_sha256_bytes"},"source_id":"2102.11306","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6e74e03c285d5648d74d6c7c02231e6e0ed9872b4330d059e7542c4b311c1c61","sha256:a76196eaa7bb9527e827871bccaba00ce54e9b3dd5b09d3afd6c3c7fef5dd6d2"],"state_sha256":"d3b115ef0d94fd47ecbe1a93f7dcf4ed1a1b499f0c84ef828f4760c358e587c5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AwXCwbGQEAaSxbERztvBkGv6V3FRyWUvqwdqTzax3tWogPmrkbabW2ZSTiM5RvrBrJff4b/wGXgGCj16D/uwCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T04:38:54.686013Z","bundle_sha256":"4c0b997f439a9671c7cf176bb86e057d75debaca6eb7eaf966d1d42ccf9da6c3"}}