{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:6DCRKHZS3PPCXSB22TAPRQ2V2I","short_pith_number":"pith:6DCRKHZS","canonical_record":{"source":{"id":"2411.13702","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-11-20T20:39:41Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"ef86521c0645cc5da1f5160513e5e3d08d40f2ef0e4891b2c4e5a799f432cdc1","abstract_canon_sha256":"63e8e423c9a0f882deb5937003000de38626038e3a3e386571fb010e99b0ce6c"},"schema_version":"1.0"},"canonical_sha256":"f0c5151f32dbde2bc83ad4c0f8c355d22bf9d979a63dcdd1386f2e332d9586d3","source":{"kind":"arxiv","id":"2411.13702","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.13702","created_at":"2026-07-05T09:38:35Z"},{"alias_kind":"arxiv_version","alias_value":"2411.13702v1","created_at":"2026-07-05T09:38:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.13702","created_at":"2026-07-05T09:38:35Z"},{"alias_kind":"pith_short_12","alias_value":"6DCRKHZS3PPC","created_at":"2026-07-05T09:38:35Z"},{"alias_kind":"pith_short_16","alias_value":"6DCRKHZS3PPCXSB2","created_at":"2026-07-05T09:38:35Z"},{"alias_kind":"pith_short_8","alias_value":"6DCRKHZS","created_at":"2026-07-05T09:38:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:6DCRKHZS3PPCXSB22TAPRQ2V2I","target":"record","payload":{"canonical_record":{"source":{"id":"2411.13702","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-11-20T20:39:41Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"ef86521c0645cc5da1f5160513e5e3d08d40f2ef0e4891b2c4e5a799f432cdc1","abstract_canon_sha256":"63e8e423c9a0f882deb5937003000de38626038e3a3e386571fb010e99b0ce6c"},"schema_version":"1.0"},"canonical_sha256":"f0c5151f32dbde2bc83ad4c0f8c355d22bf9d979a63dcdd1386f2e332d9586d3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:38:35.926516Z","signature_b64":"BFmFL/xLIMA4vsQ2HrncGX4E8Mpfp2Y+XkuoUG0NS51t1L7GdKdpBAS9G8n3zsrYFOXJC+UN7hvenBBkXDV/Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f0c5151f32dbde2bc83ad4c0f8c355d22bf9d979a63dcdd1386f2e332d9586d3","last_reissued_at":"2026-07-05T09:38:35.926010Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:38:35.926010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.13702","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":"2026-07-05T09:38:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8Q4VCuwN1eGGW8MofRdWiDxlb6/qCzl4thHvPjxtu9LrUoaUGtVnxNSRMOVUnQedH3NzJt48ST9l6Vq0KrTZCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T03:39:33.134665Z"},"content_sha256":"ac3403d875e9e889a910505a372b490b7e8df736dfb5fad2e08d7a6903386cd9","schema_version":"1.0","event_id":"sha256:ac3403d875e9e889a910505a372b490b7e8df736dfb5fad2e08d7a6903386cd9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:6DCRKHZS3PPCXSB22TAPRQ2V2I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Veronese polytopes: Extending the framework of cyclic polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.CO","authors_text":"Marie-Charlotte Brandenburg, Roland P\\'u\\v{c}ek","submitted_at":"2024-11-20T20:39:41Z","abstract_excerpt":"This article introduces the theory of Veronese polytopes, a broad generalisation of cyclic polytopes. These arise as convex hulls of points on curves with one or more connected components, obtained as the image of the rational normal curve in affine charts. We describe their facial structure by extending Gale's evenness condition, and provide a further combinatorial characterisation of facets via $\\sigma$-parity alternating sequences. Notably, we establish a bijective correspondence between combinatorial types of Veronese polytopes and partitions of finite sets equipped with a cyclic order, ca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.13702","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/2411.13702/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":"2026-07-05T09:38:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W7sHbKMl42JFanicPWXCZz28GrjVYdez5UA/MBz+RGTWSvMV6SzZwjWxkMV5pbGzW/Xe5nBalGhnl9wiU9SsCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T03:39:33.135178Z"},"content_sha256":"2b027fba0b95365e42024f16e4ad65a5f6fa71c790f20b0f5c8124a8f78d6f9c","schema_version":"1.0","event_id":"sha256:2b027fba0b95365e42024f16e4ad65a5f6fa71c790f20b0f5c8124a8f78d6f9c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6DCRKHZS3PPCXSB22TAPRQ2V2I/bundle.json","state_url":"https://pith.science/pith/6DCRKHZS3PPCXSB22TAPRQ2V2I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6DCRKHZS3PPCXSB22TAPRQ2V2I/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":"2026-08-13T03:39:33Z","links":{"resolver":"https://pith.science/pith/6DCRKHZS3PPCXSB22TAPRQ2V2I","bundle":"https://pith.science/pith/6DCRKHZS3PPCXSB22TAPRQ2V2I/bundle.json","state":"https://pith.science/pith/6DCRKHZS3PPCXSB22TAPRQ2V2I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6DCRKHZS3PPCXSB22TAPRQ2V2I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:6DCRKHZS3PPCXSB22TAPRQ2V2I","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":"63e8e423c9a0f882deb5937003000de38626038e3a3e386571fb010e99b0ce6c","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-11-20T20:39:41Z","title_canon_sha256":"ef86521c0645cc5da1f5160513e5e3d08d40f2ef0e4891b2c4e5a799f432cdc1"},"schema_version":"1.0","source":{"id":"2411.13702","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.13702","created_at":"2026-07-05T09:38:35Z"},{"alias_kind":"arxiv_version","alias_value":"2411.13702v1","created_at":"2026-07-05T09:38:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.13702","created_at":"2026-07-05T09:38:35Z"},{"alias_kind":"pith_short_12","alias_value":"6DCRKHZS3PPC","created_at":"2026-07-05T09:38:35Z"},{"alias_kind":"pith_short_16","alias_value":"6DCRKHZS3PPCXSB2","created_at":"2026-07-05T09:38:35Z"},{"alias_kind":"pith_short_8","alias_value":"6DCRKHZS","created_at":"2026-07-05T09:38:35Z"}],"graph_snapshots":[{"event_id":"sha256:2b027fba0b95365e42024f16e4ad65a5f6fa71c790f20b0f5c8124a8f78d6f9c","target":"graph","created_at":"2026-07-05T09:38:35Z","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/2411.13702/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This article introduces the theory of Veronese polytopes, a broad generalisation of cyclic polytopes. These arise as convex hulls of points on curves with one or more connected components, obtained as the image of the rational normal curve in affine charts. We describe their facial structure by extending Gale's evenness condition, and provide a further combinatorial characterisation of facets via $\\sigma$-parity alternating sequences. Notably, we establish a bijective correspondence between combinatorial types of Veronese polytopes and partitions of finite sets equipped with a cyclic order, ca","authors_text":"Marie-Charlotte Brandenburg, Roland P\\'u\\v{c}ek","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-11-20T20:39:41Z","title":"Veronese polytopes: Extending the framework of cyclic polytopes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.13702","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:ac3403d875e9e889a910505a372b490b7e8df736dfb5fad2e08d7a6903386cd9","target":"record","created_at":"2026-07-05T09:38:35Z","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":"63e8e423c9a0f882deb5937003000de38626038e3a3e386571fb010e99b0ce6c","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2024-11-20T20:39:41Z","title_canon_sha256":"ef86521c0645cc5da1f5160513e5e3d08d40f2ef0e4891b2c4e5a799f432cdc1"},"schema_version":"1.0","source":{"id":"2411.13702","kind":"arxiv","version":1}},"canonical_sha256":"f0c5151f32dbde2bc83ad4c0f8c355d22bf9d979a63dcdd1386f2e332d9586d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f0c5151f32dbde2bc83ad4c0f8c355d22bf9d979a63dcdd1386f2e332d9586d3","first_computed_at":"2026-07-05T09:38:35.926010Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:38:35.926010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BFmFL/xLIMA4vsQ2HrncGX4E8Mpfp2Y+XkuoUG0NS51t1L7GdKdpBAS9G8n3zsrYFOXJC+UN7hvenBBkXDV/Bg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:38:35.926516Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.13702","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac3403d875e9e889a910505a372b490b7e8df736dfb5fad2e08d7a6903386cd9","sha256:2b027fba0b95365e42024f16e4ad65a5f6fa71c790f20b0f5c8124a8f78d6f9c"],"state_sha256":"66fca603d977e4d8368a085cd698650097dce3407d4e5316691c4e244540437d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VD3k3Rxhz9/TtykS61BTstij0XRwRef8QI2PwaHZrlmHfkWu2/dP/SAtNPt6YGixSMLaqDf5rsiYo7Chl11dBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T03:39:33.140457Z","bundle_sha256":"143db0418f54d17de19bf03d377ef5a4374d611a501096b4622713740ce0ce3b"}}