{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:DID3ZM6X7KSTVUHFJHUQ2QJIYF","short_pith_number":"pith:DID3ZM6X","schema_version":"1.0","canonical_sha256":"1a07bcb3d7faa53ad0e549e90d4128c14243885ad4bddd038d602064055c9771","source":{"kind":"arxiv","id":"2606.17755","version":1},"attestation_state":"computed","paper":{"title":"Tridendriform algebras on hypergraph polytopes, the other way around","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"B\\'er\\'enice Delcroix-Oger, Jovana Obradovi\\'c, Pierre-Louis Curien","submitted_at":"2026-06-16T10:17:49Z","abstract_excerpt":"Hypergraph polytopes (or nestohedra) form a broad class of polytopes obtained by truncating faces of a simplex according to a hypergraph. In earlier work, the authors constructed q-tridendriform algebras on the set of faces of certain families of hypergraph polytopes, including associahedra and permutohedra. The well-definedness of these structures relied on a connectedness property on the hypergraphs involved, called strictness. Nevertheless, notable examples of hypergraph polytopes such as cyclohedra fell outside this setting. We introduce a new connectedness condition, called anti-strictnes"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2606.17755","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-06-16T10:17:49Z","cross_cats_sorted":[],"title_canon_sha256":"eaf3477d208446ce6abc62abab349af6979183d68b5621f286130982249450f5","abstract_canon_sha256":"0cb8661e2f38795027abed5371d065e09806682816f61c83404bf020d437de7f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:10:21.055885Z","signature_b64":"DygTjcwYS900knpBLTxYHSTsl1hcTuNB5VJqi09FAT7A5aMdNoxXIXhP8i1+JezFoM/Bc51i+8HzV2fxkXMsBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1a07bcb3d7faa53ad0e549e90d4128c14243885ad4bddd038d602064055c9771","last_reissued_at":"2026-06-19T16:10:21.055552Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:10:21.055552Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tridendriform algebras on hypergraph polytopes, the other way around","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"B\\'er\\'enice Delcroix-Oger, Jovana Obradovi\\'c, Pierre-Louis Curien","submitted_at":"2026-06-16T10:17:49Z","abstract_excerpt":"Hypergraph polytopes (or nestohedra) form a broad class of polytopes obtained by truncating faces of a simplex according to a hypergraph. In earlier work, the authors constructed q-tridendriform algebras on the set of faces of certain families of hypergraph polytopes, including associahedra and permutohedra. The well-definedness of these structures relied on a connectedness property on the hypergraphs involved, called strictness. Nevertheless, notable examples of hypergraph polytopes such as cyclohedra fell outside this setting. We introduce a new connectedness condition, called anti-strictnes"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.17755","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.17755/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2606.17755","created_at":"2026-06-19T16:10:21.055612+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.17755v1","created_at":"2026-06-19T16:10:21.055612+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.17755","created_at":"2026-06-19T16:10:21.055612+00:00"},{"alias_kind":"pith_short_12","alias_value":"DID3ZM6X7KST","created_at":"2026-06-19T16:10:21.055612+00:00"},{"alias_kind":"pith_short_16","alias_value":"DID3ZM6X7KSTVUHF","created_at":"2026-06-19T16:10:21.055612+00:00"},{"alias_kind":"pith_short_8","alias_value":"DID3ZM6X","created_at":"2026-06-19T16:10:21.055612+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DID3ZM6X7KSTVUHFJHUQ2QJIYF","json":"https://pith.science/pith/DID3ZM6X7KSTVUHFJHUQ2QJIYF.json","graph_json":"https://pith.science/api/pith-number/DID3ZM6X7KSTVUHFJHUQ2QJIYF/graph.json","events_json":"https://pith.science/api/pith-number/DID3ZM6X7KSTVUHFJHUQ2QJIYF/events.json","paper":"https://pith.science/paper/DID3ZM6X"},"agent_actions":{"view_html":"https://pith.science/pith/DID3ZM6X7KSTVUHFJHUQ2QJIYF","download_json":"https://pith.science/pith/DID3ZM6X7KSTVUHFJHUQ2QJIYF.json","view_paper":"https://pith.science/paper/DID3ZM6X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.17755&json=true","fetch_graph":"https://pith.science/api/pith-number/DID3ZM6X7KSTVUHFJHUQ2QJIYF/graph.json","fetch_events":"https://pith.science/api/pith-number/DID3ZM6X7KSTVUHFJHUQ2QJIYF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DID3ZM6X7KSTVUHFJHUQ2QJIYF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DID3ZM6X7KSTVUHFJHUQ2QJIYF/action/storage_attestation","attest_author":"https://pith.science/pith/DID3ZM6X7KSTVUHFJHUQ2QJIYF/action/author_attestation","sign_citation":"https://pith.science/pith/DID3ZM6X7KSTVUHFJHUQ2QJIYF/action/citation_signature","submit_replication":"https://pith.science/pith/DID3ZM6X7KSTVUHFJHUQ2QJIYF/action/replication_record"}},"created_at":"2026-06-19T16:10:21.055612+00:00","updated_at":"2026-06-19T16:10:21.055612+00:00"}