{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:BSREET35L6DHD2KIQ3YYJ3PICH","short_pith_number":"pith:BSREET35","canonical_record":{"source":{"id":"1704.02496","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-08T13:55:35Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"68e815aa75710f678f5e6b0331cd6d2374bb568420aa65c59c023b3c99320012","abstract_canon_sha256":"f25118a6a9b5aacf3ad5d6e6d6a45550a6fdde65bdd8e1acfec00320160fc347"},"schema_version":"1.0"},"canonical_sha256":"0ca2424f7d5f8671e94886f184ede811d86cf9a6e230564fb827d76645e5b520","source":{"kind":"arxiv","id":"1704.02496","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.02496","created_at":"2026-05-18T00:46:07Z"},{"alias_kind":"arxiv_version","alias_value":"1704.02496v2","created_at":"2026-05-18T00:46:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.02496","created_at":"2026-05-18T00:46:07Z"},{"alias_kind":"pith_short_12","alias_value":"BSREET35L6DH","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BSREET35L6DHD2KI","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BSREET35","created_at":"2026-05-18T12:31:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:BSREET35L6DHD2KIQ3YYJ3PICH","target":"record","payload":{"canonical_record":{"source":{"id":"1704.02496","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-08T13:55:35Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"68e815aa75710f678f5e6b0331cd6d2374bb568420aa65c59c023b3c99320012","abstract_canon_sha256":"f25118a6a9b5aacf3ad5d6e6d6a45550a6fdde65bdd8e1acfec00320160fc347"},"schema_version":"1.0"},"canonical_sha256":"0ca2424f7d5f8671e94886f184ede811d86cf9a6e230564fb827d76645e5b520","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:07.430698Z","signature_b64":"DL/vmOm9hRsAcDpHGmvjaJQ1sDTp3syRXFU0vp4pv7nOlvb75ObeNc+JwRAOxyR20QhoLyqjBSs+qkKy5X1TAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ca2424f7d5f8671e94886f184ede811d86cf9a6e230564fb827d76645e5b520","last_reissued_at":"2026-05-18T00:46:07.430187Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:07.430187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.02496","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":"2026-05-18T00:46:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wnpSo+f2GMXn9Nd0giyGVr/o2i/lWaH9wbkhJFMgkSvEwT84MIsgYF+7FHrQrmwYeQYvrlOZUBTzMRUX0OAbAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T16:34:54.995558Z"},"content_sha256":"56ead4e9759b336d9e0d57e133098496164adf9a9dde2294d9a77743b86af00f","schema_version":"1.0","event_id":"sha256:56ead4e9759b336d9e0d57e133098496164adf9a9dde2294d9a77743b86af00f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:BSREET35L6DHD2KIQ3YYJ3PICH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Monotonicity of expected $f$-vectors for projections of regular polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.PR","authors_text":"Christoph Th\\\"ale, Zakhar Kabluchko","submitted_at":"2017-04-08T13:55:35Z","abstract_excerpt":"Let $P_n$ be an $n$-dimensional regular polytope from one of the three infinite series (regular simplices, regular crosspolytopes, and cubes). Project $P_n$ onto a random, uniformly distributed linear subspace of dimension $d\\geq 2$. We prove that the expected number of $k$-dimensional faces of the resulting random polytope is an increasing function of $n$. As a corollary, we show that the expected number of $k$-faces of the Gaussian polytope is an increasing function of the number of points used to generate the polytope. Similar results are obtained for the symmetric Gaussian polytope and the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.02496","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":"2026-05-18T00:46:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zd9zzkSE3VOjir6PWXCHmRvqIkqz4WpwsTK2XZojb3N2znk+p40TwA03BYKu6AMBbxaDuSarLm4csqPorkidCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T16:34:54.996211Z"},"content_sha256":"3d4c486a0938b8ffed6213f2f40444e78ef75d6214c9dda98840c4c118242aba","schema_version":"1.0","event_id":"sha256:3d4c486a0938b8ffed6213f2f40444e78ef75d6214c9dda98840c4c118242aba"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BSREET35L6DHD2KIQ3YYJ3PICH/bundle.json","state_url":"https://pith.science/pith/BSREET35L6DHD2KIQ3YYJ3PICH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BSREET35L6DHD2KIQ3YYJ3PICH/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":"2026-05-25T16:34:55Z","links":{"resolver":"https://pith.science/pith/BSREET35L6DHD2KIQ3YYJ3PICH","bundle":"https://pith.science/pith/BSREET35L6DHD2KIQ3YYJ3PICH/bundle.json","state":"https://pith.science/pith/BSREET35L6DHD2KIQ3YYJ3PICH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BSREET35L6DHD2KIQ3YYJ3PICH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:BSREET35L6DHD2KIQ3YYJ3PICH","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":"f25118a6a9b5aacf3ad5d6e6d6a45550a6fdde65bdd8e1acfec00320160fc347","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-08T13:55:35Z","title_canon_sha256":"68e815aa75710f678f5e6b0331cd6d2374bb568420aa65c59c023b3c99320012"},"schema_version":"1.0","source":{"id":"1704.02496","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.02496","created_at":"2026-05-18T00:46:07Z"},{"alias_kind":"arxiv_version","alias_value":"1704.02496v2","created_at":"2026-05-18T00:46:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.02496","created_at":"2026-05-18T00:46:07Z"},{"alias_kind":"pith_short_12","alias_value":"BSREET35L6DH","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BSREET35L6DHD2KI","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BSREET35","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:3d4c486a0938b8ffed6213f2f40444e78ef75d6214c9dda98840c4c118242aba","target":"graph","created_at":"2026-05-18T00:46:07Z","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":"Let $P_n$ be an $n$-dimensional regular polytope from one of the three infinite series (regular simplices, regular crosspolytopes, and cubes). Project $P_n$ onto a random, uniformly distributed linear subspace of dimension $d\\geq 2$. We prove that the expected number of $k$-dimensional faces of the resulting random polytope is an increasing function of $n$. As a corollary, we show that the expected number of $k$-faces of the Gaussian polytope is an increasing function of the number of points used to generate the polytope. Similar results are obtained for the symmetric Gaussian polytope and the","authors_text":"Christoph Th\\\"ale, Zakhar Kabluchko","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-08T13:55:35Z","title":"Monotonicity of expected $f$-vectors for projections of regular polytopes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.02496","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":"sha256:56ead4e9759b336d9e0d57e133098496164adf9a9dde2294d9a77743b86af00f","target":"record","created_at":"2026-05-18T00:46:07Z","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":"f25118a6a9b5aacf3ad5d6e6d6a45550a6fdde65bdd8e1acfec00320160fc347","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-08T13:55:35Z","title_canon_sha256":"68e815aa75710f678f5e6b0331cd6d2374bb568420aa65c59c023b3c99320012"},"schema_version":"1.0","source":{"id":"1704.02496","kind":"arxiv","version":2}},"canonical_sha256":"0ca2424f7d5f8671e94886f184ede811d86cf9a6e230564fb827d76645e5b520","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ca2424f7d5f8671e94886f184ede811d86cf9a6e230564fb827d76645e5b520","first_computed_at":"2026-05-18T00:46:07.430187Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:07.430187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DL/vmOm9hRsAcDpHGmvjaJQ1sDTp3syRXFU0vp4pv7nOlvb75ObeNc+JwRAOxyR20QhoLyqjBSs+qkKy5X1TAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:07.430698Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.02496","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:56ead4e9759b336d9e0d57e133098496164adf9a9dde2294d9a77743b86af00f","sha256:3d4c486a0938b8ffed6213f2f40444e78ef75d6214c9dda98840c4c118242aba"],"state_sha256":"02d70d1a1b1e1894ab5e543a90d1d4b4afaa032f4b28b02a199fc413cbb519e7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"edN7776AYxu7igIAhAkYQqzEPC/10J239CrPCMN3kMEtU5RvUjmEzpuqP17n3Z9E3ziYdvo42ZhoQ1Qd3/iWAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T16:34:55.002688Z","bundle_sha256":"e438c63fc94bbb87a2026f09c99b2c948bf7907c71f44540ca736d26e7b34a24"}}