{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:WE32E5TSOPGJIXHRJIXGBENKDE","short_pith_number":"pith:WE32E5TS","canonical_record":{"source":{"id":"2411.14036","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-11-21T11:39:11Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"ffceb369f3e8180269cb0c2a28300e65ecea08d06e47fbecfce26e42ab1f799f","abstract_canon_sha256":"2ec8989571d58b101fb5a16a0cf9fb21f42077589095749a606a603eb1abc79c"},"schema_version":"1.0"},"canonical_sha256":"b137a2767273cc945cf14a2e6091aa191cdefc95a5105b2bf13cbd29185ee993","source":{"kind":"arxiv","id":"2411.14036","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.14036","created_at":"2026-07-05T09:38:40Z"},{"alias_kind":"arxiv_version","alias_value":"2411.14036v1","created_at":"2026-07-05T09:38:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.14036","created_at":"2026-07-05T09:38:40Z"},{"alias_kind":"pith_short_12","alias_value":"WE32E5TSOPGJ","created_at":"2026-07-05T09:38:40Z"},{"alias_kind":"pith_short_16","alias_value":"WE32E5TSOPGJIXHR","created_at":"2026-07-05T09:38:40Z"},{"alias_kind":"pith_short_8","alias_value":"WE32E5TS","created_at":"2026-07-05T09:38:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:WE32E5TSOPGJIXHRJIXGBENKDE","target":"record","payload":{"canonical_record":{"source":{"id":"2411.14036","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-11-21T11:39:11Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"ffceb369f3e8180269cb0c2a28300e65ecea08d06e47fbecfce26e42ab1f799f","abstract_canon_sha256":"2ec8989571d58b101fb5a16a0cf9fb21f42077589095749a606a603eb1abc79c"},"schema_version":"1.0"},"canonical_sha256":"b137a2767273cc945cf14a2e6091aa191cdefc95a5105b2bf13cbd29185ee993","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:38:40.780295Z","signature_b64":"BpoHjO6TPyGGhjnwMsvNFk0fVEsHAFiHfX3EBLKzdyWRLaaFLnFUuKC3Tt6YvRSIJYESFRHdZ+syB6gMRLv5Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b137a2767273cc945cf14a2e6091aa191cdefc95a5105b2bf13cbd29185ee993","last_reissued_at":"2026-07-05T09:38:40.779865Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:38:40.779865Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.14036","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":"2026-07-05T09:38:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uqJe2kl64sfz/clMXPo94BBh6LUiybblncegJcMwU+/hFQr0JsTuDu/oFTmYM3FJclkmUR9sVOi+V2lAivelBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T23:17:24.746585Z"},"content_sha256":"f820ed3f910899e31fc565ac5a8e83c481c49bdba1a6e31cc23d72f8b37c511b","schema_version":"1.0","event_id":"sha256:f820ed3f910899e31fc565ac5a8e83c481c49bdba1a6e31cc23d72f8b37c511b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:WE32E5TSOPGJIXHRJIXGBENKDE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Simplicial vs. cubical spheres, polyhedral products and the Nevo-Petersen conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.CO","authors_text":"Ivan Limonchenko, Rade \\v{Z}ivaljevi\\'c","submitted_at":"2024-11-21T11:39:11Z","abstract_excerpt":"We prove that a Murai sphere is flag if and only if it is a nerve complex of a flag nestohedron and classify all the polytopes arising in this way. Our classification implies that flag Murai spheres satisfy the Nevo-Petersen conjecture on $\\gamma$-vectors of flag homology spheres. We continue by showing that a Bier sphere is minimally non-Golod if and only if it is a nerve complex of a truncation polytope different from a simplex and classify all the polytopes arising in this way. Finally, the notion of a cubical Bier sphere is introduced based on the polyhedral product construction, and we st"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.14036","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/2411.14036/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":"2026-07-05T09:38:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7aH+smt+sEL5q8i4p6DlMQsBLCziN4wkLdQHyiVb10jVPOHuVR2aFPKW0V/P8TRerLeaznHjE0wY/RF7TlEVBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T23:17:24.747001Z"},"content_sha256":"0dab7e197c89f61ffd329e6a830ebdd69bde06768a6c246dc5664cf60d2aeb40","schema_version":"1.0","event_id":"sha256:0dab7e197c89f61ffd329e6a830ebdd69bde06768a6c246dc5664cf60d2aeb40"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WE32E5TSOPGJIXHRJIXGBENKDE/bundle.json","state_url":"https://pith.science/pith/WE32E5TSOPGJIXHRJIXGBENKDE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WE32E5TSOPGJIXHRJIXGBENKDE/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":"2026-08-12T23:17:24Z","links":{"resolver":"https://pith.science/pith/WE32E5TSOPGJIXHRJIXGBENKDE","bundle":"https://pith.science/pith/WE32E5TSOPGJIXHRJIXGBENKDE/bundle.json","state":"https://pith.science/pith/WE32E5TSOPGJIXHRJIXGBENKDE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WE32E5TSOPGJIXHRJIXGBENKDE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:WE32E5TSOPGJIXHRJIXGBENKDE","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":"2ec8989571d58b101fb5a16a0cf9fb21f42077589095749a606a603eb1abc79c","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-11-21T11:39:11Z","title_canon_sha256":"ffceb369f3e8180269cb0c2a28300e65ecea08d06e47fbecfce26e42ab1f799f"},"schema_version":"1.0","source":{"id":"2411.14036","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.14036","created_at":"2026-07-05T09:38:40Z"},{"alias_kind":"arxiv_version","alias_value":"2411.14036v1","created_at":"2026-07-05T09:38:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.14036","created_at":"2026-07-05T09:38:40Z"},{"alias_kind":"pith_short_12","alias_value":"WE32E5TSOPGJ","created_at":"2026-07-05T09:38:40Z"},{"alias_kind":"pith_short_16","alias_value":"WE32E5TSOPGJIXHR","created_at":"2026-07-05T09:38:40Z"},{"alias_kind":"pith_short_8","alias_value":"WE32E5TS","created_at":"2026-07-05T09:38:40Z"}],"graph_snapshots":[{"event_id":"sha256:0dab7e197c89f61ffd329e6a830ebdd69bde06768a6c246dc5664cf60d2aeb40","target":"graph","created_at":"2026-07-05T09:38:40Z","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/2411.14036/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that a Murai sphere is flag if and only if it is a nerve complex of a flag nestohedron and classify all the polytopes arising in this way. Our classification implies that flag Murai spheres satisfy the Nevo-Petersen conjecture on $\\gamma$-vectors of flag homology spheres. We continue by showing that a Bier sphere is minimally non-Golod if and only if it is a nerve complex of a truncation polytope different from a simplex and classify all the polytopes arising in this way. Finally, the notion of a cubical Bier sphere is introduced based on the polyhedral product construction, and we st","authors_text":"Ivan Limonchenko, Rade \\v{Z}ivaljevi\\'c","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-11-21T11:39:11Z","title":"Simplicial vs. cubical spheres, polyhedral products and the Nevo-Petersen conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.14036","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:f820ed3f910899e31fc565ac5a8e83c481c49bdba1a6e31cc23d72f8b37c511b","target":"record","created_at":"2026-07-05T09:38:40Z","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":"2ec8989571d58b101fb5a16a0cf9fb21f42077589095749a606a603eb1abc79c","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-11-21T11:39:11Z","title_canon_sha256":"ffceb369f3e8180269cb0c2a28300e65ecea08d06e47fbecfce26e42ab1f799f"},"schema_version":"1.0","source":{"id":"2411.14036","kind":"arxiv","version":1}},"canonical_sha256":"b137a2767273cc945cf14a2e6091aa191cdefc95a5105b2bf13cbd29185ee993","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b137a2767273cc945cf14a2e6091aa191cdefc95a5105b2bf13cbd29185ee993","first_computed_at":"2026-07-05T09:38:40.779865Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:38:40.779865Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BpoHjO6TPyGGhjnwMsvNFk0fVEsHAFiHfX3EBLKzdyWRLaaFLnFUuKC3Tt6YvRSIJYESFRHdZ+syB6gMRLv5Cw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:38:40.780295Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.14036","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f820ed3f910899e31fc565ac5a8e83c481c49bdba1a6e31cc23d72f8b37c511b","sha256:0dab7e197c89f61ffd329e6a830ebdd69bde06768a6c246dc5664cf60d2aeb40"],"state_sha256":"42df5d3aa1a6f95d997f3b634479ab889957491b3ee9817db520040b62cf69a4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aAc4GH8iaXWyRmkhbb7csPLnNqGnIG3b1lYzlUm4+o+3UeP6jCC3jpchpzhPiYSNIg9cNVqrvCi3oDdtLBgxBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T23:17:24.750373Z","bundle_sha256":"6bf51d43c071b6a15f09d3fe545741f897db03b49629f5fc57e2b6d259325d19"}}