{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:PUNDM277RCK43MDHPWLZQ22VBP","short_pith_number":"pith:PUNDM277","canonical_record":{"source":{"id":"2605.22194","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-21T08:59:40Z","cross_cats_sorted":[],"title_canon_sha256":"38693318fc32baacf1851350885a601eefb8c39f757be8ed15f267b948d2b2cf","abstract_canon_sha256":"802bbf6b37f64fa29a8122e492e791fc063a856eec82b33adce91d56091a07b6"},"schema_version":"1.0"},"canonical_sha256":"7d1a366bff8895cdb0677d97986b550bca63d0a5e55ca6ac51d2c9cda672a45d","source":{"kind":"arxiv","id":"2605.22194","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.22194","created_at":"2026-05-22T01:04:31Z"},{"alias_kind":"arxiv_version","alias_value":"2605.22194v1","created_at":"2026-05-22T01:04:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.22194","created_at":"2026-05-22T01:04:31Z"},{"alias_kind":"pith_short_12","alias_value":"PUNDM277RCK4","created_at":"2026-05-22T01:04:31Z"},{"alias_kind":"pith_short_16","alias_value":"PUNDM277RCK43MDH","created_at":"2026-05-22T01:04:31Z"},{"alias_kind":"pith_short_8","alias_value":"PUNDM277","created_at":"2026-05-22T01:04:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:PUNDM277RCK43MDHPWLZQ22VBP","target":"record","payload":{"canonical_record":{"source":{"id":"2605.22194","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-21T08:59:40Z","cross_cats_sorted":[],"title_canon_sha256":"38693318fc32baacf1851350885a601eefb8c39f757be8ed15f267b948d2b2cf","abstract_canon_sha256":"802bbf6b37f64fa29a8122e492e791fc063a856eec82b33adce91d56091a07b6"},"schema_version":"1.0"},"canonical_sha256":"7d1a366bff8895cdb0677d97986b550bca63d0a5e55ca6ac51d2c9cda672a45d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-22T01:04:31.229475Z","signature_b64":"oXiJLGmnAjOABD2ObEwitMYLwSbaPW5MEacXw8AjhStXZq0Jih1VnGmnpfVuF/jReVOauLijfIT1a/RadukaAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7d1a366bff8895cdb0677d97986b550bca63d0a5e55ca6ac51d2c9cda672a45d","last_reissued_at":"2026-05-22T01:04:31.228714Z","signature_status":"signed_v1","first_computed_at":"2026-05-22T01:04:31.228714Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.22194","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":"2026-05-22T01:04:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BIeXZCjp+ILOq07lnhhGFQ0+A8lrxnmATEZT2Wz7qnI3F33GpE0g7QrO57ms71SgcMPLiQx6h9Fv3rJKECUcDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T06:11:07.268810Z"},"content_sha256":"3d4a9e8fceb91bc00881bdf5bf526021d95fac9a3184c45609f8fa74abfb962d","schema_version":"1.0","event_id":"sha256:3d4a9e8fceb91bc00881bdf5bf526021d95fac9a3184c45609f8fa74abfb962d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:PUNDM277RCK43MDHPWLZQ22VBP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Segre Varieties and Desarguesian Spreads","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Antonio Cossidente, Francesco Pavese, Giuseppe Marino, John Sheekey, Paolo Santonastaso","submitted_at":"2026-05-21T08:59:40Z","abstract_excerpt":"Let $\\mathrm{PG}(n-1,q)$ denote the $(n-1)$-dimensional projective space over $\\mathbb{F}_q$. We investigate the intersection of two Desarguesian $(h-1)$-spreads of $\\mathrm{PG}(kh-1,q)$ and show that it is determined by a subgeometry over a suitable extension field. Our approach combines a characterization of subsets of points of $\\mathrm{PG}(k-1,q^h)$ closed under $q$-order subgeometries with a matrix model for Desarguesian spreads based on Moore matrices. This leads naturally to the notion of generalized Segre varieties $\\mathcal S^r_{kr-1,h-1}(q)$ and a geometric description of their maxim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.22194","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/2605.22194/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":"2026-05-22T01:04:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QrKNdi33Jjb126enBexr0xQHfcjHb2uM+bukdGzWle0eosY9VgR8SYFTT/HV6MlDvotIHZU0gzhIEfPq1ysOCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T06:11:07.269554Z"},"content_sha256":"531fa40b6284782220c59667428bb405e610addf19fcba4dd24bb08ea54633bd","schema_version":"1.0","event_id":"sha256:531fa40b6284782220c59667428bb405e610addf19fcba4dd24bb08ea54633bd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PUNDM277RCK43MDHPWLZQ22VBP/bundle.json","state_url":"https://pith.science/pith/PUNDM277RCK43MDHPWLZQ22VBP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PUNDM277RCK43MDHPWLZQ22VBP/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":"2026-05-30T06:11:07Z","links":{"resolver":"https://pith.science/pith/PUNDM277RCK43MDHPWLZQ22VBP","bundle":"https://pith.science/pith/PUNDM277RCK43MDHPWLZQ22VBP/bundle.json","state":"https://pith.science/pith/PUNDM277RCK43MDHPWLZQ22VBP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PUNDM277RCK43MDHPWLZQ22VBP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:PUNDM277RCK43MDHPWLZQ22VBP","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":"802bbf6b37f64fa29a8122e492e791fc063a856eec82b33adce91d56091a07b6","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-21T08:59:40Z","title_canon_sha256":"38693318fc32baacf1851350885a601eefb8c39f757be8ed15f267b948d2b2cf"},"schema_version":"1.0","source":{"id":"2605.22194","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.22194","created_at":"2026-05-22T01:04:31Z"},{"alias_kind":"arxiv_version","alias_value":"2605.22194v1","created_at":"2026-05-22T01:04:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.22194","created_at":"2026-05-22T01:04:31Z"},{"alias_kind":"pith_short_12","alias_value":"PUNDM277RCK4","created_at":"2026-05-22T01:04:31Z"},{"alias_kind":"pith_short_16","alias_value":"PUNDM277RCK43MDH","created_at":"2026-05-22T01:04:31Z"},{"alias_kind":"pith_short_8","alias_value":"PUNDM277","created_at":"2026-05-22T01:04:31Z"}],"graph_snapshots":[{"event_id":"sha256:531fa40b6284782220c59667428bb405e610addf19fcba4dd24bb08ea54633bd","target":"graph","created_at":"2026-05-22T01:04:31Z","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/2605.22194/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\mathrm{PG}(n-1,q)$ denote the $(n-1)$-dimensional projective space over $\\mathbb{F}_q$. We investigate the intersection of two Desarguesian $(h-1)$-spreads of $\\mathrm{PG}(kh-1,q)$ and show that it is determined by a subgeometry over a suitable extension field. Our approach combines a characterization of subsets of points of $\\mathrm{PG}(k-1,q^h)$ closed under $q$-order subgeometries with a matrix model for Desarguesian spreads based on Moore matrices. This leads naturally to the notion of generalized Segre varieties $\\mathcal S^r_{kr-1,h-1}(q)$ and a geometric description of their maxim","authors_text":"Antonio Cossidente, Francesco Pavese, Giuseppe Marino, John Sheekey, Paolo Santonastaso","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-21T08:59:40Z","title":"Segre Varieties and Desarguesian Spreads"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.22194","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":"sha256:3d4a9e8fceb91bc00881bdf5bf526021d95fac9a3184c45609f8fa74abfb962d","target":"record","created_at":"2026-05-22T01:04:31Z","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":"802bbf6b37f64fa29a8122e492e791fc063a856eec82b33adce91d56091a07b6","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-21T08:59:40Z","title_canon_sha256":"38693318fc32baacf1851350885a601eefb8c39f757be8ed15f267b948d2b2cf"},"schema_version":"1.0","source":{"id":"2605.22194","kind":"arxiv","version":1}},"canonical_sha256":"7d1a366bff8895cdb0677d97986b550bca63d0a5e55ca6ac51d2c9cda672a45d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7d1a366bff8895cdb0677d97986b550bca63d0a5e55ca6ac51d2c9cda672a45d","first_computed_at":"2026-05-22T01:04:31.228714Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-22T01:04:31.228714Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oXiJLGmnAjOABD2ObEwitMYLwSbaPW5MEacXw8AjhStXZq0Jih1VnGmnpfVuF/jReVOauLijfIT1a/RadukaAQ==","signature_status":"signed_v1","signed_at":"2026-05-22T01:04:31.229475Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.22194","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d4a9e8fceb91bc00881bdf5bf526021d95fac9a3184c45609f8fa74abfb962d","sha256:531fa40b6284782220c59667428bb405e610addf19fcba4dd24bb08ea54633bd"],"state_sha256":"9a875460d2c860884757bfe49a7c69b7e6ebfe875c1aaccb794af43d64522aa9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"INjRcgQ7gtEA7PIBSkYUqBFtDIjfMUNYoZy+XJr2GzfQZ3KL8ZUNynrmhq1GVIcVtkwCqMRagrUWzUiics4ODw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T06:11:07.273557Z","bundle_sha256":"7182386d34152d314b8f513d3673d8dee28083069f7da53cb35fa7865da5d6c9"}}